Relationship Between Unsignalised Intersection Geometry ... · PDF fileRelationship Between...

Relationship Between Unsignalised

Intersection Geometry and Accident Rates

Owen Kingsley Arndt, B.E. (Civil), M. Eng

This thesis is submitted as a requirement of the Doctor of Philosophy course (IF49).

School of Civil Engineering, Faculty of Built Environment and Engineering,

Queensland University of Technology, March 2003.

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Keywords

Intersections, Unsignalized intersections, T-intersections, Cross-roads, Accident

prevention, Collision prediction, Collision avoidance, Crash avoidance, Road

geometry, Road design standards.

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Abstract

The aim of this research is to determine the effect of unsignalised intersection

geometry on the rates of the various types of accidents occurring at unsignalised

intersections. A literature review has identified that there is little consistency

between the results of previous studies. Some studies found that particular

parameters had an opposite effect to what was expected. With this in mind, the

research identified reasons for these results and developed two basic approaches to

mitigate some of the problems with multi-factor type studies. These approaches are

‘maximise the efficiency of data collection’ and ‘develop techniques for analysing

less than perfect data’. A database consisting of 206 unsignalised intersection sites

from throughout Queensland was used for analysis. The outcome of this research

confirms the validity of several of the current design standards for unsignalised

intersections, in addition to identifying new engineering procedures.

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Table of Contents List of Tables ............................................................................................................................viii List of Figures .............................................................................................................................xi Statement of Original Authorship .............................................................................................xiii Acknowledgements...................................................................................................................xiv

Part A

1 INTRODUCTION ...........................................................................................................1 1.1 Objectives of the Study......................................................................................................1 1.2 Background to this Research .............................................................................................2 1.3 The Roundabout Study - Arndt (1998)..............................................................................2 1.4 Potential Benefits of Undertaking Research at Unsignalised Intersections.......................4 1.5 Definitions .........................................................................................................................4 1.6 Outline of this Thesis.........................................................................................................6

2 LITERATURE REVIEW ...............................................................................................9 2.1 Multi-factor Studies ...........................................................................................................9 2.2 Matched Group Studies ...................................................................................................24 2.3 Before and After Studies .................................................................................................25 2.4 Traffic Conflict Studies ...................................................................................................28 2.5 Studies Relating Traffic Volumes to Accident Rates ......................................................29 2.6 Driver Behaviour .............................................................................................................31 2.7 Literature Review Summary............................................................................................38 2.8 Discussion........................................................................................................................41

3 THESIS APPROACH ...................................................................................................45 3.1 Problems with Multi-factor Studies.................................................................................45 3.2 Maximise Efficiency of Data Collection .........................................................................48 3.3 Develop Techniques for Analysing less than Perfect Data..............................................50 3.4 Discussion of the Approaches Taken in this Study .........................................................57

Part B

4 SELECTION OF UNSIGNALISED INTERSECTION SITES ................................61 4.1 Obtaining a Wide Range of Variable Values...................................................................61 4.2 Excluding Very Low Volume Intersections ....................................................................64 4.3 Types of Intersections Selected .......................................................................................65 4.4 Overview of Intersection Sample ....................................................................................75

5 ACCIDENT DATA........................................................................................................76 5.1 Source of Accident Data..................................................................................................76 5.2 Selected Analysis Periods................................................................................................77 5.3 Categorisation of the Accident Data................................................................................78

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6 GEOMETRIC AND OTHER VARIABLES ...............................................................88 6.1 Selection of Variables ......................................................................................................88 6.2 Collection of Geometric and Other Variable Data...........................................................90 6.3 Speed Prediction Model ...................................................................................................91 6.4 Vehicle Path Model..........................................................................................................95 6.5 Geometric Data Coding and Overview ............................................................................96

7 TRAFFIC FLOW DATA ............................................................................................101 7.1 Selection of Traffic Volume Variables and Collection of Data .....................................101 7.2 Conversion of Traffic Volume Data to the Same Time Period......................................101 7.3 Conversion of Calculated AADT Values to Average AADT Values ............................101 7.4 Overview of Traffic Volume Data .................................................................................102

Part C

8 DATA COLLECTION SUMMARY AND PRELIMINARY ANALYSIS PROCEDURE ..............................................................................................................105

8.1 Data Collection Summary ..............................................................................................105 8.2 Preliminary Analysis Procedure.....................................................................................105

9 ANGLE-MINOR VEHICLE ACCIDENTS ..............................................................107 9.1 Vehicle Types ................................................................................................................108 9.2 Accident Severity...........................................................................................................110 9.3 Effect of Weather and Light Conditions ........................................................................111 9.4 Time of Day ...................................................................................................................113 9.5 Day of Week ..................................................................................................................113 9.6 Month of Year................................................................................................................114 9.7 Contributing Circumstance ............................................................................................115 9.8 Distribution of Data .......................................................................................................117 9.9 Geometric and Other Effects..........................................................................................118

10 ANGLE-MAJOR VEHICLE ACCIDENTS..............................................................122 10.1 Vehicle Types ................................................................................................................123 10.2 Accident Severity...........................................................................................................125 10.3 Effect of Weather and Light Conditions ........................................................................125 10.4 Contributing Circumstance ............................................................................................126 10.5 Distribution of Data .......................................................................................................127 10.6 Geometric and Other Effects..........................................................................................128

11 REAR-END-MAJOR VEHICLE ACCIDENTS.......................................................131 11.1 Vehicle Types ................................................................................................................132 11.2 Accident Severity...........................................................................................................134 11.3 Effect of Weather and Light Conditions ........................................................................134 11.4 Contributing Circumstance ............................................................................................135 11.5 Geometric and Other Effects..........................................................................................136

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12 SINGLE-THROUGH VEHICLE ACCIDENTS ......................................................140 12.1 Vehicle Types ................................................................................................................142 12.2 Accident Severity ..........................................................................................................143 12.3 Effect of Weather and Light Conditions........................................................................144 12.4 Contributing Circumstance............................................................................................145 12.5 Geometric and Other Effects .........................................................................................145

13 LOW FREQUENCY INTERSECTION ACCIDENTS ...........................................148 13.1 Rear-End-Minor.............................................................................................................148 13.2 Single-Minor-Turn.........................................................................................................150 13.3 Single-Major-Turn.........................................................................................................151 13.4 Incorrect Turn ................................................................................................................153 13.5 Overtaking-Intersection .................................................................................................154 13.6 Sideswipe-Major-Auxiliary ...........................................................................................156 13.7 Other Accidents .............................................................................................................156

14 LOW FREQUENCY THROUGH ACCIDENTS.....................................................157 14.1 Pedestrian.......................................................................................................................157 14.2 U-Turn ...........................................................................................................................159 14.3 Changed Lanes ..............................................................................................................159 14.4 Single-Object .................................................................................................................160 14.5 Overtaking .....................................................................................................................160 14.6 Other Accidents .............................................................................................................161

15 PRELIMINARY ANALYSIS SUMMARY...............................................................162 15.1 Types and Numbers of Accidents Recorded..................................................................162 15.2 Parameters Over Represented in the Accident Data ......................................................162

Part D

16 STATISTICAL MODELLING ISSUES ...................................................................165 16.1 Analysis Process ............................................................................................................165 16.2 Correlation between Parameters ....................................................................................166 16.3 Relationships between Variables and Accident Rates ...................................................173 16.4 Interaction between Variables .......................................................................................178 16.5 Regression Techniques ..................................................................................................179 16.6 Acceptance and Rejection of Parameters from the Regression Analysis ......................182 16.7 Diagnostic Checks .........................................................................................................185 16.8 Validation of the Accident Models................................................................................186

17 ANGLE-MINOR VEHICLE ACCIDENTS..............................................................189 17.1 Categorisation of the Data .............................................................................................189 17.2 Variables Selected for Analysis.....................................................................................189 17.3 Results of the Regression Analysis................................................................................190 17.4 Discussion of the Regression Analysis Results .............................................................196

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18 ANGLE-MAJOR VEHICLE ACCIDENTS..............................................................211 18.1 Categorisation of the Data..............................................................................................211 18.2 Variables Selected for Analysis .....................................................................................211 18.3 Discussion of the Regression Analysis Results .............................................................213

19 REAR-END-MAJOR VEHICLE ACCIDENTS.......................................................217 19.1 Categorisation of the Data..............................................................................................217 19.2 Variables Selected for Analysis .....................................................................................218 19.3 Discussion of the Regression Analysis Results .............................................................223

20 SINGLE-THROUGH VEHICLE ACCIDENTS ......................................................230 20.1 Categorisation of the Data..............................................................................................230 20.2 Variables Selected for Analysis .....................................................................................232 20.3 Discussion of the Regression Analysis Results .............................................................235 20.4 Alternative Single-Through Vehicle Accident Models..................................................238

21 LOW FREQUENCY INTERSECTION ACCIDENTS............................................242 21.1 Rear-End-Minor .............................................................................................................242 21.2 Single-Minor-Turn .........................................................................................................246 21.3 Single-Major-Turn .........................................................................................................253 21.4 Overtaking-Intersection .................................................................................................257 21.5 Remaining Intersection Accidents .................................................................................262

Part E

22 COMBINED RESULTS ..............................................................................................265 22.1 Traffic Flow Variables ...................................................................................................265 22.2 Speed Parameters ...........................................................................................................267 22.3 Potential Measures to Reduce Vehicle Speed and Accident Rates ................................269 22.4 Intersection Type............................................................................................................273 22.5 Relative Accident Rate of the Various Conflict Types ..................................................277 22.6 Parameters Relating to Visibility Restrictions ...............................................................280 22.7 Free Left-turn Lanes.......................................................................................................283 22.8 Warrants for the Various Major Road Turn Types ........................................................284 22.9 Variables Found Unimportant in this Study...................................................................292 22.10 Variables Yielding Unreasonable or Illogical Results ...................................................293

23 IMPLICATIONS FOR ROAD DESIGNS STANDARDS .......................................294 23.1 Intersection Design Philosophy......................................................................................294 23.2 Measures to Reduce Vehicle Speed ...............................................................................295 23.3 Intersection Type............................................................................................................295 23.4 Parameters Relating to Visibility Restrictions ...............................................................296 23.5 Warrants for Turn Types................................................................................................298 23.6 Effect of Median Width on BAR, AUR and MNR Turn Treatments ............................301 23.7 Widened Shoulder for LSR Treatments .........................................................................301

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23.8 Free Left-turn Lanes ......................................................................................................302 23.9 Line Marking .................................................................................................................302 23.10 Approach Visibility .......................................................................................................303

24 ACCIDENT COSTS AND APPLICATION OF THE RESULTS OF THIS STUDY..........................................................................................................................304

24.1 Accident Costs ...............................................................................................................304 24.2 Application of the Results of this Study ........................................................................305

25 FUTURE WORK.........................................................................................................308 25.1 Update of Road Design Standards.................................................................................308 25.2 Implications for Further Analysis of Unsignalised Intersections Using the Techniques Developed in this Study ...........................................................................................................308 25.3 Reanalyse the Data in Arndt (1998) ..............................................................................308 25.4 Combine the Results of this Study with the Updated Results of Arndt (1998) .............309 25.5 Analysis of All Forms of Roadways and Intersections..................................................309

26 CONCLUSIONS..........................................................................................................311 26.1 Results of the Literature Review ...................................................................................311 26.2 Approaches Taken in this Study ....................................................................................311 26.3 Analysis Results ............................................................................................................313

27 RECOMMENDATIONS ............................................................................................317 27.1 Implications for Road Design Standards .......................................................................317 27.2 Future Work...................................................................................................................318

Appendices Appendix A - Accident Categories Appendix B - Vehicle Path Model Appendix C - Geometric Variables Appendix D - Costs of the Various Turn Types Appendix E - Turn Types used in this Study

Bibliography

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List of Tables

Table 2.1 - Speed of Minor Road Drivers Involved in Failure to Give Way Accidents using Data from the Study Kanda and Ishida (2000) .......... 37

Table 2.2 - Summary of Results of the Various Studies Reviewed ........................... 40 Table 3.1 - Combination of Variables in Multi-factor Studies .................................. 48 Table 4.1 - Intersection Types Selected/Rejected ...................................................... 66 Table 4.2 - Location of Intersections in Analysis ...................................................... 75 Table 4.3 - Types of Intersections in Analysis........................................................... 75 Table 5.1 - Selection of Analysis Period.................................................................... 77 Table 5.2 - Two Methods of Categorising the Data used........................................... 79 Table 5.3 - Methods of Categorising the Data ........................................................... 80 Table 5.4 - Initial Accident Classification ................................................................. 81 Table 5.5 - ‘Not Included in Analysis’ Accident Category........................................ 82 Table 5.6 - Major Accident Categories ...................................................................... 85 Table 6.1 - Geometric and Other Variables Identified............................................... 89 Table 6.2 - Possible Changes to Variables and .......................................................... 92 Table 6.3 - Number of Major Road Lanes ................................................................. 97 Table 6.4 - Control Type versus Number of Minor Legs........................................... 98 Table 6.5 - Median Width on Major Road versus Number of Intersection Sites..... 100 Table 7.1 - Range of Traffic Volumes Recorded on the Minor Legs ...................... 102 Table 7.2 - Range of Traffic Volumes Recorded on the Major Legs....................... 103 Table 9.1 - Types of Conflicts Recorded in the ....................................................... 108 Table 9.2 - Minor Road Vehicle Involvement Rate versus Vehicle Types.............. 110 Table 9.3 - Major Road Vehicle Involvement Rate versus Vehicle Types.............. 110 Table 9.4 - Angle-Minor Vehicle Accident Rates versus Light Conditions ............ 112 Table 9.5 - Angle-Minor Vehicle Accident Rate versus Day of Week.................... 114 Table 9.6 - Contributing Circumstances for Angle-Minor Vehicle Accidents ........ 115 Table 9.7 - Other Contributing Factors to Angle-Minor Vehicle Accidents ........... 116 Table 9.8 - Comparison of Recorded Angle-Minor Vehicle Accidents................... 117 Table 9.9 - Angle-Minor Vehicle Accident Rates for the Various Conflicts........... 120 Table 9.10 - Angle-Minor Vehicle Accident Rates.................................................. 121 Table 10.1 - Vehicle Movements - Angle-Major Vehicle Accidents ...................... 123 Table 10.2 - Turning Major Road Vehicle............................................................... 124 Table 10.3 - Oncoming Major Road Vehicle........................................................... 124 Table 10.4 - Angle - Major Vehicle Accident Rates Versus Light Conditions ....... 126 Table 10.5 - Contributing Circumstances for Angle-Major Vehicle Accidents ...... 127 Table 10.6 - Additional Contributing Factors to Angle-Major Vehicle

Accidents ............................................................................................ 127 Table 10.7 - Comparison of Recorded Angle-Major Vehicle Accidents................. 128 Table 10.8 - Angle-Major Vehicle Accident Rates for Various Conflicts............... 129 Table 11.1 - Front Vehicle Turning Movements - ................................................... 132 Table 11.2 - Rear Vehicle Involvement Rate versus Vehicle Types ....................... 133 Table 11.3 - Front Vehicle Involvement Rate versus Vehicle Types ...................... 133 Table 11.4 - Rear-End-Major Vehicle Accident Rates Versus Light Conditions.... 135 Table 11.5 - Contributing Circumstances for Rear-End-Major Vehicle

Accidents ............................................................................................ 136 Table 11.6 - Rear-End-Major Accident Rates for Various Turn Treatments........... 137 Table 11.7 - Length of Right-turn Slots in Austroads (1988) and in this Study ...... 138

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Table 12.1 - Single-Through Vehicle Accidents...................................................... 141 Table 12.2 - Single-Through Vehicle Accident Rate versus Vehicle Type............. 143 Table 12.3 - Single-Through Vehicle Accident Rates Versus Light Conditions..... 145 Table 12.4 - Contributing Circumstances for Single-Through Vehicle

Accidents ............................................................................................ 145 Table 12.5 - Single-Through Vehicle Accident Rates ............................................. 146 Table 12.6 - Single-Through Vehicle Accident Rates ............................................. 146 Table 13.1 - Front Vehicle Movements - ................................................................. 149 Table 13.2 - Rear-End-Minor Vehicle Accident Rates for Front Vehicle

Movements ......................................................................................... 150 Table 13.3 - Vehicle Movements -........................................................................... 150 Table 13.4 - Single-Minor-Turn Vehicle Accident Rates........................................ 151 Table 13.5 - Vehicle Movements -........................................................................... 152 Table 13.6 - Single-Major-Turn Vehicle Accident Rates ........................................ 153 Table 13.7 - Overtaking-Intersection Vehicle Accident Rates for the Various

Right-Turn Types and Line Marking Treatments (Two-Lane Roads Only)........................................................................................ 155

Table 15.1 - Types and Numbers of Accidents Recorded in the Study ................... 163 Table 15.2 - Parameters Over Represented in the High Frequency Accident

Types .................................................................................................. 164 Table 16.1 - Combined Variables ............................................................................ 169 Table 16.2 - Secondary Variables Omitted from the Regression Analysis.............. 172 Table 17.1 - Variables and Function Types for Angle-Minor Vehicle Accidents ... 191 Table 17.2 - Results of the Regression Analysis for Angle-Minor Vehicle

Accidents ............................................................................................ 192 Table 17.3 - Alternative Variables for Angle-Minor Vehicle Accidents................. 193 Table 17.4 - Regression Analysis Results for the .................................................... 195 Table 17.5 - Effect of the Variable ‘Driver Recognition of an ................................ 204 Table 18.1 - Variables and Results of the Regression Analysis .............................. 212 Table 18.2 - Alternative Variables ........................................................................... 213 Table 18.3 - Regression Analysis Results for the .................................................... 213 Table 19.1 - Front Vehicle Turning Movements - ................................................... 217 Table 19.2 - Variables and Results of the Regression Analysis .............................. 219 Table 19.3 - Alternative Variables for Rear-End-Major.......................................... 221 Table 19.4 - Regression Analysis Results for the .................................................... 222 Table 19.5 - Percentage of Sites in Each Category of Road Width ......................... 229 Table 20.1 - Variables and Results of the Regression Analysis .............................. 233 Table 20.2 - Regression Analysis Results for the .................................................... 235 Table 20.3 - Alternative Single-Through Vehicle Accident Models ....................... 239 Table 20.4 - Predicted Single-Through Vehicle Accident Rates for Various

Cases................................................................................................... 240 Table 21.1 - Variables and Results of the Regression Analysis .............................. 243 Table 21.2 - Regression Analysis Results for the ‘Turn’ Accident Subcategory .... 244 Table 21.3 - Variables and Results of the Regression Analysis .............................. 247 Table 21.4 - Alternative Variables for Single-Minor-Turn...................................... 248 Table 21.5 - Regression Analysis Results for the ‘Turn’ Accident Subcategory .... 250 Table 21.6 - Single-Minor-Turn Vehicle Accident Rates........................................ 251 Table 21.7 - Variables and Results of the Regression Analysis .............................. 254 Table 21.8 - Final Regression Analysis Results ...................................................... 255 Table 21.9 - Variables and Results of the Regression Analysis .............................. 258

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Table 21.10 - Alternative Variables ......................................................................... 259 Table 21.11 - Final Regression Analysis Results for the ......................................... 259 Table 22.1 - Power Constants of the Traffic Flow Variables for the ....................... 265 Table 22.2 - Significance of the Speed Parameters for the ...................................... 267 Table 22.3 - Relative Accident Rate for 100 and 60 km/h Speeds .......................... 268 Table 22.4 - Relative Accident Rate for Four Leg Intersections versus .................. 275 Table 22.5 - Angle-Minor and Angle-Major............................................................ 277 Table 22.6 - Rates of the Various Accident Types and............................................ 279 Table 22.7 - Effect of Free Left-turn Lanes on Accident Rates............................... 284 Table 24.1 - Average Cost per Accident for the Various Accident Types............... 305

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List of Figures

Figure 2.1 - Error of Drivers Failing to Give way at Unsignalised Intersections ...... 35 Figure 4.1 - Types of Right-Turn Treatments on Two-Lane, Two-Way Roads ........ 69 Figure 4.2 - Types of Right-Turn Treatments on Multi-lane Roads .......................... 70 Figure 4.3 - Types of Left-Turn Treatments .............................................................. 71 Figure 4.4 - Subcategories of Type LSR and MNR................................................... 72 Figure 4.5 - Subcategories of Type AUR Turn Treatments Used in this Study ........ 73 Figure 4.6 - Subcategories of Type CHR Turn Treatments Used in this Study......... 74 Figure 5.1 - High Frequency Intersection and Through Accident Types .................. 86 Figure 5.2 - Low Frequency Intersection Accident Types......................................... 86 Figure 5.3 - Low Frequency Through Accident Types.............................................. 87 Figure 6.1 - 85th Percentile Car Speed versus Horizontal Curve Radius ................... 93 Figure 6.2 - Type and Number of Minor Road Approach Lanes............................... 98 Figure 6.3 - Speed Limit and Speed Environment Prior to Intersection.................... 99 Figure 6.4 - Speed Limit and Speed Environment Prior to Intersection.................... 99 Figure 9.1 - Number of Angle-Minor Vehicle Accidents ........................................ 107 Figure 9.2 - Type of Vehicles versus Number of Angle-Minor Vehicle

Accidents ............................................................................................ 109 Figure 9.3 - Severity of Angle-Minor Vehicle Accidents........................................ 111 Figure 9.4 - Effect of Weather and Light Conditions on Number of....................... 111 Figure 9.5 - Time of Day versus Number of Angle-Minor Vehicle Accidents ....... 113 Figure 9.6 - Month of Year versus Number of Angle-Minor Vehicle Accidents .... 114 Figure 9.7 - Types of Conflicts Recorded in the...................................................... 119 Figure 10.1 - Number of Angle-Major Vehicle Accidents Compared to the

Total Number of Accidents ................................................................ 122 Figure 10.2 - Type of Vehicle versus Number of Angle-Major Vehicle

Accidents ............................................................................................ 123 Figure 10.3 - Severity of Angle-Major Vehicle Accidents ...................................... 125 Figure 10.4 - Effect of Weather and Light Conditions on Number of..................... 126 Figure 10.5 - Types of Conflicts Recorded in the.................................................... 129 Figure 11.1 - Number of Rear-End-Major Vehicle Accidents................................. 131 Figure 11.2 - Type of Vehicles versus Number of................................................... 132 Figure 11.3 - Severity of Rear-End-Major Accidents versus Number of

Accidents ............................................................................................ 134 Figure 11.4 - Effect of Weather and Light Conditions on Number of Rear-End-

Major Vehicle Accidents (Out of the 121 Rear-End-Major vehicle accidents, 58 were listed as unknown weather and light conditions) .......................................................................................... 135

Figure 11.5 - Types of Conflicts Recorded in the.................................................... 136 Figure 12.1 - Number of Single-Through Vehicle Accidents.................................. 140 Figure 12.2 - Distance from Centre of Intersection Versus Number of Single-

Through Vehicle Accidents................................................................ 142 Figure 12.3 - Type of Vehicle Versus Number of ................................................... 142 Figure 12.4 - Severity of Single-Through Vehicle Accidents.................................. 143 Figure 12.5 - Effect of Weather and Light Conditions on Number of Single-

Through Vehicle Accidents (Out of the 167 Single-Through vehicle accidents,................................................................................ 144

Figure 13.1 - Number of Low Frequency Intersection Accidents ........................... 148

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Figure 13.2 - Severity versus Number of Rear-End-Minor Vehicle Accidents ....... 149 Figure 13.3 - Severity versus Number of Single-Minor-Turn Vehicle Accidents ... 151 Figure 13.4 - Severity versus Number of Single-Major-Turn Vehicle Accidents ... 152 Figure 13.5 - Conflict Types Recorded in the Incorrect Turn Accident Category... 153 Figure 13.6 - Severity versus Number of Incorrect Turn Vehicle Accidents .......... 154 Figure 13.7 - Severity versus Number of Overtaking-Intersection Vehicle

Accidents ............................................................................................ 154 Figure 14.1 - Number of Low Frequency Through Accidents................................. 157 Figure 14.2 - Distance from Centre of Intersection Versus Number of

Pedestrian Accidents .......................................................................... 158 Figure 14.3 - Severity versus Number of Pedestrian Accidents .............................. 158 Figure 14.4 - Severity versus Number of Changed Lanes Vehicle Accidents ......... 159 Figure 14.5 - Severity versus Number of Single-Object Vehicle Accidents ........... 160 Figure 16.1 - Relationships between Geometric and ............................................... 177 Figure 17.1 - Effect of the 85th Percentile Minor Road Approach Speed ................ 198 Figure 17.2 - Effect of Sight Distance on Angle-Minor Vehicle Accidents ............ 201 Figure 17.3 - Effect of Observation Angle on Angle-Minor Vehicle Accident

Rates ................................................................................................... 202 Figure 18.1 - Effect of Sight Distance on Angle-Major Vehicle Accidents ............ 214 Figure 19.1 - Effect of Sight Distance on Rear-End-Major Vehicle Accidents....... 225 Figure 19.2 - Effect of Median Width on Rear-End-Major Vehicle........................ 226 Figure 20.1 - Effect of Vehicle Path Radius on Single-Through Vehicle

Accidents ............................................................................................ 236 Figure 20.2 - Location of Single-Through Vehicle Accidents on Horizontal

Geometric Elements in the ‘Major’ Accident Subcategory................ 238 Figure 21.1 - Effect of Minor Road Approach Speed .............................................. 251 Figure 22.1 - Effect of Sight Distance on Accident Rates ....................................... 282 Figure 22.2 - Potential Warrants for Right-Turn Treatments for an 85th

Percentile Speed of 110km/h Using the ‘By Accident Rate’ Method (estimated accident rate limited to one right-turn Rear-End-Major vehicle accident in ten years) ........................................... 286

Figure 22.3 - Potential Warrants for Right-turn Treatments for an 85th Percentile Speed of 70km/h Using the ‘By Accident Rate’ Method (estimated accident rate limited to one right-turn Rear-End-Major vehicle accident in ten years) ........................................... 287

Figure 22.4 - Potential Warrants for Right-turn Treatments for a New Intersection for an 85th Percentile Speed of 110km/h Using the ‘By Benefit / Cost Analysis’ Method (based on a benefit / cost ratio of one and an design life of 20 years) ........................................ 290

Figure 22.5 - Potential Warrants for Upgrading an AUR Intersection for an 85th Percentile Speed of 70km/h Using the ‘By Benefit / Cost Analysis’ Method (based on a benefit / cost ratio of one and an design life of 20 years) ....................................................................... 290

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Statement of Original Authorship

“The work contained in this thesis has not been previously submitted for a degree or

diploma at any other higher education institution. To the best of my knowledge and

belief, the thesis contains no material previously published or written by another

person except where due reference is made”.

Owen Arndt

March 2004

xiv

Acknowledgements

The author wishes to acknowledge the assistance of the following individuals and

authorities in the preparation of this study.

The following staff from the Queensland University of Technology:

• Professor Rod Troutbeck - for his continued encouragement, support and

guidance throughout the duration of this thesis and for that given throughout

previous projects.

• Mr Gareth Ridall - for his guidance and technical support

The following Queensland Department of Main Roads staff and offices:

• Mr Arthur Hall - for his support of this work

• Mr Jon Douglas - for his support of this work

• Mr Mark Logan - for supply of accident data

• Traffic Engineering and Road Use Management Division - for the supply of

traffic data

• Various engineers, designers and traffic personnel from within the following Main

Roads district offices for the supply of information:

South Coast Hinterland

North Coast Hinterland

Southern

South West

Border

Central

Mackay

Northern

Peninsula

Wide Bay

Metropolitan

Part A

1

Relationship Between Unsignalised Intersection Geometry and Accident Rates

1 INTRODUCTION

1.1 Objectives of the Study

The aim of this thesis is to determine the effect of unsignalised intersection geometry

on the rates and various types of accidents occurring at unsignalised intersections. To

determine the effect of unsignalised intersection geometry, the effects of traffic

volume and speed must also considered. Therefore, there are three specific objectives

of the study:

Objective 1

Objective 1 is to determine relationships between traffic volumes and accident rates.

Objective 2

Objective 2 is to determine relationships between unsignalised intersection geometry

and accident rates. In particular, this includes the following geometric parameters:

• Number of legs at the intersection

• Angle between the major and minor legs

• Horizontal curvature on the major and minor legs

• Left and right-turn treatments

• Median width

Objective 3

Objective 3 is to determine relationships between the following speed parameters and

accident rates:

• 85th percentile speeds on the major and minor legs

• Relative speed between major and minor road vehicles

• Decrease in speed between successive horizontal geometric elements

The purpose of determining these relationships is to build a model that enables

2

practitioners to check the likely safety performance of unsignalised intersection

designs. This will highlight any potential safety problems.

The model will also enable practitioners to understand whether there are major local

influences affecting accidents at an existing intersection by comparing recorded

accident rates with those predicted by the model (the average estimated accident

rate).

This study will also enable the accuracy and importance of some of the current

design standards to be verified. An update of the existing standards and the

development of new standards may then result.

1.2 Background to this Research

Many road geometric design standards within the various state and national road

design documents are based on theoretical models and the experience of

practitioners. These models often aim to set absolute and/or desirable minimum

standards to achieve an appropriate balance between perceived safety and cost. Many

of these models, although logical, have little objective safety evidence to support the

minimum standards set, or even to support the expected effect of particular

parameters within the model.

Geometric design standards can also be based on studies that relate accident rates to

geometric parameters using statistical analysis. However, the findings of these

studies can be quite limited and inconsistent. An expected reason for this result is as

follows. It is difficult to accurately identify the effect of all but the most important

geometric parameters due to the many variables that affect accidents, the relative

scarcity of accidents, and the interrelationships that exists between the parameters.

The approach taken in this study adopts techniques undertaken in a study of

roundabouts titled ‘Relationship Between Roundabout Geometry and Accident

Rates’ - Arndt (1998) in addition to new techniques developed in this study. This

approach attempts to obtain better and more usable results than those in previous

studies. A summary of the roundabout study and the techniques adopted is given

below.

1.3 The Roundabout Study - Arndt (1998)

Arndt (1998) selected one hundred roundabouts from throughout Queensland for

3

analysis. Relevant authorities provided data on geometry, traffic volume and major

accidents for these roundabouts.

A preliminary analysis was undertaken to review the accident data for any common

factors that applied in any of the crashes. Factors considered included driver error,

traffic conditions, types of vehicles involved, weather and light conditions, and road

geometry. Following the preliminary analysis, a regression analysis was undertaken

on the data to relate the roundabout geometry to accident rates.

Several different techniques were used in the regression analysis. A generalised

linear model with a Poisson error distribution was chosen to develop the final

equations for each major accident type. This method of analysis is appropriate for

accident data (which is not normally distributed) where the dispersion of the

dependent variable (ratio of variance to mean of the observed accident rates) is

approximately equal.

The initial accident models explained little of the variability in the data and few

parameters were found to be significant. It was later realised that better accident

models could be developed based on:

• The identification of primary and secondary parameters

• The importance of appropriate mathematical relationships between parameters

• The concept of exposure and propensity

• Selecting parameters relating to driver behaviour

Design guidelines were developed in the final report, based on the results of the

roundabout study. These were incorporated in Chapter 14 ‘Roundabouts’ of the

interim Queensland Department of Main Roads ‘Road Planning and Design Manual’

- QDMR (2000).

The results of the roundabout study have been incorporated into a draft computer

program titled ARNDT ‘A Roundabout Numerical Design Tool’. ARNDT is a useful

tool for determining the potential safety performance of a roundabout, by identifying

potentially hazardous geometry.

4

1.4 Potential Benefits of Undertaking Research at Unsignalised Intersections

The potential benefits of studying the relationship between unsignalised intersection

geometry and accident rates are expected to be similar to those obtained for the

roundabout study. Such benefits include:

• Production of updated design standards to enable practitioners to design

unsignalised intersections of optimal safety.

• Reduction of the number and severity of accidents at unsignalised intersections.

• Ability to determine if recorded accident rates at particular intersections are

similar to those that could be expected or whether local factors are influencing the

accident rates.

• Ability to determine if the savings in accidents of a particular unsignalised

intersection design outweigh the additional construction costs.

• Minimisation of potential litigation by avoiding poor design practices.

Upon completion of this study, the resulting accident equations can be combined

with those developed for roundabouts ie placed in the software program ‘ARNDT’.

In addition, practitioners will be able to determine whether a roundabout or an

unsignalised at-grade intersection will potentially yield the lowest accident rate at a

particular location for the given traffic flows and right-of-way constraints.

1.5 Definitions

Accident

NAASRA (1988) refers to vehicle collisions and other traffic incidents on the road

system which result in death, injury, or property damage as ‘road crashes’. The

reason given is that recent publications indicate that many of these incidences are not

accidental occurrences. However, this thesis uses the term ‘accidents’ instead of

‘road crashes’. Justification for using this term is as follows:

• Not all authors agree with the reasoning in NAASRA (1988). Hauer (1997)

disputes the way some practitioners reject the word ‘accident’. He believes that

the ‘fatalistic interpretation of accident’, such as that given by NAASRA (1988)

5

makes no sense and ‘...why intervene if accidents are preordained or

unavoidable’.

• Most references on road crashes at intersections have used the word ‘accidents’ in

lieu of ‘crashes’ (especially international references).

• The descriptor field within the most important databases related to this subject use

the word ‘accident’ in lieu of ‘crash’.

• It was desired to make the title of this thesis consistent with the previous study at

roundabouts Arndt (1998).

Accident Rate

Unless otherwise stated in this thesis, ‘accident rate’ is the number of accidents per

year. When this term is used for comparative purposes, all variables are held constant

(eg traffic volumes, speed, visibility) except those as stated.

Factorial Variable

The term ‘factorial variable’ has been used in this thesis to describe a variable that

comprises various categories. Factorial variables are input into the regression

analysis with codes to describe the categories.

Major Road

The term ‘major road’ refers to the approach legs of an unsignalised intersection that

are continuous through the intersection and have priority ie they do not contain stop

or giveway signs.

Minor Road

The term ‘minor road’ refers to the approach legs of an unsignalised intersection that

do not have priority ie they either end at a T-intersection (where the standard T-

intersection road rule applies) or they contain stop or giveway signs.

Turn Treatment Types

The rural turn treatment codes (A, B and C) listed in Austroads (1988) ‘Part 5 -

Intersections at-grade’ have not been adopted in this thesis. Instead, modified turn

treatment codes from QDMR (2000) and Austroads (2003) have been used.

6

Austroads (2003) is the final draft update of Austroads (1988).

The QDMR (2000) and Austroads (2003) codes were used as a basis because this is

current Queensland practice and is expected to become the national practice. These

codes were modified to adequately describe the various turn treatments in existence.

The modified QDMR (2000) and Austroads (2003) codes are listed in Section 4.3.

The codes are repeated in Appendix E, to enable easy reference for the reader.

Variable

The term ‘variable’ has been used in this thesis to describe traffic volume, geometric

and other parameters that are related to the dependent variable ‘accident rate’. This

term is used in lieu of the traditional term ‘independent variable’, as favoured

amongst statisticians. Unlike the term ‘covariate’, the term ‘variable’ was found to be

more useful because it describes both measured parameters (covariates) and

transformed parameters.

1.6 Outline of this Thesis

A basic outline of this thesis is given below.

Chapter 2 - Literature Review: This chapter documents the results of studies that

have attempted to relate intersection geometry to accident rates. This chapter also

reviews studies relating traffic conflicts, traffic volumes and driver behaviour to

accident rates at unsignalised intersections. A comparison of the results of the

literature review to the objectives of this study is then made.

Chapter 3 - Thesis Approach: This chapter presents the approach taken in this

thesis in order to mitigate the problems identified with previous multi-factor studies.

Chapter 4 - Selection of Unsignalised Intersection Sites This chapter discusses

techniques used to choose a number of intersection sites, the types of numbers of

intersections selected and an overview of the selected intersections.

Chapter 5 - Accident Data: This chapter discusses the source and collection of

accident data and the selection of analysis periods. It then outlines the method used

to categorise the data and an overview of these categories.

Chapter 6 - Geometric and Other Variables: This chapter discusses techniques

used for the selection of geometric and other parameters, the methods used in

7

measuring these parameters and an overview of the collected data.

Chapter 7 - Traffic Flow Data: This chapter discusses techniques used for the

selection of traffic flow parameters, the method used in measuring these parameters

and an overview of the collected data.

Chapters 8 to 15 - Preliminary Analysis: These chapters document the preliminary

analysis undertaken on the collected data to determine how the factors ‘driver error’,

‘traffic conditions’, ‘environmental conditions’ and ‘road geometry’ affect the

various accident types recorded. This analysis was performed on each of the accident

types by using simple tabular and graphical techniques. The purpose was to obtain a

‘feel’ for the data to help identify appropriate techniques for analysing the data in the

regression analysis. A summary of the results of the preliminary analysis is given in

Chapter 15.

Chapter 16 - Statistical Modelling Issues: This chapter discusses techniques used

to perform the regression analysis including the treatment of highly correlated

variables, identification of appropriate model forms, the diagnostic checks used and

the validation of the results.

Chapters 17 to 21 - Regression Analysis: These chapters discuss the results of

applying the techniques in Chapter 16 to each accident type. This forms the

regression analysis of the data. Methods of sub-dividing each accident type and the

variables selected for analysis are firstly discussed in each chapter. The best accident

models are then selected and validated followed by a discussion of the results of the

analysis.

Chapter 22 - Combined Results: This chapter combines the results obtained in

Chapters 17 to 21 to determine overall trends in the data.

Chapter 23 - Implications for Road Designs Standards: This chapter lists the

outcomes of this study by referencing relevant sections of this thesis and discusses

the implications of these outcomes on current intersection design standards.

Chapter 24 - Accident Costs and Application of the Results of this Study: This

chapter shows the method of calculation of accident costs for each of the accident

types in the study. It also recommends how the results of this study should be applied

to the future design of unsignalised intersections.

8

Chapter 25 - Future Work: This chapter recommends what future work should be

undertaken to obtain maximum benefits of this study. It also discusses how the

findings of this study can be used to undertake research at other forms of

intersections and roadways.

Chapter 26 - Conclusions

Chapter 27 - Recommendations

9

2 LITERATURE REVIEW

This literature review is divided into several sections. Section 2.1 reviews all ‘multi-

factor studies’ found in the literature search that have analysed geometric, traffic

volume and accident data at unsignalised intersections in order to determine the

relationship between geometry and accident rates.

Various studies have gathered data in order to find the relationship between one

particular geometric parameter on accident rates. These studies are referred to as

‘matched group studies’ and the results of such studies identified in the literature

search are shown in Section 2.2.

Another method of determining the effect of geometry on accident rates is to

undertake ‘before and after’ studies of unsignalised intersections. The results of such

studies identified in the literature search are discussed in Section 2.3.

An alternative method of determining the effect of geometry on safety is to undertake

studies to relate geometry to an observed number of traffic conflicts. Some studies

undertaken in this area are discussed in Section 2.4.

Section 2.5 reviews the results of studies relating traffic volumes to accident rates at

unsignalised intersections. These studies do not consider any effect from geometric

parameters.

Section 2.6 reviews literature on driver behaviour at unsignalised intersections. The

purpose was to gain an appreciation of what errors are being committed by drivers

involved in accidents.

A summary of the reviewed literature is given in Section 2.7. Finally, Section 2.8

discusses the results of the literature search compared to the objectives of this study.

2.1 Multi-factor Studies

OECD (1971) defined ‘multi-factor studies’ as those considering simultaneously the

effects of many factors on the incidence of accidents. These studies aimed to indicate

the extent of the contribution of each factor, in each situation, to the accident

incidence eg by providing a mathematical equation representing the number of

accidents as some function of the factors considered.

The literature review has revealed that several multi-factor studies from around the

10

world have been undertaken to relate unsignalised intersection geometry and traffic

volumes to accident rates. These have been undertaken by collecting geometric data,

traffic volume data and accident data, then undertaking a regression analysis of this

data to determine relationships.

Approaches Taken within Multi-factor Studies

There was considerable variation in the approaches taken in the various multi-factor

studies. The types of sites selected, the method of site selection, the number of

intersections selected, the method of categorising the accident data (or lack of), and

the variables selected for trial all varied significantly between the various studies.

This is not surprising considering that the safety of an intersection results from the

operation of a complex system of variables as reported by OECD (1971). In general,

no single variable can be shown to be responsible for an accident, but rather, it can

be shown to have resulted from the presence and interaction of a number of

conflicting variables. This complexity of interaction between variables results in the

possibility of many different approaches to this type of study.

The various approaches taken in the reviewed literature are given in the following

sections.

Types of Sites Selected

Some studies chose to analyse a narrow category of intersections. Pickering, Hall et

al (1986) studied 300 priority T-intersections on rural single carriageway roads. The

intersections had a speed limit of 50 mph or more, were on roads without continuous

frontage development and had no kerbed islands on the major road. This is a very

specific type of intersection chosen for analysis.

Other studies chose a wide range of intersection types, control and geometry. Bauer

and Harwood (1996), for example, chose three-leg and four-leg intersections in urban

and rural areas comprising stop and signalised intersection control.

Method of Site Selection

The method of selecting sites for analysis varied between studies. Some studies

selected sites at random. Agent (1988), however, selected 65 high-speed rural

intersections in such a way as to provide a variety of traffic volume, roadway

11

geometrics, and traffic control. In a similar way, Pickering, Hall et al (1986) sampled

sites to obtain traffic flows in as wide a range as possible in order to provide an

adequate basis for subsequent analysis.

Number of Intersections Selected/Categorising of the Accident Data

Some multi-factor studies comprised a very large sample of intersections. Bauer and

Harwood (1996) analysed 11,165 intersections of various configurations. It was

possible to analyse such a large number of intersections because all data used for the

analysis was already contained within an existing database or was derived from it.

However, a number of geometric, traffic control, and traffic volume variables of

potential interest were not available in the existing database. To check the

importance of these variables, a subset of these intersections were selected and the

variables measured in the field.

Another study comprising a large number of intersections was undertaken by Huang

and May (1991) who developed accident prediction models for 11,786 unsignalised

and 2,488 signalised intersections.

Studies comprising large numbers of intersections generally did not involve the

categorisation of accident data into various accident types and therefore did not

identify potential parameters affecting the safety of each particular accident type.

Studies that comprise a smaller number of intersections generally involve some

categorisation of the accident data. For example, Pickering, Hall et al (1986)

analysed 300 rural T-intersections and initially categorised the data into 43 accident

types. However, for the purposes of analysis, these were amalgamated into 13

accident types.

In an analysis of 149 four-leg unsignalised intersections, Belanger (1994) stated that

breaking accidents into patterns constitutes a more powerful tool of analysis because

they can provide a detailed identification of abnormal situations. Such an example is

a site having a total number of accidents not significantly higher than the average

total for similar sites but which shows an abnormal frequency of right-angle

collisions.

The following section lists the major types of accidents recorded in various studies

that have categorised accident data.

12

Accident Types Identified

Summersgill, Kennedy et al (1996) identified the most common accidents at three-

leg priority intersections on urban single-carriageway roads by using the categories

pedestrian (31.7%), right-turn from minor leg (16.6%), rear-end on major leg

(13.8%), right-turn from major leg (12.1%), single vehicle on major leg (6.9%),

head-on and U-turn (3.9%) and left-turn from minor leg (2.8%).

Layfield (1996) identified the most common accidents at urban priority crossroads

and staggered intersections were right-angle (40.9%), right-turn (35.8%), pedestrian

(9.6%), left-turn (7.2%), rear-shunts and lane changing (2.7%), and single vehicle

(2.1%).

Pickering, Hall et al (1986) classified accidents at rural T-intersections into two main

groups: 0 - 20m from the intersection (674 accidents) and 20 - 100m from the

intersection (296 accidents). In the 0-20m group, the most common accidents were

categorised as right-turn from minor leg (27.4%), right-turn from major leg (22.1%),

rear-end (19.7%), single vehicle (14.4%), head-on (8.2%) and left-turn (3.4%). In the

20-100m group, the most common accidents were categorised as single vehicle

(42.2%), head-on (26%), rear-end (19.6%) and pedestrian (6.8%).

In a study of 65 rural high speed intersections with all forms of intersection control,

Agent (1988) used the categories angle (46.6%), rear-end (21.1%) and opposing left-

turn (equivalent to right-turn in Australia - 20.5%) and single vehicle (4%).

Hanna, Flynn et al (1976) found that rural intersections with stop or yield control

contained 49% angle accidents, 29% rear-end accidents, and 10% sideswipe

accidents.

From the above studies, the most common vehicle accidents at unsignalised

intersections appeared to be angle (right-turn or through-movement from minor leg

colliding with a vehicle on the major road travelling through), right-turn from major

leg (colliding with an oncoming vehicle on the major road), and rear-end. Single

vehicle, head-on, sideswipe and left-turn from minor (colliding with a major road

vehicle) are common but are less in number.

Analysis Types

Several different methods of analysing the accident, traffic and geometric data have

13

been used in the multi-factor studies. These are discussed in the following sections.

Use of Multiple Regression Analysis Studies up to the early 1980’s were likely to have used stepwise multiple linear

regression analysis techniques that assume normal distribution of data. Kitto (1980)

is one example.

Bauer and Harwood (1996) stated that the use of multiple regression is inappropriate

for developing relationships between accident rates and geometric variables for the

following reasons:

• Accidents do not follow a normal distribution. Traffic accidents are random,

discrete events that are sporadic in nature. Normalising accident frequencies with

exposure estimates, such as million vehicle-miles of travel or million vehicles

entering an intersection, to make the accident rate appear to be a continuous

random viable does not change the fundamentally discrete nature of accident data.

• Accident frequencies for particular intersections or relatively small roadway

sections are typically very small integers, even if several years of accident data are

obtained for those intersection or roadway sections. In fact, it is not uncommon

for a substantial proportion of the sites in an accident study to have experienced

no accidents at all during the study period. Small integer counts, often zero or

close to zero, do not typically follow a normal distribution.

• Accident frequencies and accident rates are necessarily non-negative. However,

there is nothing to constrain traditional multiple regression models from

predicting negative accident frequencies or accident rates, which confronts the

accident analyst trying to use the predictive model with a meaningless result.

Bauer and Harwood (1996) stated that the use of the Poisson and negative binomial

distributions are appropriate for rare events like traffic accidents counts where the

number of events in a given time period is likely to be zero or a small integer.

Distributional Assumptions Other than Normal Studies after 1980 have tended to assume non-normal distributions, especially the

Poisson distribution eg Agent (1988). Use of negative binomial models as in Vogt

(1999) and lognormal models as in Bauer and Harwood (1996) are also common.

Maren (1980) transformed the accident data for each intersection that recorded no

14

accidents by adding a value of 1.0 to each calculated accident rate and taking the

square root. Although it was stated that accidents are an infrequent event that follow

a Poisson distribution, stepwise regression using a normal distribution appeared to be

used in the analysis.

Different approaches have been taken in selecting which model to use for various

types of accident data. Several authors eg Bauer and Harwood (1996) explained that

use of the Poisson distribution is only relevant where the variance in the accident

data is equal to the mean. Over-dispersion, which occurs when the variance of the

accident-frequency data is greater than its mean, can result in biased model

coefficients and erroneous standard errors. The negative binomial can be used to

overcome the over-dispersion concern.

Kulmala (1997) explained that the variation in the number of accidents is a

combination of systematic variation between the expected number of accidents at

different intersections and the random variation. The systematic part of the variation

is the part that is explained by modelling techniques. Kulmala (1997) assumed the

random variation followed either a Poisson or negative binomial distribution. An

opinion was given that the accuracy and appropriateness of a Poisson model should

be measured by how much of the systematic variation of the response variable the

model can explain.

TRL research projects Summersgill, Kennedy et al (1996) and Layfield (1996) stated

that when the mean number of accidents per intersection is less than 0.5, the scaled

deviance is reduced below that expected for the generalised Pearson χ2 function.

Summersgill, Kennedy et al (1996) used a quasi-likelihood method to take into

account of the over-dispersion in the presence of low mean values. This approach has

been discussed earlier in Maycock and Maher (1988). Each model was initially

calculated assuming a Poisson distribution. The amount of over-dispersion was then

determined by calculating the ratio of the generalised Pearson χ2 function, to the

number of degrees of freedom (df) for each model. This provided a revised estimate

of the scale factor (s).

Bauer and Harwood (1996) analysed data using Poisson, negative binomial,

lognormal and logistic distributions and concluded that these methods of analysis are

better suited to the modelling of accident relationships than the normal distribution. It

15

was recommended that the form of the statistical distribution selected for any

particular modelling should be based on a review of the data to be modelled. The

Poisson distribution was preferred where the data was not over or under dispersed.

The negative binomial distribution is preferred where over or under dispersion

occurs. The lognormal distribution was found to be the most appropriate choice of

modelling two of the intersection types in the study.

Harwood et al. (1995) found Poisson regression useful for analysing accident

frequencies for rural and urban unsignalised intersections that included many

intersections with no or very few accidents. The Poisson approach was found

unsuitable for analysing accident frequencies at urban signalised intersections that

did not include many intersections with very few accidents. A lognormal regression

approach was found to be more appropriate for analysing the data for this

intersection type.

Huang and May (1991) used a three level modelling approach. The level 1 approach

(the base model) was a regression model relating accident rates to traffic volumes

only. A grouping and classification technique called Classification and Regression

Tree (CART) was used for developing the second level model. This model was used

to analyse the residuals of the base model by grouping together those intersections

with similar characteristics (based on geometric and other parameters) and which

have higher or lower accident records than other intersections in general. The level

three model considered the accident history of individual intersections.

Model Forms

Most studies reviewed have used variants of the following model:

A = k Q1a Q2

bexp(Σci Gi) Equation 2.1

Where A = accident frequency

k, a, b and ci are constants to be estimated

Q1 = first traffic flow variable

Q2 = second traffic flow variable (multiple vehicle accidents only)

Gi = geometric variables

Bauer and Harwood (1996) used the following model form for the lognormal and

log-linear regression models:

16

Y = exp(β0)(ADT1)β1(ADT2)β2exp(β3Xi3) x … x exp(βqXiq) Equation 2.2

Where Y = accident frequency

β0 to βq = constants to be estimated

ADT1, ADT2 = traffic volume variables

Xi = geometric and other variables

Vogt (1999) used the following model:

µ1 = exp(β1 +ΣXijβj) Equation 2.3

Where µ1 = accident rate

β1 to β = constants to be estimated

Xij = intersection variables

When the value of a geometric variable in the above models is zero, the

multiplicative term becomes e0 = 1, and is omitted. Therefore, a value of a geometric

variable of zero has no effect on the accident rate.

General Findings

Traffic Flow Variables Most studies have found traffic flow to be an important parameter affecting accident

rates. Bauer and Harwood (1996) found that the traffic volume accounted for most of

the variability in the accident data at all forms of at-grade intersections. Huang and

May (1991) found traffic intensity to be the most important single factor in

predicting accident rates at signalised and unsignalised intersections. Pickering, Hall

et al (1986) found functions of flows were highly significant predictors of accident

frequency for rural T-intersections.

Del Mistro (1981) found traffic volumes to be by far the most important variable for

a sample of intersections that included all types of traffic control: signalised, all way

stop and other control. Kulmala (1997) found that the most important variables at

three and four-leg intersections were those describing the magnitude and distribution

of traffic volumes. In an analysis of rural three and four-leg intersections with stop

sign control, Vogt and Bared (1998) concluded that exposure and traffic counts are

the chief highway variables contributing to accidents.

17

Relationships developed between traffic volumes and accident rates for the various

studies reviewed are given in the following section titled ‘Relationships Between

Traffic Volumes and Accident Rates’.

Geometric Variables In general, studies relating unsignalised intersection geometry to safety have yielded

inconsistent results. If a particular study did identify an important geometric

parameter, it was often not considered by other studies, was not found to be

important or was found to have the opposite effect. Vogt and Bared (1998) and Bauer

and Harwood (1996) found certain geometric parameters to be significant, however,

some of the effects were the opposite of what was expected.

Geometric parameters found important by the various studies are given in the

following section titled ‘Geometric and Other Parameters Found Important’.

Variability in the Accident Data Even the best equations developed (which included traffic flow) did not explain most

of the variability in the data. Bauer and Harwood (1996) found that geometric

parameters, traffic control, and traffic volume parameters explained between 16 and

38 percent of the variability in the accident data. In an analysis of four-leg, right-

angle intersections comprising all forms of intersection control, Kitto (1980) found

that over 60 percent of the variability in the data was not explained.

Relationships between Traffic Volumes and Accident Rates

Pickering, Hall et al (1986) found that when accidents were divided in various

groups, traffic flows were highly significant predictors of accidents, in most cases,

the best fitting flow functions being those directly connected with that type of

accident.

Del Mistro (1981) used several traffic volume indices and the one found to combine

ease of computation with accuracy in modelling the accident data was the ‘product

volume’ index. This is the product of the sum of minor road approach flow/s and the

sum of major road approach flows.

Kulmala (1997) found that the total accident rate was proportional to the total

number of entering vehicles raised to a power of around 1. Crossing accidents were

proportional to the minor road traffic to a power of around 0.8 and to the major road

18

of between 0.3 to 0.5. From this, Kulmala (1997) concluded that for crossing

accidents, the minor road flow is a more important parameter than the major road

flow. For all other accident types, the major road flow was more important.

Vogt (1999) found ADT to play an important role at unsignalised three-leg

intersections, less at unsignalised four-leg intersections, and lesser again at signalised

intersections.

Geometric and Other Parameters Found Important

As discussed previously, if a particular study did identify an important geometric

parameter, it was often not identified as important in other studies or was sometimes

found to have the opposite effect. The following findings have been summarised

from the various studies.

Intersection Type

Cross Intersection versus T-intersection Most studies have shown that T-intersections are safer than cross-intersections, when

taking into account traffic volumes. Leong (1973) found that the mean accident rate

at three-arm intersections was lower than the mean accident rate at four-arm

intersections for similar types of traffic control. Hanna, Flynn et al (1976) found that

accident rates at four-leg rural intersections are 69 percent higher than at T-

intersections. O'Brien (1976) found that rural cross intersections had five times the

accident rate of T-intersections.

David and Norman (1975) found that cross intersections tend to have higher total

accident rates than do T-intersections for a given ADT. A further study, David and

Norman (1979), found that at urban intersections with stop signs, the accident rates

were very similar for four-leg and T-type designs with an average ADT of under

20,000. Once above that plateau, the accident rate doubled for four-leg when

compared with T-type intersections.

Cross-intersections versus Staggered T-intersections Del Mistro (1979) related accident rates to the volume index - the product of the sum

of the minor road approach flow/s and the sum of the major road approach flows

‘VP’. The following results were obtained:

• For VP > 23 000 000, cross-intersections are safer than T-intersections

19

• For VP in the range 3 300 000 to 23 000 000, cross-intersections have similar

accident rates to T-intersections

• For VP < 3 300 000, cross-intersections are less safe than T-intersections

Kulmala (1997) found that a four-leg intersection is safer than two three-leg

intersections, for low proportions of minor road flow, but less safe for high

proportions of minor road flow. This is an opposite result to the above finding by Del

Mistro (1979). Therefore, there is conflicting evidence as to whether or not a

staggered T-intersection is safer than a cross intersection.

Traffic Control Type

Although the studies reviewed revealed conflicting evidence, a greater number of

studies indicated that when taking into account traffic volumes, signalised

intersections record a greater number of accidents than unsignalised intersections.

David and Norman (1975) found that signalised cross intersections showed

considerably higher accident rates than stop-controlled cross intersections. Hanna,

Flynn et al (1976) found that for a given intersection and ADT, rural signalised

intersections have a higher accident rate than those intersections with stop or yield

sign control.

Maren (1980) found that multi-lane unsignalised intersections have a lower number

of accidents per million conflicts than signalised intersections. The number of

accidents per million conflicts was used as the independent variable as this variable

was found to better describe the accident potential of high accident locations than

one utilising the intersectional entering volume. Leong (1973), however, found that

the presence of traffic signals reduced the mean accident rate at four-arm

intersections, but had little effect at three-arm intersections.

Kitto (1980) found that intersections with give way signs recorded similar accident

rates to those with stop signs. Stockton, Brackett et al (1981) concluded that at low-

volume intersections, the control type has no appreciable effect on accident rates.

Number of Lanes

Transport Research Laboratory (TRL) studies Summersgill, Kennedy et al (1996)

and Layfield (1996), found that an increase in the number of traffic lanes increased

the number of rear end and lane-changing accidents.

20

Size of Intersection Conflict Area

Maren (1980) found that at large unsignalised intersections (those with a large

distance across the intersection), the number of accidents per million conflicts was

higher than at small unsignalised intersections.

Provision of Auxiliary Lanes

Within the studies, there is conflicting evidence of the benefits of right-turn lanes.

Kulmala (1997) found that a left-turn lane on the major road (equivalent to right-turn

in Australia) reduced the number of rear-end accidents on the major road. For four-

leg intersections, Vogt (1999) found that a 38.4 percent reduction in total accidents

occur by the presence of one or more left-turn lanes (equivalent to right in Australia).

David and Norman (1975), however, found that intersections with opposing left-turn

lanes (equivalent to right-turn lanes in Australia) recorded more accidents than those

without left-turn lanes. Also, Pickering, Hall et al (1986) found diverging lanes to

have no significant effect on accidents.

Kulmala (1997) found that the accident rate is lower at intersections with a separate

right-turn lane (equivalent to left-turn in Australia) on the major road.

Minor Road Approach Geometry

Kulmala (1997) found accident rates to be often lower than average at intersections

with a curve on the minor road approach before the intersection especially at four-leg

intersections.

Grades

Pickering, Hall et al (1986) found that downhill approaches were found to be

associated with higher accident rates. Hanna, Flynn et al (1976), however, found that

intersections with severe grades generally operate safely, although they are obviously

potential hazards.

Sight Distance

There is inconsistency between the results obtained of the effect of visibility on

accident rates. David and Norman (1975) indicated that intersections with an ADT

greater than 15,000, and with obstructions within the first 20ft (6.1m) back from the

21

stop lines, recorded 83 percent more accidents per year than did intersections

unobstructed within that distance. Hanna, Flynn et al (1976) found that rural

intersections with poor sight distance on one or more approaches tend to have higher

than normal accident rates.

Pickering, Hall et al (1986), however, found that visibility from the minor arm was a

significant predictor for only one relatively small accident class, where better

visibility to the right resulted in a higher accident frequency. Stockton, Brackett et al

(1981) found that at low-volume intersections, sight distance has no discernible

effect on accident rates.

Signing and Delineation

David and Norman (1975) found that high volume intersections using street signs

with white lettering on a dark background have an average of 96 percent more

accidents per year than those having dark lettering on a white background. However,

it is considered unlikely that such a difference in signage could have this much

effect.

Maren (1980) found that larger stop signs on the minor legs were found to decrease

the number of accidents per million vehicle conflicts.

David and Norman (1975) found that intersections with raised pavement markers

recorded fewer accidents than those without raised pavement markers.

Agent (1988) concluded that providing the driver adequate warning of the

intersection is of primary importance at rural high speed intersections because of the

many accidents which occurred in which a driver on a side street did not observe the

through vehicle and consequently pulled into its path.

Road Classification

Huang and May (1991) found that intersections with stop signs on main streets

recorded a higher accident rate than intersections with stop signs on minor streets.

The anticipated reason for this was that motorists might not generally expect stop

signs on main streets.

Restricted Turning Movements

Huang and May (1991) found that intersections with no left-turn permitted

22

(equivalent to right-turn in Australia) recorded a lower accident risk.

Presence of Lane Dividers

There is conflicting evidence relating to the value of medians and islands. Leong

(1973) found that the presence of narrow-kerbed medians on main roads reduced the

mean accident rate at three-arm intersections, but had little effect at four-arm

intersections. David and Norman (1979) found that multi-vehicle accident

involvement decreases when lane dividers (raised reflectors, painted lines, barriers,

medians) are used. Summersgill, Kennedy et al (1996) found that the presence of an

island on the minor leg was associated with increases in several accident types. An

island on the major right leg of a T-intersection reduced accidents for some accident

groups.

Layfield (1996) found that the presence of an island on the major road had a mixed

effect. Some accident types were lower whilst others were higher. Pickering, Hall et

al (1986) found that at higher flow intersections, the presence of ghost islands

(painted hatched medians/islands) resulted in a 35 percent reduction in accident rates

for the 0 - 20m accident group (accidents occurring within 20m of the intersection).

However, greater road width at the intersection was found to have broadly the same

benefit as ghost islands.

Maren (1980) found that median barriers were found to increase the accident rate

considerably.

Harwood, Pietrucha et al (1995) found that at rural, unsignalised intersections, the

frequency of both accidents and undesirable driving behaviour decreases as median

width increases. Conversely, at suburban unsignalised intersections, the frequency of

both accidents and undesirable driving behaviour increases as median width

increases. The frequency of undesirable driving behaviour increases as median-

opening length increases at rural intersections and decreases for suburban

intersections.

Length between Staggered T-intersections

Layfield (1996) analysed accidents at urban priority crossroads and staggered

intersections. The particular staggered intersections used for the study were those

where the absolute value of the stagger length exceeds 5m, but is less than 20m.

23

Longer stagger lengths between the minor legs were found to result in fewer total

vehicle and right-angle accidents.

Pedestrian Crossing Facilities

Transport Research Laboratory studies by Summersgill, Kennedy et al (1996) and

Layfield (1996) found that the presence of pedestrian crossing facilities at T-

intersections and at crossroads (including staggered intersections) were associated

with more pedestrian accidents. However, the mean number of accidents per

pedestrian crossing the road was less at those intersections with pedestrian crossing

facilities than those without.

Speed Parameters

Pickering, Hall et al (1986) found that variables representing major road traffic

speeds at the intersection were significant in models for 5 classes of 0 - 20m

accidents (accidents occurring within 20m of the intersection), however, in only two

cases did higher mean speeds give rise to higher accident rates. Summersgill,

Kennedy et al (1996) found a similar result in that there was no evidence that the

speed of vehicles on either the major or minor roads influenced accident occurrence

when other variables were taken into account. Summersgill, Kennedy et al (1996)

suspected that this result was obtained because the some of the significant variables

found to influence accidents do so by modifying speeds.

The above results are not unexpected, however, for the following reason. Pickering,

Hall et al (1986) analysed only rural intersections with speed limits above 50mph.

Summersgill, Kennedy et al (1996) analysed only T-intersections on 30 and 40-mph

roads. Each study comprises only a narrow band of speed data. A significant

relationship between speed and accidents is unlikely to be found using such a narrow

band of data.

When determining the effect of a particular variable on accident rates, a wide range

of values of the independent variable is desirable. This was the approach taken by

Agent (1988) and the approach proposed in this study as discussed in Chapter 3.

Pickering, Hall et al (1986) used this same concept to select a wide range of traffic

volumes for analysis.

24

2.2 Matched Group Studies

OECD (1971) defined the objective of ‘matched group studies’ as the investigation

of the effects of a single factor. The method uses two groups of situations that are

similar, except in the representation of the factor under study; it will be present in

one group and not in the other. The results of the matched group studies identified in

the literature search are shown below:

Lipinski and Wortman (1976) compared accident rates of rural intersections with and

without lighting. It was found that night accidents reduced by 45 percent when

illumination was installed. The presence of channelisation at illuminated

intersections further reduced accident rates.

Morrison (1998) compared accidents at six intersections that comprise Minor

Intersection Sign Treatment ‘MIST’ with all stop sign controlled intersections within

their respective council areas. MIST included a kerbed median traffic island with

keep left and oversized stop signs on the island, and oversized stop signs on the

right-side footpath in addition to the existing stop sign on the left footpath. This

treatment resulted in a 50 percent reduction in crashes for sites that had the following

characteristics:

• Road hierarchy is unclear or traffic volumes for each of the two intersecting roads

are similar;

• The left hand side stop sign is obscured or faded; and

• There is a sight distance problem

Pant, Park et al (1999) compared the safety effectiveness of beacon-controlled

intersections with stop-controlled intersections. At a two-way stop-controlled

intersection, beacons flash yellow on the major road and red on the minor road. The

following conclusions were given:

• Intersection control beacons generally reduced vehicular speeds in the major

directions particularly at intersections with inadequate sight distance;

• Intersection control beacons had little or no effect on accepted or rejected gaps

and on service delays; and

• Intersection control beacons did not appear to be effective in reducing accidents.

25

2.3 Before and After Studies

OECD (1971) defines ‘before and after’ studies as two matched groups of situations

formed to test the effects of one factor. They are different to ‘matched group’ studies

in that each situation is matched with itself, first without and then with the factor

present.

At intersections, geometric, traffic volume and accident data is collected prior to and

after a particular change to an intersection. When comparing the accident rates before

and after the change, it is common for researchers to correct for ‘regression to the

mean’ effects eg Kulmala (1994).

Results of the ‘before and after’ studies identified in the literature search are given

below.

Accident Categories

Brude (1991) found that left-turns (equivalent to right-turns in Australia) and

crossing movements are the most dangerous movements at intersections. In rural

environments, left-turns (right-turns in Australia) from the major road were found to

be the most dangerous. In urban environments, however, left-turns (right-turns in

Australia) were found to be more dangerous from the minor road.

Belanger (1994) found that right-angle accidents at unsignalised four-leg

intersections account for 42 percent of all accidents involving two or more vehicles.

The next most common accident was between a right-turn and a through vehicle.

Gambard (1988) found that crossing conflicts (vehicles coming straight from two

different legs) represented approximately 60% of the total number of injury accidents

at four-leg intersections and 30% at three-leg intersections. Left-turn conflicts

(equivalent to right-turn in Australia), which comprised rear-end or head-on

collisions with vehicles turning off the major road to the left (right in Australia),

represented about 20% of the total number of injury accidents at four-leg

intersections and 30% at T-intersections.

The accident types identified in the above studies are consistent with those found in

the multi-factor studies.

26

Traffic Flow Variables

Poch and Mannering (1996) found that increasing left-turn volumes (equivalent to

right-turn in Australia) increased accident frequencies. Increased right-turn volumes

(left-turn in Australia) also increased the likelihood of an accident.

Intersection Type

Brude (1991) found the accident rate on average to be 1.5 - 2 times higher for four-

leg intersections than for three-leg under comparable traffic conditions. Gambard

(1988) found that the frequency of accidents on four-leg intersections was about

twice as high as three-leg intersections. These finding are consistent with those found

in multi-factor studies.

Traffic Control

King and Goldblatt (1975) found no clear cut evidence that the installation of signals

would reduce the adverse effects of accidents, especially for cases where traffic

signals were not warranted by traffic volume.

Polus (1985) studied 160 unsignalised intersections in Israel to determine whether an

increase in traffic control is beneficial for safety. The following increases in traffic

control were considered:

• Uncontrolled intersection to give way sign on the minor road

• Uncontrolled intersection to stop sign on the minor road

• Give way sign on the minor road to stop sign on the minor road

It was found that an increase in the level of control tended to cause more vehicle

accidents and less pedestrian accidents. A similar result was obtained by Poch and

Mannering (1996), who found that having no control on an approach, compared to a

stop or give way sign, decreased accident frequencies. In contrast, the multi-factor

study Stockton, Brackett et al (1981), found control had no influence on accident

rates at low-volume intersections.

Presence of Lane Dividers

Brude (1991) found that traffic islands on the secondary road reduced the number of

accidents by around 10 percent. There was conflicting evidence in the multi-factor

studies on this issue.

27

Lighting

The presence of intersection lighting appears to correlate with lower accident rates.

Brude (1991) found that during the hours of darkness, the number of intersection

accidents was 30 percent less with lighting, than without. Kulmala (1994) found that

none of the changes to the three and four-leg intersections investigated were

statistically significant, except for a change in all accidents at three-leg intersections

following the implementation of road lighting.

Walker and Roberts (1976) concluded that a 49 percent reduction in night accidents

occurred after the installation of lighting. The effect at the 19 unchannelised

intersections within the study was not statistically significant, however.

Sight Distance

Poch and Mannering (1996) found that the presence of a sight distance restriction

was found to significantly increase accident frequency.

Use of Beacons

King and Goldblatt (1975) found that the installation of flashing beacons to

supplement stop sign control generally appeared to have a favourable effect on

accident patterns. This result is different to that obtained by the ‘matched group’

study Pant, Park et al (1999).

Turn Lane Type

Poch and Mannering (1996) found that intersection approaches with a combined

through-left lane (equivalent to through-right in Australia) were found to have higher

accident frequencies than approaches not having these conditions.

Harwood, Bauer et al (2002) found that adding a single left-turn lane (equivalent to

right-turn in Australia) on the major road would be expected to reduce total

intersection accidents by 28 percent at rural four-leg intersections and 44 percent at

rural three-leg intersections. At urban unsignalised intersections, the installation of a

left-turn lane on one approach would be expected to reduce total intersection

accidents by 27 percent at rural four-leg intersections and 33 percent at rural three-

leg intersections.

The addition of right-turn lanes (equivalent to left-turn in Australia) also reduced

28

total intersection accidents at unsignalised intersections. The reductions in accidents,

however, were not as high as those for the addition of left-turn lanes.

Rimiller, Garrick et al (2003) found that the addition of left-turn lanes (equivalent to

right-turn in Australia) improved safety. Three-leg intersections experienced greater

safety benefits than four-leg intersections. The left-turn lanes were found to perform

better at sites with two lanes rather than four lanes on the major road.

Intersection Realignment Combined with the Addition of a Left-Turn Lane

Yuan, Ivan et al (2001) studied the combined effect of intersection realignment with

the addition of a left-turn lane (equivalent to right-turn lane in Australia) on accident

rates. Intersection realignment comprised either a curve on the main road being

straightened or a skewed intersection approach leg on the side road being aligned.

The combination of these treatments did not appear to have additional benefits in

reducing the total number of crashes.

Speed Parameters

Brude (1991) found that lower permitted speeds improved intersection safety. This

differs to the results found by the Transport Research Laboratory multi-factor studies

Pickering, Hall et al (1986) and Summersgill, Kennedy et al (1996), where speed was

found to have little effect.

2.4 Traffic Conflict Studies

OECD (1971) listed traffic conflict studies undertaken as early as 1954. However, in

describing the use of a computer simulation model used to study traffic conflicts at

unsignalised intersections, Sayed (1997) reported that the concept of traffic conflicts

was first proposed by Perkins and Harris (1967) as an alternative to accident data,

which in many cases is scarce, unreliable, or unsatisfactory. It was stated that an

internationally accepted definition of a traffic conflict is ‘an observable situation in

which two or more road users approach each other in space and time for such an

extent that there is a risk of collision if their movements remain unchanged’.

A variety of observation methods have been developed to measure traffic conflicts

including the observation of driver behaviour and recording the number of near

misses or avoidance manoeuvres. Salman and Al-Maita (1995) used traffic conflict

29

techniques to collect data at 18 three-leg unsignalised intersections and concluded

that accidents and conflicts are related by a linear relationship.

Several studies attempting to relate geometry to safety at unsignalised intersections

have been undertaken by measuring and using traffic conflicts in lieu of accident

data. Cooper (1973), for instance describes a study undertaken to evaluate various

models for the prediction of accident occurrence at intersections. Variables

considered were traffic volumes, vehicular manoeuvre times, traffic conflicts and

violations. The results of the study did not indicate a very efficient or practical

application.

Conflicts were found to be extremely volume dependent and could not account for

difference in accidents when corrected for volume exposure. It was found that the

best accident predictor models were those based on vehicular volumes. This result is

similar to the general result of the multi-factor studies: traffic flow is by far the most

important independent variable with geometric parameters having only a small

effect.

2.5 Studies Relating Traffic Volumes to Accident Rates

There have been many studies undertaken relating accident rates to traffic volumes

for various configurations of unsignalised intersections. Typically, these studies have

analysed a large number of intersections e.g. Agent (1993) analysed 6,707

intersections.

Golob, Ruhl et al (1988) had similar objectives when analysing 500 non-signalised

intersections in the Netherlands. Golob, Ruhl et al (1988) concluded that interaction

terms between the traffic volumes on various intersection approaches are important

explanatory traffic intensity variables. Furthermore, unique types of non-signalised

arterial road intersections exhibited different forms of relationships between accident

rates and traffic intensities.

Golias (1992) selected 43 urban unsignalised four-leg intersections to have similar

road features and operational characteristics so that variation of accident number is

mainly due to the different traffic flows. The percentage variability in the number of

accidents explained by the final proposed model was found to be 78 percent. The

model related accidents to exposure indices, which are formed by the sum of the

functions of cross products of traffic stream flows, which take into account the

30

interaction between traffic streams. It was concluded that the dominant factor

influencing the accident potential of the intersections studied is an expression of the

interacting traffic stream flows.

Comparative Importance of the Minor and Major Road Flows

Most of the studies reviewed relating traffic volume to accident rates have shown

that the minor road flow has a greater effect on total accident rates than does the

major road flow. This is in agreement with the results of the multi-factor study

Kulmala (1997).

Sayed and Rodriguez (1999) found that for stop-controlled T-intersections, the

accident rate (total) was proportional to the AADT on the major road divided by

1000 raised to a power of 0.45, and proportional to the AADT on the minor road

divided by 1000 raised to a power of 0.58. For four-leg intersections, these values

were 0.45 and 0.65 respectively. Using these results, the ratio of the minor road flow

exponent to the major road flow exponent equals 1.3 at T-intersections and 1.4 at

four-leg intersections.

In an analysis of two-way stop-controlled intersections, Bonneson and McCoy

(1993) found that the accident frequency was proportional to the AADT on the major

road divided by 1000 raised to a power of 0.256 and proportional to the AADT on

the minor road divided by 1000 raised to a power of 0.831. Using these results, the

ratio of the minor road flow exponent to the major road flow exponent equals 3.2.

In a study of 150 divided-highway intersections, McDonald (1953) found accident

rates to be proportional to the ADT on the major road raised to a power of 0.455 and

proportional to the ADT on the minor road raised to a power of 0.633. Using these

results, the ratio of the minor road flow exponent to the major road flow exponent

equals 1.4.

In the above studies, the ratio of the minor road flow exponent to the major road flow

exponent varies between 1.3 and 3.2. The results of these studies therefore suggest

that the minor road flow may be between 1.3 and 3.2 times more important in

predicting accident rates than the major road flow. These findings are in agreement

with the results of the multi-factor study Kulmala (1997).

Stark (1994) summarised the results of TRL research into the relationship between

31

traffic flows and accident rates. It was stated, however, that accidents are relatively

insensitive to flow changes on the minor arms, so that the risk to entering vehicles is

very high at low flows. This is the opposite effect found by most other studies.

In summary, the majority of studies have identified that the minor road flow affects

total accidents rates more than the major road flow.

2.6 Driver Behaviour

Arndt (1998) has shown that gaining knowledge of driver behaviour helps to form a

framework for the selection of the geometric parameters most likely to affect

accident rates. This section reviews literature on driver behaviour at unsignalised

intersections in order to gain an appreciation of driver perception issues, what errors

drivers involved in accidents are committing, issues of speed and how driver

expectancy can be violated.

Driver Perception

To drive correctly and safely at intersections, OECD (1971) has listed the following

information as required to be perceived:

• The Intersection and its Approach-roads

Need for changes in speed

Choice of routes across the intersection and choice of position when

approaching the intersection

Decision about the possible approach of other road-users

• Traffic Controls

• Traffic at the Intersection and on the Approach Roads

Types of other road users

Their position with regard to the intersection and to themselves

Their speed

The route that other road users will follow at the intersection

Signals given by road-users concerning slowing down, stopping and turning

• Position and Speed of the Road-user

• Special Circumstances, such as a slippery pavement or a diversion

The above list shows that drivers need to perceive a great deal of information and

32

make many decisions within a short time in order to safely negotiate an intersection.

Any misjudgement in perception or decision-making at any of these stages increases

the likelihood of an accident.

Berthelon and Mestre (1993) experimented with visual displays that simulated the

curvilinear approach of an intersection. It was found that judgement of a moving

vehicle on an adjacent leg becomes increasingly difficult when driving on small

curve radii because relative visual motion becomes ambiguous. A spatial reference

point near the intersection (eg a road sign) improved performance.

Driver Error

Cairney (1983) analysed all urban casualty accidents at intersections reported in the

state of Victoria during the year 1981. Crossroads with stop and give way signs

resulted in a very high proportion of cross traffic accidents. T-intersections with stop

or give way signs recorded a high proportion of ‘right-near’ collisions. These

accidents are the result of a minor road vehicle turning right and colliding with a

major road vehicle approaching from the right. These accident patterns are similar to

those found in the majority of other studies reviewed.

Cairney (1983) found that the proportion of collisions occurring at the different types

of intersections analysed was found to be largely unaffected by age, gender, or

alcohol content of the driver, or whether the collision happened during the day or at

night.

Cairney and Catchpole (1991) investigated road user behaviour that contributes to

accidents at urban arterial/local intersections. The most striking finding was the very

large number of drivers (61 percent) who did not see another vehicle or pedestrian in

time to avoid a collision. Approximately 25 percent of drivers were found to be

effected from visual obstructions. Almost 70 percent of these obstructions were

manoeuvring vehicles and only 12 percent were parked vehicles.

Russell, Stokes et al (1999) analysed accidents resulting from failure to give way at

rural two-way stop-controlled intersections. No evidence was found to support a

conclusion that crashes were directly related to stop sign violations. Based on this

outcome, it was hypothesised that most drivers on the minor road involved in angle

accidents fail to pick an acceptable gap in the major traffic stream rather than fail to

stop. It was expected that failure to pick an acceptable gap was due to driver inability

33

to accurately estimate the speeds of the major road vehicles.

They further suggested that if their hypothesis was correct, effective solutions to the

failure to give way problem needs to focus on the entire intersection, including the

major roadway approaches. Treatments to reduce the speeds of vehicles on the major

roadway approaches were suggested. These included advance warning signs with

advisory speed plates and reduced speed zones.

Catchpole and Cairney (1990) stated that changing the behaviour of drivers,

however, is notoriously difficult to achieve. They did not believe that enforcement

was the answer since most of the errors did not involve breaches of traffic

regulations. They also stated that a reduction in driver error seems to call for traffic

engineering measures to either simplify or eliminate the need for the judgement and

detection tasks which road users fail to carry out correctly.

Harkey (1996) found that older drivers are over involved in failure to give way

accidents at intersections. Potential causes for this were given as misjudging the

available gap and/or oncoming vehicle speed, assuming the oncoming driver was

going to stop or turn, simply not seeing the other vehicle, misjudging the time

required to clear the intersection, inability to accelerate through the intersection in

time to avoid the conflict, or misunderstanding the traffic control device.

Parsonson, Isler et al (1996) concluded that all drivers appear to be at risk because of

poor gap and speed estimation. Older drivers’ visual and physical deficits and slower

reaction time and acceleration times increase the magnitude of the risk of an

accident. The most evident problem for all drivers was estimating speeds of vehicles

exceeding 100km/h.

Ueyama (1997) discussed the results of a model for research of accident mechanisms

that employs data from an automatic accident recording system (TAAMS). The

results showed that under certain circumstances, dangers have been overlooked

because the driver received a clear indication of some safety factor, either external or

internal. It was suggested that, rather than indicating a temporary lack of vigilance on

the part of the driver, this phenomenon can be interpreted as a complete lack of any

vigilance and can be assumed to stem from a basic human characteristic.

Teply, Abou-Henaidy et al (1997) investigated behaviour of drivers turning left from

a major road onto a minor road through oncoming traffic (equivalent to a right-turn

34

in Australia). The probability of accepting a gap was found to be very high for

drivers who did not stop.

Lloyd, Bitter et al (1996) discussed the development of an Intersection Collision

Avoidance (ICA) countermeasure that will mitigate causal factors by warning drivers

of potential errors and pre-empting driver control of the vehicle to avoid a collision.

The need for such countermeasures was based on a causal analysis of a data sample

that concluded that nearly 75% of intersection collisions were due to driver error,

including driver inattention (28.7%), faulty perception (33.9%), and vision

impaired/obstructed (11.1%).

Mounce (1980) found that the violation rate at low-volume intersections with stop

sign control decreased with increasing major roadway volume. The violation rate

was higher at sites with unrestricted visibility than at sites with restricted visibility.

However, it was found that there was no correlation between violation rates and

accident rates.

Larson, Hopkins et al (1997) described an alternative traffic control approach for

unsignalised intersections. A Collision Countermeasures System (CCS) has been

developed to enhance driver awareness of approaching or crossing traffic. This

system uses vehicle detectors to track approaching vehicles and illuminate warning

messages at the intersection via ‘active’ signs.

Kanda and Ishida (2000) analysed human factors of drivers failing to give way at

unsignalised intersections in Japan. Priority at these intersections is given by stop

signs, road width, ‘give way to the left’ rule and other treatments. Human factors

found important in 101 of these accidents are shown in Figure 2.1.

With the exception of patterns 9 and 10, the remaining patterns in Figure 2.1 could

be summarised into the following two broad categories:

• Category 1 - The driver on the minor road has adequately perceived the

intersection and determined that they are required to give way. However, the

driver either fails to see a major road vehicle or misjudges the speed and position

of that vehicle. This category would comprise patterns 1, 3, 4 and 6.

• Category 2 - The minor road driver has not adequately recognised the presence of

the intersection or the need to give way. This category would comprise patterns 2,

5, 7, and 8.

35

Figure 2.1 - Error of Drivers Failing to Give way at Unsignalised Intersections from the Study Kanda and Ishida (2000)

The findings in Category 2 are a very different result to that obtained by Russell,

Stokes et al (1999) who indicated that ‘no evidence was found to support a

conclusion that crashes were directly related to stop sign violations’. This outcome

may partially be due to the difference in intersection layouts and the difference in

assigning priority at intersections, between Japan and the USA.

36

Summary The following may be concluded from the studies above:

• The most common accident type at unsignalised intersections is failing to give

way on the minor legs and colliding with a vehicle on the major road.

• Common faults of drivers failing to give way are not seeing the other vehicle,

misjudging the speed and position of the other vehicle, not recognising the

intersection and not recognising the need to give way.

• Some failure to give way accidents involve obstruction to vision particularly by

other vehicles.

Speed

Several studies of driver behaviour have shown the importance of speed on safety.

Horswill and McKenna (1997) identified speed choice as having one of the strongest

associations with accident involvement of any behavioural measure. Maycock (1997)

discussed research into the relationship between speed and accidents. One method of

relating speed to accidents is at the ‘aggregate’ level. At the aggregate level,

statistical relationships between accident rates and key characteristics of the speed

distribution of traffic are formed. As expected, a number of research projects have

shown that on a given road, accident rates increase as the mean speed increases.

Maycock, Brocklebank et al (1999) discussed the results of experimental studies

relating road layout to driver behaviour. One concluding factor was that primarily its

gross geometric features would determine the average absolute speed of traffic on a

road. The concept of an 85th percentile speed which links the geometric elements of a

design to an overall measure of driver behaviour (speed) would therefore appear to

be a sound and practical one.

Zaidel, Hakkert et al (1986) undertook a ‘before and after study’ to find the effect of

paint stripes and rumble strips on the speed of vehicles approaching an intersection

on the minor legs. Stop signs were the method of control on the minor legs. Paint

stripes were found to have only minor influence on driver behaviour, whereas rumble

strips lowered speeds by an average of 40 percent. Both treatments had a small,

though positive, effect on compliance with the stopping requirement and the effects

on driver behaviour did not diminish after a one-year period.

37

Jarvis and Jordan (1990) examined the effects of yellow bar markings on driver

approach speeds to isolated rural intersections. It was found that the markings

reduced the approach speed of vehicles, including those identified as approaching in

the highest speed ranges. Bars placed further from the intersection (200m or more)

had a greater effect on speed reduction.

Kanda and Ishida (2000) determined whether minor road drivers slowed before the

intersection for the 10 patterns of driver behaviour identified in Figure 2.1. Their

findings have been summarised in Table 2.1.

Table 2.1 - Speed of Minor Road Drivers Involved in Failure to Give Way Accidents using Data from the Study Kanda and Ishida (2000)

Number of Accidents

Pattern Number

Driver Stopped at

Intersection

Driver Decelerated

Prior to Intersection

Driver Maintained Speed Prior

to Intersection

Unknown

Total

1 4 6 9 3 22 2 0 0 16 0 16 3 0 5 7 2 14 4 6 5 2 0 13 5 0 0 10 1 11 6 2 5 3 0 10 7 0 4 0 0 4 8 0 0 4 0 4 9 0 0 0 4 4 10 0 0 0 3 3 Total 12 25 51 13 101

Table 2.1 indicates that at least half of the minor road drivers involved in failure to

give way accidents in Japan have not slowed prior to the intersection.

Violation of Driver Expectancy

Kammann (1976) discussed the possibility that non-standard situations at

intersections (eg non-standard intersection geometry or signing) create driver

uncertainty, which leads in turn to a higher accident rate.

Thomson and Kammann (1979) discussed three ways in which the road environment

can reduce drivers’ performance. The first was a violation of general expectancy that

can be caused by factors such as non-standard signing arrangements and one-way

streets. The second was violations of specific expectancy when familiar intersections

38

or familiar intersection rules are changed. The third was information overload, which

is caused by the driver being presented with too much information from which to

select. It was recommended that traffic engineers should obtain human factors

consultation before making any major change.

Summersgill, Kennedy et al (2001) compared data of a study of junctions with one or

more one-way arms with that for corresponding studies of junctions with all two-way

arms. The sites included priority and signalised junctions. They found that accident

risk was related to whether arms (or adjacent or opposite arms) were one-way or

two-way. In general, more conflict points were found to be associated with a higher

risk. This result may not support the above discussions on violation of driver

expectancy.

2.7 Literature Review Summary

This literature review has discussed the results of several studies that attempt to

relate geometric and other variables to safety at unsignalised intersections. ‘Multi-

factor’, ‘matched group’, ‘before and after’, and ‘traffic conflict’ are some of the

various methods used in these studies. General results found in these studies are

discussed in the following sub-sections.

Multi-factor Studies

The approaches taken in the various multi-factor studies vary considerably. The

types of sites selected, the method of site selection, the number of intersections

selected, the method of categorising the accident data (or lack of), and the variables

selected for trial all vary significantly between the various studies.

The most recent multi-factor studies have tended to analyse accident data using non-

normal distributions, especially the Poisson distribution. Use of negative binomial

models is also common. Most multi-factor studies reviewed have used variants of the

model shown by Equation 2.1 in Section 2.1.

Types of Accidents

The most common vehicle accidents at unsignalised intersections appear to be angle

(right-turn or through-movement from minor leg colliding with a vehicle travelling

through on the major road), right-turn from major road (colliding with an oncoming

39

major road vehicle), and rear-end. Single vehicle, head-on, sideswipe and left-turn

from minor road (colliding with a vehicle travelling through on the major road) are

common, but are less in number.

General Results

Many studies (including ‘multi-factor’, ‘before and after’ and ‘traffic conflict’) have

found traffic flow to be the most important variable affecting safety, with geometric

parameters having only a small effect. If a particular study did identify an important

variable (other than traffic volume), it was often not considered by other studies, was

not found to be important or was found to have the opposite effect. Even the best

equations developed (which included traffic flow) did not explain most of the

variability in the data.

The majority of studies have identified that the minor road flow affects accident rates

more than does the major road flow.

Geometric and Other Parameters Found Important

Several statistically significant geometric and other parameters have been found in

the various studies. However, there is little consistency between the results of these

studies. If a particular study did identify an important parameter (other than traffic

volume), it was often not considered by other studies, was not found to be important

or was found to have the opposite effect. A summary of the results of these studies is

given in Table 2.2. This table shows the results of studies that identified the effect of

individual parameters. It excludes those studies of the effect of combined parameters

on accident rates.

The only results found consistent across two or more independent studies (those

studies undertaken by different organisations) are as follows:

• T-intersections are safer than cross-intersections, when taking into account traffic

volumes.

• Lit intersections record lower accident rates than do unlit intersections

• Larger stop signs on the minor legs result in a lower accident rate

40

Table 2.2 - Summary of Results of the Various Studies Reviewed Multi-Factor Studies Match.

Group Before and After Studies

Change to Geometric or

Other Parameter D

avid

and

Nor

man

(197

5)

Dav

id a

nd N

orm

an (1

979)

D

el M

istro

(197

9)

Han

na, F

lynn

et a

l (19

76)

Har

woo

d, P

ietru

cha

et a

l (19

95)

Hua

ng a

nd M

ay (1

991)

K

itto

(198

0)

Kul

mal

a (1

997)

La

yfie

ld (1

996)

Le

ong

(197

3)

Mar

en (1

980)

O

'Brie

n (1

976)

Pi

cker

ing,

Hal

l et a

l (19

86)

Stoc

kton

, Bra

cket

t et a

l (19

81)

Sum

mer

sgill

, Ken

nedy

et a

l V

ogt (

1999

) Li

pins

ki a

nd W

ortm

an (1

976)

M

orris

on (1

998)

Pa

nt, P

ark

et a

l (19

99)

Bru

de (1

991)

G

amba

rd (1

988)

K

ing

and

Gol

dbla

tt (1

975)

H

arw

ood,

Bau

er e

t al (

2002

) K

ulm

ala

(199

4)

Poch

and

Man

nerin

g (1

996)

Po

lus (

1985

) R

imill

er, G

arric

k et

al (

2003

) W

alke

r and

Rob

erts

(197

6)

T-to Cross Intersection + + + + + + + Cross to Staggered T-Intersection

V V

Unsignalised to Signalised Intersection

+ + V + 0

Give way to Stop Sign Control

0 -

No Control to Give way and Stop-control

0 +

Increase Number of Lanes + + Increase Size of Intersection Conflict Area

+

Provide Auxiliary Turn Lanes

+ - 0 - - - -

Provide a Curve on Minor Road Approach

-

Increase/Decrease Grades 0 + Increase Sight Distance - - 0 0 - Increase Number and Size of Stop Signs

- -

Provide Raised Pavement Markers

-

Increase Minor Road Classification

+

Restrict Turning Movements

-

Provide Medians and Islands

- V V V - V - -

Provide Roadside Barriers - + Increase Length Between Staggered T-intersections

-

Provide Pedestrian Crossing Facilities

- -

Provide Lighting - - - -Provide Beacons 0 - Increase in Road Speed 0 0 +

Notes: + indicates that the change to the particular geometric or other parameter described was found to result in an increase in accident rate/s

- indicates that the change to the particular geometric or other parameter described was found to result in a decrease in accident rate/s

0 indicates that the change to the particular geometric or other parameter described was not found to significantly affect accident rate/s

V indicates that the change to the particular geometric or other parameter described was found to have a variable affect on accident rate/s

41

Driver Error

The following may be concluded from the studies of driver behaviour:

• The most common accident type at unsignalised intersections is failing to give

way on the minor road and colliding with a vehicle on the major road.

• Common faults of drivers failing to give way are not seeing the other vehicle,

misjudging the speed and position of the other vehicle, not recognising the

intersection and not recognising the need to give way.

• Some failure to give way accidents involve obstruction to vision particularly by

other vehicles.

2.8 Discussion

The three specific objectives of this study given in Section 1.1 are discussed below in

relation to the results of studies reviewed.

Objective 1 - Effect of Traffic Volumes

As discussed in the previous section, most studies have found traffic flows to be by

far the most important variables affecting accident rates at unsignalised intersections.

The majority of studies have identified that the minor road flow affects total

accidents rates more than the major road flow.

Most of the studies in this literature review relating traffic volumes to accident rates

at unsignalised intersections are international studies. Adopting the developed

accident equations of one particular study directly for Queensland conditions may

give poor results. One reason for this result is that the magnitude to which the minor

road has more effect than the major road varies between the various studies. It would

be uncertain as to which study results to adopt.

Another reason why poor results may be obtained is that driver behaviour, which

affects the nature of accidents, may change between different countries. As stated by

Cairney (1983), it is unwise to generalise from one country’s driving population to

that of another.

Objective 2 - Effect of Geometric Parameters

As shown in the literature review (and summarised in Table 2.2), there is little

42

consistency between the results of the various studies of the effect of geometry on

accident rates. In addition, most studies have found that geometric parameters have

only a small effect on accident rates. It is therefore of little use to try to adopt the

results of other studies to build mathematical relationships between unsignalised

intersection geometry and accident rates.

In addition, the geometric layout, signing, and other features of at-grade intersections

analysed by the international studies may be considerably different to those

encountered in Australia.

Objective 3 - Effect of Speed Parameters

Very few of the studies reviewed considered the effect of speed parameters on

accident rates. Of those studies that did, none developed mathematical relationships

between speed parameters and accidents at unsignalised intersections.

It is considered that speed parameters, however, are very important parameters for

the following reasons. The principal national document for the design of at-grade

intersections, Austroads (1988), states that safety depends largely on low relative

speeds. Arndt (1998) has shown this to be true for each major multiple vehicle

accident type occurring at roundabouts. Austroads (1988) discusses the importance

of limiting the decrease in design speeds between successive geometric elements for

safety. Arndt (1998) has also found this to be true for single vehicle accident rates at

roundabouts.

Effect of Speed on Multiple Vehicle Accidents at Unsignalised Intersections Minor road vehicles failing to give way and colliding with major road vehicles are a

major accident type at unsignalised intersections. In order to determine whether the

major and minor road speeds are an important predictor of these accidents, two

scenarios may be considered:

• Scenario 1 - in this scenario, the driver on the minor road has adequately

perceived the intersection and slowed to a safe negotiating speed. However, the

driver then either fails to see a major road vehicle or misjudges the speed and

position of that vehicle and pulls out across its path, causing a collision between

the two vehicles. This concept is supported by Ueyama (1997). In this scenario, it

may be expected that the major road speed only would be an important predictor

of failure to give way accidents. This was the hypothesis stated in Russell, Stokes

43

et al (1999). The findings of Kanda and Ishida (2000), however, show that this

does not occur for all accidents of this type.

• Scenario 2 - in this scenario, the minor road driver has not slowed down

sufficiently to safely negotiate the intersection and collides with a major road

vehicle (ie the driver is travelling too fast to take the appropriate action to avoid a

collision). This may have been caused by inadequate recognition of the

intersection or inadequate recognition of the need to give way. In this scenario,

the minor road approach speed may be considered important. Higher minor road

speeds could be expected to result in more drivers failing to take the appropriate

action to avoid a collision. There are two possible alternatives for this scenario as

given below:

Alternative 1 - in this alternative, the minor road speed alone may be

important.

Alternative 2 - in this alternative, the relative speed between major and minor

road vehicles may be important. The relative speed can be calculated by using

the 85th percentile major and minor road vehicle speeds and an assumed 90

degree angle between vehicle paths. In this case, both the minor and major road

speeds are important.

If the speed parameter in Scenario 1 is found to be a better predictor of ‘failure to

give way’ accidents than those in Scenario 2, then increased safety at intersections

(particularly high-speed rural intersections) can potentially be achieved by reducing

vehicle speeds on the major approaches only. Little benefit, if any, would be gained

by introducing treatments on the minor road to reduce vehicle speed.

In contrast, if the first alternative speed parameter in Scenario 2 was found to be a

better predictor of ‘failure to give way’ accidents than the second alternative

parameter or the parameter in Scenario 1, then increased safety at intersections can

potentially be achieved by reducing the minor road speed only.

If the second alternative speed parameter in Scenario 2 was found to be a better

predictor of ‘failure to give way’ accidents than the first alternative parameter or the

parameter in Scenario 1, then increased safety at intersections can potentially be

achieved by reducing speeds on both the major and/or minor roads.

Treatments which may have the potential to reduce speeds (as incorporated at

44

particular major intersections in Queensland), include:

• For Scenario 1 (reduction of speed on the major road only), speed limit reduction

on the major approaches, combined with methods to locally reduce the major road

speed environment e.g. introduction of medians, dense planting close to the edges

of the carriageway, reduction in lane widths, guide posts at decreasing spacing.

• For the first alternative of Scenario 2 (reduction of speed on the minor road only),

treatments as per Scenario 1 to minor road approaches only and/or curvature and

rumble strips on the minor approach/s.

• For the second alternative of Scenario 2 (reduction of speed on both the major and

minor roads), treatments as per Scenario 1 to both major and minor road

approaches and/or curvature and rumble strips on the minor approach/s.

None of the objectives listed in this section can be met by using the results of the

studies reviewed. To undertake a study in Queensland using the same approach and

parameters as those discussed in the literature review is expected to yield similar

results. Therefore, a different approach is required to meet the above objectives. Such

an approach is discussed in the next chapter.

45

3 THESIS APPROACH

As discussed in the previous chapter, none of the objectives listed can be met by

using the results of the studies reviewed. A different approach is required and the

purpose of this chapter is to explain this approach.

3.1 Problems with Multi-factor Studies

The best method to identify the effect of a particular variable on a dependent

parameter is to hold all other variables constant. Hauer (1997) identified this fact.

The effect on the dependent parameter can then be measured by varying the

magnitude of this one variable. This procedure could then be applied to all possible

combinations of values of the other variables to determine if the same relationship

applies. If the relationship is different, then there is an identified interaction between

variables.

Such a purely experimental approach is impossible within a study such as this (as in

several other fields) because of legal and ethical issues. Intersections cannot be built

with particular features and then tested for accidents. This is especially true in the

case of deliberately building an intersection with sub-standard features (eg extremely

poor visibility) in order to determine its effect on accidents.

To determine the effect of unsignalised intersection geometry on accident rates,

several study types are available as discussed in the literature review. These are

‘multi-factor’, ‘matched group’ and ‘before and after’ studies. Each type is an

observational study and has its own advantages and shortcomings. Hauer (1997)

states that ‘Observation studies are a very imperfect source of knowledge...’.

Observational studies determine correlations in data, which can be used to

hypothesise causes. Unlike experimental studies, they cannot determine causality.

For the reasons listed previously, experimental studies are not possible in this field.

Instead, observational studies (imperfect as they are) are the only tool available for

practitioners to determine relationships between geometry and accidents.

A multi-factor approach has been chosen for use in this study. One reason for

adopting this approach was that a single multi-factor study could potentially identify

the effect of many factors on accident rates. Another reason was that most of the

studies that identified opposite relationships to that expected were multi-factor

46

studies. By undertaking a multi-factor study, reasons for the previous results could

potentially be identified and new techniques developed to overcome these problems.

Multi-factor studies consider simultaneously the effects of many factors on the

incidence of accidents using a sample of collected data. Usually, a regression

technique is then applied to find trends in the data.

Multi-factor studies have the following problems. To discuss these problems, the

example in Table 3.1 has been produced. This table shows three combinations of

particular variables relating to unsignalised intersections. The results of multi-factor

studies will potentially yield many highly significant parameters and explain much of

the variability in the data only if the data sample comprises the following data

properties:

1. An adequate amount of accident data. This includes an adequate exposure

(number of vehicles over time) for each selected site to be confident of the

resulting accident rate. For this to occur, the exposure would need to be high

enough to produce a few accidents at every site in the sample as a minimum. For

lower volume sites, this may involve an analysis period of hundreds of years.

Obtaining such an amount of data is unlikely to be achieved.

2. A wide range of values for each variable. To accurately determine the effect of

each variable on accident rates, sites must contain a broad range of values for each

of the variables. For example, the effect of visibility on accident rates is unlikely

to be determined if there are no intersections with poor visibility in the sample.

For any particular variable in Table 3.1, a range of values from that given in

Variable Set 1 to that given in Variable Set 3 must be available within the selected

sites. Failure to do this will likely show that a particular variable does not affect

accident rates. In reality though, it may have a significant effect.

3. Accurate measurements of each variable. Each variable must be capable of

being accurately measured and the value/s of this variable must be representative

for the period of the analysis. In practice, however, this is rarely the case. As an

example, accurately measuring visibility can be difficult because the amount of

visibility can change over time. The presence of parked vehicles, varying heights

of vegetation and the various paths from which vehicles travel will all affect the

amount of visibility provided.

47

4. Sites that cover every possible combination of variables. Accurate results are

likely to be obtained only if the sample sites meet the criteria in Variable Sets 1 to

3 in Table 3.1 and every combination of variables possible between these variable

sets. This is termed ‘full factorial experimental design’. As an example, some sites

would need to meet all of the criteria in Variable Set 1 except that they need to be

in high-speed areas.

Given that there are eight variables and three variable sets, the total number of

sites required in order to have just one site per combination is 38 = 6561. Such a

number of sites with the required combinations would be virtually impossible to

find. Given that a study such as this usually comprises many more than eight

variables and three variable sets, the total number of sites would be much greater

than this.

Failure to apply this technique introduces potential problems with correlation

between variables. An example of this is if all sites with wide medians are on

roads with high traffic volumes and all sites with narrow medians are on low

volume roads. This will produce high levels of correlation between the variables

‘median width’ and ‘traffic volume’.

Problems with correlation are dominant in multi-factor studies because the values

of many geometric parameters chosen from road design standards are often

dependent on traffic volumes and 85th percentile speeds. Therefore, many of the

geometric parameters in these standards are expected to correlate these parameters

and each other.

If it is shown that both of these variables significantly affects accident rates if

applied in isolation, it often becomes very difficult to determine the exact effect of

each variable on accident rates. This is because a stepwise regression analysis will

often reject one of the variables or will show one to have an opposite effect to that

considered reasonable.

Failure to apply this technique also introduces problems in determining

interactions between variables. Complex interactions between variables are not

likely to be identified unless the sites cover every possible combination of

variables.

48

Table 3.1 - Combination of Variables in Multi-factor Studies Variable Variable

Set 1 Variable

Set 2 Variable

Set 3 Speed Low Medium High Median Width Zero Medium Wide Traffic Volume Low Medium High Number of Major Road Lanes

2 4 6

Curvature Zero Medium Tight Visibility Poor Average Good Level of Lighting None Average High Level of Signage None Average High

The problems discussed in the four dot points above can be summarised as follows:

the collected data is likely to be insufficient in determining all relationships between

variables. It is highly unlikely that any multi-factor study could ever meet all of the

criteria listed in the four dot points above. As a result, problems can occur as

discussed in the dot points. It is expected that these problems are the main reasons

why previous multi-factor studies have found that many geometric variables do not

affect accident rates and some variables have an opposite effect to that considered

reasonable.

It is important that strategies be developed to overcome or allow for these problems.

Such strategies proposed for this study can be categorised into two basic approaches,

as follows:

• Maximise Efficiency of Data Collection

• Develop Techniques for Analysing Less than Perfect Data

These basic approaches are discussed in the next two sections. The approaches differ

from previous studies in that they incorporate techniques used in Arndt (1998) (as

discussed in Section 2.1) in addition to other techniques developed during the study.

None of the previous studies identified have used all these techniques, although some

of the techniques have been used previously. The combination of these techniques

make this study unique in its approach.

3.2 Maximise Efficiency of Data Collection

This study has adopted two techniques for the selection of sites to maximise the

efficiency of data collection. These techniques involve an experimental approach to

49

the selection of sites rather than selecting sites at random. The techniques are

discussed below.

Obtain a Wide Range of Values of Each Variable

This issue was outlined in the second data property in Section 3.1. In order to predict

the effect of the variables (traffic volume, speed and geometric data) on accident

rates, it is desirable to obtain a relatively even spread of a wide range of values.

Agent (1988) identified that this method produced the most confident result.

Should the values of a particular variable only cover a narrow range, the regression

analysis is likely to show that it is not a significant parameter. In reality though, it

may have a major influence but its effect is being masked because only a narrow

band of data was used. This is one reason why it is expected that the studies in the

literature review found most variables were not significant predictors of accident

rates.

Another effect that can occur is that if this narrow range of data contains a few

outliers in the data, these outliers will have a major influence on the result. This

concept shows the importance of checking the values of each variable to see if a wide

range exists.

To minimise this problem, preliminary data can be collected on a larger number of

intersections than will be used in the analysis. From this preliminary data sample, a

smaller sample of intersections can be selected to provide the greatest range of these

variables (those considered to be the most important).

The method of obtaining a wide range of values for each variable is discussed further

in Section 4.1.

Exclude Very Low Volume Intersections The first data property in Section 3.1 discussed the issue of obtaining an adequate

amount of data for analysis. With limited time and resources, the amount of data

collected is usually less than that desired. For this reason, it is advantageous to

maximise the data collected. One way to achieve this is to exclude intersections with

very low traffic volumes from the study.

This approach seeks to optimise the data collected by avoiding the addition of

intersections to the sample that comprise very little accident data resulting from low

50

exposure. This ensures that the time spent in data collection maximises the likely

results. In order to confidently analyse intersections with very low volumes, a very

large number of sites would be required. This is considered impractical, given time

and budget constraints.

The method of excluding very low volume intersections is discussed further in

Section 4.2.

3.3 Develop Techniques for Analysing less than Perfect Data

This study has adopted several techniques for analysing data that is less than perfect.

These techniques are discussed below.

Categorise the Accident Data

Some studies identified in the literature review did not involve categorising the data

according to the various accident types. Instead, all accident types were analysed

together. A problem with this technique is that variables affecting a particular

accident type/s but not others (or having an opposite effect on others) will not

normally be identified.

Knowing these effects is important because they potentially identify the most

appropriate mitigating treatments for reducing each accident type. For this reason,

accidents recorded in this study were grouped according to what principle event/s

and driver behavioural factors gave rise to each accident. This technique is discussed

in Section 5.3.

Selection of Variables

This study has adopted several techniques for the selection of variables for analysis.

These are discussed below.

Select Variables that are Expected to Relate to Accident Rates

Variables for each accident type have been carefully selected based on logical

relationships with accident rates. Variables that logically would have very little or no

influence were not included. For example, the level of approach signage on the minor

road would logically have no influence on single vehicle accidents occurring to

through vehicles on the major road.

This technique was adopted because variables with very little or no influence on

51

accident rates may be correlated with other more important variables. Through this

correlation, an analysis may show that they are important predictors of accidents.

However, their effect is only being reflected through the other, more important

variables. It is even possible that variables that have nothing to do with the particular

intersection can be shown to be important.

This method of selecting variables is discussed in Section 6.1.

Develop Driver Behavioural Models During the initial phase of the study, no consideration was given to the driver

behaviour that gave rise to the accidents when selecting geometric parameters for

trial in the regression analysis. The resulting equations explained little of the

variability in the data and few parameters were found significant. However, by

selecting parameters for trial based on the known or expected behaviour of drivers

involved in accidents, it was found that much more significant equations could be

developed.

Speed Model The selection of speed parameters is one example of the selection of parameters

based on driver behaviour. The selected speed parameters used in Arndt (1998) are

based on a model of measured speeds adopted by drivers under a number of

conditions as given in Chapter 2 of Austroads (1989). McLean (1978) originally

developed this model from data measurements on rural roads.

In Arndt (1998), the statistical significance of the developed accident equations

showed that there was a strong correlation between accident rates and the predicted

speeds. The same model has been adopted for the unsignalised intersection study to

obtain consistency between the intersection types. This model is discussed further in

Section 6.3.

Vehicle Path Model On a particular geometric element, the radius of the vehicle path is required in order

to calculate the 85th percentile speed by the model discussed in the previous section.

Vehicle path models were developed in Arndt (1998), because the vehicle path radii

can be significantly larger than the radii of the individual geometric elements of

roundabouts.

Similar vehicle path models are required at unsignalised intersections. These vehicle

52

path models are also necessary to determine the collision angle between vehicles,

which in turn, is needed to calculate the relative speed between vehicles. The adopted

vehicle path models are discussed in Section 6.4.

Determine Suitable Methods of Measuring Variables

The third data property in Section 3.1 shows that measurements of some of the

variables can be difficult due to changes over time, amongst other issues. To measure

such variables, this study makes a number of assumptions. For example, assumptions

made in the measurement of observation angle include all those required to

construction representative vehicle paths and the choice of a distance behind the give

way line where drivers will stop. The accuracy of the final models will only be as

good as these assumptions.

Assumptions made in the measurement of variables in this study are given in

Appendix C - Geometric Variables.

Determine Suitable Methods of Dealing with Correlation between Variables

The fourth data property in Section 3.1 discussed problems with multi-factor studies

when the sample sites do not comprise every possible combination of variables. This

was found to be a major problem in this thesis because several geometric parameters

recorded high levels of correlation with each other (as discussed in Section 16.2).

Harwood, Council et al (2000) state that ‘... if the independent variables in the model

are strongly correlated to one another, it is difficult to separate their individual

effects’.

A major reason for these high levels of correlation is that values of many geometric

parameters chosen from road design standards are often dependent on traffic volumes

and 85th percentile speeds. Therefore, many of the geometric parameters in these

standards correlate with these parameters and each other.

When these geometric parameters are used as variables in a regression equation, this

high level of correlation often yields results opposite to that expected. It can also

result in a particular variable being shown to be unimportant. Vogt and Bared (1998)

and Bauer and Harwood (1996) found such results.

An example of this outcome within this study was for the variables ‘traffic volume’

53

and ‘number of lanes’. These variables are highly correlated because higher traffic

volumes are generally accompanied by a greater number of lanes.

To minimise the problem with correlation, a number of methods have been

developed as discussed in Section 16.2.

Model Forms

Identify Appropriate Relationships between Variables and Accident Rates Most studies in the literature review have used variants of the model shown as

Equation 2.1 in Section 2.1. In this equation, accident rates are made proportional to

the following:

• Traffic flow parameters.

• Exponential of the sum of the values of geometric parameters multiplied by a

constant.

This equation considers interactions between variables to be the same ie they have an

additive effect. This may not be the case. Choosing such an equation sets a rigid

framework that is unlikely to identify trends in the data for variables that do not

follow this relationship.

When, in the model above, the value of a geometric parameter is zero, the parameter

has no effect on the accident rate. Using this model, a low value of a particular

parameter may not have much effect on the resulting accident rates if the range of

parameter values is high.

This aspect of the model, however, does not necessarily give a reasonable result for

all parameters. For example, single vehicle accidents would logically increase as the

length of the geometric element or the absolute speed increases. Should the length or

the absolute speed approach zero, the single vehicle accident rate would logically

approach zero (having a major influence on the accident rate). This was the approach

taken in Arndt (1998), where logical relationships between the variables and

dependent variables were derived. However, when low values are used in the above

model, these terms will have little effect on the accident rate.

In the case of a parameter such as side friction, single vehicle accident rates are not

proportional to side friction because single vehicle accidents occur even though the

side friction is zero (ie for a horizontal geometric element comprising a straight). The

54

model above may be appropriate in this instance. However, an appropriate

relationship between the side friction factor and single vehicle accident rate may also

be a polynomial equation which cannot be modelled with Equation 2.1.

This study identifies the most logical form of mathematical relationships between the

variables and the dependent parameters. Being a more logical approach, it is more

easily understood by practitioners.

This method of selecting relationships is discussed further in Section 16.3.

Develop Suitable Methods of Dealing with Interaction between Variables As discussed in the previous section, Equation 2.1 sets a rigid framework for the

acceptance of variables in the regression analysis. The opposite extreme to this is

setting a very flexible framework. Early in this study, all possible interactions

between parameters (using a multiplicative component of the variables for up to a

three-level interaction) were analysed in addition to allowing many parameters to

form polynomial relationships with accident rates. This was originally undertaken

because some very complex interactions are likely to exist between the various

parameters.

This scenario explained much of the variability in the data but produced results that

were illogical and impractical to apply. It was seen that such a flexible framework

does not produce reasonable results due to the problem discussed in the fourth data

property in Section 3.1. That is, there are usually far too few sites to cover every

possible combination of variables. Therefore, a more rigid framework is required.

For this reason, adding a multiplicative component of the variables to address

interactions was not adopted. A study such as this is therefore only likely to identify

major interactions between parameters.

If interactions between parameters were considered likely, alternative methods of

considering interaction were used. These include dividing the accident data into

smaller categories and checking the consistency across the categories, combining

variables, and/or creating dummy variables.

Interactions between variables are discussed further in Section 16.4.

Identify Suitable Regression Analysis Techniques

Initially in this study, Poisson techniques were used to analyse the various accident

55

categories. Each model developed was then tested for over or under-dispersion.

Many of the final accident models were found to be under-dispersed. It was seen that

the levels of categorisation used (ie the degree of division of the data sample into

smaller subsets) increased the levels of under-dispersion. The large number of under-

dispersed data samples in this study was reflecting the degree of categorisation used.

No suitable methods of allowing for the under-dispersion in the data were identified.

The standard errors within the final accident models were therefore inaccurate. The

trend identified, though, was likely to be the same. When the larger accident types

with over-dispersed or non-dispersed data were divided into smaller, under-dispersed

accident subcategories, similar estimates were obtained for most variables.

Therefore, it is not expected that the results will be in error to any large degree.

It is considered that the advantages of creating the smaller accident subcategories

outweigh the disadvantages. This method of analysis is discussed further in Section

16.5.

Determine Methods of Accepting and Rejecting Parameters in the Regression Analysis

To determine the more important variables in each accident model, a stepwise

regression analysis technique has been chosen. Stepwise regression techniques have

commonly been used in the identification of important variables in multi-factor type

studies.

Application of stepwise regression techniques in this study removed variables that

explained little of the variability in the data. However, some of the remaining

variables yielded illogical or unreasonable results even with the principals adopted in

the previous sections.

The purpose of developing predictive models is to explain as much variation as

possible in the data. Significant variables yielding illogical or unreasonable results

explain a greater amount of variation in the data but are not useful for this study.

Instead, the purpose of this study is to develop explanatory models that infer causal

relationships between geometric parameters and accident rates. An explanatory

model does not include illogical or unreasonable relationships. For this reason, unless

a logical mechanism could be established to explain why the variable should affect

accident rates in the particular way, the result was rejected.

56

The assumptions used as the basis of this decision are documented in this thesis. This

includes variables that form an opposite relationship to that found in previous

studies. Most variables forming an opposite relationship to that expected were those

highly correlated to other important variables or were those most likely to be

upgraded at an existing unsignalised intersection to improve safety. Reasons for

these types of variables producing these results are given in Sections 16.2 and 16.6

respectively.

For the major accident types, a stepwise regression technique was applied across all

of the subcategories. If a particular variable has only been selected in a

proportionally small amount of the subcategories, it has not been included in the final

accident model. In some cases, though, the individual subcategories may be adopted

as the final accident models eg where there is a logical interaction between variables.

These methods of accepting and rejecting variables are discussed further in Sections

16.6 and 16.8.

Determine Suitable Methods of Validating the Data

Two methods of validating the models have been used in this study. These are as

described below:

Dividing the Accident Data into Subcategories This method consisted of dividing the accident types into subcategories based on the

values of particular variables. The results of applying a stepwise regression analysis

across the subcategories were reviewed for consistency. This was usually only

possible for the major accident types with larger data samples.

If the results for a particular variable were inconsistent across the subcategories, the

variable was rejected. In some cases, though, the individual subcategories may be

adopted as the final accident models eg there is a logical interaction between

variables. Where relatively consistent results were obtained, the original larger

accident model would usually be adopted. Inconsistent results were deemed to be as

follows:

• Where a variable was significant in less than half of the accident subcategories

• Where the estimates of a variable were much different across the accident

subcategories

57

Cross Validation Using 90 Percent of the Data Cross validation comprises removing a number of observations from the data sample

and attempting to predict these using the remaining data. The degree of validation is

the closeness of the predicted results to the omitted observations. This method of

validation was not particularly useful in this study because the final accident models

are poor predictors of accident rates.

As discussed previously, the purpose of the accident equations are to be explanatory

models, not predictive models. For this reason, a different cross validation technique

to the traditional one was used. This technique consists of randomly removing ten

percent of the observations and applying a stepwise regression procedure to select

variables. This procedure was repeated 100 times and recordings were made of the

number of times that each variable from the original model was selected.

The purpose of applying this method of model validation was to record the level of

confidence in the final result, rather than influence the result as per the previous

method of validation. Therefore, all variables in the final models have been retained,

regardless of their stability.

These methods of validating the data are discussed further in Section 16.8.

3.4 Discussion of the Approaches Taken in this Study

The problems with multi-factor studies discussed in Section 3.1 were summarised as

follows: the collected data is likely to insufficient in determining all relationships

between variables. Two strategies proposed in this study to allow for or to overcome

these problems are as follows:

• Maximise Efficiency of Data Collection as discussed in Section 3.2.

• Develop Techniques for Analysing Less than Perfect Data as discussed in Section

3.3.

Some of the techniques discussed under the second dot point make assumptions

based on the results of previous research, observation of driver behaviour on-site,

experience, and logical or reasonable outcomes and relationships. These form the

framework on which the results are based. Some of these assumptions are required

simply to measure the values of certain variables.

The results of this study will only be as good as these assumptions and the suitability

58

of the data collected. Regardless of the amount of data collected (even when

adopting the techniques discussed in dot point number one above), it will usually be

inadequate to obtain results that yield many highly significant variables and explain

much of the variability in the data. For this reason, the framework on which the

results are based needs to be rigid enough to avoid results that do not make sense.

All assumptions made in the study are documented in this thesis and form the

framework on which the results are based. If certain assumptions are inaccurate,

particular relationships may not be identified. Even worse, a suspect result may be

produced. Where it is not clear which assumption is best for a particular case,

alternative assumptions have been applied and the results compared.

All authors of multi-factor studies make assumptions, whether consciously or

otherwise. For example, adopting the use of Equation 2.1 in Section 2.1 assumes that

the relationships between variables (interactions) and the relationships between

variables and accident rates will be in accordance with this model.

Some of the techniques discussed in Section 3.3 form a more rigid framework than

previous studies and are likely to produce fewer results eg accepting and rejecting

variables based on their consistency across subcategories. These techniques are

designed to remove variables likely to give inconsistent or unreasonable results.

Some techniques, though, form a less rigid framework than previous studies and are

likely to produce more results eg use of alternative relationships between variables

and accident rates.

The overall approach taken in this study seeks to identify the important variables

affecting accident rates and produce a logical result. Relationships for variables

having only a small effect on accident rates are unlikely to be determined. In the

same way, only strong interactions between variables are likely to be determined.

This approach is not dissimilar to that discussed in Hauer (1997) who stated ‘... the

statistical interpretation of observation studies is messy, involves ambiguity, may

require judgement, and, in general, does not provide the intellectual pleasures of

clear logic, systematic deduction and uncontrovertible proof’.

It is considered that this type of study forms part of an evolutionary or iterative

process to obtain better results. The results of this study can identify where more data

is required to overcome the problems associated with multi-factor studies as

59

discussed in Section 3.1. This data can then be collected and added to the existing

data in the study.

An example of this concept is the need to obtain a wider range of data to identify

stronger tends. The range of values required to develop more robust relationships

with accident rates is more clearly identified using the results of the regression

analysis. For example, what constitutes poor visibility (those values of visibility that

cause a significantly higher accident rate) is more likely to be understood from the

results of a study such as this.

If visibility was not found important, it is likely that sites with less visibility than

those originally included in the sample need to be obtained. If visibility was found

important but its level of validation was low, a greater number of sites with visibility

towards the lower end of the sample are required.

Such an evolutionary process to obtain better results would involve large amounts of

time, expenditure and resources. It would likely be beyond the scope of most road

authorities.

Part B

61

4 SELECTION OF UNSIGNALISED INTERSECTION SITES

This chapter describes the process used to select a number of suitable unsignalised

intersections for analysis, and an overview of the selected intersections.

4.1 Obtaining a Wide Range of Variable Values

As discussed in Section 3.2, it is considered desirable to obtain a relatively even

spread of a widest possible range of the values of each the variables. As identified in

Agent (1988), it is expected that this procedure will more likely identify trends in the

data and produce the most confident result. Taylor and Young (1988) states that ‘the

lack of variation of a variable of interest will result in the variable appearing to have

little impact,… Attempts should always be made to overcome these problems’.

If the values of a particular variable are all the same, it is obvious that no correlation

between this variable and accident rates can be determined. If the values of a

particular variable predominantly cover only a narrow range, a few sites with values

well outside this range will have a major influence on the result. If these sites have

limited exposure, a very small amount of accident data will have a major influence

on the model developed.

Examples of obtaining the widest possible range of variables values are given below:

• Continuous variables eg approach speed- select intersection samples that cover

a wide range of approach speeds ie low speed to high speed. Ensure that there are

a relatively even spread of sites through the range of approach speed.

• Discrete variables eg number of major road lanes - select intersection samples

that cover two lane and multi-lane roads. Ensure that there are enough sites in

each.

• Categorical variables eg turn treatments - select intersection samples that cover

all turn treatment types. Ensure that there are an adequate number of sites for each

turn type.

In order to obtain a relatively even spread of a widest possible range of the values of

each variable, intersection sites have not been chosen completely at random. Instead,

preliminary data was collected on a larger number of intersections than was used in

the analysis (these intersections were chosen largely at random). From these

preliminary intersections, a smaller sample of intersections was selected to provide

62

the greatest range of values of the variables.

Sample Size

As discussed above, a wide range of the values of the variables (traffic volume,

geometric and other parameters) is desirable in order to predict their effect on

accident rates. To achieve this, preliminary data were gathered on approximately 600

unsignalised intersections throughout Queensland. These intersections were

essentially selected at random except that very low volume intersections were not

selected (refer to Section 4.2 for the criteria used to omit intersections on the basis of

insufficient traffic volumes). Of these 600 intersections, 206 were chosen for

analysis. These were subjectively selected as to provide the widest possible range of

the values of the following variables:

• Number of legs - three-leg and four-leg

• Turn treatments - LSR, AUR, CHR, MNR, BAL and AUL (refer to Figures 4.1 to

4.3 in Section 4.3 for the various turn treatment codes)

• Control - stop or give way

• Number of stand-up lanes on the minor road - one lane and two lane with or

without free left-turn lanes

• Number of lanes on the major road - two lane to six lane

• Median width - no median to wide median

• Road type - urban or rural

• Speed environment on major and minor legs- low to high speed

• Traffic volumes on major and minor road - low to high volumes

Justification for Using Other than Random Sampling

Random sampling is often used to find attributes of the total population eg average

accident rate per intersection in Queensland. In this process, the total population may

be known or unknown. In this study, however, attributes of the total population are

not required. Instead, the effects of particular geometry on accident rates are

required.

In order to obtain the widest possible range of variable values, the experimental

63

approach listed in the previous section has been used. In addition to the benefits of

this approach discussed in the previous section, this approach seeks to optimise the

data collected by avoiding the collection of many similar data. This ensures that the

time spent in data collection maximises the likely results. In addition, a spread of the

values of the variables enables better predictions at values near the extremes.

The sites selected for analysis using this experimental design have no known bias.

They have not been chosen in any way based on some method of selection of the

dependent variable ‘accident rates’. Values of the dependent variable are not known

until all sites have been selected and resulting data collected.

It would be desirable to apply some form of ‘weighting’ to each variable and their

values to ensure enough intersection sites within each category. However, finding

intersections with the required features to fit within such a system would be

extremely difficult, if not impossible due to the large number of variables that would

require ‘weighting’ together. Choosing an intersection sample to weight the values of

just one variable will result in difficulty weighting a second variable, let alone at

least ten variables.

Expected Results Using Random Sampling

For intersection sites to be selected at random, all intersections within Queensland

would need to be identified and listed. Some method of sampling from this list would

then need to be performed. Problems with this method are then:

• This process would be difficult and time consuming.

• There would be difficultly in distinguishing between some of the lower volume

intersections and accesses and driveways.

• Many of the Type LSR and AUR intersections selected would comprise very low

traffic volumes producing inadequate amounts of accident data for analysis. This

issue is discussed in Section 4.2.

• This process does not address the issues identified in the previous section as

discussed below.

It is expected that very few intersections with the following criteria would be chosen

by random selection. This is based on the amount of effort that was undertaken in

finding such intersections for the analysis.

64

• Type AUR intersections

• High traffic volumes on the minor road

• Greater than one stand-up lane on the minor road

• Wide medians

• Multi-lane roads

• High speed minor legs

• Crossroads with significant through volumes from the minor legs

Initially in this study, a sampling method more random than described in the

previous section was undertaken. It was found that random sampling selected very

few Type AUR intersections (refer to Figure 4.1 in Section 4.3 for details of Type

AUR turn treatments). Predictive equations for Type AUR intersections would then

only be based on a small amount of data resulting in a low degree of confidence in

the outcome. However, the final sampling method used (choosing a sample of

intersections from a larger preliminary sample to provide the greatest range of values

of the variables) ensures that enough Type AUR intersections will be selected to be

reasonably confident of the results.

4.2 Excluding Very Low Volume Intersections

As discussed in Section 3.2, intersections with very low traffic volumes have been

excluded from the study. This is for the following reasons:

• Intersections with very low traffic volumes (as defined by those meeting the

criteria in the first row of Table 5.1 in Section 5.2) are expected to have too much

influence on the developed accident models. This is because just one accident

recorded at one of these sites will produce an extremely high accident rate

(accidents per number of vehicles). This potentially results in the regression

equations predicting that the geometry at this type of intersection significantly

affects accident rates, especially if only a few low volume sites exist in the

sample. Conversely, if no accidents are recorded, the zero accident rate will

potentially show that the geometry at this intersection is good.

• This approach seeks to optimise the data collected by avoiding the addition of

intersections to the sample that comprise very little accident data resulting from

65

low exposure. This ensures that the time spent in data collection maximises the

likely results. In order to confidently analyse intersections with very low volumes,

a very large number of sites would be required. This is considered impractical,

given time and budget constraints.

By choosing to exclude intersections with very low volumes from the analysis, the

resulting models can be judged to strictly apply to intersections other than low

volume. However, the highest traffic volume product in the study (minor flow

multiplied by the major flow) is approximately 3000 times higher than the accepted

minimum for intersections to be added to the sample. Therefore, the range of traffic

volumes excluded from the study is actually very low in comparison with the total

sample. In the absence of an enormous amount of data required for the low volume

sites, the best predictor of accidents at the low volume sites will be the equations

developed in this study. This is because the wide spread of traffic volume data

enables reasonable predictions near the extremes (were the low volume intersections

lie).

Criteria for the inclusion of intersection sites based on minimum traffic volumes is

given in Section 5.2.

4.3 Types of Intersections Selected

Relatively uncommon intersections were excluded from the analysis because

inadequate samples of these intersections exist in order for them to be placed in

separate categories. If relatively uncommon intersection types were combined with

common ones into an overall sample, the uncommon types are expected to have too

much influence on the outcome of the results. Table 4.1 lists the types of

intersections selected for analysis and those rejected, based on how commonly they

occur.

Due to the relative ease in obtaining the necessary geometric, traffic volume and

accident data, only intersections under the jurisdiction of the Queensland Department

of Main Roads were selected (ie no intersections under the jurisdiction of local

authorities).

The selected intersections were checked with the appropriate Main Roads District

Office to ensure that the physical layout of the intersection had not changed over the

analysis period, or that no major work had been undertaken at the intersection over

66

this time. Some districts used data from the asset management system ARMIS ‘A

Road Management Inventory System’ to determine this. For those districts that did

not have such data available, an engineer with an extensive knowledge of the road

system was contacted in order to verify this from memory.

Table 4.1 - Intersection Types Selected/Rejected Intersection Type

Parameter Included in Analysis (relatively common

intersections)

Excluded from Analysis (relatively uncommon intersections)

Number of legs / Shape of intersection

• Three-leg T-intersections

• Four-leg intersections

• Y-intersections (particularly old rural intersections)

• Intersections with greater than four legs

• Seagull intersections

• Staggered T-intersections with an offset greater than the width of the minor road.

• Intersections with very wide medians >50m

Control • T-intersections with no control; intersections with give way or stop-control on minor legs - both major legs to have no control.

• Four-leg intersections with no control on any leg or one leg only

• Intersections with give way or stop-control on major legs including four-way stop-control intersections

Traffic flow direction

• Intersections on two-way roads

• Intersections where major or minor roads comprise one-way traffic flow only

Turning movements

• Intersections with unrestricted turning movements

• Intersections with restricted movements due to continuous medians, channelisation, or full or part time signage

Turn types • Turn types LSR, AUR, CHR, MNR, LSL, AUL and combinations of these (refer Figures 4.1 to 4.3).

• Intersections with greater than one auxiliary lane per turning movement (excluding through movements)

Through lanes

• Intersections with continuous through lanes on the major road (two lane to six lane)

• Intersections where a through lane on the major road becomes an exclusive turning lane

67

Intersection Turn Types

The standard rural intersection turn type codes BAR, AUR, and CHR used in QDMR

(2000) and Austroads (2003) were found insufficient for use in this study for the

following reasons:

• They do not cover urban applications

• They only cover two-lane, two-way roads

• They do not include cases of right-turn treatments with no specific turn facilities.

For the reasons above, a code was selected for each of the intersection turn types

used in this study. The original rural codes from QDMR (2000) and Austroads

(2003) were adopted where the intent of these turn treatments were the same as the

turn treatments used in the study. Where this intent was achieved, the original codes

were used to describe turn treatments for urban and rural areas, even though the

original codes were specifically set for rural areas only.

The codes adopted and the reasons are given below. Figures 4.1 to 4.3 show

diagrams of these treatments. These diagrams are repeated in Appendix E - Turn

Types Used in this Study for ease of reference by the reader.

• LSR ‘Low Standard Right-Turn Treatment on Two-Lane, Two-Way Roads’ -

This code was adopted to describe right-turn types that comprised no specific turn

facilities and those that comprised a shoulder area of various sizes (including a

widened shoulder) for passing a right-turning vehicle on a two-lane, two-way

road. The code BAR was not adopted because it does not adequately describe all

of these cases.

• AUR ‘Auxiliary Right-turn Treatment on Two-Lane, Two-Way Roads’ - This

code was adopted from QDMR (2000) and Austroads (2003) where a marked

auxiliary lane allowed drivers to pass a right-turn vehicle on the left. Dimensions

of the auxiliary lanes of the sites in the study were often different to those given in

QDMR (2000) and Austroads (2003).

• CHR ‘Channelised Right-Turn’ - This code was adopted from QDMR (2000) and

Austroads (2003) where a formal right-turn bay has been provided. This term has

been adapted to both single and multi-lane roads. Dimensions of the right-turn

68

slots of the sites in the study were often different to those given in QDMR (2000)

and Austroads (2003).

• MNR ‘Multi-lane Road with No Specific Right-Turn Facility’ - This code was

adopted to describe right-turn types that comprised no specific turn facilities on a

multi-lane road.

• LSL ‘Low Standard Left-Turn Treatment’ - This code was adopted to describe

left-turn types that comprised no specific turn facilities and those that allowed a

left-turn vehicle to turn from the shoulder. The code BAL was not adopted

because it does not adequately describe both of these cases. This term has been

adapted to both single and multi-lane roads.

• AUL ‘Auxiliary Left-Turn Treatment’ - This code was adopted from QDMR

(2000) and Austroads (2003) where a marked auxiliary lane allowed drivers to

turn left from the auxiliary lane. This term has been adapted to both single and

multi-lane roads. Dimensions of the auxiliary lanes of the sites in the study were

often different to those given in QDMR (2000) and Austroads (2003).

Subcategories of right-turn treatments are given in Figures 4.4 to 4.6. These

subcategories were developed because the line marking or other features of each

intersection turn type differed significantly as discussed below:

• Intersections with medians but no right-turn slots or auxiliary lanes were

classified as Type MNR2 as shown in Figure 4.4.

• Intersections with Type AUR turn treatments comprised various forms of line

marking as shown by Types AUR1 to AUR5 in Figure 4.5. Type AUR turn

treatments with medians are shown as Types AUR6 and AUR7.

• Intersections with Type CHR turn treatments comprised various forms of line

marking as shown by Types CHR1 to CHR3 in Figure 4.6. Types CHR2 and

CHR3 were included as Type CHR because all through drivers observed

(travelling from the right to the left in Figure 4.6) moved to the left side of the

intersection in the same manner as for a Type CHR1. This is different to driver

behaviour at Type LSR and AUR turn treatments where through drivers were

observed to stay near the centreline (unless passing a right-turning vehicle).

69

Figure 4.1 - Types of Right-Turn Treatments on Two-Lane, Two-Way Roads Analysed in this Study and Selected Descriptive Codes

Notes: (1) At three-leg LSR turn treatments, a sealed or unsealed shoulder may be provided on the left side

of the carriageway for through vehicles to pass right-turning vehicles. (2) For the four-leg AUR turn treatment shown, it can be difficult to determine whether this type of

intersection is a Type AUR or a Type AUL with acceleration lanes. On-site observations indicate that it operates both ways.

70

Figure 4.2 - Types of Right-Turn Treatments on Multi-lane Roads Analysed in this Study and Selected Descriptive Codes

71

Figure 4.3 - Types of Left-Turn Treatments Analysed in this Study and Selected Descriptive Codes

Note: Two lane roadways only are shown. The same turn types apply to multi-lane roadways.

72

Figure 4.4 - Subcategories of Type LSR and MNR

Turn Treatments Used in this Study Note: Number of sites with the particular turn treatment is shown in brackets.

73

Figure 4.5 - Subcategories of Type AUR Turn Treatments Used in this Study

Note: Number of sites with the particular turn treatment is shown in brackets.

74

Figure 4.6 - Subcategories of Type CHR Turn Treatments Used in this Study

Notes: (1) Two lane roadways only are shown. (2) Number of sites with the particular turn treatment is shown in brackets.

75

4.4 Overview of Intersection Sample

The number of intersections selected within each Main Roads District is given in

Table 4.2.

Table 4.2 - Location of Intersections in Analysis District Number

District Name Number of Sites

1 South Coast Hinterland 16 2 North Coast Hinterland 26 3 Southern 20 4 South West 4 5 Border 11 6 Central 12 8 Mackay 10 9 Northern 11 11 Peninsula 13 12 Wide Bay 10 13 Metropolitan 73

Total 206

The number and type of intersections selected for analysis is shown in Table 4.3.

Table 4.3 - Types of Intersections in Analysis Number of Intersections in Analysis Right-Turn

Treatment Three-leg T-Intersections

Four-leg Intersections

Type LSR 43 15 Type AUR 33 5 Type CHR 53 32 Type MNR 14 4 Combination Type LSR/Type AUR

N/A 3

Combination Type LSR/Type CHR

N/A 2

Combination Type MNR/Type AUR

N/A 1

Combination Type MNR/Type CHR

N/A 1

Total 143 63

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5 ACCIDENT DATA

This chapter describes the method of accident data collection for each unsignalised

intersection. An overview of the recorded accident types and the method of

categorising the accident data are then given.

5.1 Source of Accident Data

For this study, accident data has been taken from the Department of Main Roads

accident database ‘Road Crash 2’, which is part of the asset management system

ARMIS. Accident data contained within this database is collected as follows:

• The Queensland Police Service completes a PT51 traffic incident report for each

major crash and log the recorded data onto its computer system.

• The Office of Economic and Statistical Research accesses the police database and

enters data into the Queensland Transport road crash database.

• Individual Main Roads districts access the Queensland Transport database and

add further information to it to create the Road Crash 2 database.

Road Crash 2 lists all reported personal injury accidents and/or property damage

greater than $2,500 occurring on declared roads in Queensland. Crash incident

reports were obtained for all accidents occurring within 200m of the intersection

(except on minor legs under the control of local authorities, in which case the

maximum distance of 50m was used). The distance of 200m was chosen to ensure

that the complete geometry of rural intersections was contained within the selected

distance. Rural intersections containing long left-turn lanes and large splitter islands

can extend well over 100m from the centre of the intersection.

The crash incident reports described each accident. In most cases, the description

was sufficient to identify the type of accident and the direction of vehicles involved.

This applied for accidents at the selected unsignalised intersections as well as those

at adjacent intersections, driveways and mid-block locations.

77

Using the Road Crash 2 database, the following parameters were recorded for each

accident:

• Date of accident

• Time of accident

• Type of accident (including DCA Code)

• Type of vehicles involved in the accident

• Contributing factor/s

• Accident severity

• Atmospheric conditions at time of accident

• Light conditions at time of accident

• Road surface conditions at time of accident

5.2 Selected Analysis Periods

Table 5.1 shows the analysis periods selected. Intersections meeting the criteria in

the first row (very low volume intersections) were excluded because they were

expected to have too much influence on the developed accident models. Preliminary

calculations revealed that they were unlikely to record one angle type accident over a

period of five years. This issue was discussed in Section 4.2.

Table 5.1 - Selection of Analysis Period Cross Product

of Traffic Flows (1)

Intersections in this Range Included

Analysis Period

Selected

Length of Analysis

Period (years)

Number of Sites Selected

< 5 x 104 No N/A N/A 0

> 5 x 104 and < 5 x 105 Yes

1 January 1992 -

31 December 2001

10 20

1 July 1994 - 30 June 1999 5 170 > 5 x 105 Yes

Varies 5 (minimum) 16 Total 206

Note: (1) The values in the first column equal the cross product of the traffic flow per day approaching on

the minor leg multiplied by the sum of the traffic volume per day approaching on the major legs (veh/d)2

78

An analysis period of ten years was selected for the low volume intersections

meeting the criteria given in the second row. It was felt that an analysis period

longer than five years was required for these intersections because of the relatively

low frequency of accidents. Intersections in this category were only selected if

sufficient evidence was available that their layout did not change in this period.

These low volume intersections generally comprised Type LSR turn lane treatments.

An analysis period of five years was selected for the majority of the intersections that

meet the criterion given in the last row of Table 5.1. It would be preferable to have a

longer analysis period, however, for several cases it could not be reliably ascertained

that the intersection layout has remained the same over a longer period. Several of

the intersections meeting this criterion had varying analysis start and end dates

because of changes to the layout of the intersection. The minimum analysis period

for these intersections was selected as five years.

5.3 Categorisation of the Accident Data

Some studies identified in the literature review comprised a very large sample of

intersections. These studies generally did not involve categorising the data according

to the various accident types. Instead, all accident types were analysed together. A

problem with this technique is that variables affecting a particular accident type/s but

not others (or having an opposite effect on others) will not normally be identified.

These types of studies were generally unsuccessful in relating geometry to accident

rates.

Knowing these effects is important because they potentially identify the most

appropriate mitigating treatments for reducing each accident type. Arndt (1998)

found that increasing the value of some variables had a positive effect on some

accident categories whilst having a negative effect on others. It was found possible to

increase the value of a particular variable to minimise one accident type, whilst

introducing other treatments to minimise another accident type. These other

treatments offset the increase in accident rate with an increase in value of the

particular variable for the second accident type.

Studies that comprised a smaller number of intersections generally involved some

categorisation of the data by accident type. Separate analyses were then undertaken

on each individual accident type.

79

Table 5.2 lists two common methods of categorising the accident data used in the

various multi-factor studies identified in the literature review. One of these methods

was ‘by intersection type’. This table shows that most studies analysed three and

four-leg intersections separately.

The other method was ‘by accident type’. Some studies did not categorise according

to accident type (mostly those with large intersection samples as discussed

previously) whilst others categorised to different levels. Three studies categorised by

individual conflict points, the largest degree of categorising by accident type.

Table 5.2 - Two Methods of Categorising the Data used in the Various Multi-factor Studies

Method of Categorising the Accident

Data

Level of Categorisation of the Accident Data

Number of

Studies

All intersection types (three and four-leg) analysed together

2

Three and/or four-leg intersections analysed separately

12

By Intersection Type

Unknown 2 All accident types analysed together 5 Each accident type analysed separately eg angle, rear end

4

Each accident type from the major or minor road analysed separately eg angle from minor, rear-end from major

2

Each individual conflict analysed separately

3

By Accident Type

Unknown 2

The two methods of categorising the data in Table 5.2 were the most common.

However, other methods of categorising the data were also used. Table 5.3 lists such

methods in addition to those already discussed above. Potential advantages and

disadvantages of each method are also shown.

In some ways, it is desirable to categorise the data into many accident subsets using

most of the methods in Table 5.3. However, little data would then remain in most of

the accident subsets unless data on an enormous number of intersections were

collected. Such a study would be beyond most practical limits.

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Table 5.3 - Methods of Categorising the Data Method of

Categorising the Data

Advantages/Disadvantages of Each Method

None Few relationships are likely to be identified unless an extremely complex model using dummy variables to cater for the various accident subtypes is used. This is because variables that may affect one accident sub-type may not affect another or may have the opposite effect. In addition, a variable relevant to one accident subtype may not be relevant to another.

By intersection type eg three or four-leg

Similar to the issues in row number one except that the effect of intersection type on the total number of accidents is likely to be identified.

By accident nature eg angle, rear-end

Particular accident natures can comprise different accident subtypes. In this case, the issues in row number one apply.

By movement type eg left, through, right

Irrelevant unless used in conjunction with other methods eg ‘by location’ and ‘accident nature’.

By individual conflict type

Best method if large amounts of data are available. If not, particular conflicts types contain too little data to adequately analyse. May need to be combined with other methods eg ‘by intersection type’ unless dummy variables are used.

By accident severity eg injury or death

Similar to the issues in row number one except that rates for various accident severities are likely to be identified.

By location eg major or minor road

Irrelevant unless used in conjunction with other methods eg ‘by movement type’ and ‘by accident nature’.

By environment eg urban or rural

Similar to the issues in row number one except that the effect of environment on the total number of accidents is likely to be identified.

By distance from intersection

Similar to the issues in row number one unless used in conjunction with other methods eg ‘by accident nature’.

By driver error which lead to the accident

More readily identifies possible parameters affecting each accident subtype. Enables particular accident subtypes to be combined creating larger samples for analysis. May need to be combined with other methods eg ‘by intersection type’ unless dummy variables are used.

A combination of any or all of the above

Enables numerous models to be developed and tested. Some will take a more logical form than others. If similar results are obtained for more than one method, greater confidence can be placed in the result.

It is desirable to divide the total accident sample into smaller categories such that the

variables selected for trial in each accident subset are least relevant to that accident

subset. An example of this is as follows. Accidents involving two major road

vehicles colliding in a rear-end type manner would logically be unaffected by the

variable ‘minor road speed limit’. If this variable was selected for trial, it should only

81

be used in those accident subsets for which it is relevant.

The next section discusses the process used to categorise the accident data into major

accident types for use in this study. The regression analysis further divides these

accident types into smaller accident subsets as detailed in Chapters 17 to 21.

The smaller accident subsets have been created by combining particular

categorisation methods listed in Table 5.3, as discussed in the last row of this table.

For practical reasons, it is not possible to trial all possible methods.

Initial Accident Classification

A total of 1678 accidents were recorded from the Road Crash 2 database. These

accidents were initially classified according to the nature of the collision (considering

the number of vehicles involved and the original direction of travel of the vehicles).

A summary of the initial classification is shown in Table 5.4.

Table 5.4 - Initial Accident Classification Accident Category Number of Accidents

Recorded Not Included in Analysis 587 Angle 602 Rear-end 148 Single Vehicle 211 Head-on 55 Sideswipe 35 Pedestrian and Cyclist Crossing 40

Total 1678

In Table 5.4, the ‘Not Included in Analysis’ accident type shows 587 accidents that

were excluded from the analysis because they were at the wrong location, were

unable to be accurately located, or were accidents at nearby intersections or other

features that were readily identified as being primarily influenced by the existence of

these features. Table 5.5 gives a breakdown of the various accident types in this

category.

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Table 5.5 - ‘Not Included in Analysis’ Accident Category Accident Symbol

Assigned

Accident Description Number of

Accidents Recorded

A

Nearby intersection accidents - accidents at nearby intersections that were readily identified as being primarily influenced by the existence of the nearby intersection. Pedestrian accidents included if crossing at a signalised crossing. Rear-end accidents at the intersection under consideration were included if the cause of the accident was a queue banked up from a nearby intersection.

274

D Driveway accidents - resulting from drivers pulling into or out of driveways 100

P Parking accidents - resulting from drivers pulling into or out of parking bays, or from running into or avoiding a parked vehicle

43

PE Accidents at pedestrian crossings- including collisions with pedestrians and rear-end accidents resulting from stopping at the crossing

13

R Roadwork accidents - resulting primarily due to roadworks eg rear end in queue at roadworks with traffic signal control

8

RC Accidents at railway level crossings - train collided with a car 6

RE

Rear-End-Through accidents - rear-end accidents occurring to two or more through vehicles. No indication was given in the data as to why the front vehicle stopped or slowed. These accidents predominantly occurred near an urban intersection that recorded high rear-end vehicle accident rates. It is suspected that most of these rear-end-through accidents have occurred because of right-turning vehicles at nearby Type LSR intersections or queues at traffic signals.

34

U Insufficient information to accurately locate accident or insufficient information to determine nature of accident

50

W Wrong location given for accident 59 Total 587

Final Accident Classification

It is considered inappropriate to analyse the accident data according to the

classification in Table 5.4. This is because different factors (e.g. driver behaviour,

conflict type, geometry) are applicable to the various accidents within each category.

For this reason, the accident data (except the ‘Not Included’ category) were

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reclassified according to what principle event/s gave rise to each accident.

The major accident types within the final accident classification are shown in Table

5.6. Figures 5.1 to 5.3 show simple conflict diagrams of each accident category.

These categories are consistent with the results of previous studies as identified in the

literature review in Section 2.1.

Criteria for this classification are given below.

Number of Accidents Accidents were categorised according to the number of accidents in each category.

Accident types that recorded greater than or equal to 40 accidents were classified as

‘high frequency’ accidents whilst those that recorded less than 40 accidents were

classified as ‘low frequency’ accidents. The cut-off of 40 accidents was based on a

convenient gap in the number of accidents in Table 5.6 ie from 39 to 107.

Location Accidents that could only occur because of the physical presence of the intersection

were classified ‘Intersection’ accidents. An example of this type of accident was

failing to give way on the minor leg and colliding with a major road vehicle.

All other accidents that could occur at any location along the major or minor roads

(including within the intersection conflict area) were classified as ‘Through’

accidents. An example of this type of accident was a single vehicle accident on the

major road where a driver has lost control of the vehicle due to excessive speed for

the geometric feature. This classification was made on the subjective basis that the

physical presence of the intersection could not have had any perceived effect on

these accidents.

Driver Behaviour Accidents were classified according to what driver behavioural factors principally

lead to the accident occurring. As an example, an ‘angle’ accident involving a minor

road vehicle failing to give way and colliding with a major road vehicle was placed

into the same category (Angle-Minor) as a ‘single vehicle’ accident occurring due to

a major road vehicle avoiding a minor road vehicle that has failed to give way. In

both these cases, the principal driver error was the minor road driver failing to give

way.

It was found that the only successful way to determine the events that lead to the

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accident (and hence the driver behaviour) was to read the description on every crash

incident report combined with the other data boxes on the form.

Leg Type For most accident types, the accidents were classified according to which leg the

erroneous driver behaviour was performed ie major or minor leg.

Based on the above, the following four broad accident categories have been selected:

• High frequency intersection accidents

• Low frequency intersection accidents

• High frequency through accidents

• Low frequency through accidents

Appendix A ‘Accident Categories’ details the types and numbers of sub-accident

types recorded for each major accident category listed in Table 5.6. These have not

been included in this section because of the large space requirements.

85

Table 5.6 - Major Accident Categories Broad

Accident Category

Major Accident Type

Principal Cause of Accident No. Total

Angle-Minor Failure to give way by a minor road vehicle

466

Rear-End-Major Not adequately negotiating a slowed or stopped turning major road vehicle

121 High Frequency Intersection Accidents

Angle-Major Failure to give way by a major road vehicle turning right at intersection

107

694

Rear-End-Minor Not adequately negotiating a slowed or stopped minor road vehicle at intersection

27

Single-Minor-Turn

Loss of control whilst turning from minor leg

23

Single-Major-Turn

Loss of control whilst turning from major leg

17

Incorrect Turn Undertaking an incorrect turning manoeuvre

17

Overtaking-Intersection

Unsafe overtaking on the major road at an intersection

13

Sideswipe-Major-Auxiliary

Hit another vehicle by moving from deceleration lane onto through lane

4

Low Frequency Intersection Accidents

Other 8

109

High Frequency Through Accidents

Single-Through

Loss of control whilst travelling through on the major or minor legs

167

167

Pedestrian Hit a pedestrian or cyclist crossing road

39

U-Turn Hit whilst undertaking a U-turn at midblock

33

Changed Lanes Changed lanes when unsafe 16 Single-Object Hit or avoid object or animal 16 Overtaking Unsafe overtaking 7

Low Frequency Through Accidents

Other 10

121

Total 1091

86

Figure 5.1 - High Frequency Intersection and Through Accident Types

Figure 5.2 - Low Frequency Intersection Accident Types (excludes 8 ‘Other’ accidents)

87

Figure 5.3 - Low Frequency Through Accident Types (excludes 10 ‘Other’ accidents)

88

6 GEOMETRIC AND OTHER VARIABLES

This chapter describes the method used for selecting variables and the collection of

geometric data (and data for other variables) for each of the intersections and an

overview of the collected data.

6.1 Selection of Variables

To undertake a regression analysis on the effects of unsignalised intersection

geometry on accident rates, all geometric and other variables that may be expected to

have an influence on accident rates must be determined. This has been undertaken

by:

• Reviewing literature on this topic (as discussed in Sections 2.1 to 2.4)

• Considering the possible effect of geometric variables on driver behaviour by:

Reviewing literature on this topic (as discussed in Section 2.6)

Analysing the contributing factors for each accident category given by police

in the Crash Incident Reports

Observing driver behaviour on-site

Obtaining the views of drivers

• Considering Exposure and Propensity concepts

Exposure is defined as the number of opportunities for accidents to occur of a given

type, in a given time, in a given area. Propensity is the conditional probability that an

accident will occur, given the opportunity for one. Each selected variable is either an

exposure term or a propensity term. Identification of these terms aids the

development of accident equations.

Some of the variables identified by the procedure above could not be used in the

regression analysis. One reason for this was that not all variables could be readily

quantified. Such variables are listed in Table 6.1.

As discussed in Sections 3.2 and 4.1, a relatively even spread of a wide range of the

values of the variables is desirable in order to predict their effect on accident rates.

Variables that were considered to have a very limited range were not used in the

regression analysis. Such variables are listed in Table 6.1.

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Table 6.1 - Geometric and Other Variables Identified but not Used in the Regression Analysis

Variable Variable Readily Quantifiable Wide Range of

Values Available

Presence of islands and medians

No. The number and type of islands and medians (raised, depressed, painted) and the width and length vary which would require a complex model to be developed. Median width can be used separately, though.

Yes

Use of delineation No. The type of delineation varies between intersections and over time. Data is not reliable.

No

Change in land use No. Would require a complex model to be developed. No Special treatments eg rumble strips

Yes. No - few sites available

Gradient of major and minor roads

No. Varies over length on vertical curves No - few steep sites

Road surface type and condition

No. Varies over time. Data is not reliable. No

Major road bunching

No. Could use distance since last potential stop condition. However, the number of vehicles stopping at say traffic signals varies. In addition, bunching is dependent on number of overtaking opportunities on two-lane rural roads. Inadequate time and resources available to measure this parameter. Subjective measurement expected to be too inaccurate

Yes

Number of vehicles parking / leaving parked areas

No. Inadequate time and resources available to measure this parameter. Subjective measurement expected to be too inaccurate.

No

Differential in major rd vehicle speed

No. Intersections on steep grades, intersections on roads with inappropriate speed limits, and intersections where there are a considerable number of vehicles accelerating on the major road may cause a differential in vehicle speeds. This may make it more difficult for drivers to adequately perceive these vehicles. Inadequate time and resources available to measure this parameter. Subjective measurement expected to be too inaccurate.

No

Number of Heavy Vehicles Turning

Unsure. Large numbers of turning heavy vehicles may cause increased blockage to visibility. Inadequate time and resources available to measure this parameter.

Yes

Number of roadside hazards

No. The type, number and extent of roadside hazards vary considerably which would require a complex model to be developed.

Yes

Crossfall of major road

No. Crossfall varies over superelevation development lengths. This makes it very difficult to quantify.

No

Stopping sight distance

No. Stopping sight distance varies along length of roadway. Yes

All the values of all variables identified by this method (shown in the previous dot

points in this section), excluding those in Table 6.1, were either measured or

calculated and are shown in Appendix C - Geometric Variables. These eighty-five

variables include other parameters identified after initial analysis of the data as

discussed in Section 16.1. Information on these variables (including issues regarding

their measurement) has not been included in this section because of the large amount

90

of space required.

As discussed in Section 3.3, variables have been carefully selected based on logical

relationships with accident rates. Variables that logically would have only very little

or no influence were not included. An example of this is as follows. The level of

approach signage on the minor road would logically have no influence on single

vehicle accidents occurring to through vehicles on the major road.

This technique was adopted because variables with very little or no influence on

accident rates may be correlated with other more important variables. Through this

correlation, an analysis may show that they are important predictors of accidents.

However, their effect is only being reflected through the other, more important

variables. It is even possible that variables that have nothing to do with the particular

intersection can be shown to be important.

Another example of this was the variable ‘presence of a free left-turn lane from the

minor road’. This variable was found to be a very significant predictor of failure to

give way accident rates (Angle-Minor). It logically would have the most effect for

accidents involving left-turn drivers from the minor road who fail to give way rather

than for through and right-turning drivers.

However, the number of accidents resulting from left-turn drivers from the minor

road failing to give way was very low and this variable was not a significant

predictor of this accident subcategory. It was seen that the significance of the

variable ‘presence of a free left-turn lane from the minor road’ was being reflected

through correlation with the variables ‘traffic volume’ and ‘minor road approach

speed’.

6.2 Collection of Geometric and Other Variable Data

Values of the chosen variables in the previous section were obtained for all the

unsignalised intersection sites. Initially, plans of each intersection were requested in

order to determine some of these values. In several cases, however, it was found

unsuitable to use plans for the following reasons:

• No plans were available, particularly if the intersection had remained unchanged

over a long period.

• Details on plans were different to what was built in the field.

91

• Plans gave inadequate details of the intersection.

Aerial photographs were obtained where it was unsuitable to use plans for the

reasons given above. In some cases, however, aerial photographs were also

unsuitable for the following reasons:

• Only three Main Roads Districts had good aerial photograph coverage of their

roads.

• Some intersections were obscured by a large amount of vegetation.

Where plans or aerial photographs could not be obtained for a particular intersection,

it was not selected as a sample site. The only exception to this was if the intersection

comprised extremely simple geometry that could be measured on-site.

Change in Parameter Values over the Analysis Period

Values of several of the variables selected for analysis (as given in Appendix C -

Geometric Variables) were measured on-site. Although it was verified that there

were no major changes to each intersection over the analysis period (refer Section

4.1), it was not possible to verify that the values of every variable measured

remained unchanged. This is for reasons of lack of documentation and practical

considerations.

It is possible that in some circumstances, particular variables will have changed.

Table 6.2 lists such possible changes and methods used during data collection to help

identify such changes. Where such changes to variables were identified, the start and

end dates of the analysis period were changed so that the change to the variable did

not occur during the analysis period.

Site inspections were undertaken at each of the selected intersections. Some of the

variables required (eg sight distance) could only be measured on-site.

6.3 Speed Prediction Model

To estimate speeds on horizontal curves and straights, the speed prediction model

developed in Arndt (1998) has been used. This model was based on the speed

environment model in Chapter 2 of Austroads (1989) which was originally

developed by McLean (1978) from data measurements on rural roads.

92

Table 6.2 - Possible Changes to Variables and Methods Used to Help Identify Such Changes

Variable Method

Speed limit District personnel were contacted to verify whether the current speed limit existed over the analysis period for other than the following cases: 1. 60km/h in an established urban environment 2. 100km/h in a rural environment If district personnel could not verify this from records, other methods of verification were used. This included door knocks of residents around the intersection that had been in the area long enough to verify the duration of the speed limit from memory.

Location of holding line

None. The location of the holding line may have changed with remarking and/or overlays but this is difficult to determine.

Shoulder widths at Type LSR intersections

None. Small amounts of additional seal material may have been added to the shoulder as part of maintenance schemes during the analysis period. The degree to which this occurred would probably not be documented.

Level of Control If the method of control was different to that shown on the plans or aerial photographs, district personnel were contacted to verify whether the current level of control existed over the analysis period.

Lighting If light poles at the intersection looked relatively new, district personnel were contacted to verify whether the current level of lighting existed over the analysis period.

Other variables If any other variable not discussed above was different to that shown on the plans or aerial photographs, district personnel were contacted to verify whether the variable had changed over the analysis period. An example of this was the addition of pavement arrows and the modification of line marking.

Arndt (1998) modified the original work by McLean (1978) for the following

reasons:

• By definition of speed environment concepts, it is believed that each desired

driver speed curve should reach an 85th percentile speed equal to the speed

environment at large values of horizontal curve radii.

• The curves shown on McLean’s graph do not predict speeds for very small radii

or speed environments less than 60 km/h (the curves were not intended to do so).

93

Some of the roundabouts comprised very small curve radii so prediction of speeds

on these elements was required.

To achieve the first requirement above, the original desired driver speed equations

were modified so that each desired speed curve would reach an 85th percentile speed

equal to the speed environment at large values of horizontal curve radii. The form of

the original desired driver speed equations were changed and were placed through

the centre of each set of data and through a point equal to the speed environment at

zero curvature.

To achieve the second requirement above, an equation was developed to predict 85th

percentile speeds in the range of the lower curve radii. This equation was set at a co-

efficient of side friction of 0.5, which appeared as a general maximum recorded by

McLean. This equation therefore limited the coefficient of side friction to 0.5 in the

range of the lower horizontal curve radii. The speed prediction models developed

were applied to roundabouts by assuming that there was no acceleration between

curves. The resultant graph of the developed desired speed curves is shown in Figure

6.1.

Speed Environment (km/h)(Desired Driver Speed)

Horizontal Curve Radius (m)

85th

Per

cent

ile C

ar S

peed

(km

/h)

130120110

100

90

80

70

60

50

40

100090080070060050040030020010000

20

40

60

80

100

120

Figure 6.1 - 85th Percentile Car Speed versus Horizontal Curve Radius

94

Arndt (1998) considered that the speeds predicted by this method would not

necessarily be same as the actual 85th percentile speeds at roundabouts. However,

on-site inspections at roundabouts revealed that there was potential for drivers to

travel at these predicted speeds. The statistical significance of the developed accident

equations in the roundabout study showed that there was a strong correlation

between accident rates and these predicted speeds. It is possible that the speed of

drivers involved in accidents at roundabouts were closer to the 85th percentile speed

predicted by this method than the actual 85th percentile speeds.

Adopting the speed prediction model from Arndt (1998) for the unsignalised

intersection study is expected to yield the following results:

• The predicted 85th percentile speeds on the major roads are expected to be

reasonably accurate because the presence of the intersections is considered to

have little effect on these speeds.

• The predicted 85th percentile speeds on the minor roads away from the

intersections are also expected to give good results for the reason given above.

• The predicted 85th percentile speeds approaching the intersection from the minor

road (eg around horizontal curves immediately before the intersection) may be

somewhat different to the actual speeds due to braking at the intersection.

Speed Parameters Selected for Analysis

Speed parameters on both the major and minor road include:

• Speed limit prior to intersection.

• Speed limit reduction at the intersection (if applicable).

• School/bus zone speed limits (if applicable).

• Speed environment prior to the intersection.

• 85th percentile approach speed.

Early regression analysis results have shown that it is not practical to include all the

parameters above in the final equations for reasons of practicality, high correlation

levels, and the presentation of a logical result. Section 16.2 discusses this issue in

regard to the high levels of correlation between parameters. For this reason, it was

decided to exclude the following speed parameters:

95

• Speed limit prior to the intersection - this parameter was removed because it

was considered a less accurate measure of the typical speeds approaching and

through the intersection because it does not take into account parameters such as:

Horizontal curvature prior to the intersection that can significantly decrease

approach speeds.

Short length roads where actual speeds may be significantly below the speed

limit.

Roadways for which no speed limit signs were provided.

Roadways of high geometric standard where actual speeds may be 10 - 20

km/h above the speed limit.

• School and bus zone speed limits - Calculation of the percentage of vehicles per

year affected by school zones were undertaken using the data collected in this

study. These calculations showed that generally between 11 and 14 percent of the

total number of vehicles per year travelling through school and bus zones travel

during the reduced speed limit. As this percentage is relatively small and because

there is uncertainty about the proportion of vehicles that actually slow down and

to what extent, it is considered that this parameter may only have a small total

effect on overall speeds. For this reason, it has been excluded from the regression

analysis.

6.4 Vehicle Path Model

Vehicle path models were required in order to determine the following parameters:

• Curve radii for determination of 85th percentile speeds.

• Angles between vehicle paths at each conflict point.

On-site inspections undertaken in Arndt (1998) revealed that drivers tend to

transition their path to obtain the largest possible radii. This was most noticeable on

small radius, small length geometric elements. On-site inspections at unsignalised

intersections revealed a similar result.

Assumptions for Vehicle Path Construction

Actual vehicle paths comprise a series of straights, circular curves and spirals.

Spirals occur because drivers cannot instantaneously turn the steering wheel from

one position to another. To model vehicle paths using spirals is far too complex for

96

the scope of this study. If spirals were used, it is not expected that the results

obtained from this study would be significantly better. For these reasons, only

straights and circular curves were modelled in this study.

Arndt (1998) modelled the behaviour of drivers through roundabouts based on on-

site inspections of travelled paths. Arndt (1998) found that drivers would typically

travel at a location to keep the following distances from the edge of their vehicles to

the particular geometric features:

• 0.5m from a road centreline

• 0.5m from concrete kerbing

• 0m from a painted edge line or chevron

Assuming an average vehicle 2m wide, the distance from the centre of the vehicle to

the geometric factors above became:

• 1.5m from a road centreline

• 1.5m from concrete kerbing

• 1m from a painted edge line or chevron

On-site inspections at unsignalised intersections revealed that adopting the above

distances would give indicative vehicle paths at unsignalised intersections. These

inspections also indicated that most drivers stay within their own lane and do not cut

across adjacent lanes. Therefore, the vehicle path models developed for this study

assume drivers remain in their correct lane.

The vehicle path model developed for this study is detailed in Appendix B - Vehicle

Path Model. The details of the vehicle path model have not been included in this

section due to the large space requirement.

6.5 Geometric Data Coding and Overview

Each of the variables was input into spreadsheets under the various accident

categories. The software program Microsoft Excel was used for this purpose.

Table 6.3 shows the number of lanes on the major road versus the number of

intersection sites. Approximately 70 percent of the intersection sites were on two-

lane roadways and 26 percent were on four-lane roadways.

97

Table 6.3 - Number of Major Road Lanes Number of Lanes on

the Major Road Number of

Intersections 2 144 3 5 4 54 6 3

Total 206

Figure 6.2 shows the type and number of minor road approach lanes. Forty-two of

the minor road legs comprised a free left-turn lane in addition to the number of

approach lanes listed in this table. Most minor road legs comprised only one marked

approach lane, although a significant portion of the one lane approaches were wide

enough to be marked as two lane. Observations of driver behaviour revealed that the

wide single lane approaches can be used as two lanes because drivers pulled up

alongside each other behind the give way line.

Table 6.4 shows the type of control used versus the number of minor legs.

Approximately 62 percent of the minor legs comprised give way control, 34 percent

comprised stop sign control whilst nine T-intersections comprised no control. These

nine intersections were included because they contained values of particular

geometric or other features desirable to increase the total value range of these

features (refer Section 4.1).

Figure 6.3 shows the speed limit and speed environment on the minor legs (prior to

the intersection) versus the number of minor legs. The speed limit was taken as the

posted speed of the roadway. Further information on this parameter is given in Table

C4 of Appendix C – Geometric Variables. The speed environment was the estimated

85th percentile speed of free passenger cars on the longer sections of roadway before

the intersection that comprised horizontal straights or large radius horizontal curves.

Further information on this parameter is given in Tables C5 and C6 of Appendix C –

Geometric Variables.

Few minor legs had speed limits other than 60 and 100km/h. The speed environment

on the minor legs, however, was much more distributed over the 60 - 100km/h range

than the speed limits. Eleven out of the 269 minor legs were in school zones.

Twenty-four minor legs had a reduced regulatory speed sign immediately prior to the

intersection whilst four legs had an increased speed regulatory sign.

98

Figure 6.2 - Type and Number of Minor Road Approach Lanes

Note: Number of sites with the particular approach treatment is shown in brackets.

Table 6.4 - Control Type versus Number of Minor Legs Control Type Number of Minor legs

Stop 93 Give way 160 Give way (includes an additional give way sign in median)

7

None (minor leg of T-intersection where the T-intersections rule applies)

9

Total 269

99

0

20

40

60

80

100

120

140

160

180

Num

ber o

f Min

or L

egs

40 50 60 70 80 90 100 110Speed (km/h)

Speed Limit Prior toIntersectionSpeed EnvironmentPrior to Intersection

Figure 6.3 - Speed Limit and Speed Environment Prior to Intersection

on the Minor Legs versus Number of Minor Legs

Figure 6.4 shows the speed limit and speed environment on the major legs (prior to

the intersection) versus the number of major legs. There is a reasonable distribution

of speed limits and speed environments across the 60 - 100km/h range. Fourteen of

the 412 major legs were in school zones. Thirty-four of the major legs had a reduced

regulatory speed sign immediately prior to the intersection whilst three legs had an

increased speed regulatory sign.

0

20

40

60

80

100

120

140

160

Num

ber o

f Maj

or L

egs

40 50 60 70 80 90 100 110Speed (km/h)

Speed Limit Prior toIntersectionSpeed EnvironmentPrior to Intersection

Figure 6.4 - Speed Limit and Speed Environment Prior to Intersection

on the Major Legs versus Number of Major Legs

100

Table 6.5 shows the median width on the major road versus the number of

intersection sites. Approximately half of the sites comprised no median on the major

road. Approximately 23 percent comprised a median width greater than 4m up to and

including 6m. Seventeen sites comprised a wide median (greater than 8m).

Table 6.5 - Median Width on Major Road versus Number of Intersection Sites Median Width on Major Road (m)

Number of Intersection Sites

0 (No median) 106 0.01 - 2 10 2.01 - 4 21 4.01 - 6 47 6.01 - 8 5

> 8 17 Total 206

101

7 TRAFFIC FLOW DATA

This chapter describes the method of collecting the traffic volume data for each

intersection site and the method of converting the traffic volumes to the same time

period. An overview of the recorded traffic volume data is then given.

7.1 Selection of Traffic Volume Variables and Collection of Data

The use of Annual Average Daily Traffic (AADT) volumes were expected to best

represent the average traffic volume over the length of the analysis period and were

selected for this purpose. Intersections with proportionally high peak hour volumes

(relative to the rest of the day) may record somewhat different accident rates to those

with lower peak hour volumes but this is difficult to determine.

Traffic data showing volumes for each movement through the intersection were

collected from each of the relevant Main Roads districts. If particular intersections

had no traffic data available, separate one to three hour counts were undertaken on-

site.

7.2 Conversion of Traffic Volume Data to the Same Time Period

The traffic volume data obtained were for various time periods are given below:

• Average annual daily traffic (AADT) volumes

• 12 hour traffic counts

• One to three hour traffic counts

To analyse the traffic flow data, all traffic volume data was required to be of the

same time period. Conversion of the traffic counts of other time periods to AADT

values was therefore required. Traffic data from the closest permanent counting

station on the same road type was used for this purpose. This data enabled

conversion factors to be calculated for each of the non-AADT counts.

7.3 Conversion of Calculated AADT Values to Average AADT Values

The supplied or calculated AADT values were volumes at the date of the traffic

count. The AADT volumes required for analysis needed to be the average volumes

over the analysis period. Once the average AADT values were known, multiplication

102

by the analysis period would estimate the total number of vehicles that had

negotiated the intersection during the analysis period. This value was necessary to

compare the number of accidents obtained in the analysis period to the total number

of vehicles that negotiated the intersection ie it gives the accident rate (number of

accidents/number of vehicles).

Growth rates (increase in traffic volumes over time) for all intersections were

obtained from each district. These values were used in the compounding growth

formula to find the average AADT from the calculated AADT.

7.4 Overview of Traffic Volume Data

Table 7.1 shows the range of traffic volumes recorded on the minor legs approaching

the intersections. These were generally less than 2000 vehicles per day. Whilst a

greater range of volumes would have been preferable, unsignalised intersections with

high minor road volumes are relatively few in number and are usually converted to

signalised intersections or roundabouts.

Table 7.1 - Range of Traffic Volumes Recorded on the Minor Legs Traffic Volume on the Minor Leg

Approaching Intersection (One way traffic volume - vehicles/day)

Number of Minor Legs

0 - 999 197 1000 - 1999 67 2000 - 2999 12 3000 - 3999 8 4000 - 4999 2

≥5000 1 Total 269

At least eight out of the twenty-three intersections in the study with minor road

volumes over 2000 vehicles per day were changed, or were about to be changed,

within one year of data collection. These changes included the addition of traffic

signals, the replacement by a roundabout, the replacement by an interchange or the

addition of right-turn bans. The minor road traffic flow for an additional five of the

twenty-three intersections consisted of a high volume left-turn.

Table 7.2 shows the range of traffic volumes recorded on the major legs approaching

the intersections. Most major leg volumes were less than 10000 vehicles per day.

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Table 7.2 - Range of Traffic Volumes Recorded on the Major Legs Traffic Volume on Major Leg

Approaching Intersection (One way traffic volume - vehicles/day)

Number of Major Legs

0 - 4999 243 5000 - 9999 102

10000 - 14999 37 15000 - 19999 23 20000 - 24999 4

≥25000 3 Total 412

Part C

105

8 DATA COLLECTION SUMMARY AND PRELIMINARY ANALYSIS PROCEDURE

This chapter briefly summarises the data collected and describes the process used in

the preliminary analysis.

8.1 Data Collection Summary

A brief summary of the data collected is as follows:

• 206 unsignalised intersections through Queensland comprising 143 T-

intersections and 63 four-leg intersections

• Total number of minor legs is 269 and the total number of major legs is 412

• 93 minor legs contained stop signs, 167 contained give way signs and 9 contained

no priority signage (minor legs of T-intersections where the T-intersection rule

applies)

• 1091 accidents from Road Crash 2 over an analysis period that varies between 5

and 10 years

8.2 Preliminary Analysis Procedure

The purpose of the preliminary analysis was to review the accident data for any

common factors that applied within each of the accident types by using simple

tabular and graphical techniques. This was performed to obtain a "feel" for the data

thereby helping to identify appropriate techniques for analysing the data in the

regression analysis.

This was undertaken by determining if any factors listed below were common

between a majority of the accidents that occurred within each accident type.

• Driver Error - any particular mistake that a driver made to cause the accident as

per the listed contributing circumstances

• Traffic Conditions – eg traffic movements and conflicts, types of vehicles

involved

• Environmental Conditions – eg weather and light conditions

• Road Geometry - any geometric parameters of the intersection or roadways

The following six chapters discuss the results of applying the preliminary analysis

106

process described above to the accident classifications developed in Section 5.3. The

preliminary analysis is summarised in Chapter 15.

107

9 ANGLE-MINOR VEHICLE ACCIDENTS

This chapter presents the results of undertaking the preliminary analysis process

described in Chapter 8 to the Angle-Minor vehicle accident category. The number of

Angle-Minor vehicle accidents as compared to the total number of accidents is

shown in Figure 9.1.

Total Accidents 1091 acc.

100%

High Frequency

Intersection Accidents 694 acc.

64%

Angle-Minor 466 acc.

Low Frequency Intersection Accidents 109 acc.

10%

High Frequency Through

Accidents 167 acc.

15%

Low Frequency Through

Accidents 121 acc.

11%

Rear-End-Major 121 acc.

Angle-Major 107 acc.

Figure 9.1 - Number of Angle-Minor Vehicle Accidents Compared to the Total Number of Accidents

A total of 466 accidents were recorded, making this the largest accident category.

These accidents are primarily the result of a minor road vehicle failing to give way.

As identified in the literature review and by the contributing factors listed in the

Crash Incident Reports, these accidents are commonly the result of drivers not seeing

the other vehicle or misjudging the speed and position of the other vehicle. These

accidents, however, sometimes result from a minor road driver not adequately

perceiving the intersection, followed by not stopping or slowing in time to avoid an

accident.

Five of these accidents were the result of a major road vehicle losing control or being

run into after avoiding a minor road vehicle that failed to give way. Six of these

108

accidents resulted from a minor road vehicle failing to give way and colliding with a

minor road vehicle on the opposite approach. Except for another seven accidents

with unknown movements, all other accidents were the result of a minor road vehicle

failing to give way and colliding with a major road vehicle.

Table 9.1 shows the types of conflicts recorded within this category.

Table 9.1 - Types of Conflicts Recorded in the Angle-Minor Vehicle Accident Category

Location and Movement of Vehicle Not at Fault Major leg on left

of minor road Minor road opposite (g)

Major leg on right of minor

road

Movement of Minor

Road Vehicle

(a) L T R L T R L T R

Other

Total

L - - - - - 0(b) - 13 - 0 13 T 0(c) 121 0 - - (d) - 83 0 2 206 R - 35 3 0(e) 5 1(-) - 189 1 2(f) 236

Other 0 2 0 0 0 0 0 6(f) 0 3 11 Total 0 158 3 0 5 1 0 291 1 7 466

Notes: L = left-turn movement T = through movement R = right-turn movement Other = unknown movement or overtaking movement - = not a crossing path (under normal conditions) (a) This represents the minor road vehicle at fault (that has failed to give way) (b) The minor road vehicle (the vehicle normally at fault as listed in column 1) is at fault only if a

splitter island exists for the left-turn from the minor road (c) The minor road vehicle is at fault only if a splitter island does not exist for the left-turn from the

major road (d) The minor road vehicle is not at fault in this case (e) The minor road vehicle is at fault only if a splitter island does not exist for the left-turn on the

opposite minor leg (f) One of these accidents involved a U-turning vehicle (g) An opposite minor road exists only at four-leg intersections

9.1 Vehicle Types

Figure 9.2 shows a graph of the types of vehicles involved in the Angle-Minor

vehicle accidents. For any particular vehicle type, a vehicle is just as likely to be

located as a minor road vehicle as a major road vehicle. Therefore if there is a

considerable difference between the number of minor road vehicles to the number of

major road vehicles for any particular vehicle type, then there is likely be an over or

under representation as a minor road or major road vehicle. From Figure 9.2, it

would appear that the car/station wagon category might be a little over represented as

minor road vehicles whilst the remaining vehicle categories may be over represented

as major road vehicles.

109

9

22

322

78

8

8

17

2

2

3

375

67

3

9

0

7

0 100 200 300 400

Bicycle

Motor Cycle

Car, Station Wagon

Utility, Panel Van

Omnibus

Truck

Articulated Vehicle

Other or Unknown

Vehi

cle

Type

Number of Accidents

Minor Road VehicleMajor Road Vehicle

Figure 9.2 - Type of Vehicles versus Number of Angle-Minor Vehicle Accidents

Note: The major road vehicle category in this figure includes six accidents occurring to vehicles on the opposite minor leg

Tables 9.2 and 9.3 show the vehicle involvement rates versus type of vehicle for the

minor and major road vehicles respectively. No particular vehicle type is well over

represented as a minor road vehicle in Table 9.2.

Table 9.3 shows that motorcyclists are well over represented as major road vehicles.

A similar conclusion was found for motorcyclists as circulating vehicles at

roundabouts in Arndt (1998), in the entering/circulating vehicle accident type. These

statistics show that motorcycles, which are relatively small vehicles, are hit much

more regularly. This would appear logical when considering that a common reason

used by drivers of minor road vehicles that fail to give way is that they did not see

the other vehicle. As vehicle size decreases, the probability of it being seen is

decreased and the therefore the chance of it being hit is increased.

110

Table 9.2 - Minor Road Vehicle Involvement Rate versus Vehicle Types Number of Percentage Relative Standardised

Vehicle Type Accidents of km Accident Accident RateRecorded Travelled Rate Passenger

(A) per Vehicle (A/B) Car = 1.0Type (B) (1) (A/B/4.8)

Motor Cycle 3 0.6 5.0 1.0Car, Station Wagon 375 77.6 4.8 1.0Utility, Panel Van 67 14.1 4.8 1.0Omnibus 3 1.0 3.0 0.6Truck 9 3.7 2.4 0.5Articulated Vehicle 0 3.0 0.0 0.0

Table 9.3 - Major Road Vehicle Involvement Rate versus Vehicle Types

Number of Percentage Relative StandardisedVehicle Type Accidents of km Accident Accident Rate

Recorded Travelled Rate Passenger(A) per Vehicle (A/B) Car = 1.0

Type (B) (1) (A/B/4.1)Motor Cycle 22 0.6 36.7 8.8Car, Station Wagon 322 77.6 4.1 1.0Utility, Panel Van 78 14.1 5.5 1.3Omnibus 8 1.0 8.0 1.9Truck 8 3.7 2.2 0.5Articulated Vehicle 17 3.0 5.7 1.4

Note: (1) The values in the third column of these tables are the estimated percentage of kilometres

travelled per vehicle type as calculated in Arndt (1998).

9.2 Accident Severity

The severity versus the number of Angle-Minor vehicle accidents is shown in Figure

9.3. This figure illustrates that approximately half of the Angle-Minor vehicle

accidents are property damage, whilst the remainder are mostly treated and

hospitalised. As expected, these accidents were generally more severe than

entering/circulating accidents at roundabouts (failure to give way) as identified in

Arndt (1998).

111

199

56

124

77

10

0 50 100 150 200 250

Property Damage

Minor

Treated

Hospitalised

Fatal

Seve

rity

Number of Accidents

Figure 9.3 - Severity of Angle-Minor Vehicle Accidents versus Number of Accidents

9.3 Effect of Weather and Light Conditions

Figure 9.4 is a bar chart of the type of weather versus the number of Angle-Minor

vehicle accidents for the various light conditions.

0

50

100

150

200

250

Num

ber o

f Acc

iden

ts

Clear RainingWeather Conditions

DarknessDawn/DuskDaylight

Figure 9.4 - Effect of Weather and Light Conditions on Number of

Angle - Minor Vehicle Accidents (Out of the 466 Angle-Minor accidents, 205 were listed as unknown weather and light conditions)

Figure 9.4 shows that the majority of Angle-Minor vehicle accidents occurred in

clear weather. In order to determine whether any particular weather condition is over

represented, the average hours of wet weather per year for the various intersection

locations are required. The Bureau of Meteorology has advised that considerable

112

time and finance is required to determine this information, making it outside the

scope of this study.

As the ratio of total hours of wet weather to total hours of dry weather for any year

would be quite low, it is suggested that wet weather may be a little over represented

for this accident type.

Accident rates during the different light conditions are shown in Table 9.4. These

values were based on data obtained from the Lands Department together with data

from the Queensland Department of Main Roads permanent traffic counting stations,

as used in Arndt (1998). For the purposes of these calculations, the following

assumptions were made:

• Dawn - period between nautical twilight (morning) and sunrise.

• Day - period between sunrise and sunset.

• Dusk - period between sunset and nautical twilight (evening).

• Dark - period between nautical twilight (evening) and nautical twilight

(morning).

Table 9.4 - Angle-Minor Vehicle Accident Rates versus Light Conditions Number of Percentage Relative Standardised

Light Conditions Accidents of Vehicles Accident Accident RateRecorded Using Rate Daylight = 1.0

(A) Roadway (A/B) (A/B/2.9)(B) (1)

Daylight 222 77 2.9 1.00Dawn/Dusk 13 7 1.9 0.64Darkness 26 16 1.6 0.56

Note: (1) The values in the third column are the estimated percentage of vehicles that use the roadway

during the given light condition as calculated in Arndt (1998). The accident rate during the hours of darkness is approximately half that during the

daylight hours. No firm conclusions can be drawn from this. Possibly, vehicles with

lights operating are easier to perceive at night than vehicles without lights operating

during the day. However, it is also possible that because traffic volumes and delays

are greater in the hours of daylight, drivers accept smaller gaps in the traffic stream

in daylight hours thereby taking greater risks and increasing their likelihood of being

involved in an accident.

113

9.4 Time of Day

Figure 9.5 shows the time of day during which the Angle-Minor vehicle accidents

occurred versus the number of accidents.

The general shape of the chart in Figure 9.5 approximately follows the pattern of

traffic volumes during a day. This suggests that these accidents will be significantly

related to traffic volumes, which was one of the few agreements between studies

identified in the literature review.

The morning peak appears a little lower than that expected, whilst the values around

midday may be higher than that expected.

2 1 0 0 02

20

14

40

2932

47

39

3027

39 39 40

32

1113

4 41

05

101520253035404550

12:0

0AM

2:00

AM

4:00

AM

6:00

AM

8:00

AM

10:0

0AM

12:0

0PM

2:00

PM

4:00

PM

6:00

PM

8:00

PM

10:0

0PM

Time of Day

Num

ber o

f Acc

iden

ts

Figure 9.5 - Time of Day versus Number of Angle-Minor Vehicle Accidents

9.5 Day of Week

Table 9.5 lists the accident rates for the various days of the week. This table shows

that the Angle-Minor vehicle accident rate (number of accidents/number of vehicles)

is somewhat similar for all days of the week.

114

Table 9.5 - Angle-Minor Vehicle Accident Rate versus Day of Week Number of Percentage Relative Standardised

Day of Week Accidents of Vehicles Accident Accident RateRecorded Using Rate Monday = 1.0

(A) Roadway (A/B) (A/B/4.4)(B) (1)

Sunday 59 13.2 4.5 1.02Monday 62 14.2 4.4 1.00Tuesday 55 14.1 3.9 0.89Wednesday 74 14.2 5.2 1.19Thursday 66 14.7 4.5 1.03Friday 89 15.5 5.7 1.32Saturday 61 14.1 4.3 0.99

Note: (1) The values in the third column are the percentage of vehicles that use the roadway during the

particular day of the week as calculated in Arndt (1998).

9.6 Month of Year

Month of the year versus the number of Angle-Minor vehicle accidents is shown in

Figure 9.6. The number of accidents for each month is relatively constant except for

a slight peak in July, August and November. For roundabouts, Arndt (1998) found a

large peak for July.

3532

4037

41

30

4946

3338

4540

0

10

20

30

40

50

60

Janu

ary

Febr

uary

Mar

ch

Apr

il

May

June July

Aug

ust

Sep

tem

ber

Oct

ober

Nov

embe

r

Dec

embe

r

Month

Num

ber o

f Acc

iden

ts

Figure 9.6 - Month of Year versus Number of Angle-Minor Vehicle Accidents

115

9.7 Contributing Circumstance

The most common contributing circumstances given in the Crash Incident Reports

are given in Table 9.6. These were listed for the unit on the minor road that failed to

give way. Some crashes recorded more than one contributing circumstance.

Table 9.6 - Contributing Circumstances for Angle-Minor Vehicle Accidents Contributing Circumstance Percent of Total

Violation - disobey stop sign 29Violation - disobey giveway sign 23Violation - undue care and attention 10Driver - inexperience/lack of expertise 10Driver - age (lack of perception, power or concentration) 8Violation - fail to give way 3Road - wet/slippery 2Other 15

Other contributing factors to each Angle-Minor vehicle accident can be found in the

accident descriptions in the crash incident reports. Some of these factors are listed in

Table 9.7. These factors have been classified according to whether or not the minor

road driver has perceived the intersection in time to stop safely.

Table 9.7 shows that it was not possible to classify a majority of the contributing

factors according to whether or not the minor road driver perceived the intersection

in time to stop safely (291 cases). Of those accidents that were classified with a

reasonable degree of confidence, most were the result of a driver perceiving the

intersection followed by not seeing or misjudging a major road vehicle (160 cases).

Only 15 cases were the result of a minor road driver not perceiving the intersection in

time to stop safely. This is quite a different result than that obtained in the Japanese

study Kanda and Ishida (2000).

Taking the results from the first two rows of Table 9.7 in isolation would indicate

that most accidents involving drivers failing to give way on the minor road result

from not seeing or misjudging a major road vehicle in lieu of not perceiving the

intersection in time to stop safely. However, because of the high number of accidents

that were unable to be classified (a reasonable portion that may well have been the

result of not perceiving the intersection in time to stop safely), it is considered that

little confidence can be placed in such a result.

116

Table 9.7 - Other Contributing Factors to Angle-Minor Vehicle Accidents Accident Number of Total

Classification Accidents No. ofAccidents

Not perceive Did not see stop or give way sign 9intersection Out of control through intersection 1 15until too late Though intersection at speed 5

Stopped at stop or give way sign 134Moved slowly through stop or give way sign 8Major road vehicle on right had left indicator on 2View obscured due to adjacent minor road vehicle 2View obscured by left turning major vehicle on the right 7 160View obscured by parked major vehicle on the right 1View obscured by traffic queue on major road 2Followed front vehicle without looking 2Became impatent because of a long wait 1Confusion with minor road vehicle on opposite leg 1Did not stop at stop sign 52Drove into path of major road vehicle refer (1)

Unable toFailed to give way and collided with major road vehicle refer (1)

classify Failed to obey a stop or give way sign refer (1)

(TypicalDriven straight through the give way signs refer (1) 291

descriptions Disobeyed give way sign refer (1)shown) Has gone through the give way sign refer (1)

Proceeded straight through give way sign refer (1)Failed to give way at the intersection refer (1)Travelled past a give way sign refer (1)

Not see or misjudge a major road

vehicle

Contributing Factors Taken from the Accident Descriptions within the

Crash Incident Reports

Note: (1) Counts were not made of the number of times that each of these contributing factors were listed. Out of the 15 accidents where minor road drivers failed to perceive the intersection,

11 occurred at crossroads and four occurred at T-intersections.

117

9.8 Distribution of Data

Table 9.8 compares the recorded Angle-Minor vehicle accident data with the

expected results if the accidents were randomly distributed (using a Poisson

distribution as shown in Equation 9.1 with λ = 466 accidents / 269 minor legs =

1.73).

P(x) = e(-λ t) x (λ t)x / x! Equation 9.1 where P(x) = probability of x accidents per minor road approach λ = average number of accidents per minor leg per unit time t = time interval (all time intervals were made equal to one) x = number of accidents

Table 9.8 - Comparison of Recorded Angle-Minor Vehicle Accidents with a Random Distribution of these Accidents

0-1 2-3 4-5 >5Number of Legs (A1) 172 61 16 20Percentage of Legs (A1 / 269) x 100 63.9 22.7 5.9 7.4Number of Accidents (B1) 64 148 70 184Percentage of Accidents (B1 / 466) x 100 13.7 31.8 15.0 39.5Number of Legs (A2)ΣP(x) x 269 130 113 24 2Percentage of Legs (A2 / 269) x 100 48.3 41.9 8.9 0.9Number of Accidents (B2)Σ(P(x) x x) x 269 82 266 102 15Percentage of Accidents(B2 / 466) x 100 17.7 57.2 22.0 3.2

Category Parameter No. of Accidents Per Minor Leg (x)

Recorded Data

Predicted Data (Poisson

Distribution)

Table 9.8 shows that 63.9% of the minor legs recorded less than two Angle-Minor

vehicle accidents. This table also shows that if randomly distributed, 48.3% of the

minor legs could have expected to record less than two Angle-Minor vehicle

accidents. Table 9.8 also shows that 7.4% of the minor legs recorded greater than

five accidents and that the number of accidents in this category is 39.5% of the total

number of accidents. By random distribution, it is predicted that the number of legs

in this category would be 0.9% and that the number of accidents in this category

would be 3.2% of the total number of accidents.

The above figures show that the accidents are not randomly distributed. A majority

118

of the legs record fewer accidents than could be expected, whilst others legs record a

greater accident rate than would be expected if randomly distributed. Therefore, there

must be particular variables that have a significant impact on these accidents. This

verifies the need for a more in-depth study to determine what these variables are, and

their relationship to these accidents.

9.9 Geometric and Other Effects

Figure 9.7 shows the various conflicts possible within the Angle-Minor vehicle

accident category. Table 9.9 lists the accident rate (accidents divided by the square of

vehicle volume) for the various conflicts shown in Figure 9.7.

The following conclusions have been drawn from Table 9.9:

• Conflicts Involving a Left-Turn from the Minor Road (LRT): Minor road

drivers failing to give way when turning left record low accident rates (accidents

per traffic volume product), in comparison with many of the other Angle-Minor

vehicle accident conflicts.

• Conflicts Involving a Through Movement from the Minor Road (TRT, TLR,

TLT, TLL, TRR): All minor road drivers failing to give way when travelling

through were hit by a major road vehicle also travelling through. No turning major

road vehicles were hit. A greater number of minor road vehicles travelling

through the intersection (ie at four-leg intersections only) that are involved in

Angle-Minor vehicle accidents collide with a major road vehicle from the left

(TLT conflict). Minor road vehicles failing to give way when travelling through

the intersection record the highest accident rates (accidents per traffic volume

product) in comparison to all other Angle-Minor vehicle accident conflicts.

• Conflicts Involving a Right-turn from the Minor Road (RRT, RLR, ROR,

RRR, ROT, RLT, ROL): Most minor road drivers failing to give way when

turning right were hit by a major road vehicle travelling through from the right

(RRT conflicts). This conflict type records a relatively high accident rate

(accidents per traffic volume product) in comparison to all other Angle-Minor

vehicle accident conflicts. Substantially fewer minor road drivers are hit by major

road drivers travelling through from the left (RLT conflicts). This conflict type

records a relatively low accident rate (accidents per traffic volume product) in

comparison to other Angle-Minor vehicle accident conflicts. Ten accidents

119

involved turning major road vehicles. Accident rates (accidents per traffic volume

product) for turning major road vehicle conflicts are comparatively low. Accident

rates (accidents per traffic volume product) for conflicts involving vehicles

travelling through from the opposite minor road approach (ROT conflicts) are

comparatively moderate to high.

Figure 9.7 - Types of Conflicts Recorded in the Angle-Minor Vehicle Accident Category

Notes: (1) Vehicle paths shown as full lines are the paths of vehicles at fault. (2) For TLL conflicts, the through vehicle from the minor road is not at fault in this circumstance if

a splitter island exists for the left-turn from the major road. (3) For ROL conflicts, the right-turn vehicle from the minor road is not at fault in this circumstance

if a splitter island exists for the left-turn from the minor road. (4) For LOR conflicts, the left-turn vehicle from the minor road is only at fault in this circumstance

if a splitter island exists for the left-turn from the minor road. (5) U-turn movements are not shown in this diagram.

120

Table 9.9 - Angle-Minor Vehicle Accident Rates for the Various Conflicts No. of Traffic Accidents Standarised

Conflict Accidents Volume /Volume RateType (A) Product (A/B) LRT = 1.0

(B) (1) (A/B/5.73E-15)LRT 13 2.27E+15 5.73E-15 1.0TRT 83 3.55E+14 2.34E-13 40.8TLR 0 3.50E+13 0 0.0TLT 121 3.55E+14 3.41E-13 59.5TLL 0 3.94E+13 0 0.0TRR 0 3.47E+13 0 0.0RRT 189 1.64E+15 1.15E-13 20.1RLR 3 1.62E+14 1.85E-14 3.2ROR 1 1.43E+13 6.99E-14 12.2RRR 1 3.42E+13 2.92E-14 5.1ROT 5 3.37E+13 1.48E-13 25.9RLT 35 1.62E+15 2.16E-14 3.8

ROL/LOR 0 3.40E+13 0 0.0Total 451 6.63E+15 - -

Notes: (1) The values in the third column equal the sum of the number of vehicles undertaking the

particular movement from the minor road multiplied by the total number of vehicles undertaking the particular movement from the major road during the analysis period.

(2) Unknown movements and U-turn movements are not shown in this table.

These results are consistent with the general findings of the literature review and

with the reported accident statistics for unsignalised intersections in QDMR (2000)

and Austroads (2003).

The two conflicts recording the highest accident rates in Table 9.9 involve through

movements from the minor road. This shows that four-leg intersections are likely to

have greater accident rates than T-intersections. This result is also consistent with the

findings from the literature review.

Angle-Minor vehicle accident rates for the various minor road approach speeds are

shown in Table 9.10. Higher minor road approach speeds appear to result in a higher

Angle-Minor vehicle accident rates. Several of the intersections in the analysis

comprised horizontal curvature on the minor legs that reduced vehicle approach

speed. Judging by the results in this table, this treatment may be worthwhile in

minimising Angle-Minor vehicle accident rates.

121

Table 9.10 - Angle-Minor Vehicle Accident Rates for the Various Minor Leg Approach Speeds

Minor Number of Traffic Accident StandardisedRoad No. of Accidents Volume Rate Accident

Approach Sites Recorded Product (acc/veh) RateSpeed (A) (B) (1) (A/B) Sp 0 - 40 =1.0(km/h) (A/B/3.31E-14)0 - 40 37 29 8.76E+14 3.31E-14 1.0

40 - 60 125 247 6.08E+15 4.06E-14 1.260 - 80 54 93 2.36E+15 3.93E-14 1.2

80 - 100 37 70 6.73E+14 1.04E-13 3.1100 - 120 16 26 2.00E+14 1.3E-13 3.9

Note: (1) The values in the fourth column equal the sum of the number of vehicles approaching on the

minor road multiplied by the total number of vehicles on the major road during the analysis period.

122

10 ANGLE-MAJOR VEHICLE ACCIDENTS


described in Chapter 8 to the Angle-Major vehicle accident category. The number of

Angle-Major vehicle accidents as compared to the total number of accidents is



100%

High Frequency


64%



10%


Accidents 167 acc.

15%


Accidents 121 acc.

11%



Figure 10.1 - Number of Angle-Major Vehicle Accidents Compared to the Total Number of Accidents

A total of 107 accidents were recorded in this category. These accidents are primarily

the result of a major road vehicle failing to give way when turning right (or

undertaking a U-turn) and colliding with an oncoming major road vehicle. It is

expected that similar driver behaviour factors apply in these accidents as to the

Angle-Minor vehicle accidents ie that they are commonly caused by drivers not

seeing the other vehicle and misjudging the speed and position of the other vehicle.

This was not specifically identified in the literature review or by the contributing

factors listed in the Crash Incident Reports.

Table 10.1 shows the turning movements of the vehicles involved in these accidents.

Two of these accidents were the result of a right-turning major road vehicle failing to

123

give way and colliding with an oncoming major road vehicle turning left at the

intersection. Three of these accidents were the result of a major road vehicle

undertaking a U-turn and colliding with an oncoming major road vehicle. All the

remaining accidents were the result of a right-turning major road vehicle failing to

give way and colliding with an oncoming major road vehicle travelling through the

intersection.

Table 10.1 - Vehicle Movements - Angle-Major Vehicle Accidents Turning

Movement Oncoming Movement

Number of Accidents

Right Left 2 Right Through 102

U-Turn Through 3 Total 107

10.1 Vehicle Types

A graph of the types of vehicles involved in the Angle-Major vehicle accidents is

given in Figure 10.2. For any particular vehicle type, a vehicle is just as likely to be

located as the turning major road vehicle as the oncoming vehicle. Therefore, if there

is a considerable difference between the number of turning major road vehicles to the

number of oncoming major road vehicles for any particular vehicle type, then there is

an over or under representation.

2

11

77

14

0

2

1

0

1

2

81

17

1

3

1

1

0 20 40 60 80 100

Bicycle

Motor Cycle

Car, Station Wagon

Utility, Panel Van

Omnibus

Truck

Articulated Vehicle

Other or Unknown

Vehi

cle

Type

s

Number of Accidents

Turning MajorRoad Vehicle

Oncoming MajorRoad Vehicle

Figure 10.2 - Type of Vehicle versus Number of Angle-Major Vehicle Accidents

124

Motorcyclists appear over represented as oncoming vehicles. This would be

consistent with the findings for the Angle-Minor vehicle accident category.

Vehicle involvement rates versus type of vehicle for turning and oncoming major

road vehicles are shown in Tables 10.2 and 10.3 respectively.

Table 10.2 shows that no particular vehicle type is over represented as a turning

major road vehicle (some of the vehicle types record a low number of accidents and

therefore, the results for these types cannot be relied upon).

Table 10.3 verifies the results concluded from Figure 10.2 that motorcyclists are well

over represented as oncoming major road vehicles.

Table 10.2 - Turning Major Road Vehicle Involvement Rate versus Vehicle Types




Table 10.3 - Oncoming Major Road Vehicle

Involvement Rate versus Vehicle Types Number of Percentage Relative Standardised




Note: (1) The values in the third column of these tables are the percentage of kilometres travelled per

vehicle type as calculated in Arndt (1998).

125


Figure 10.3 shows the severity versus the number of Angle-Major vehicle accidents.

The shape of this graph is approximately similar to that for Angle-Minor vehicle

accidents with the exception that the ‘fatal’ category is smaller.

42

12

28

24

1

0 10 20 30 40 50

Property Damage

Minor

Treated

Hospitalised

Fatal

Seve

rity

Number of Accidents

Figure 10.3 - Severity of Angle-Major Vehicle Accidents Versus Number of Accidents


Figure 10.4 provides a bar chart of the type of weather versus the number of Angle-

Major vehicle accidents for the various light conditions. This figure shows that most

Angle-Major vehicle accidents occur in clear weather. Because data of the average

percentage of wet weather per year was not available, it is not possible to calculate

the effect of wet weather. However, as for Angle-Minor vehicle accidents, it is

anticipated that rain may be a little over represented in this accident type.

Angle-Major vehicle accident rates during the different light conditions is provided

in Table 10.4. This table shows that the accident rate during the hours of darkness for

Angle-Major accidents is greater than that during the hours of daylight. This result is

opposite to that identified in Table 9.4 for Angle-Minor vehicle accidents. No

adequate explanation for these diametrically opposed results was identified.

126

0

10

20

30

40

50

60N

umbe

r of A

ccid

ents



Figure 10.4 - Effect of Weather and Light Conditions on Number of

Angle-Major Vehicle Accidents (Out of the 107 Angle-Major accidents, 48 were listed as unknown weather and light conditions)

Table 10.4 - Angle - Major Vehicle Accident Rates Versus Light Conditions

Number of Percentage Relative StandardisedLight Conditions Accidents of Vehicles Accident Accident Rate

Recorded Using Rate Daylight = 1.0(A) Roadway (A/B) (A/B/0.5)

(B) (1)Daylight 42 77 0.5 1.00Dawn/Dusk 3 7 0.4 0.79Darkness 15 16 0.9 1.72


given light condition as calculated in Arndt (1998).


Table 10.5 lists the most common contributing circumstances given in the Crash

Incident Reports. These were listed for the unit turning on the major road that failed

to give way. Some crashes recorded more than one contributing circumstance.

Additional contributing factors to each Angle-Major vehicle accident can be found in

the accident descriptions in the crash incident reports. Specific contributing factors

from these reports and the number of times recorded are shown in Table 10.6.

127

Table 10.5 - Contributing Circumstances for Angle-Major Vehicle Accidents Contributing Circumstance Percent of Total

Violation - turn in face of oncoming traffic 55Driver - inexperience/lack of expertise 11Violation - undue care and attention 9Driver - age (lack of perception, power or concentration) 9(dawn/dusk/reflection) 2Violation - fail to give way 2Other 12

Table 10.6 - Additional Contributing Factors to Angle-Major Vehicle Accidents Contributing Factors Taken from the Number of

Accident Desciptions within the AccidentsCrash Incident Reports

Stopped at intersection 13Did not stop at intersection 2Slowed at intersection 3Oncoming traffic queued through intersection 6View obscured by oncoming right turn vehicle 1Other or unknown 82

Tables 10.5 and 10.6 do not provide a great deal of help in determining potential

driver behaviour contributing to this type of accident. It is interesting to note,

however, that six of these accidents occurred at intersections where the major road

traffic was queued through the intersection. Three of these accidents involved a

driver of a queued major road vehicle signalling to the turning driver to commence

the turn. This scenario also occurred for two Angle-Minor vehicle accidents where a

queue was reported through the intersection.

10.5 Distribution of Data

The Angle-Major vehicle accidents did not appear to be randomly distributed

amongst all of the major legs because particular legs tended to record high numbers

of accidents, while a large number of legs recorded zero accidents.

Table 10.7 compares the recorded Angle-Major vehicle accidents data with the

expected results if the accidents were randomly distributed (using a Poisson

distribution as shown in Equation 9.1 with λ = 107 accidents / 269 minor legs =

0.40).

128

Table 10.7 shows that 74% of the minor legs recorded no Angle-Major vehicle

accidents. It also shows that if randomly distributed, 67.1% of the minor legs could

have expected to record no Angle-Major vehicle accidents. Table 9.7 also shows that

2.6% of the minor legs recorded greater than two accidents and that the number of

accidents in this category is 29% of the total number of accidents. By random

distribution, it is predicted that the number of legs in this category would be 0.8%

and that the number of accidents in this category would be 6% of the total number of

accidents.

Table 10.7 - Comparison of Recorded Angle-Major Vehicle Accidents with a Random Distribution of these Accidents

0 1 2 >2Number of Legs (A1) 199 50 13 7Percentage of Legs (A1 / 269) x 100 74.0 18.6 4.8 2.6Number of Accidents (B1) 0 50 26 31Percentage of Accidents (B1 / 466) x 100 0.0 46.7 24.3 29.0Number of Legs (A2)P(x) x 269 181 72 14 2Percentage of Legs (A2 / 269) x 100 67.2 26.7 5.3 0.8Number of Accidents (B2)P(x) x x x 269 0 72 29 6Percentage of Accidents(B2 / 466) x 100 0.0 67.2 26.7 6.0

Category Parameter No. of Accidents Per Minor Leg (x)

Predicted Data (Poisson

Distribution)

Recorded Data

The above figures show that a small proportion of the minor legs recorded a larger

accident rate than would be expected if randomly distributed.


Figure 10.5 shows the various conflicts possible within the Angle-Major vehicle

accident category. Table 10.8 lists the accident rate (accidents divided the square of


As expected, Table 10.8 shows that the accident rate for left-turn oncoming vehicles

(RL) is lower than for through vehicles (RT). This is probably due to the lower

relative speed between vehicles for the RL conflict. The two accidents occurring to

left-turning oncoming vehicles (RL) occurred at high speed left-turn splitter islands.

129

Figure 10.5 - Types of Conflicts Recorded in the Angle-Major Vehicle Accident Category

Notes: (1) Vehicle paths shown as full lines are paths of vehicles at fault. (2) For an RL conflict, the right-turn vehicle from the major road is not at fault in this circumstance

if a splitter island exists for the opposing left-turn from the major road.

Table 10.8 - Angle-Major Vehicle Accident Rates for Various Conflicts No. of Traffic Accidents Standarised

Conflict Accidents Volume /Volume RateType (A) Product (A/B) Through = 1.0

(B) (1) (A/B/4.02E-14)RL 2 2.03E+14 9.85E-15 0.25RT 102 2.54E+15 4.02E-14 1.00

Notes: (1) The values in the third column equal the sum of the number of vehicles undertaking right-turn

from the major road multiplied by the total number of oncoming vehicles travelling left or through on the major road during the analysis period.

130

The three accidents resulting from vehicles undertaking U-turns were not included in

this table because traffic data for these movements were not available for all of the

intersection samples.

Out of the 269 sites with left-turn movements from a major leg, 42 were free left-

turns and most were slow speed turns. Given that the only two accidents for this

conflict occurred on high speed left-turn lanes, it is quite possible that splitter islands

for high speed left-turns from the major road generate higher Angle-Major vehicle

accident rates.

A preliminary review of the accident data for through oncoming vehicles did not

identify any geometric features over represented in these types of accidents.

131

11 REAR-END-MAJOR VEHICLE ACCIDENTS


described in Chapter 8 to the Rear-End-Major vehicle accident category. The number

of Rear-End-Major vehicle accidents as compared to the total number of accidents is



100%

High Frequency


64%



10%


Accidents 167 acc.

15%


Accidents 121 acc.

11%



Figure 11.1 - Number of Rear-End-Major Vehicle Accidents Compared to the Total Number of Accidents


the result of a through major road vehicle inadequately negotiating a slowed or

stopped turning major road vehicle.

Seven of these accidents were the result of a major road vehicle losing control after

avoiding a turning major road vehicle. Three accidents involved a major road vehicle

avoiding a turning major road vehicle and colliding with another major road vehicle.

All other accidents in this category resulted from major road vehicles colliding in a

rear-end type accident. Most of these accidents involved a major road vehicle

colliding with the turning major road vehicle. Some of the accidents, however,

comprised more than two vehicles colliding in a rear-end manner and some did not

132

directly involve the turning vehicle.

The turning movement of the front vehicles involved in accidents within this

category is given in Table 11.1.

Table 11.1 - Front Vehicle Turning Movements - Rear-End-Major Vehicle Accidents

Turning Movement of Front Vehicle

Number of Accidents

Left 5 Right 111

U-Turn 3 Unknown 2

Total 121

Table 11.1 shows that the majority of these accidents occurred as a major road

vehicle was undertaking a right-turn at the intersection.

11.1 Vehicle Types

A graph of the types of vehicles involved in the Rear-End-Major vehicle accidents is


0

0

91

17

2

3

0

8

0

1

84

22

0

5

8

1

0 20 40 60 80 100

Bicycle

Motor Cycle

Car, Station Wagon

Utility, Panel Van

Omnibus

Truck

Articulated Vehicle

Other or Unknown

Vehi

cle

Type

Number of Accidents

Rear VehicleFront Vehicle

Figure 11.2 - Type of Vehicles versus Number of

Rear-End-Major Vehicle Accidents

For any particular vehicle type, a vehicle is just as likely to be located as the front

turning major road vehicle as rear through vehicle. Therefore, if there is a

133

considerable difference between the number of these vehicles for any particular

vehicle type, then there is an over or under representation. No particular vehicle type

appears significantly over or under represented, other than the possibility that

articulated vehicles are under represented as front vehicles.

Tables 11.2 and 11.3 show the vehicle involvement rates versus type of vehicle for

the rear and front vehicles respectively. Table 11.2 shows that articulated vehicles

may be over represented as rear vehicles, whilst Table 11.3 shows that articulated

vehicles might be under represented as front vehicles.

Table 11.2 - Rear Vehicle Involvement Rate versus Vehicle Types Number of Percentage Relative Standardised




Table 11.3 - Front Vehicle Involvement Rate versus Vehicle Types




Note: (1) The values in the third column of these tables are the percentage of kilometres travelled per

vehicle type as calculated in Arndt (1998). In Arndt (1998), articulated vehicles were found under represented as front vehicles

in Approaching Rear-end vehicle accident rates at roundabouts. These vehicles do

not brake as quickly as the majority of other vehicle types, and it is therefore less

likely that the vehicle behind them will not be able to stop in time to avoid a

134

collision. In addition, they are significantly easier to see because of their size.


Figure 11.3 shows the severity versus the number of Rear-End-Major vehicle

accidents. A comparison of the rear-end accident data from Figure 11.3 with that at

roundabouts in Arndt (1998) has revealed that rear-end accidents on the major

roadway at unsignalised intersections are considerably more severe.

54

21

30

13

3

0 10 20 30 40 50 60

Property Damage

Minor

Treated

Hospitalised

Fatal

Seve

rity

Number of Accidents

Figure 11.3 - Severity of Rear-End-Major Accidents versus Number of Accidents


Figure 11.4 provides a bar chart of the type of weather versus the number of Rear-

End-Major vehicle accidents for the various light conditions. This figure indicates

that most Rear-End-Major vehicle accidents occur in clear weather. Because data of

the average percentage of wet weather per year was unable to be obtained, it is not

possible to calculate the effect of wet weather.

Rear-End-Major vehicle accident rates during the different light conditions are

shown in Table 11.4. The accident rate during the hours of darkness for Rear-End-

Major vehicle accidents in this table is somewhat less that during the hours of

daylight. This is a similar result to that in Table 9.4 for Angle-Minor vehicle

accidents.

135

0

10

20

30

40

50

60

Num

ber o

f Acc

iden

ts



Figure 11.4 - Effect of Weather and Light Conditions on Number of Rear-End-Major Vehicle Accidents (Out of the 121 Rear-End-Major vehicle accidents, 58 were listed

as unknown weather and light conditions)

Table 11.4 - Rear-End-Major Vehicle Accident Rates Versus Light Conditions Number of Percentage Relative Standardised


(A) Roadway (A/B) (A/B/0.7)(B) (1)






are given in Table 11.5. These were listed for the rear vehicle on the major road that

failed to evade the turning vehicle. Some crashes recorded more than one

contributing circumstance.

136

Table 11.5 - Contributing Circumstances for Rear-End-Major Vehicle Accidents Contributing Circumstance Percent of Total

Violation - undue care and attention 47Driver - inexperience/lack of expertise 20Violation - follow too closely 13Road - wet/slippery 5Atmospheric - rain 2Lighting - sunlight glare (dawn/dusk/reflection 2Other 11


Figure 11.5 shows the various conflicts possible within the Rear-End-Major vehicle

accident category. Table 11.6 lists the accident rate (accidents divided the square of


Figure 11.5 - Types of Conflicts Recorded in the Rear-End-Major Vehicle Accident Category

Notes: (1) Full lines show paths of vehicles at fault. (2) The right-turn vehicle from the major road is not at fault in this circumstance if a splitter island

exists for the opposing left-turn from the major road.

137

Table 11.6 - Rear-End-Major Accident Rates for Various Turn Treatments Confl. Turn No. of Median Sealed No. No. Traffic Accid. StandarisedType Type Major Width Should. of of Volume /Volume Rate-Type

Road (m) Width Sites Acc. Product (A/B) CHR = 1.0Lanes (m) (A) (B) (1) (A/B/2.58E-15)

LSR 2 0 Varies 75 44 1.47E+14 2.99E-13 116.1R LSR/MNR 2,4 ≥ 1 N/A 19 11 1.98E+14 5.56E-14 21.6

MNR 4 0 N/A 8 23 8.91E+13 2.58E-13 100.2AUR 2 0 N/A 47 28 1.59E+14 1.76E-13 68.3CHR 2,4,6 Varies N/A 120 5 1.94E+15 2.58E-15 1.0LSL 2 N/A < 2 63 3 1.94E+14 1.55E-14 6.0

L LSL 2 N/A ≥ 2 26 0 3.07E+14 0 0.0LSL 2 N/A Parking 13 0 5.31E+13 0 0.0LSL 4,6 N/A N/A 56 0 7.23E+14 0 0.0AUL 2,4,6 N/A N/A 111 2 9.11E+14 2.2E-15 0.9

Notes: (1) The values in the eighth column are equal to the sum of the number of vehicles undertaking a left

or right-turn from the major road multiplied by the total number of vehicles travelling through on the major road (one way only) during the analysis period.

(2) Accident rates are shown for left and right conflicts only. Accidents resulting from vehicles undertaking U-turns were not included in this table because traffic data for these movements were not available for all of the intersection samples

From Table 11.6, the accident rate for a right-turn movement into a turn slot (type

CHR treatment) has been standardised at unity. It must be remembered that

comparisons of the standardised accident rates are approximate only because they do

not account for other parameters within the various categories such as approach

speed.

Table 11.6 shows that the accident rate for a right-turn movement into an auxiliary

lane (Type CHR treatment) is very similar to that for a left-turn movement into an

auxiliary lane (Type AUL treatment). Where a left-turn auxiliary lane does not exist

(Type LSL treatment), and the sealed shoulder width is less than 2m, the accident

rate for a left-turn movement is 6/0.9 = 6.7 times higher than where a left auxiliary

lane has been provided. This value shows the benefit in providing left-turn auxiliary

lanes. However, this value is only based a small number of accidents in each

category.

A right-turn Type AUR treatment records an accident rate 68.3 times higher than a

right-turn Type CHR treatment. Type LSR and MNR treatments record an accident

rate 116.1 and 100.2 times higher respectively, than a Type CHR treatment. These

values clearly show the advantage in providing Type CHR turn treatments. In

138

addition, a significant number of the Type CHR turn slots were of shorter length than

the values recommended in Austroads (1988) as shown in Table 11.7.

Table 11.7 - Length of Right-turn Slots in Austroads (1988) and in this Study Speed Length of Right Intersection Study

Environment Turn Slot from No. of Minimum Average Maximumof Major Leg Austroads (1988) Sites Slot Slot Slot

(m) (m) Length Length Length(1) (m) (m) (m)

40 - 1 32 32 3250 60 (60) 0 - - -60 80 (60) 18 32 68 11670 100 (60) 36 25 61 13480 120 12 50 80 13890 140 20 51 122 185

100 170 8 64 98 161110 - 25 47 128 207

Note: (1) The values in the second column are taken from Table 5.6 ‘Length of Deceleration Lanes’ of

Austroads (1988), for vehicles to decelerate to a stop condition. Values shown in brackets are stated values for urban areas where a full-length deceleration lane cannot be provided. Values not shown were not provided.

Table 11.7 shows that the average right-turn slot length in this study is generally less

than the recommended values in Austroads (1988), particularly in the higher speed

environments. The minimum right-turn slot length in each category is well below the

recommended values in Austroads (1988). Although particular intersections within

this study comprised substandard length right-turn slots, it does not appear to have

much influence on the accident rates. This indicates that a substandard right-turn slot

is still much safer than Type LSR, MNR or AUR right-turn treatments.

It is interesting to note in Table 11.6 that Type LSR and MNR right-turn treatments

with medians have a significantly lower accident rate than those without medians.

This suggests that motorists who can position their vehicle further away from the

through traffic lane are safer, although they need to decelerate to a slow speed before

moving into this position (creating ‘friction’ with the through traffic). This fact,

combined with the fact that right-turn vehicles have much higher accident rates than

left-turn vehicles at Type LSL treatments and the fact that substandard right-turn

slots still perform well, suggest the following. It is more important to keep stationary

right-turn vehicles (who are waiting for a gap in the oncoming traffic) off the through

carriageway than it is to be concerned with the length of the right-turn slot (and thus

139

the deceleration within the through traffic stream). In other words, the length of time

(exposure) that a vehicle is stopped waiting for the gap is important.

140

12 SINGLE-THROUGH VEHICLE ACCIDENTS


described in Chapter 8 to the Single-Through vehicle accident category. The number

of Single-Through vehicle accidents compared to the total number of accidents is



100%

High Frequency Intersection Accidents 694 acc.

64%


10%


Accidents 167 acc.

15%


Accidents 121 acc.

11%

Single-Through 167 acc.

Figure 12.1 - Number of Single-Through Vehicle Accidents Compared to the Total Number of Accidents


the result of a major or minor road vehicle losing control. This category does not

include single vehicle accidents involving collisions with or avoiding an object or

animal on the roadway. Nor does it cover single vehicle accidents occurring to

vehicles turning at the intersection. The latter accident type was excluded because the

presence of the intersection was deemed to have a direct influence on these

accidents.

Locations of the vehicles involved in these accidents are given in Table 12.1. Most

accidents were recorded on the major road.

141

Table 12.1 - Single-Through Vehicle Accidents Location Number of

Accidents Major Road 154 Minor Road 13

Total 167

Figure 12.2 shows a plot of the distance from the centre of the intersection versus the

number of Single-Through vehicle accident locations. The 0 - 49.99m category

appears somewhat over represented, suggesting that the presence of the intersection

is influencing these accidents. However, it is anticipated that these accidents are

largely unaffected by the presence of the intersection and that this over

representation is probably due to the reasons given below:

• Accidents occurring on minor legs under the jurisdiction of a local authority were

only recorded up to 50m from the intersection (all others were recorded up to

200m).

• Over half the accidents occurring in the 0 - 49.99m category were listed at the

intersection ie at 0m. It is believed that some police officers list an accident

occurring near the intersection as at the intersection. This was seen in the accident

subcategory ‘Wrong Location for Accident’ in the ‘Not Included in Analysis’

accident category, where accidents at locations greater than 200m away (up to

several kilometres) were recorded as at the intersection.

• Several intersections in the analysis comprised tight horizontal curves on the

minor road immediately prior to the intersection with horizontal straights before

the curves. Most studies show that high single vehicle accident rates are recorded

on tight horizontal curves. It is possible that the over representation in the 0 -

49.99m category is partially due to the concentration of these accidents on these

tight horizontal curves on the minor road.

• Several intersections in the analysis comprised tight horizontal curves on the

major road through the intersection, with horizontal straights either side of the

curves (tangent points located less than 200m from the intersection). Because

most studies show that high single vehicle accident rates are recorded on tight

horizontal curves, it is possible that the over representation in the 0 - 49.99m

142

category is partially due to the concentration of these accidents on these tight

horizontal curves on the major road.

0 10 20 30 40 50 60 70

Number of Accidents

0 - 49.99

50 - 99.99

100 - 149.99

150 - 200

Dis

tanc

e fr

om C

entr

e of

In

ters

ectio

n (m

)

Figure 12.2 - Distance from Centre of Intersection Versus Number of Single-

Through Vehicle Accidents

12.1 Vehicle Types

Figure 12.3 provides a graph of the types of vehicles involved in the Single-Through

vehicle accidents. Table 12.2 shows the Single-Through vehicle accident rates for the

various vehicle types.

2

9

129

23

0

0

3

1

0 20 40 60 80 100 120 140

Bicycle

Motor Cycle

Car, Station Wagon

Utility, Panel Van

Omnibus

Truck

Articulated Vehicle

Other or Unknown

Vehi

cle

Type

Number of Accidents

Figure 12.3 - Type of Vehicle Versus Number of Single-Through Vehicle Accidents

143

Motorcyclists appear to be over represented whilst heavy vehicles appear to be under

represented. Arndt (1998) found motorcyclists to be over represented in single

vehicle accidents at roundabouts. Unlike these results, however, Arndt (1998) also

found that heavy vehicles were over represented.

Table 12.2 - Single-Through Vehicle Accident Rate versus Vehicle Type




Note: (1) The values in the third column are the percentage of kilometres travelled per vehicle type as

calculated in Arndt (1998).


Severity versus the number of Single-Through vehicle accidents is shown in Figure

12.4. By observation with the severity graphs of other accident types in this study,

these accidents record high rates for the ‘hospitalised’ and ‘fatal’ categories.

67

19

29

44

8

0 10 20 30 40 50 60 70 80

Property Damage

Minor

Treated

Hospitalised

Fatal

Seve

rity

Number of Accidents

Figure 12.4 - Severity of Single-Through Vehicle Accidents

144


Figure 12.5 illustrates the type of weather versus the number of Single-Through

vehicle accidents for the various light conditions.

0

10

20

30

40

50

60

Num

ber o

f Acc

iden

ts



Figure 12.5 - Effect of Weather and Light Conditions on Number of Single-Through

Vehicle Accidents (Out of the 167 Single-Through vehicle accidents, 80 were listed as unknown weather and light conditions)

Figure 12.5 indicates that weather and light conditions have a major effect on single

vehicle accidents. Thirty-four percent of the accidents occurred in wet weather. For

any year, the ratio of total hours of wet weather/total hours of dry weather is

expected to be quite low, certainly much lower than 34%. For this reason, it is

expected that wet weather conditions are over-represented. A similar result was

found in Arndt (1998) for single vehicle accidents at roundabouts and on steep

downgrades in Shelton and Arndt (1992).

Table 12.3 presents the Single-Through vehicle accident rates during the different

light conditions. This table shows that the accident rate at night is approximately 3.5

times higher than during the hours of daylight, indicating that light conditions have a

major impact on single vehicle accidents. This result is expected because driving at

night requires more concentration to perform the driving task, and there is more

likelihood of making a mistake that leads to an accident under conditions that require

more concentration. A similar result was also found in Arndt (1998) for single

vehicle accidents at roundabouts and on steep downgrades in Shelton and Arndt

(1992).

145

Table 12.3 - Single-Through Vehicle Accident Rates Versus Light Conditions Number of Percentage Relative Standardised


(A) Roadway (A/B) (A/B/0.6)(B) (1)






are given in Table 12.4. Some crashes recorded more than one contributing

circumstance. The factors listed in Table 12.4 are similar to those found in Arndt

(1998) for single vehicle accidents at roundabouts.

Table 12.4 - Contributing Circumstances for Single-Through Vehicle Accidents Contributing Circumstance Percent of Total

Road - wet/slippery 19Driver - inexperience/lack of expertise 15Violation - undue care and attention 11Atmospheric - rain 8Violation - over prescribed concentration of alcohol (must have BAC) 7Driver - fatigue/fell asleep 5Other 35


Horizontal geometric elements on which high Single-Through vehicle accident rates

(number of Single-Through vehicle accidents divided by the traffic volume) were

recorded tended to be horizontal curves comprising a large decrease in speed

between successive geometric elements.

Table 12.5 and Table 12.6 show Single-Through vehicle accident rates on the major

and minor roads respectively. These tables compare the accident rates for various

ranges of the decrease in speed between successive horizontal geometric elements

based on the speed prediction and vehicle path models in Sections 6.3 and 6.4. The

146

accident rate for a horizontal geometric element with a zero decrease in speed

between successive geometric elements (predominantly horizontal straights) has

been standardised at unity.

It must be remembered that comparisons of the standardised accident rates are

approximate only because they do not account for other parameters within the

various categories such as the length of each geometric element. Both tables show

that there is a strong correlation between decrease in speed and the resulting accident

rates.

Table 12.5 - Single-Through Vehicle Accident Rates on the Major Road for Various Decreases in Speed

Decrease Number of Total Accident StandardisedIn No. of Accidents No. of Rate Accident

Speed Sites Recorded Vehicles (acc/veh) Rate∆S (A) (B) (A/B) ∆S of 0 = 1.0

(km/h) (A/B/1.22E-8)0 308 39 3.19E+09 1.22E-08 1.0

0 - 10 168 56 1.42E+09 3.96E-08 3.210 - 20 20 25 1.46E+08 1.71E-07 14.0

Table 12.6 - Single-Through Vehicle Accident Rates on the Minor Road for Various Decreases in Speed

Decrease Number of Total Accident StandardisedIn No. of Accidents No. of Rate Accident

Speed Sites Recorded Vehicles (acc/veh) Rate∆S (A) (B) (A/B) ∆S of 0 = 1.0

(km/h) (A/B/3.02E-09)0 198 1 3.31E+08 3.02E-09 1.0

0 - 10 41 1 7.91E+07 1.26E-08 4.210 - 20 12 2 2.27E+07 8.82E-08 29.220 - 30 9 2 1.83E+07 1.09E-07 36.230 - 40 7 3 1.19E+07 2.53E-07 83.6

>40 2 1 4.19E+06 2.38E-07 78.9

From Table 12.5, a decrease in speed between successive horizontal elements on the

major road of up to 10km/h gives a 3.2 times greater accident rate than a horizontal

element with a zero decrease in speed. A decrease in speed on the major road of 10 -

20 km/h gives a 14 times greater accident rate than a horizontal element with a zero

decrease in speed. This trend is quite similar for the minor road, even though the total

number of accidents for the minor road is very small.

147

From Table 12.6, a decrease in speed of greater than 40km/h on the minor road gives

a 78.9 times greater accident rate than a horizontal element with a zero decrease in

speed. These values show the importance of limiting the decrease in speed between

successive geometric elements to minimise single vehicle accident rates.

148

13 LOW FREQUENCY INTERSECTION ACCIDENTS


described in Chapter 8 to the Low Frequency Intersection accident category. Figure

13.1 shows the number of Low Frequency Intersection accidents as compared to the

total number of accidents. Also shown in Figure 13.1 is a break up of the accident

subsets that form the Low Frequency Intersection accident category.


100%


64%

Low Frequency


10%


Accidents 167 acc.

15%


Accidents 121 acc.

11%

Rear-End-Minor: 27 acc. Single-Minor-Turn: 23 acc. Single-Major-Turn: 17 acc. Incorrect Turn: 17 acc. Overtaking Intersection: 13 acc. Sideswipe-Major-Auxiliary: 4 acc. Other: 8 acc.

Figure 13.1 - Number of Low Frequency Intersection Accidents Compared to the Total Number of Accidents

A total of 109 accidents were recorded in this category. The accident subsets within

this category are discussed below.

13.1 Rear-End-Minor

These 27 accidents are primarily the result of a minor road vehicle colliding in a rear-

end type collision with another slowed or stopped minor road vehicle, at the

intersection. Movement of the front vehicle involved in these accidents is given in

Table 13.1. The majority of minor road vehicles that were hit were turning left at the

149

intersection.

Table 13.1 - Front Vehicle Movements - Rear-End-Minor Vehicle Accidents

Front Vehicle Movement

Number of Accidents

Left 15 Through 3

Right 4 Unknown 5

Total 27

Severity versus the number of Rear-End-Minor vehicle accidents is shown in Figure

13.2. There are a comparatively high proportion of treated cases relative to the other

categories (and relative to the other severity plots in this study). These accidents are

generally less severe than most of the other accident types.

8

8

10

1

0

0 2 4 6 8 10 12

Property Damage

Minor

Treated

Hospitalised

Fatal

Seve

rity

Number of Accidents

Figure 13.2 - Severity versus Number of Rear-End-Minor Vehicle Accidents

Table 13.2 shows the accident rate for various front vehicle movements. It appears

that rear-end accidents involving right-turning front vehicles may be a little under

represented, at least compared to left-turning front vehicles.

150

Table 13.2 - Rear-End-Minor Vehicle Accident Rates for Front Vehicle Movements Front No. of Traffic Accidents Standarised

Vehicle Accidents Volume /Volume RateMovement (A) Product (A/B) Right = 1.0

(B) (1) (A/B/5.38E-15)Left 15 7.50E+14 2.00E-14 3.72

Through 3 1.21E+14 2.48E-14 4.61Right 4 7.44E+14 5.38E-15 1

Notes: (1) The values in the third column equal the sum of the number of vehicles undertaking the

particular turn from the minor road multiplied by the total number of vehicles on the minor leg approaching the intersection during the analysis period.

(2) The five accidents which recorded an unknown front vehicle movement are not included in this table.

13.2 Single-Minor-Turn

These 23 accidents are primarily the result of a minor road vehicle losing control

whilst turning (or intending to turn) at the intersection. Some of the accidents at T-

intersections involved collisions with the side opposite to the minor leg. Table 13.3

shows the movement of the vehicle involved in these accidents. This table indicates

that the majority of these vehicles were turning right at the intersection.

Table 13.3 - Vehicle Movements - Single-Minor-Turn Vehicle Accidents

Vehicle Movement

Number of Accidents

Left 8 Through 0

Right 14 Unknown 1

Total 23

Severity versus the number of Single-Minor-Turn vehicle accidents is given in

Figure 13.3. These accidents appear less severe than those recorded in the Single-

Through vehicle accident category (single vehicle accidents occurring to through

vehicles on the major and minor roads).

Table 13.4 shows the accident rate for various vehicle movements. It appears that the

right-turn manoeuvre is over represented.

151

12

2

5

4

0

0 2 4 6 8 10 12 14

Property Damage

Minor

Treated

Hospitalised

Fatal

Seve

rity

Number of Accidents

Figure 13.3 - Severity versus Number of Single-Minor-Turn Vehicle Accidents

Table 13.4 - Single-Minor-Turn Vehicle Accident Rates for the Various Vehicle Movements No. of Total Accidents Standarised

Vehicle Accidents Number of /Volume RateMovement (A) Vehicles (A/B) Left = 1.0

(B) (1) (A/B/3.46E-8)Left 8 2.31E+08 3.46E-08 1.00

Through 0 5.17E+07 0.00E+00 0.00Right 14 1.84E+08 7.61E-08 2.20

Notes: (1) The values in the third column equal the total number of vehicles undertaking the particular turn

from the minor road during the analysis period. (2) The two accidents which recorded an unknown front vehicle movement are not included in this

table.

Half the left-turn accidents occurred on free left-turn lanes. However, only 16

percent of the minor legs comprised a free left-turn lane.

Five of these twenty-three accidents occurred on the minor leg of one T-intersection.

This minor leg was a national highway in a high-speed environment. Other than this

minor leg, there appeared to be no consistent geometry amongst the minor legs on

which high Single-Minor-Turn vehicle accident rates (number of Single-Minor-Turn

vehicle accidents divided by the minor leg volume) were recorded.

13.3 Single-Major-Turn

These 17 accidents are primarily the result of a major road vehicle losing control

152

whilst turning at the intersection. The movements of the vehicles involved in these

accidents are given in Table 13.5.

Table 13.5 - Vehicle Movements - Single-Major-Turn Vehicle Accidents

Vehicle Movement

Number of Accidents

Left 8 Right 9

Unknown 0 Total 17

Figure 13.4 shows the severity versus the number of Single-Major-Turn vehicle

accidents. As for Single-Minor-Turn vehicle accidents, these accidents appear less

severe than those recorded in the Single-Through vehicle accident category (single

vehicle accidents occurring to through vehicles on the major and minor roads).

11

3

1

2

0

0 2 4 6 8 10 12

Property Damage

Minor

Treated

Hospitalised

Fatal

Seve

rity

Number of Accidents

Figure 13.4 - Severity versus Number of Single-Major-Turn Vehicle Accidents

Accident rates for various vehicle movements are shown in Table 13.6. It appears

that the left and right-turn movements record similar accident rates.

There appeared to be no consistent geometry amongst the major legs on which high

Single-Major-Turn vehicle accident rates (number of Single-Major-Turn vehicle

accidents divided by the major leg turning volume) were recorded.

153

Table 13.6 - Single-Major-Turn Vehicle Accident Rates for the Various Vehicle Movements No. of Total Accidents Standarised

Vehicle Accidents Number of /Volume RateMovement (A) Vehicles (A/B) Left = 1.0

(B) (1) (A/B/3.9E-8)Left 8 2.05E+08 3.90E-08 1.00

Right 9 2.37E+08 3.8E-08 0.97 Note: (1) This values in the third column equal the total number of vehicles undertaking the particular turn

from the minor road during the analysis period.

13.4 Incorrect Turn

Figure 13.5 shows the various conflict types recorded within this accident category.

Ten of these seventeen accidents involved a vehicle turning at the intersection and

then travelling onto the wrong carriageway (eight accidents were left-turns, two were

unknown). The other seven accidents involved turning from the wrong side of

another vehicle.

Figure 13.5 - Conflict Types Recorded in the Incorrect Turn Accident Category

Note: The numbers shown in this figure are the number of accidents recorded for each conflict type. Two accidents involved unknown turning movements and are not included in this figure.

154

Nine of the ten accidents that involved turning at an intersection, and then travelling

onto the wrong carriageway, occurred on roadways with no median.

Severity versus the number of Incorrect Turn vehicle accidents is given in Figure

13.6.

9

2

3

2

1

0 2 4 6 8 10

Property Damage

Minor

Treated

Hospitalised

Fatal

Seve

rity

Number of Accidents

Figure 13.6 - Severity versus Number of Incorrect Turn Vehicle Accidents

13.5 Overtaking-Intersection

These thirteen accidents occurred because of an overtaking vehicle on the major road

hitting the overtaken vehicle that was turning right at the intersection. Figure 13.7

shows the severity versus the number of Overtaking-Intersection vehicle accidents.

10

0

1

2

0

0 2 4 6 8 10 12

Property Damage

Minor

Treated

Hospitalised

Fatal

Seve

rity

Number of Accidents

Figure 13.7 - Severity versus Number of Overtaking-Intersection Vehicle Accidents

155

As expected, all Overtaking-Intersection vehicle accidents occurred at intersections

on two-lane roads. The Overtaking-Intersection vehicle accident rate for the various

right-turn types and line marking treatments is given in Table 13.7.

Table 13.7 - Overtaking-Intersection Vehicle Accident Rates for the Various Right-Turn Types and Line Marking Treatments (Two-Lane Roads Only)

Barrier No. No. Traffic Accidents StandarisedInter. Line of of Volume /Volume Rate-Type LSRType Marking Sites Acc. Product (A/B) Barrier = 1.0

(A) (B) (1) (A/B/1.87E-14)LSR N 26 6 6.80E+13 8.82E-14 4.7LSR Y 52 2 1.07E+14 1.87E-14 1.0AUR N 9 5 4.38E+13 1.14E-13 6.1AUR Y 38 0 1.15E+14 0.00E+00 0.0CHR Y 61 0 4.77E+14 0.00E+00 0.0

Note: (1) The values in the fifth column equal the sum of the number of vehicles undertaking a right-

turn from the major road multiplied by the total number of vehicles travelling through on the major road (one way only) during the analysis period.

Table 13.7 shows that five of these accidents occurred at Type AUR turn treatments,

whilst the remaining eight occurred at Type LSR turn treatments. Two accidents

occurred at intersections that contained barrier line marking (these intersections

comprised Type LSR turn treatments).

The accident rate for Type LSR turn types without barrier line marking is higher than

those with barrier marking. This value may not necessarily totally reflect the benefits

of having barrier line marking because many of the Type LSR turn treatments with

barrier line marking had reduced oncoming visibility. The lower accident rate at

these intersections may be at least partially reflecting the fact that less overtaking

manoeuvres are likely to occur at these locations. However, offsetting this fact is the

uncertainty that the intersections with barrier line marking may not have comprised

this line marking over the full period of analysis.

It was noted that some Type LSR turn treatments did contain barrier line marking,

though oncoming visibility was more than adequate. It is considered that this line

marking may have introduced to minimise these accidents.

Of the Type AUR turn treatments that recorded the five accidents, none contained

barrier line marking. However, QDMR (2000) and Austroads (2003) show that

156

barrier marking must be used at Type AUR turn treatments. The accident rate at the

Type AUR turn types without line marking is similar to that at Type LSR turn types

without line marking.

An expected result was that none of these accidents occurred at Type CHR turn

treatments. This is probably because little overtaking occurs where there are medians

provided (although some medians are only painted).

All thirteen accidents occurred in high-speed environments.

13.6 Sideswipe-Major-Auxiliary

These four accidents occurred as a driver in an auxiliary lane moved onto the main

carriageway and collided with a major road vehicle. Three of these accidents

occurred on Type AUL deceleration lanes. In one of these accidents, the driver

mistook a Type AUL deceleration lane for an overtaking lane that starts in the

middle of the intersection. A similar accident occurred at this site shortly before the

author undertook a site inspection of the intersection.

The other accident occurred as a driver mistook a Type AUR auxiliary lane as an

overtaking lane. In this case, the Type AUR auxiliary lane was quite long.

13.7 Other Accidents

The seven ‘other’ accidents consisted of seven infrequent intersection accident types.

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14 LOW FREQUENCY THROUGH ACCIDENTS


described in Chapter 8 to the Low Frequency Through accident category, of which a

total of 121 accidents were recorded. The number of Low Frequency Through

accidents as compared to the total number of accidents is shown in Figure 14.1. This

figure also shows a break up of the accident subsets that form the Low Frequency

Through accident category.


100%


64%


10%


Accidents 167 acc.

15%


Accidents 121 acc.

11%

Pedestrian: 39 acc. U-Turn: 33 acc. Changed Lanes: 16 acc. Single-Object: 16 acc. Overtaking: 7 acc. Other: 10 acc.

Figure 14.1 - Number of Low Frequency Through Accidents Compared to the Total Number of Accidents

A total of 121 accidents were recorded in this category. The accident subsets within

this category are discussed below.

14.1 Pedestrian

These 39 accidents were primarily the result of a vehicle colliding with a pedestrian

or cyclist who were crossing the major or minor road. This category excludes

accidents occurring at designated pedestrian crossings eg at zebra crossing or traffic

signals. All but two of these accidents occurred on the major roadway.

158

Figure 14.2 shows a plot of the distance from the centre of the intersection versus the

number of Pedestrian accident locations. There is a tendency for the number of these

accidents to increase towards the centre of the intersection. This may be due to the

method of police reporting as discussed in Chapter 12, or alternatively, it may be due

to a greater number of pedestrians crossing near intersections than at mid-block.

0 5 10 15

Number of Accident Locations

0 - 49.99

50 - 99.99

100 - 149.99

150 - 200

Dis

tanc

e fr

om C

entr

e of

In

ters

ectio

n (m

)

Figure 14.2 - Distance from Centre of Intersection Versus Number of Pedestrian

Accidents Severity versus the number of Pedestrian accidents is given in Figure 14.3. As

expected, the relative severity of this accident category is very high due to the

unprotected nature of pedestrians.

0

4

12

20

3

0 5 10 15 20 25

Property Damage

Minor

Treated

Hospitalised

Fatal

Seve

rity

Number of Accidents

Figure 14.3 - Severity versus Number of Pedestrian Accidents

159

Intersection sites recording greater than one pedestrian accident were mostly in low

speed commercial areas where high pedestrian activity occurs.

14.2 U-Turn

These 33 accidents are primarily the result of a vehicle undertaking a U-turn on the

major or minor road and colliding with a vehicle from behind (26 accidents) or

colliding with an oncoming vehicle (7 accidents). All but two of the accidents were

recorded on the major road. There appeared to be no any consistent factors between

the sites that recorded U-turn accidents.

14.3 Changed Lanes

These 16 accidents are primarily the result of a major road vehicle making an unsafe

change into an adjacent lane (same direction of travel). Nine of these accidents

involved colliding with a vehicle in the adjacent lane and seven accidents involved a

major road vehicle losing control whilst avoiding the vehicle changing lanes.

Figure 14.4 shows the severity versus the number of Changed Lanes vehicle

accidents. The severity of this accident category is higher than one may normally

expect where relative speeds of vehicles are low. The seven single vehicle accidents

resulting from avoiding a vehicle changing lanes tended to record much higher

severity ratings than the nine accidents involving colliding with a vehicle in the

adjacent lane.

9

0

5

2

0

0 2 4 6 8 10

Property Damage

Minor

Treated

Hospitalised

Fatal

Seve

rity

Number of Accidents

Figure 14.4 - Severity versus Number of Changed Lanes Vehicle Accidents

160

There tended to be an over representation of Type MNR turn treatments in this

category, particularly those sites that recorded high Rear-End-Major vehicle accident

rates. The expected reason is that vehicles are changing lanes more often at these

locations to avoid queues behind right-turning vehicle/s at the intersection and this

increases the chance of Change Lanes vehicle accidents occurring. There was

insufficient information in the Crash Incident Reports to verify this.

14.4 Single-Object

These 16 accidents are primarily the result of a major road vehicle hitting an object

or animal (10 accidents) or avoiding an animal or object (6 accidents).

Severity versus the number of Single-Object vehicle accidents is shown in Figure

14.5.

8

3

3

2

0

0 2 4 6 8 10

Property Damage

Minor

Treated

Hospitalised

Fatal

Seve

rity

Number of Accidents

Figure 14.5 - Severity versus Number of Single-Object Vehicle Accidents

14.5 Overtaking

These seven accidents are primarily the result of a major road vehicle overtaking

unsafely. Of these, two involved a major road vehicle losing control after avoiding

the overtaking vehicle, one involved the overtaking vehicle losing control, three

involved an overtaking vehicle colliding with an oncoming vehicle and one involved

the overtaking vehicle hitting the overtaken vehicle.

161

14.6 Other Accidents

The ten ‘other’ accidents consisted of seven infrequent through accident types.

162

15 PRELIMINARY ANALYSIS SUMMARY

This chapter lists the types and numbers of accidents in each accident category and

summarises the findings of the preliminary analysis for each high frequency accident

type.

15.1 Types and Numbers of Accidents Recorded

A total of 1091 accidents have been analysed for the 206 intersections in this study.

These accidents have been placed into the categories shown in Table 15.1.

15.2 Parameters Over Represented in the Accident Data

Table 15.2 summarises the results of the preliminary analysis for the high frequency

accident types shown in Table 15.1 by identifying trends and parameters that

appeared to be over represented in the data.

This thesis now describes the issues regarding the statistical analysis techniques

adopted for use in the regression analysis.

163

Table 15.1 - Types and Numbers of Accidents Recorded in the Study Broad

Accident Category

Major Accident Type



466




107

694


27

Single-Minor-Turn


23

Single-Major-Turn


17


17



13



4


Other 8

109


Single-Through


167

167


39

U-Turn Hit whilst undertaking a U-turn at midblock

33



Other 10

121

Total 1091

164

Table 15.2 - Parameters Over Represented in the High Frequency Accident Types Accident Type Factor

Angle-Minor Angle-Major Rear-End-Major

Single-Through

Contributing Factor

• Disobey stop/ give way sign

• Undue care and attention

• Inexperience/ lack of expertise

• Turn in face of oncoming traffic

• Undue care and attention

• Inexper-ience/lack of expertise

• Road wet/ slippery

• Inexper-ience/lack of expertise

Movements

• Through minor road vehicles colliding with through major road vehicles

• Right-turn minor road vehicles colliding with through major road vehicles from the right

• Oncoming major road vehicles travelling through

• Right-turning vehicles from the major road

• N/A

Vehicle Types

• Motorcyclists as major road vehicles

• Possibly smaller vehicle types as minor road vehicles

• Motor-cyclists as oncoming vehicles

• Possibly articulated vehicles as rear vehicles

• Motor-cyclists

Weather Conditions

• Possibly wet weather

• Possibly wet weather

• None • Wet weather

Light Conditions

• Daylight • Darkness • None • Darkness

Geometry

• Four-leg intersections

• Minor legs with high approach speed

• High speed splitter islands for left-turns from the major road

• Type LSR, MNR and AUR turn treatments

• Possibly, Type LSL turn treatments

• Horizontal curves with a large decrease in speed

Part D

165

16 STATISTICAL MODELLING ISSUES

This chapter describes the various statistical modelling techniques used in the study.

Accident types within the Low Frequency Through accident category were not

analysed because they were deemed to be unaffected by the presence of the

intersection. Accident types within the High Frequency Through accident category

were analysed because it was desirable to determine the effect on single vehicle

accidents of introducing minor road approach curvature at rural intersections.

16.1 Analysis Process

The analysis process used to develop predictive equations for each accident category

was very iterative. The following steps describe this process, though many of the

early iterative steps have been omitted:

1. Identify potential exposure and propensity variables for each accident category

used in the preliminary analysis. Section 6.1 discussed methods that were used as

a framework for the selection of these variables. These variables are listed in


2. Identify all variables correlated at values of 40 percent or more. Apply the

methods developed in Section 16.2 to minimise the amount of correlation.

3. Identify appropriate relationships between each variable and accident rates as

discussed in Section 16.3.

4. Identify potential interactions between variables and consider methods to allow

for these interactions. This is discussed in Section 16.4.

5. Develop accident subcategories (if the data sample is large enough) and trial

different sets of variables. Perform a stepwise regression analysis using the

techniques discussed in Sections 16.5 and 16.6. Apply the techniques in Section

16.6 to reject all variables not forming reasonable relationships with accident

rates. Re-analyse with all of the original variables (excluding those forming

unreasonable relationships) until no more unreasonable relationships are found.

6. Undertake a series of diagnostic checks on the data by using the following

techniques discussed in Section 16.7. Use Cook’s Distance to identify any

outliers and check data input of these points for accuracy. Review plots of each

variable versus the Pearson Residuals. Trial different relationships for any

variables if indicated by the plots. Consider if there are any common factors

166

evident in the outlying residuals that have not been considered in the model.

7. Select any common factors identified in Step 6 as new variables and determine

their values for each data point. These variables form additional exposure or

propensity variables. This process may suggest the need for other methods of

sub-categorising the accident models. If this occurs, develop new categories as

appropriate.

8. Redo Steps 5 to 7 using the new variables identified plus any new categories of

the data as relevant. Repeat these steps until no additional variables can be

readily identified and no other practical methods of analysis become apparent.

Reject those variables recording little consistency across subcategories. Select

the best predictive model.

9. Perform a cross validation technique on the final model in Step 5, as described in

Section 16.8. Select this model as the best equation to identify influential

variables and their relationship to accident rates.

16.2 Correlation between Parameters

The variables selected using the procedure in Section 6.1 were initially used in the

regression analysis. It was quickly identified from the results that the effects of some

of these variables were opposite to that expected. This same result was found by

Vogt and Bared (1998) and Bauer and Harwood (1996).

A check of these variables found that most were correlated at levels 40 percent or

more with other variables. An expected reason for this high level of correlation is

that values of many geometric parameters chosen from road design standards are

often dependent on traffic volumes and 85th percentile speeds. Therefore, many of

the geometric parameters in these standards are expected to correlate these

parameters and each other. Examples of intersection standards in QDMR (2000)

relating geometric parameters to other parameters are given below:

• The type of turn treatment (provision of auxiliary lanes, right-turn slots etc)

chosen for an intersection depends on traffic volumes (may also depend on

existing accident rates).

• The length of auxiliary lane depends on 85th percentile speed.

• The minimum amount of sight distance depends on 85th percentile speed

• The required number of lanes depends on traffic volumes

167

Other parameters can be dependent on a greater number of parameters than those

above. As an example, the type and level of signage depends on 85th percentile

speed, available sight distance and existing accident rates.

Taylor and Young (1988) state that ‘…while correlation will result in one of the

correlated variables contributing little to the explanation offered by the data.

Attempts should always be made to overcome these problems’. To improve the

results of the regression analysis, it was found that variables correlated at values 40

percent or more could not be used simultaneously within each accident model. A

method to reduce the amount of correlation between variables in the study was

required. Methods considered and used to achieve this included the following.

Increase the Data Sample

In this method, the number of intersections with certain features would need to be

increased. An example of this is as follows. The variables ‘major road traffic flow’

and ‘median width’ were correlated at a level of 42 percent. Median width tended to

increase as traffic volumes increase.

To reduce the amount of correlation, a greater number of intersections with wide

medians but lower traffic volumes would be needed. Much more time and resources

would be required to adopt this method, which is outside the practical limit of this

study. Much time and effort was already placed into this study in an attempt to obtain

a wide range of values of particular variables as discussed in Section 4.1.

Creating Subcategories of Accident Types

If the data sample was of reasonable size, it was possible to divide the sample into

smaller subcategories such that the level of correlation was reduced or removed. The

dummy variable ‘driver recognition of an opposite minor leg’ (coded as DR4) and

‘number of legs at the intersection’ (coded as NLEG) were correlated at the 72

percent level.

By creating subcategories for through conflicts only, the variable NLEG was

considered in the creation of the subcategory ie only four-leg intersections were used.

This allowed the variable DR4 to be used in the analysis without the NLEG variable.

The disadvantage of this technique is that each subcategory contains lesser amounts

of data.

168

Mathematically Combining the Variables

Use Principal Components Techniques This method mathematically combines correlated variables into alternative variables

with lower correlation. The alternative variables are used in the regression analysis in

lieu of the original variables. For two correlated variables A and B, the two

alternative variables produced are as follows:

1) The average of the variables: (A+B)/2

2) The difference between the variables: A-B

This method was not found to be particularly successful. Often, the stepwise

regression would accept only one of the alternative variables. If it was the first

alternative variable listed above (the average), the result implied that each original

variable had an equal influence. This may well not be the case. If only the second

alternative variable above was selected (the difference), the result may well have not

produced a logical relationship with accident rates.

For these reasons, the method of using principal components was not adopted.

Using Other Methods of Mathematically Combining the Variables It was sometimes possible to use other techniques to mathematically combine two

variables into one alternative variable. An example of this was the major and minor

road speeds that were correlated at a level of 54 percent. Instead of allowing each as

a separate variable, they can be combined within the single variable ‘relative speed

between vehicles’. The statistical significance of the combined variable can be

compared to that obtained for each separate variable. Table 16.1 shows variables that

were combined by this procedure. The disadvantage with this technique is that the

relative effects of each variable were not known.

169

Table 16.1 - Combined Variables First Variable Second Variable/s and

Level of Correlation (%) Method of Combination

LIGHTS - Level of lighting on the minor road

LIGHTM - Level of lighting on the major road @ 68%

Create new variable LIGHT (level of lighting at the intersection) equal to the average of LIGHTS and LIGHTM.

SSAP - 85th percentile minor road approach speed

SMT - 85th percentile through speed on the major road @ 54%

Create new variable SR (relative speed between major and minor vehicles) calculated by the major and minor road speeds and the angle between vehicle paths

Creating New Variables

It was sometimes found possible to create new variables in place of one of the

correlated variables. An example of this is for the variables ‘speed environment on

the minor road’ (coded as SES) and ‘85th percentile minor road approach speed -

potential speed allowing for approach curvature, reductions in speed limit and other

features’ (coded as SSAP). These variables were correlated at the 90 percent level. The

new variables created were as follows:

• SRCS - the potential reduction in 85th percentile speed due to approach curvature

• SRSLS - the potential reduction in 85th percentile speed due to a reduction in

speed limit at the intersection

• SROS - the potential reduction in 85th percentile speed due to other features in

close proximity to the intersection

The variables then used in the regression analysis were SES, SRCS, SRSLS and

SROS. These variables were not highly correlated. However, this approach can only

be used when comparing variables with the same terms.

A potential problem with this approach is that the initial two variables were highly

correlated because of an inadequate range of data. The results may then be based on

only a small amount of data points. An example of this is if the variables SES and

SSAP were highly correlated because few minor road approaches contained approach

curvature, reduced speed limits or other features.

170

Trial each Variable Separately

This method places each correlated variable in a separate analysis. The variable

yielding the most statistically significant result may be considered the more

important variable. Where the variables have the same terms, this may be a

reasonable approach eg for the variables ‘SES’ and ‘SSAP’ as discussed in the

previous section. It may not be appropriate for other variables especially if it is

considered reasonable that one of these forms a fundamental relationship with

accident rates. This point is discussed in the next section.

Apply Primary and Secondary Variable Techniques

This technique was developed by the author. In this technique, two correlated

variables (at a level greater than 40 percent) were compared and a subjective decision

made as to which one was likely to have the most fundamental effect on accident

rates. This variable was labelled the Primary Variable and was used in the final

analysis. This variable often formed a logical relationship with accident rates even

when used with the other correlated variable in the regression analysis.

The other variable was labelled the Secondary Variable and was not included in the

final analysis. In the absence of the primary variable, this variable often formed a

logical relationship with accident rates. However, this variable usually gave a result

opposite to that expected, or was not significant when used with the primary variable

in the regression analysis.

The following were considered primary variables:

• Traffic volumes -These variables are fundamental because they are a measure of

exposure. Variables highly correlated with traffic volumes are treated as

secondary variables eg number of lanes.

• Speed - These variables are fundamental because they are based on the laws of

physics. Vehicles colliding at higher speeds will do more damage and are more

likely to be reported. Variables highly correlated with speed are treated as

secondary variables eg driver alertness.

• Particular geometric parameters - An example of this is the variables ‘presence

of a free left-turn lane’ and ‘minor road entry width’. These variables were

correlated at negative 45 percent. The presence of free left-turn lanes are usually

171

accompanied by a smaller minor road entry width. This is because the entry width

does not have to cater for left-turning vehicles. It is considered that the presence

of a free left-turn lane is the primary parameter in this case.

Table 16.2 shows secondary variables that were omitted from the analysis. Some of

these variables were measurements of a very similar factor to that for the primary

variables eg speed environment and speed limit.

A disadvantage of this technique was that it assumed the secondary variable did not

affect accident rates. Instead, the primary variable was assumed to take the full

effect. As no alternative techniques were known, it was considered that this method

would at least yield some indicative results by showing what likely effect the primary

variables were having on accident rates. Therefore, the results of these studies, at

best, are indicative only and are likely to only find major effects of the variables on

accident rates.

Such studies as this do not consider the effects of many other parameters (eg road

surface condition, position of the sun etc) that may have an effect on accident rates.

Should any of these parameters be highly correlated to the variables in this study,

different results may be obtained if data on these other parameters are used in the

regression analysis.

Discussion

As discussed previously, several variables correlated at levels 40% or more gave

unexpected or unreasonable results in this study. Expected reasons for such low

correlation levels causing problems in this study are given below.

There are 206 intersection sites and 907 accidents analysed in this study.

Approximately 85 variables have been identified for analysis. It is probable that there

are simply not enough sites or enough accident data to confidently predict the effect

of all 85 variables on accident rates.

172

Table 16.2 - Secondary Variables Omitted from the Regression Analysis Secondary Variable Primary Variable/s and level of

Correlation (%) General Effect on Using Secondary

Variable in the Accident Models SIGNS - Level of signage on the minor road

SSAP - 85th percentile minor road approach speed @ 42% RCS - Minor road classification @ 70%

Increase in SIGNS either had no effect on accident rates or increased accident rates.

SIGNM - Level of signage on the major road

SMT - 85th percentile major road through speed @ 54%

Increase in SIGNM either had no effect on accident rates or increased accident rates.

SMT - 85th percentile major road through speed

SSAP - 85th percentile minor road approach speed @ 54%

Increase in SMT had no effect on accident rates Sometimes, an increase in SMT decreased accident rates.

SLS - Speed limit on the minor road


Not undertaken - (1)

SLM - Speed limit on the major road

SMT - 85th percentile major road through speed @ 92%

Not undertaken - (1)

DAS - Level of driver alertness on the minor road


Sometimes DAS was important, sometimes SSA - (2)

DAM - Level of driver alertness on the major road

SMT - 85th percentile major road through speed @ 82% QM - Major road traffic volume @ 46%

Sometimes DAM was important, sometimes SSA - (2)

DRS - Driver recognition of the intersection from the minor road approach

NLEG - number of legs at the intersections @ 50%

Increase in DRS had no effect on accident rates

NLM - Number of lanes on the major road

QM - Major road traffic volume @ 73%. Sometimes NLM was important, sometimes QM, occasionally both.

WS - Entry width of the minor road

FLTLS - Presence of a free left-turn lane from the minor road @ -45%

Increase in WS had no effect on accident rates

WM - Width of the major road traffic lanes

NLM - Number of lanes on the major road @ 96% QM - Major road traffic volume @ 71%

Sometimes WM was important, sometimes NLM, sometimes QM.

WMED - width of the median on the major road

QM - Major road traffic volume @ 42% Increase in WMED had no effect on accident rates

LM - length of vehicle path on a horizontal geometric element of the major road

RM - vehicle path radius on a horizontal geometric element of the major road @ 48%

An increase in LM increased accident rates

fS - side friction used on the minor road horizontal element

RS - vehicle path radius on a horizontal geometric element of the minor road @ -84%

Not undertaken

fM - side friction used on the major road horizontal element

RM - vehicle path radius on a horizontal geometric element of the major road @ -74%

Not undertaken

∆SS - Decrease in 85th percentile speed on the minor road horizontal element

RS - vehicle path radius on a horizontal geometric element of the minor road @ -57%

Not undertaken

∆SM - decrease in 85 percentile speed on the major road horizontal element

RM - vehicle path radius on a horizontal geometric element of the major road @ -64%

Not undertaken

Notes: (1) It was considered that 85th percentile speed is a more appropriate measurement of actual speeds

than the speed limit. Some roads with high speed limits had low operating speeds. Some rural roads had no speed limits and had low operating speeds.

(2) It is considered that 85th percentile speed is a more appropriate measurement than driver alertness. Driver alertness was estimated using a very subjective model and is strongly correlated to 85th percentile speed.

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A study such as this is only likely to identify variables that have a major effect on

accident rates. For many of the other variables, a relationship is not likely to be

identified unless much more accident data is obtained and many more sites are

selected.

Obtaining more accident data alone is likely to be impractical because this study has

already maximised the analysis period for each intersection. Many intersections

change over time so there is little use in waiting another 10 years to gain additional

accident data.

Adding more intersection sites alone may not yield much better results. Bauer and

Harwood (1996) analysed 11,165 intersections but several results were still

unexpected or unreasonable. It is expected that the data must consist of a relatively

even spread of a widest possible range of the values of each the variables as

discussed in Section 4.1. This method may, however, still produce high levels of

correlation between some of the variables. To overcome this problem, sites with

particular features need to be added to the sample.

An example of this is the variables ‘major road median width’ (coded as WMED) and

‘major road traffic volume’ (coded as QM) that were correlated at the 42 percent

level. Wider medians tended to be found on higher volume roads. To lower the

correlation, more sites with wider medians need to be found on lower volume roads.

This may or may not even be feasible. This approach would need to be applied to

each variable with high levels of correlation.

It is envisaged that the results of this study can only be improved by adopting all the

principles used in this study, in addition to increasing the sample of intersections

with particular features. An experimental approach to the selection of these sites is

required. This approach must seek to maximise the range of data and minimise the

amount of correlation. Such an approach is probably outside the scope of what any

road authority could realistically afford.

16.3 Relationships between Variables and Accident Rates

As discussed in Section 3.3, the developed models have been based on identifying

appropriate forms of mathematical relationships between parameters. This is

important because not all of the variables may form the same types of relationships

with accident rates. Choice of an inappropriate relationship may show that an

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important variable does not significantly influence accident rates. For example, the

regression analysis revealed that visibility was not important in two cases until an

inverse function was used. Persaud, Lord et al (2002) states that ‘...the specification

of the mathematical form is not a trivial task’.

A general equation to meet these requirements is given by Equation 16.1.

A = k x Q1a x Q2

b x FPRi x FEXi x FINi x FPOi x….. Equation 16.1 Where A = accident rate (accidents per year)

k, a, and b are constants to be estimated

Q1 = first traffic flow variable

Q2 = second traffic flow variable (for multiple vehicle accidents only)

FPri = proportional function (refer below)

FExi = exponential function (refer below)

FIni = inverse function (refer below)

FPoi = polynomial function (refer below)

The following discusses how the various function terms above were selected for each

of the variables:

• Proportional (PR) - This function was used when the geometric or other variable

was expected to be proportional to the accident rate. Accident rates will approach

zero when the values of these variables approach zero. Examples of such variables

are 85th percentile speed and geometric element length in the single vehicle

accident models. This relationship is shown by the top left graph in Figure 16.1.

Equation 16.2 below refers to this relationship.

FPRi = GPRic Equation 16.2

Where FPri = proportional function

c = a constant

GPri = values of the particular variable

• Exponential (EX) - This function was used when the geometric or other variable

was expected to form an exponential relationship with the accident rate. The

accident rate will be unaffected when the values of these variables approach zero.

Examples of such variables are categorical and dummy variables. This

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relationship is shown by the top right graph in Figure 16.1. Equation 16.3 refers to

this relationship.

FEXi = exp(d GEXi) Equation 16.3 Where FExi = exponential function

d = a constant

GExi = values of the particular variable

• Inverse (IN) - This function was used when the geometric or other variable was

expected to form an exponential inverse relationship with the accident rate. The

accident rate will be unaffected when the values of these variables approach

infinity. An example of such a variable is sight distance. This relationship is

shown by the bottom left graph in Figure 16.1. Equation 16.4 below refers to this

relationship.

FINi = exp(e / GINi) Equation 16.4 Where FIni = inverse function

e = a constant

GIni = values of the particular variable

• Polynomial (PO) - This function was used when the geometric or other variable

was expected to form an exponential polynomial relationship with the accident

rate. The accident rate will be unaffected when the values of these variables

approach zero. An example of such a variable is horizontal curvature in the single

vehicle accident models. This relationship is shown by the bottom right graph in

Figure 16.1. Equation 16.5 below refers to this relationship for a second order

polynomial.

FPOi = exp(f GPOi2 + g GPOi) Equation 16.5

Where FPoi = polynomial function

f and g are constants

GPoi = values of the particular variable

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Substituting Equations 16.2 to 16.5 into 16.1 gives Equation 16.6:

A = k x Q1a x Q2

b x GPRic x exp(d GEXi) x exp(e / GINi) x

exp(f GPOi2 + g GPOi) x….. Equation 16.6

In order to analyse Equation 16.6, the dependent variable ‘A’ is made equal to the

number of accidents for a given time period ‘N’ rather than the rate of accidents/year.

Therefore, both sides of Equation 16.6 must be multiplied by the intersection

analysis period (T) as shown by Equation 16.7.

N = k x T x Q1a x Q2

b x GPRic x exp(d GEXi) x exp(e / GINi) x

exp(f GPOi2 + g GPOi) x….. Equation 16.7

where N = number of accidents over the intersection analysis period = A x T

T = intersection analysis period (years)

Before fitting, the model is transformed to the linear form by taking logs of both

sides of Equation 16.7 as shown below:

log(N) = log(k) + log(T) + a x log(Q1) + b log (Q2) + c log(GPRi) +

d GEXi + e / GINi + f GPOi2 + g GPOi +….. Equation 16.8

The term log(T) is assigned as the offset variable and its coefficient is forced to be

unity in the fitting process.

RDCT (2002) is a freeware program called ‘R’, which been used to perform the

statistical analysis in this study. The program is an integrated suite of software

facilities for data manipulation, calculation and graphical display, which includes

statistical analysis.

Using the standard LOG LINK function of the GLM command in R, the dependent

variable used is the number of accidents ‘N’ in Equation 16.8 rather than the log of

this variable. In this way, values of accident rates of zero can be used in the analysis.

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Proportional (PR) Exponential (EX)

00

K

1 00

K

0

0

K

0

0

K

Inverse (IN) Polynomial (PO)

Figure 16.1 - Relationships between Geometric and Other Variables and Accident Rates

Notes: (1) The polynomial function (PO) shows a second order polynomial. Higher order polynomials are

also possible. A = accident rate G = values of geometric and other variables k, a, b are constants

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16.4 Interaction between Variables

Some very complex interactions are likely to exist between the various parameters.

Interactions between variables occur when the effect of the variables on accident

rates does not follow an additive relationship as shown in Equation 16.8. An example

of this is for the variables ‘85th percentile minor road approach speed’ (coded as

SSAP) and ‘control type’ (coded as CONT). The effect of minor road approach speed

on accident rates may be different for the various control types eg stop or give way.

Therefore, there may be an interaction between approach speed and control type.

One way to address interactions between variables is to add a multiplicative

component of the parameters to Equation 16.8 (up to a three-level interaction was

initially used in the study). This technique explained a considerable proportion of the

variability in the data. However, it produced the following disadvantages:

• The model is much more complex

• The transformation of Equation 16.8 back to Equation 16.6 is more difficult.

• The model is less easily understood by practitioners, particularly when two or

more continuous variables are combined.

• Many of the results were illogical.

For the above reasons, adding a multiplicative component of the variables to

Equation 16.8 to address interactions was not undertaken.

As discussed in Section 3.3, there is probably far too little data to enable

identification of all interactions. It is probable that a study such as this will only

identify major interactions between parameters.

If interactions between parameters were considered likely (eg whether minor road

approach speed has a different effect on accident rates at T-intersections than at

cross-intersections), alternative methods of allowing for the interaction were used.

These include the following:

• Creating dummy variables. An example of this was for an interaction between

the variables ‘number of stand-up lanes on the minor road’ and ‘conflict type’ in

the ‘CONT’ Angle-Minor vehicle accident model. For some conflict types within

this accident type, a greater number of stand-up lanes on the minor road will

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potentially result in increased restrictions to visibility for some drivers due to

adjacent vehicles. However, this was not the case for one conflict type.

A dummy variable was created to allow for this interaction. This dummy variable

was ‘number of adjacent stand-up lanes on the minor leg in the direction of the

major leg relevant to the particular conflict’. This dummy variable was used in

lieu of the variable ‘number of stand-up lanes on the minor road’.

• Combining variables. An example of this was for the variables ‘Sight Distance’

and ‘Speed’. These two variables would logically interact. A given value of sight

distance would be expected to yield a higher accident rate on a high-speed road

than a low speed road. This is because the time available to react and take an

evasive action manoeuvre is less on the higher speed road.

Combining the variables into the variable ‘time’, by dividing the sight distance by

the speed, allows for this interaction. This assumes that the interaction between

sight distance and speed is inversely proportional. This is considered a reasonable

assumption given the available amount of data.

• Dividing the Accident Data into Subcategories. This technique involved

applying the validation technique ‘Dividing the Accident Data into Subcategories’

as discussed in Section 16.8. This technique divides the accident data into

subcategories based on various values of a particular variable and checking the

consistency of the results across the subcategories. Usually, this is only possible

for the major accident types with larger data samples.

16.5 Regression Techniques

Regression Techniques in Previous Studies

Section 2.1 has documented several regression techniques that have been used to

analyse accident data at intersections. Studies up to the early 1980’s were more likely

to have used stepwise multiple linear regression analysis techniques that assume

normal distribution of data. Later studies have tended to assume non-normal

distributions, especially the Poisson distribution. Use of negative binomial models

and lognormal models are also common.

The use of the Poisson distribution is only relevant where the variance in the accident

data is equal to the mean. Over-dispersion, which occurs when the variance of the

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accident-frequency data is greater than its mean, can result in biased model

coefficients and erroneous standard errors. Some authors identified in the literature

review have used negative binominal distributions to overcome the over-dispersion

concern. Other authors used a ‘quasi-likelihood’ method to take into account of the

over-dispersion in the presence of low mean values.

Some authors identified in the literature review have used other approaches to the

analysis of accident data eg ‘a grouping and classification technique called

Classification and Regression Tree’. In addition, other techniques are available eg

GAM, Artificial Neural Networks and hierarchical models. Harwood, Council et al

(2000) used a combination of elements of multiple techniques to produce an accident

prediction algorithm.

Regression Techniques Adopted for this Study

Initially in this study, Poisson techniques were used to analyse the various accident

categories. Poisson techniques were performed using the ‘GLM’ command in the

software package ‘R’ by setting the ‘family’ category in the command to ‘Poisson’.

Each model developed was then tested for over or under-dispersion by undertaking a

Chi squared test. The degrees of freedom of the residual deviance of a given model

defined a confidence interval (5 and 95 percentile values used) for the acceptable

residual deviance of a Poisson GLM.

If the upper and lower limits of the confidence interval were not exceeded, the data

was deemed to be acceptably dispersed for analysis with a Poisson GLM. In this

case, the results of using the Poisson techniques for the particular data sample were

adopted in the final results.

If the upper limit of the confidence interval was exceeded, the data was deemed over-

dispersed. In this case, negative binomial techniques were applied using another

parameter ‘theta’ that expressed the degree of over-dispersion. To estimate theta, the

method in Section 7.4 of Venables and Ripley (1999) was adopted. This compares

the mean predicted by an ordinary Poisson GLM to the input data. Once theta has

been estimated, another GLM can be fitted from the negative binomial family using

the estimate of theta.

If the lower limit of the confidence interval was exceeded, the data was deemed

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under-dispersed. Analysis of under-dispersed data is much more difficult than for

non under-dispersed data. A distribution that describes both over and under-

dispersion is the Double Poisson. Experiments with Jim Lindsey’s generalised non-

linear regression library in the software package ‘R’ were undertaken on particular

under-dispersed data samples. Unfortunately, this did not give useful results.

Jim Lindsey was contacted regarding this issue. He advised that a Double Poisson

could not properly describe the type of under-dispersion in the data. Because no

acceptable methods for accounting for the under-dispersion in this data were

identified, the final equations for the under-dispersed data samples were analysed by

simply using a Poisson distribution as for the acceptably dispersed data.

Dispersion of Data in this Study

Using the method of testing for dispersion discussed in the previous section, many of

the final accident models in this study were found to be under-dispersed. This is a

different result to that found by several authors identified in the literature review,

who found that accident counts are usually over-dispersed eg Hauer (2001). It was

seen that greater levels of categorisation (ie dividing the data sample into smaller

subsets) increased the levels of under-dispersion. The large number of under-

dispersed data samples in this study was reflecting the degree of categorisation used.

Because no suitable methods of allowing for the under-dispersion in the data were

identified, the standard errors within the final accident models (those that were

under-dispersed) were inaccurate. However, when the larger accident types with

over-dispersed or non-dispersed data were divided into smaller, under-dispersed

accident subcategories, similar estimates were obtained for most variables. For the

Rear-End-Major vehicle accident model, the maximum differences in values of the

estimates was only four percent. It is therefore not expected that the results will be in

error to any large degree.

The only way to avoid the under-dispersion problem is to extend the analysis periods

or combine particular accident categories into larger categories. The first method was

impractical in this study because the analysis period for each intersection was already

maximised. The second method produces problems in that particular variables

relevant to an original accident category will not be relevant to all accident types in

the larger accident category. This issue was discussed in Section 5.3. The accident

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data was divided into smaller subsets originally to avoid this problem. Unfortunately,

it creates the problem with under-dispersion.

It is considered that the advantages of creating the smaller accident subcategories

significantly outweigh the disadvantages.

16.6 Acceptance and Rejection of Parameters from the Regression Analysis

The fit of a model can always be improved by increasing the number of parameters.

A model with too many parameters, however, is poor at predicting new points. In

addition, a greater number of parameters can lead to a greater number of

unreasonable relationships being produced the model. For this reason, it is desirable

to penalise complexity. A process that does this is the ‘Akaike Information Criterion’

(AIC) as defined in Sakamoto, Ishiguro et al (1986) and Venables and Ripley (1999)

and. An equation for AIC is given in the following equation.

AIC = - deviance + 2 x N Equation 16.9

Where N = the number of parameters used

deviance = -2 maximised log-likelihood

To select the most important parameters for each accident model of this study, the

‘StepAIC’ command in the software package ‘R’ has been used. This command

automates the process of stepwise selection. Both forward and backward selection

using StepAIC have been selected.

The forward analysis considers adding to the model from a list of variables to

minimise the AIC. The backward analysis considers dropping variables from the

model in order to minimise the AIC. By selecting forwards and backwards, the best

possible model is identified as defined by the AIC.

One problem with stepwise regression analysis is that it only selects one model for

each data set. In reality, though, the best model (the one which gives the most

practical and logical result) may not necessarily be the one that minimises the AIC.

Other models with a slightly higher AIC may give a more practical and logical result.

For this reason, the following techniques were used to explore various other models

to see if a reasonably consistent result was obtained:

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• Dividing the accident data into subcategories (for the larger accident categories)

and comparing the results (refer Section 16.8). Variables recording little

consistency across the subcategories were rejected.

• Using alternative sets of variables. It is possible to measure a particular geometric

feature/s in several ways. This produces alternative sets of variables. The results

of an analysis can vary significantly depending on what set of these variables are

used. This was identified in the alternative Single-Through vehicle accident

models and is discussed in Section 20.4.

Outcomes of the Application of the Stepwise Regression

Applying the stepwise regression analysis to the various accident types produced the

following scenarios:

• Scenario 1 - Some variables did not explain much of the variability in the data.

The stepwise regression analysis removed these from the model.

• Scenario 2 - Some variables explained a significant amount of variability in the

data. The stepwise regression analysis kept these in the model. These parameters

may or may not be significant at the five percent level. Either of the following

results were found to apply to these variables:

Result 1 - The variables selected by the StepAIC process yielded logical or

reasonable results eg an increase in traffic volume produced an increase in

accidents.

Result 2 - Sometimes, the variables selected by the StepAIC process yielded

illogical or unreasonable results (according to the assumptions made in the next

section of this thesis) eg stop signs produce more accidents than give way

signs, higher speeds produce lower accident rates.

Techniques used in this study for dealing with the above scenarios are given below:

• For Scenario 1, the rejection of the variable by the StepAIC process was accepted

unless there were strong reasons why the variable should be selected eg the

variable was a primary variable eg traffic volume. In the latter case, other

variables and combinations of variables were used in subsequent models to see if

any of these alternative models produced an expected result.

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• For Scenario 2, Result 1 - The inclusion of the variable into the model by the

StepAIC process was accepted.

• For Scenario 2, Result 2 - The variable forming the illogical or unreasonable

relationship was rejected. This included variables that formed an opposite

relationship to that found in several previous studies. This scenario occurred quite

commonly for particular variables as discussed in the next section.

Variables Forming Illogical or Unreasonable Relationships with Accident Rates

Most variables forming illogical or unreasonable relationships with accident rates

were those as follows. Very few variables (other than those listed below) recorded

unexpected results.

• Those variables strongly correlated with other variables. This was especially true

for variables that were correlated at levels 40 percent or above. A method to

reduce the amount of correlation between variables in the study was required.

Methods considered and/or used to achieve this have been discussed in Section

16.2.

• Those variables most likely to be upgraded at an existing unsignalised intersection

to improve safety. These include the following:

Level of control (replacement of a give way sign by a stop sign)

Number of control signs (addition of a central median with an additional stop

sign)

Level of lighting (addition of lighting at the intersection)

The results for these variables are probably reflecting the fact that these measures

are often used at the more dangerous intersections in an attempt to reduce accident

rates. Given this scenario, a multi-factor study is not likely to enable appropriate

causal relationships between such parameters and accident rates to be inferred.

Instead, multi-factor studies probably give the most reliable result for parameters

that are not easily changed eg angle of the intersection, level of sight distance,

number of legs etc. It is interesting to note that in Table 2.2, most studies which

identified logical relationships for the above parameters were either ‘before and

after’ or ‘matched group’ studies. They were not ‘multi-factor’ studies.

The accuracy of the results of this study is only as good as the accuracy of the

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assumptions made. This thesis has adopted several approaches to arrive at the final

result and each approach makes certain assumptions (as documented in this thesis).

One of these assumptions is the rejection of variables based on unreasonable or

illogical relationships. Unless a logical mechanism can be established as to why the

variable should affect accident rates in the particular way, the result was rejected.

Such assumptions made in this study include the following. Accident rates cannot

decrease with the following:

• An increase in speed

• An increase in traffic volumes

• By less advance warning and intersection signage

• By using a give way sign in lieu of a stop sign

• A decrease in the level of intersection lighting

• A decrease in the available sight distance

If any of the above assumptions are wrong, then the corresponding accident model

will be suspect.

16.7 Diagnostic Checks

There are various diagnostic checks available for detecting outliers in the data. In this

study, the following methods have been used.

Cook’s Distance

Plots of Cook’s Distance were generated to detect outliers that were unduly

influential on the model. Input data for all of the furthest outliers were checked for

accuracy and amended if necessary.

Pearson Residuals

Pearson residuals are residuals that have been standardised ie given a mean of zero

and a standard deviation of one. Plots of Pearson Residuals versus each data point

were generated to detect if there were any common factors evident in the outliers that

have not been considered in the model. If factors were identified, these were selected

as new variables and their values determined for each data point. Subsequent

analyses used these variables.

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Plots of the Pearson Residuals versus the values of each variable were also

generated. The shape of the graphs in each of these plots was used for determining

whether alternative relationships may be more appropriate. If indicated, subsequent

analyses used these alternative relationships.

16.8 Validation of the Accident Models

Sections 16.2 and 16.6 have shown that unreasonable or illogical results can be

obtained in the regression analysis. In addition, the best accident models will still

have large amounts of unexplained variability. For these reasons, the findings need to

be validated. Two method of validating the accident models have been performed for

this purpose and are discussed below.

Dividing the Accident Data into Subcategories

This method consisted of dividing the accident types into subcategories based on the

values of particular variables. The results of applying a stepwise regression analysis

across the subcategories were reviewed for consistency. This was usually only

possible for the major accident types with larger data samples.

If the results for a particular variable were inconsistent across the subcategories, the

variable was rejected. In some cases though, an individual subcategory may be

adopted as the final accident model eg where a logical interaction between variables

occurred. Where relatively consistent results were obtained, the original larger

accident model would usually be adopted. Inconsistent results were deemed to be as

follows:

• Where a variable was significant in less than half of the accident subcategories

• Where the estimates of a variable where much different across the accident

subcategories

Cross Validation Using 90 Percent of the Data

Cross validation comprises removing a number of observations from the data sample

and attempting to predict these using the remaining data. The degree of validation is

the closeness of the predicted results to the omitted observations. This method of

validation was not particularly useful in this study because the final accident models

are poor predictors of accident rates. Reasons for the poor predictive ability are given

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below:

• There are many other factors influencing accidents at unsignalised intersections

that are not considered in this study. These include factors specific to local areas.

• The study comprises a limited amount of accident data. This has been discussed in

Section 3.1.

• The study comprises a limited number of sites. This has also been discussed in

Section 3.1.

The purpose of the final accident models is not to predict accident rates for a

particular location. Rather, they are explanatory models that are used to identify the

effect of particular variables on accident rates. They can, however, be used to

determine if recorded accident rates at particular intersections are similar to those

that could be expected or whether local factors are influencing the accident rates.

Because of this, a different cross validation technique to the traditional one was

required.

A criticism of stepwise regression methods is that there is an element of uncertainty

in the way the procedure selects the best model. To test for this lack of stability, the

cross validation technique used in this study consisted of randomly removing ten

percent of the observations and applying a stepwise regression procedure to select

variables. This procedure was repeated 100 times and a record was made of the

number of times that each variable from the original model was selected. For a

variable to be recorded, the sign of the estimate must be the same. The number of

times that a particular variable was selected was a measure of the confidence that

could be placed in the result. The following subjective measure was chosen:

• Variable selected in greater than 94 percent of cases - high level of confidence and

stability

• Variable selected between 90 and 94 percent of cases - moderate level of

confidence and stability

• Variable selected in less than 90 percent of cases - lower levels of confidence and

stability

Less stable variables (those recorded in less than 90 percent of cases) are often the

result of limited number of data points in the sample.

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The purpose of applying this method of model validation was to record the level of

confidence in the final result, rather than influence the result as per the previous

method of validation. Therefore, all variables in the final models have been retained,

regardless of their stability.

The regression analysis techniques discussed in this chapter are now applied to the

accident types identified in Section 5.3. This is given in the following five chapters.

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17 ANGLE-MINOR VEHICLE ACCIDENTS

This chapter presents the results of applying the regression analysis techniques

described in Chapter 16 to the Angle-Minor vehicle accident category.

17.1 Categorisation of the Data

The 466 Angle-Minor vehicle accidents recorded were categorised according to the

following criteria:

• LegT - Angle-Minor vehicle accidents per minor leg for T-intersections only -

sample size 155 accidents and 143 minor legs.

• Leg - Angle-Minor vehicle accidents per minor leg - sample size 465 accidents

and 269 minor legs.

• Individual Conflicts - Angle-Minor vehicle accidents per major conflict type per

minor leg. This contained the major conflict subcategories LRT, TLT, TRT, RLT,

and RRT (refer Figure 9.7 for these conflict types). Sample sizes are as follows:

LRT - comprised 13 accidents and 269 conflict points

TLT - comprised 121 accidents and 126 conflict points

TRT - comprised 83 accidents and 126 conflict points

RLT - comprised 35 accidents and 269 conflict points

RRT - comprised 189 accidents and 269 conflict points

(25 accidents were not included in the above accident subcategories because

they were either unknown movements or were minor conflict types)

• CONT - Angle-Minor vehicle accidents per major conflict type per minor leg for

T-intersections only. This is the addition of all the accident subcategories listed

under ‘Individual Conflicts’ above for T-intersections- sample size 144 accidents

and 429 conflict points.

• CON - Angle-Minor vehicle accidents per major conflict type per minor leg. This

is the addition of all the accident subcategories listed under ‘Individual Conflicts’

above - sample size 441 accidents and 1059 conflict points.

17.2 Variables Selected for Analysis

Variables for each accident type have been selected by the technique in Section 6.1.

The variables selected by this technique for the Angle-Minor accident categories are

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shown in Table 17.1. For more information on these variables, refer Appendix C -


17.3 Results of the Regression Analysis

Table 17.2 shows the results of applying the regression analysis techniques discussed

in Chapter 16 to the Angle-Minor vehicle accident subcategories. Table 17.3 shows

the significance of alternative variables used in the analysis.

Comparison Between Models

Table 17.2 shows that the following variables are significant across a majority of the

accident subcategories in which they were used:

• Traffic flow from the minor leg (QSi)

• Traffic flow from a major leg (QMi)

• Speed environment of the minor road (SES)

• Visibility from the minor road to the major road measured in time (Ti)

• Driver recognition of an opposite minor leg (DR4)

• Number of stand-up lanes on the minor road (NLS)

• Observation angle (θi) - one subcategory gave an opposite result

• Level of perception of the backdrop of the intersection (BACK) - T-intersections

only

The variable ‘presence of queuing through the intersection’ was only significant for

one of the conflict types. Several accidents in the Crash Incident Reports highlighted

extended queues through the intersection for this same conflict type.

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Table 17.1 - Variables and Function Types for Angle-Minor Vehicle Accidents Variable

Code Variable Description Function

Types (1) QSi Traffic flow from the minor leg PR QMi Traffic flow from a major leg PR SES Speed environment of the minor road EX

SRSLS Potential reduction in 85th percentile speed on the minor leg due to a reduction in speed limit (used if SES is important)

EX

SROS 85th percentile speed reduction on the minor road due to devices near the intersection (used if SES is important)

EX

SRCS 85th percentile speed reduction on the minor road due to approach curvature (used if SES is important)

EX

SSAP 85th percentile minor road approach speed EX SRi Relative speed between major and minor road vehicles

for the particular conflict PR

TSAP Approach visibility on the minor road measured in time IN Ti Visibility from the minor road to the major road

measured in time IN

TiI Visibility from the minor road to the major road measured in time with a maximum value to the next signalised intersection

IN

RCS Classification of the minor road EX RCM Classification of the major road EX

LIGHT Average level of lighting at the intersection EX CONT Level of control on the minor road EX

NCONT Number of control signs EX NLEG Number of legs at the intersection EX DR4 Driver recognition of an opposite minor leg EX

BACK Level of perception of the backdrop of a T-intersection EX FOV Field of view EX

FLTLS Presence of a free left-turn lane from the minor road EX RSL Vehicle path radius of the left-turn from the minor road EX NLS Number of stand-up lanes on the minor road PR NLSi Number of adjacent stand-up lanes on the minor leg EX

θi Observation angle PO CMi Curvature of the major road EX

DHL Distance from the holding line to the continuity line EX QUEi Presence of queuing through the intersection on a multi-

lane road. EX

CONF Conflict Type - LRT, TLT, TRT, RLT, or RRT Factorial variable

Note: (1) Refer to Section 16.3 for the function types shown in the third column.

192

Table 17.2 - Results of the Regression Analysis for Angle-Minor Vehicle Accidents Accident Subcategory Variable

LegT Leg LRT TLT TRT RLT RRT CONT CON QSi ***

QSA *** QSA

** QSL

*** QST

*** QST

*** QSR

*** QSR

*** QSM

*** QSM

QMi *** QMA

*** QMA

N QMT

# QMT

N QMT

o QMT

*** QMT

*** QMT

*** QMT

SES o *** N # ** ** *** N *** SROS - N - N N N N - N SRSLS - N - N * N # - N SRCS - N - N N N N - N TSAP N C R R C N N N N

Ti * TR

* TR

N TR

# TL

N TR

N TL

* TR

o Ti

* Ti

RCS C C N R R N C R R RCM N C N C R N N C N

LIGHT R N R R N N R R R CONT N R N N R R C C R

NCONT R R R R N N R R R NLEG - *** R - - C N - - DR4 - - - # o - - - ***

BACK *** - - - - - - *** - FOV R R N R N N R R R

FLTLS - - N - - - - - - RSL - - N - - - - - -

NLS/NLSi * NLS

*** NLS

** NLSi

# NLSi

** NLSi

N NLSi

- NLSi

N NLSi

* NLSi

θi N θRRT

N θRRT

N θLRT

# θTLT

R θTRT

# θRLT

** θRRT

** θi

* θi

CMi N CMSA

R CMSA

C CMSR

C CMSL

R CMSR

C CMSL

R CMSR

N CMSi

R CMSi

DHL N C C R N N N N N QUEi N C - C * - N N N CONF - - - - - - - V V

Notes: *** = significant at the 0.1% level ** = significant at the 1% level * = significant at the 5% level o = significant at the 10% level # = not significant at the 10% level but explained enough of the variability in the data to be retained

through a StepAIC process N = not significant at the 10% level and did not explain a significant amount of variability in the

data to be retained through a StepAIC process R = explained a significant amount of variability in the data. However, the sign of the constant was

opposite to that considered to be a reasonable result or a logical mechanism could not be identified which explained why this variable was significant. The variable was therefore rejected.

C = explained a significant amount of variability in the data. However, the variable was rejected because of inconsistency across the subcategories.

V = significance varies for the terms within this factorial variable - = not applicable for the accident category

193

Table 17.3 - Alternative Variables for Angle-Minor Vehicle Accidents Accident Subcategory Orig.

Var-iable

Alter-native Var-iable

LegT Leg TLT TRT RLT RRT CONT CON

SEs SRi - - N L L L L L SES SSAP - L N G L L G L QSi QSA - - L L - - - - Ti TiI - - L

(TLI)- - L

(TRI) L L

(TiI) Notes: G = the alternative variable explained a greater amount of the variability in the data than did the original variable. L = the alternative variable explained a lesser amount of the variability in the data than did the original variable. N = the alternative variable was not significant - = not applicable for the accident category / not undertaken

Selected Accident Model

The ‘Leg’ accident model is not considered the best model because some of the

variables used were appropriate to a particular conflict or movement type, rather than

the minor leg as a whole. An example of this is the visibility terms. The creation of

additional dummy variables can help mitigate this problem for some of the variables.

For other variables, however, it is much more difficult.

The overall conflict model (CON) is considered the best model to predict Angle-

Minor vehicle accident rates. This model is relatively large (compared to the other

accident subcategories) in that it comprises most of the Angle-Minor accident data.

This is a desirable feature in order to avoid sub-dividing the data into samples that

become too small. This in turn increases the risk that an inadequate amount of data

exists in each sample to be confident of the result.

Although the model is relatively large, it is flexible enough to consider the various

major conflict types and parameters only relating to particular conflict types. It is

important that this flexibility is provided, especially for the traffic flow variables

relating to each conflict type. This is for the following reason. A minor road with a

high proportion of left-turn vehicles is likely to record a low accident rate compared

to a minor road with a high proportion of through and/or right-turning vehicles. This

is because of the low number of accidents occurring to left-turning minor road

vehicles. The overall conflict model (CON) allows for this by incorporating the

factorial variable ‘conflict type’.

194

This model assumes that several interactions between parameters are the same. By

combining all the individual major conflicts into the one model, it is assumed that

traffic flow, minor road speed, number of stand-up lanes, and visibility terms form

the same relationship with Angle-Minor vehicle accidents for each conflict type. In

addition, because both three and four leg intersections were included in the model, it

assumes that these variables will form the same relationship with Angle-Minor

vehicle accidents, regardless of the number of legs of the intersection.

With the following exceptions, it was considered that this is a reasonable approach,

given the amount of data available. It was anticipated that the minor road speed

might form a different relationship at four leg intersections than at three leg

intersections. For this reason, the significant variables in the overall conflict model

(CON) were placed in a stepwise regression analysis using the data for the three-leg

intersection conflict model (CONT). This analysis showed that the minor road speed

was also a significant predictor of Angle-Minor vehicle accidents and the estimate of

the power constant was very similar to that for the overall conflict model.

The overall conflict model (CON) also assumed that the accident rate for individual

conflict types common to both three and four leg intersections (LRT, RLT and RRT)

will not be dependent on the number of legs at the intersection. It was originally

anticipated that these conflict types would record higher accident rates at four leg

intersections than at three leg intersections. However, Table 17.2 shows that this was

true only for the conflict type ‘RLT’, which comprised a relatively small accident

sample. The conflict type ‘LRT’, which also comprised a small data sample, gave an

opposite result. By far the largest conflict type was ‘RRT’ for which the number of

legs was not a significant predictor of accident rates. These results suggest that

accident rates for these conflict types are not overly dependent on the number of legs

at the intersection.

Due to the relatively consistent results above, it was considered appropriate to

combine both three and four leg intersections into the overall conflict model (CON).

Table 17.3 shows that the alternative variable ‘85th percentile minor road approach

speed’ was a more significant predictor of Angle-Minor vehicle accident rates for

two accident subcategories than the original variable ‘speed environment of the

minor road’. For other accident subcategories, an opposite result was obtained.

195

Only one of these variables can be chosen in the final accident model. When

considering all of the accident types in this study, the speed variables that allowed for

reductions in speed limit and curvature were more significant in a majority of cases

than the speed environment variables. For this reason, and for reasons of consistency,

it was decided to place into the final accident models the speed variables that allowed

for reductions in speed limit and curvature, rather than the speed environment

variables.

The results of the regression analysis for the ‘CON’ accident subcategory are shown

in Table 17.4. This model uses the alternative variable ‘85th percentile minor road

approach speed’.

Table 17.4 - Regression Analysis Results for the ‘CON’ Accident Subcategory

Variable Estimate Standard Error

Pr(>|z|) Cross Validation

(1) k -13.7 0.879 <2E-16 100

log(QSM) 0.771 0.0464 <2E-16 100 log(QMi) 0.292 0.0580 4.70E-7 100

SSAP 0.0125 0.00278 6.40E-6 100 Ti 1.95 0.960 0.0423 84

DR4 0.330 0.0996 0.000915 100 NLSi 0.416 0.171 0.0147 92

θi 0.00750 0.00370 0.0423 88 CONF - TLT 3.18 0.382 <2E-16 - CONF - TRT 2.84 0.400 1.22E-12 - CONF - RLT 1.50 0.368 4.78E-5 - CONF - RRT 3.34 0.360 <2E-16 -

Notes: (1) The values in the last column are the number of times out of 100 that each variable was selected

by a StepAIC process using 90 percent of the data (refer Section 16.8). (2) The lower bound of the confidence interval for deviance is 958 for 1046 degrees of freedom at

the 2.5% level using a Chi-squared test. As the residual deviance is 884, the data is somewhat under-dispersed.

(3) The mean recorded accident rate (number of accidents per year per conflict) = 0.0785 The mean predicted accident rate = 0.0781 The mean error in accident rate = 0.0856 (1.09 x average recorded accident rate)

The selected Angle-Minor vehicle accident model ‘CON’ is given by Equation 17.1.

AAS = 1.10 x 10-6 x QSM0.771 x QMi

0.292 x exp(0.0125 x SSAP + 1.95 / Ti

+ 0.330 x DR4 +0.416 x NLSi + 0.00750 x θi + CONF) Equation 17.1

196

where AAS = number of Angle-Minor vehicle accidents per year per minor leg per

conflict type

QSM = turning traffic flow from the minor leg for the particular conflict -

refer Table C1 of Appendix C - Geometric Variables. The constant

‘m’ = 0.16 (veh/d)

QMi = through traffic flow on the major leg for the particular conflict (veh/d)

SSAP = 85th percentile minor road approach speed - refer Table C5 of

Appendix C - Geometric Variables (km/h)

Ti = Visibility (measured in time) from the minor road to vehicles on the

major leg relative to the particular conflict - refer table C8 of

Appendix C - Geometric Variables (s)

DR4 = Driver recognition of an opposite minor leg - dummy variable - refer

Table C15 of Appendix C - Geometric Variables

NLSi = number of adjacent stand-up lanes on the minor leg for the particular

conflict - refer Table C10 of Appendix C - Geometric Variables

θi = Observation angle for the particular conflict - refer Table C14 of

Appendix C - Geometric Variables (degrees)

CONF = conflict type - dummy variable (0 for a LRT conflict, 3.18 for a TLT

conflict, 2.84 for a TRT conflict, 1.50 for a RLT conflict, 3.34 for a

RRT conflict)

17.4 Discussion of the Regression Analysis Results

The selected accident model ‘CON’ gives the following results.

Traffic Flow

The Angle-Minor vehicle accident rate is a function of the minor road traffic flows to

a power of 0.77 and the major road traffic flows to a power of 0.29. These values are

consistent with the results of previous studies discussed in the literature review in

Section 2.5. In the review, the range of values for the minor road flows varied from

0.58 to 0.83. For the major road, these values varied from 0.26 to 0.46.

In accordance with Table C1 in Appendix C - Geometric Variables, the variable

‘turning traffic flow from the minor leg’ is calculated as follows:

• QSL (the left-turn volume from the minor leg) for a LRT conflict

197

• QST + m x (QSL+QSR) for TLT and TRT conflicts, where m is a constant and QST

is the through traffic volume from the minor leg.

• QSR (the right-turn volume from the minor leg) for RLT and RRT conflicts

The QSL and QSR terms (left and right-turn volume from the minor road respectively)

were included for the TLT and TRT conflicts (conflicts involving through

movements from the minor road) for the following reason. Some cross intersections

in the study that comprised very low through volumes from the minor road (ie high

proportions of left or right-turns) recorded high rates of TLT and TRT conflicts.

It is probable that the drivers involved in these accidents wanted to turn at the

intersection but did not perceive the intersection adequately and drove straight

through it. Therefore, the rates of the TLT and TRT conflicts will not simply be

related to the through traffic counts only, but also on some portion of the turning

volumes. This portion was made equal to the constant ‘m’.

The constant ‘m’ was calculated by an iterative process. Estimated values of ‘m’

were used and the stepwise process (discussed in Section 16.6) was undertaken to

record each subsequent AIC value. The estimate of ‘m’ that gave the lowest AIC

value was adopted. Logically, the value of ‘m’ would be between zero and one. The

iterative process showed that a value of 0.16 produced the lowest AIC.

This result indicates that 16 percent of TLT and TRT conflicts may be occurring to

drivers that should have turned at the intersection, but drove straight through. As

stated above, these drivers probably did not perceive the intersection in time to

undertake the required action.

Speed Parameters

Minor Road Speed This model shows that an increased 85th percentile minor road approach speed will

increase the Angle-Minor vehicle accident rate. A plot of the standardised Angle-

Minor vehicle accident rate (accident rate of one at an approach speed of zero) versus

the minor road approach speed is shown in Figure 17.1. From this figure, a minor

road approach speed of 110km/h will record an accident rate 1.6 times higher than a

70km/h approach speed.

198

0

1

2

3

4

5

6

7

8

9

0 20 40 60 80 100 120Minor Road Approach Speed (km/h)

Stan

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Veh

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Acc

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Estimate

Figure 17.1 - Effect of the 85th Percentile Minor Road Approach Speed on the Angle-Minor Vehicle Accident Rate

When considering all the accident types in this study, the speed variables that

allowed for reductions in speed limit and curvature were more significant in a

majority of cases than the speed environment variables. For this reason and for

reasons of consistency, it was decided to place into the final accident models the

speed variables that allowed for reductions in speed limit and curvature, rather than

the speed environment variables.

The 85th percentile minor road approach speed (which allows for curvature and

reductions in speed limit) has been used in the final Angle-Minor vehicle accident

model in lieu of the speed environment for this reason. There are simply not enough

data in the study (sites with approach curvature and reductions in speed limit) to

accurately determine which speed variable is more important or whether a particular

combination of these variables produces the most significant result.

It is possible that the speed reduction devices at intersections in the study have been

retrofitted at intersections with poor safety records. If this were true, it would offset

any potential benefits of these devices.

The choice of ‘85th percentile approach speed’ or ‘speed environment’ in this model

makes a significance difference as what measures will potentially reduce the Angle-

Minor vehicle accident rate. The selected variable ‘85th percentile approach speed’

indicates that approach curvature, rumble strips, and a reduction in speed limit on the

199

minor road will potentially reduce speeds and lower the Angle-Minor vehicle

accident rate. These measures are not likely to reduce the speed environment to any

large degree. Instead, the speed environment will likely be affected only by a

reduction in the desired driver speed achieved by the following:

• A reduction in speed limit; and

• A change in roadside environment eg rural to urban, a topography change; and/or

• A change in the standard of horizontal curvature over a significant length of the

roadway.

Therefore, the placement of either ‘85th percentile approach speed’ or ‘speed

environment’ into the final model makes a significant difference as to what devices

will potentially lower minor road speeds and reduce the Angle-Minor vehicle

accident rate. As previously stated, there is simply not enough data in the study (sites

with approach curvature and reductions in speed limit) to determine accurately which

speed variable is more important or whether a particular combination of these

variables produces the most significant result.

Therefore, the results of this study can only conclude the following:

• A lower minor road speed will produce a lower Angle-Minor vehicle accident

rate.

• The magnitude of the effect of speed reduction devices such as speed limit

reduction and approach curvature is uncertain.

Major Road Speed The major road speed has not been included in this model. This speed correlated with

the minor road speed at a level of 54 percent and was omitted from later regression

models. This was based on applying primary and secondary variable techniques to

these two variables. In the early regression models that comprised both these

variables, an increase in major road speed sometimes gave a decrease in accident

rates, but in a majority of cases, it was not found to have a significant effect.

These results showed that reducing the major road speed through a reduction in

speed limit was not likely to have much impact on Angle-Minor vehicle accident

rates.

200

Visibility from the Minor Road to Major Road Vehicles

The model shows that decreased levels of visibility will increase the Angle-Minor

vehicle accident rate. A plot of the standardised Angle-Minor accident rate (accident

rate of one at a sight distance of infinity) versus sight distance for a speed of

100km/h is shown in Figure 17.2.

The sight distance is measured between a minor road vehicle 5m behind the give way

line and major road vehicles. It is based on an eye height of 1.15m and an object

height of 1.15. This is the same method of measuring sight distance in the Safe

Intersection Sight Distance model in QDMR (2000) and Austroads (1988).

Figure 17.2 shows that the Angle-Minor vehicle accident rate increases substantially

when the sight distance is less than about 100m. For an 85th percentile speed of

100km/h and a minimum reaction time of 2 seconds, the safe intersection sight

distance is 240m. When considering this value in respect to Figure 17.2, it would

appear to give a reasonably conservative result.

Figure 17.2 is only based on a limited number of sites with poor visibility. Therefore,

the exact location of the estimate Figure 17.2 cannot be confidently relied upon. This

is highlighted by the spread of the 95 percentile confident limits in this figure. This is

also confirmed by the results of the cross validation process in Table 17.4 where this

variable was selected only 84 times.

This result may be caused from the lack of suitable data. However, in some cases, it

can also be caused by the relatively inaccurate measurements of this parameter.

Table C8 (refer Appendix C - Geometric Variables) discusses variation in sight

distance over time, due to such issues as vegetation removal, height of crops, traffic

flows from different streams, parked vehicles etc.

However, this figure does indicate that providing Safe Intersection Sight Distance

does provide a reasonably high level of safety. It is probable that sight distances

would need to be significantly less than this before a sharp increase in accident rate

occurs.

The accident rate at a distance of 500m is 12 percent higher than that at infinity.

However, a value of close to unity is considered more appropriate. This is because

perception of other vehicles becomes quite difficult at sight distances above say

500m.

201

The effect of increasing accident rate with decreasing distance (down to say at least

500m) is mainly due to the inverse function chosen to model this variable. Other

methods of modelling this parameter have not been considered because of the lack of

initial data and the extreme complexity likely in the development of such methods.

0

1

2

3

4

5

6

0 100 200 300 400 500 6001.15m to 1.15m Sight Distance for 100km/h (m)

Stan

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Veh

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Acc

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95th Percentile Confidence Limits

Estimate

Figure 17.2 - Effect of Sight Distance on Angle-Minor Vehicle Accidents

Observation Angle

A plot of the standardised Angle-Minor vehicle accident rate (a value of unity at an

angle of zero) versus observation angle is shown in Figure 17.3. ‘Observation Angle’

is the angle between a line representing the instantaneous direction of travel of minor

road drivers 4m behind the give way line and a line tangential to the major road. This

parameter is detailed in Table C14 of Appendix C - Geometric Variables. For any

particular conflict point, an increase in the observation angle will increase Angle-

Minor vehicle accident rates. This result supports the concept of Minimum Gap Sight

Distance in QDMR (2000) and Austroads (2003) which give maximum observation

angles for various conflict points.

It was originally anticipated that the shape of the graph in Figure 17.3 might be a

polynomial with a maximum accident rate at about a 150 degree observation angle.

This shape would reflect the criteria in Figure 13.4 (Sight Restrictions due to Vehicle

Design) of QDMR (2000) and Austroads (2003). However, the regression analysis

showed that a polynomial function did not fit as well as an exponential function.

202

A review of accidents for the LRT conflict type revealed that left-turn movements

with observation angles around 150 degrees did not perform worse than left-turn

movements with observation angles closer to 180 degrees. However, the LRT

conflict only consisted of 13 accidents, so the level of confidence in this result is not

high. A greater level of confidence would require more data.

Increasing the skew of an intersection increases the observation angles for particular

conflict points. Figure 17.3 shows that these conflict points will then record an

increased accident. For other conflict points, an increase in skew will lower

observation angles, and therefore decrease the accident rates.

0

1

2

3

4

5

6

7

8

40 60 80 100 120 140 160 180Observation Angle (degrees)

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Estimate

Figure 17.3 - Effect of Observation Angle on Angle-Minor Vehicle Accident Rates

Using the final accident model, an optimum skew of a minor leg could be determined

to minimise the total Angle-Minor vehicle accident rate. Factors influencing this are

as follows:

• Number of legs at the intersection - this influences the types of conflicts

applicable

• Traffic volumes for the various turning movements

• Geometry of the intersection - road and median widths, presence of a free left-turn

lane from the minor road, approach curvature etc

It is not recommended, however, to use this model in order to determine an optimum

203

skew. Rather, it is recommended that observation angles for through and right-turn

conflicts be limited to around 90 degrees, enabling a more clear view of each

direction. The minimum and maximum values given in the Minimum Gap Sight

Distance model in QDMR (2000) and Austroads (2003) should be applied.

A large single radius free left-turn will have an observation angle approaching 180

degrees. A non-free left-turn with a small single radius will have an observation

angle around 110 degrees. Figure 17.3 shows that the free left-turn will record an

Angle-Minor vehicle accident rate approximately 70 percent higher.

This supports the use of high entry angle free left-turn lanes in lieu of single radius

free left-turn lanes. High entry angle free left-turn lanes provide a smaller

observation angle than do single radius free left-turn lanes. Single radius free left-

turn lanes should only be provided if accompanied by an acceleration lane as per

QDMR (2000) and Austroads (2003).

The cross validation process in Table 17.4 shows that this parameter was only

selected 88 times. This value is less than desirable and may well be the result of an

insufficient number of sites with large skews between the major and minor roads.

However, it may also be the result of the inaccuracy of the measurement of this

parameter, as discussed in Table C14 of Appendix C - Geometric Variables. A major

issue being minor road drivers do not view major road vehicle from one point only,

which is an assumption made in the measurement of this variable.

Driver Recognition of an Opposite Minor Leg

Table 17.5 shows the effect of the variable ‘Driver Recognition of an Opposite

Minor Leg’ on Angle-Minor vehicle accident rates. This variable is a measure of the

degree that the minor road appears to continue straight ahead through cross

intersections and is detailed in Table C15 of Appendix C - Geometric Variables. This

variable is only applicable to conflicts involving a through movement from the minor

road.

Table 17.5 shows that the accident rate for through conflicts is almost double that for

four leg intersections comprising a high degree of recognition of the opposite minor

leg than for four leg intersections comprising little to no recognition of the opposite

minor leg. Minor legs with a high degree of recognition of the opposite minor leg are

horizontally aligned and on a continuous vertical grade or in a sag.

204

Table 17.5 - Effect of the Variable ‘Driver Recognition of an Opposite Minor Leg’ on Angle-Minor Vehicle Accident Rates

Value of DR4

Case Standarised Angle-Minor Accident Rate

(accident rate of 1.0 at a value of zero)

0 Little or no recognition of an opposite minor leg due to a horizontal offset between legs, small radius curves at intersection, large angle between legs, or small radius crest vertical curve

1

1 All other cases 1.4 2 Minor legs horizontal aligned and

straight for at least 50m prior to the intersection. Vertical alignment on a continuous grade or in a sag.

1.9

It is considered that the reason why this variable is important is as follows. Fully

aligned minor legs can deceive drivers as to the presence of the intersection. The

road can appear to continue straight ahead for drivers not concentrating adequately.

This is especially true if very little of the major road can be seen prior to the

intersection, due to surrounding development/vegetation or major road crossfall.

However, minor legs with little or no recognition of the opposite minor leg can

appear as T-intersections. This appearance probably helps identify the intersection.

Another reason may be that fully aligned minor legs encourage some drivers to travel

across the intersection too quickly (not slowing adequately prior to the intersection)

and accept smaller gaps in the traffic stream.

These results suggest that the introduction of minor road staggers at all four-leg

intersections would be beneficial in minimising the amount of driver recognition of

the opposite minor leg. This would be in addition to the advantages of minimising

the relative speed for particular conflict types. Table 17.5 also suggests that other

methods to minimise the amount of driver recognition of the opposite minor leg

include introducing small radius curves at intersections, a large angle between legs,

or a small radius crest vertical curves. However, these are not recommended design

treatments because they may generate other potential problems.

The cross validation process in Table 17.4 shows that this parameter was selected

100 times. This indicates that a high degree of confidence can be placed in this result.

205

Given the subjective nature of the measurement of this parameter, this is a

remarkable result. The perception of an opposite minor leg is probably far more

complex than this simple variable has measured.

The parameter ‘level of perception of the backdrop of a T-intersection’ was not used

in the selected Angle-Minor vehicle accident model because it does not apply to four

leg intersections. The Angle-Minor vehicle models for T-intersections only (the

LegT and CONT models) showed that Angle-Minor vehicle accident rates decreased

with greater levels of perception given by backdrop.

This finding, in combination with the finding for the parameter ‘driver recognition of

an opposite minor leg’ suggests the following. The level of perception of the

intersection is very important. Crossroads provide relatively little perception of the

intersection. Drivers can more easily misread cross intersections by assuming the

road simply continues ahead. This increases the Angle-Minor vehicle accident rate.

Conversely, T-intersections with significant backdrops give good driver recognition

of the need to slow down because the roadway appears to end. As for cross

intersections, drivers may more easily misread T-intersections with no backdrop by

assuming the road simply continues straight ahead.

Conflict Type

The various conflict types discussed in this section have been shown in Figure 9.7 in

Section 9.9. Standardising the Angle-Minor vehicle accident rate at unity for a LRT

type conflict, the other major conflict types in this model will yield the following

accident rates (assuming all other variables remain the same except where shown):

• TLT (DR4 = 0) - 24

• TLT (DR4 = 2) - 47

• TRT (DR4 = 0) - 17

• TRT (DR4 = 2) - 33

• RLT - 4.5

• RRT - 28

The following conclusions are made from the above results. These results are

consistent with those found in previous studies as identified in the literature review in

206

Section 2.1.

LRT Conflict Angle-Minor vehicle accident rates resulting from minor road vehicles turning left at

the intersection colliding with major road vehicles travelling through (LRT) are

relatively low compared to the other conflict types. The expected reason for this is

that drivers have to view and give way to only one traffic stream. This requires a

relatively low driver workload.

Another expected reason is that the relative speed between vehicles is low due to the

small angle between vehicle paths. In addition, the small angle between vehicle paths

may result in an easier evasive manoeuvre for major road vehicles to avoid left-turn

vehicles that have failed to give way. Based on the results from this model, an

intersection with a high proportion of left-turn vehicles from the minor road is likely

to record a relatively low total Angle-Minor vehicle accident rate.

TLT Conflict Angle-Minor vehicle accident rates resulting from minor road vehicles travelling

through an intersection colliding with major road vehicles on the left leg travelling

through (TLT) record the highest accident rate. One expected reason for this is that

drivers have had to view and give way to multiple traffic streams. This requires a

relatively high driver workload.

Another reason is that the relative speed between vehicles is high due to the angle

between vehicle paths often being around 90 degrees. It is also suspected that the

front left pillar of passenger cars may tend to block visibility of major road vehicles.

Depending on the angle of the intersection, the presence of a passenger in the front

seat and the centre left pillar may also tend to block visibility.

It is considered quite feasible that these factors may cause restrictions to visibility,

especially when considering that so many other parameters that cause restrictions to

visibility have already been identified in this model. These are observation angle,

number of stand-up lanes on the minor road, and visibility to major road vehicles.

TRT Conflict Angle-Minor vehicle accident rates resulting from minor road vehicles travelling

through an intersection colliding with major road vehicles on the right leg travelling

through (TRT) record a relatively high accident rate. Expected reasons for this are

207

the same as those given for TLT conflicts with the exception of the potential

restrictions to visibility in passenger cars.

Based on the results from this model, an intersection with a high proportion of

through vehicles from the minor road is likely to record a high total Angle-Minor

vehicle accident rate. This result suggests that a staggered T-intersection treatment

that eliminates through movements may reduce Angle-Minor vehicle accident rates.

RLT Conflict Angle-Minor vehicle accident rates resulting from minor road vehicles turning right

at the intersection colliding with major road vehicles travelling through from the left

(RLT) are relatively low. Although this conflict type records a 4.5 times higher rate

than a LRT conflict, it is significantly lower than the other major conflict types.

Although drivers turning right have to view multiple traffic streams (especially at

four leg intersections), the small angle between vehicle paths may result an easier

evasive manoeuvre for major road vehicles from the left to avoid right-turn vehicles

that have failed to give way.

RRT Conflict Angle-Minor vehicle accident rates resulting from minor road vehicles turning right

at the intersection colliding with major road vehicles on the right leg travelling

through (RRT) record a relatively high accident rate. This rate is in the same order as

that for TRT conflicts. This is expected because the situation regarding this conflict

is similar to that discussed for TRT conflicts.

Based on the results from this model, an intersection with a high proportion of right-

turning vehicles from the minor road is likely to record a moderate to high total

Angle-Minor vehicle accident rate.

Number of Stand-up Lanes on the Minor Road

This model shows that the Angle-Minor vehicle accident rate is 1.5 times higher for

those conflict points where there was an adjacent stand-up lane in the direction of the

relevant oncoming major road vehicles. This shows that minor roads with two stand-

up lanes will record higher Angle-Minor vehicle accident rates than minor roads with

one stand-up lane. In this model, a free left-turn lane does not constitute an

individual stand-up lane.

208

The expected reason for this result is that vehicles in an adjacent stand-up lane will

block visibility to major road vehicles in that direction. This is turn increases the

likelihood of not perceiving a major road vehicle and failing to give way.

On a minor road with two stand-up lanes, all conflict points except RRT will record

an Angle-Minor vehicle accident rate 1.5 times higher than for a minor road with a

single stand-up lane. Angle-Minor vehicle accident rates for RRT conflicts do not

change with the number of stand-up lanes because there are no adjacent lanes in the

direction of viewing the major road vehicles (all intersections comprised only one

right-turn movement from any given leg).

In this model, T-intersections comprised only LRT, RLT and RRT Angle-Minor

vehicle conflicts. Given that LRT and RLT conflict points record comparatively low

accident rates and that accident rates are unaffected by the number of stand-up lanes

for RRT conflicts, providing two stand-up lanes at T-intersections will not produce

high overall Angle-Minor vehicle accident rates. However, four-leg intersections

with heavy through movements from the minor legs will record much higher Angle-

Minor vehicle accident rates for minor legs with two stand-up lanes than for minor

legs with one stand-up lane.

It is recommended that only one stand-up lane be provided on minor road

approaches, particularly at four leg intersections with heavy through movements

from the minor legs. Where two lanes are required for capacity reasons, signalisation

of the intersection should be considered.

Presence of Queuing Through the Intersection

The presence of queuing through the intersection was not a significant variable in the

final accident model. It was significant, though, in the individual TRT conflict type.

This is not surprising given that Angle-Minor vehicle accidents in the Crash Incident

Reports were of this conflict type where queuing through the intersection was

documented.

It is possible to create a dummy variable in order to account for queuing through the

intersection for this conflict type only. This was not undertaken for the following

reasons:

• To avoid additional complexity in the model.

209

• Only a small benefit would be gained by using the additional term

• The results for the new term would be based on a relatively small data sample

Approach Visibility on the Minor Road

It was found that approach visibility on the minor road did not significantly affect

Angle-Minor vehicle accident rates. This variable was measured using the Approach

Sight Distance model in QDMR (2000) and Austroads (1988) in which a 1.15m eye

height and a 0m object height is used. One reason considered for this result is that an

intersection can usually be well perceived from the minor road with values of

approach sight distance far below that listed as the minimum. This is generally the

result of the intersection backdrop (eg buildings, vegetation, cut face), signage and

the presence of major road vehicles.

Approach Sight Distance on the minor road was found difficult to measure under the

certain conditions. For this reason, an alternative approach sight distance model was

developed as discussed below:

• The alternative model used the distance at which the minimum Approach Sight

Distance was first gained. This was relevant in undulating terrain where the

minimum Approach Sight Distance is gained and lost a number of times prior to

the intersection.

• The alternative model used a 0.2m object height. This made measurements of

approach sight distance easier for certain combinations of horizontal alignment,

vertical alignment and roadside obstacles.

The alternative approach sight distance model was also not a significant predictor of

Angle-Minor vehicle accidents.

Level of Control

The level of control at the intersection generally did not affect Angle-Minor accident

rates. There was a tendency for a higher level of control to increase accident rates eg

stop signs recording a higher accident rate than give way signs. This result is

consistent with the results of previous studies as identified in the literature review in

Section 2.3. An expected reason for this result is that higher levels of control are

placed at the more dangerous intersections. This is somewhat contrary to Clause

210

2.5.3 of the Queensland Department of Main Roads ‘Manual of Uniform Traffic

Control Devices’ - QDMR (1995) which states ‘For these reasons, no accident

warrant is given for the use of stop signs and in general they should not be installed

unless the sight distance restrictions above apply’.

211

18 ANGLE-MAJOR VEHICLE ACCIDENTS


described in Chapter 16 to the Angle-Major vehicle accident category.


Only one category of data has been considered for analysis, comprising all Angle-

Major vehicle accidents involving right-turns from the major road colliding with

oncoming through vehicles. Sample size is 102 accidents and 269 right-turn sites.

Angle-Major vehicle accidents involving U-turn vehicles (3 accidents) and left

oncoming movements (2 accidents) were not analysed because they were few in

number and/or traffic volume data was not available for the turn movement.


The variables selected for the Angle-Major vehicle accident category are shown in

Table 18.1, along with the results of applying the regression analysis techniques

discussed in Chapter 16. For more information on these variables, refer to Appendix

C - Geometric Variables. Table 18.2 shows the significance of alternative variables

used in the analysis.

The results of the regression analysis for the Angle-Major vehicle accident category

are shown in Table 18.3 and by Equation 18.1.

AAM = 0.000439 x QMR0.473 x QMO

0.234 x exp(4.84 / TMOPP + 0.602 x QUEO) Equation 18.1

where AAM = number of Angle-Major vehicle accidents per year per major leg

QMR = traffic flow turning right from the major leg (veh/d)

QMO = through traffic flow on the opposing major leg (veh/d)

TMOPP = visibility from a stationary right-turning vehicle at the intersection

to oncoming major road vehicles measured in time - refer table C8

of Appendix C - Geometric Variables (s)

QUEO = presence of queuing through the intersection from a downstream

set of traffic signals on a multi-lane road only - dummy variable

(refer to Table C1 of Appendix C - Geometric Variables)

212

Table 18.1 - Variables and Results of the Regression Analysis for Angle-Major Vehicle Accidents

Variable Code

Variable Description Function Types (1)

Results

QMR Right-turning traffic flow from a major leg

PR ***

QMO Opposing through traffic flow on a major leg (one direction only)

PR *

QMOR Opposing right-turn traffic flow from a major leg

PR N

QSR Right-turning traffic flow from the minor leg

EX R

SMO Opposing through 85th percentile speed on the major leg

PR N

TMOPP Visibility from intersection to oncoming major road vehicles measured in time

IN *

RCM Classification of the major road

EX N

LIGHTM Level of lighting on the major road

EX R

TTR Right-turn type from the major road- LSR, AUR, CHR, or MNR

EX N

TTL Left-turn type from the major road - LSL or AUL

EX N

CMO Curvature of the major road PO N QUEO Presence of oncoming traffic

queuing through the intersection on a multi-lane major road.

EX **

RMR Right-turn radius from the major road

EX N

Notes: (1) Refer to Section 16.3 for the function types shown in the third column. *** = significant at the 0.1% level ** = significant at the 1% level * = significant at the 5% level o = significant at the 10% level # = not significant at the 10% level but explained enough of the variability in the data to be retained






213

Table 18.2 - Alternative Variables

for Angle-Major Vehicle Accidents Original Variable

Code

Original Variable

Description

Alternative Variable

Code


Description

Results

TMOPP Visibility from intersection to oncoming major road vehicles measured in time.

TMOPPI Visibility from intersection to oncoming major road vehicles measured in time with a maximum value to the next signalised intersection

L

Notes: G = the alternative variable explained a greater amount of the variability in the data than did the original variable. L = the alternative variable explained a lesser amount of the variability in the data than did the original variable. N = the alternative variable was not significant - = not applicable for the accident category / not undertaken

Table 18.3 - Regression Analysis Results for the Angle-Major Vehicle Accident Category



(1) k -7.73 0.983 3.53E-15 100

log(QMR) 0.473 0.0900 1.48E-7 100 log(QMO) 0.234 0.111 0.0356 94

QUEO 0.602 0.217 0.00548 90 TMOPP 4.84 1.93 0.0122 90


by a StepAIC process using 90 percent of the data (refer Section 16.8). (2) The lower bound of the confidence interval for deviance is 220.9 for 264 degrees of freedom at

the 2.5% level using a Chi-squared test. The upper bound of the confidence interval for deviance is 310.9. As the residual deviance is 274.8, the data is not significantly over or under-dispersed.

(3) The mean recorded accident rate (number of accidents per year per leg) = 0.0733 The mean predicted accident rate = 0.0731 The mean error in accident rate = 0.0965 (1.32 x average recorded accident rate)


Traffic Flow Parameters The Angle-Major vehicle accident rate is related to both the turning traffic flow and

the oncoming through traffic flow. This is an expected result.

214

Visibility from Intersection to Oncoming Vehicles The model shows that decreased visibility will increase the Angle-Major vehicle

accident rate. Figure 18.1 shows a plot of the standardised Angle-Major accident rate

(accident rate of one at a sight distance of infinity) versus sight distance for a speed

of 100km/h. The sight distance is measured between a right-turning major road

vehicle and an oncoming major road vehicle. Eye and objects heights of 1.15m have

been used.

0

2

4

6

8

10

12


Stan

dard

ised

Ang

le-M

ajor

Vehi

cle

Acc

iden

t Rat

e


Estimate

Figure 18.1 - Effect of Sight Distance on Angle-Major Vehicle Accidents

Although QDMR (2000) and Austroads (1988) do not check visibility requirements

for this conflict type, Figure 18.1 shows that it is an important predictor of Angle-

Major vehicle accidents. The current use of the Safe Intersection Sight Distance

model in QDMR (2000) and Austroads (1988) (which apply the model between

minor road and major road vehicles only) does not consider restrictions to visibility

for this conflict type. Such a case is at intersections on the back of tight horizontal

curves where the amount of visibility can be significantly less for right-turning

drivers on the major road than for turning drivers on the minor road.

Figure 18.1 shows that the Angle-Major vehicle accident rate increases substantially

when the sight distance is less than about 150m. For an 85th percentile speed of

100km/h, a minimum reaction time of 2 seconds, the safe intersection sight distance

(measured 1.15m eye height to 1.15m eye height) is 240m. This value would appear

215

to give a reasonably conservative result.

The accident rate at a distance of 500m is 45 percent higher than that at infinity. A

value of close to unity, however, is considered more appropriate. This is because at

sight distances above say 500m, perception of vehicles in conflict situations becomes

quite difficult. In addition, by the time the driver travels 500m or more, the original

conflict situation may well be completely different.

As explained previously, the effect of increasing accident rate with decreasing sight

distance from infinity to say 500m is mainly due to the inverse function chosen to

model this variable. Better methods of modelling this variable have not been

considered due to the lack of initial data and the extreme complexity likely in the

development of such methods.

Like other accident types in this study, this model is only based on a limited number

of data points with particularly poor visibility. This is reflected in the cross validation

process shown in Table 18.3, where this variable was selected only 90 times. In

addition, the 95th percentile confidence limits in Figure 18.1 have a considerable

spread.

As discussed for Angle-Minor vehicle accidents, this result may be caused from the

relative inaccuracy in measuring this parameter, or from a lack of sites with very

poor visibility.

Queuing Through the Intersection The Angle-Major vehicle accident rate increases with an increase in the level of

queuing through the intersection on the opposite major road leg (the major leg on

which the right-turn vehicle is crossing). This only applies where the opposite major

leg is multilane. Vehicles travelling on the outside lane of the opposite major leg can

be hidden by stationary queued vehicles on the inside lane.

Standardising the Angle-Major vehicle accident rate at a value of one for a non-

multilane road and for a multilane road with no queuing, other levels of queuing on

multilane roads will yield the following relative accident rates:

• Moderate queuing in peak hour (typically queues will dissipate with each change

of the downstream traffic signals) - an accident rate of 1.8

216

• Heavy queuing in peak hour (typically queues will not dissipate with each change

of the downstream traffic signals over a period of at least 15 minutes) - an

accident rate of 3.3

The above results show that heavy queuing through an intersection on a multilane

road can increase the Angle-Major vehicle accident rate by more than three fold.

The cross validation process in Table 18.3 shows that this variable was selected only

90 times. This result was not unexpected as there were only a few multilane sites

comprising high levels of queuing through the intersection.

Speed Parameters The parameter ‘opposing through 85th percentile speed on the major leg’ was not a

significant predictor of Angle-Major vehicle accident rates. This was initially a

somewhat surprising result given that speed parameters were important predictors of

every accident type at roundabouts in Arndt (1998).

Right-Turn Traffic Flow from the Minor Road Table 18.1 shows that the right-turn traffic flow from the minor road is a significant

predictor of Angle-Major vehicle accidents. Greater right-turn minor road traffic

flows increased the Angle-Major vehicle accident rate. It was originally considered

that this result might be due to right-turn vehicles from the minor road propping in

the major road median and blocking visibility from right-turning major road vehicles.

For the following reasons, however, this variable was rejected:

• If the above scenario was valid, it could be expected that the Crash Incident

Reports would have identified it.

• The Angle-Major vehicle accident rate was not significantly higher at sites where

this scenario was likely to occur

This variable was therefore was rejected because a logical mechanism that supports

the statistical result could not be determined.

The right-turn traffic flow from the minor road is highly correlated with the left-turn

from the major road into the minor road. Using the left-turn traffic flow from the

major road instead of the right-turn from the minor road also showed a significant

result. However, this was also rejected because a logical mechanism could not be

determined that adequately explained why this parameter was important.

217

19 REAR-END-MAJOR VEHICLE ACCIDENTS


described in Chapter 16 to the Rear-End-Major vehicle accident category.


Table 11.1 showed the turning movement of the front vehicle involved in each Rear-

End-Major vehicle accident versus the number of accidents. This table is reproduced

as Table 19.1.

Table 19.1 - Front Vehicle Turning Movements - Rear-End-Major Vehicle Accidents

Turning Movement of Front Vehicle

Number of Accidents

Left 5 Right 111

U-Turn 3 Unknown 2

Total 121

Accidents involving a front vehicle undertaking a U-turn were not included in the

regression analysis because inadequate traffic data were available for U-turns.

Accidents with unknown front vehicle movements were also excluded.

Four subcategories of data have been considered for analysis as follows:

• LSR - accidents at Type LSR treatments - sample size 44 accidents and 78 Type

LSR sites.

• AUR - accidents at Type AUR treatments- sample size 28 accidents and 47 Type

AUR sites.

• R - accidents at all right-turn treatments (LSR, AUR, CHR and MNR) - sample

size 111 accidents and 269 right-turn treatments.

• LR - Accidents at all left and right-turn treatments (LSR, AUR, CHR, MNR,

LSL, AUL) - sample size 116 accidents and 502 left and right-turn treatments.

Type LSL sites with adjacent parking lanes have been excluded from the sample

because these sites may act as AUL sites when the parking lanes are empty.

The following accident subcategories were not analysed for the reasons given:

218

• MNR - accidents at Type MNR treatments - insufficient sites and variation in

several of the parameters

• CHR - accidents at Type CHR treatments - insufficient accident data

• L - accidents at all left-turn treatments (LSL, AUL)- insufficient accident data


The variables selected for the Rear-End-Major vehicle accident category are shown

in Table 19.2 along with the results of applying the regression analysis techniques

discussed in Chapter 16. For more information on these variables, refer Appendix C -

Geometric Variables. Table 19.3 shows the significance of alternative variables used

in the analysis.


Table 19.2 shows that the traffic flow variables are significant across the most of the

models. The speed terms are generally consistent except for the AUR model. As

most of the AUR treatments were in high-speed environments, it is not surprising

that the speed terms for this model were not significant. This result is probably only

reflecting the fact that an inadequate range of speed data exists for AUR sites to

show that the speed terms are significant.

The visibility term TMINT was only significant in the larger models. This is not an

unexpected result because there are few sites with particularly poor visibility.

The variable ‘median width of LSR, AUR, and MNR sites’ was significant across

three of the models. It was not significant for the AUR model. This is not an

unexpected result because only three of the AUR sites comprised a median.

219

Table 19.2 - Variables and Results of the Regression Analysis for Rear-End-Major Vehicle Accidents

Accident Subcategory Variable Code

Variable Description Function Types (1) LSR AUR R LR

QMi Turning traffic flow from a major leg

PR *** QMR

o QMR

*** QMR

*** QMi

QMT Through traffic flow on a major leg

PR *** # *** ***

SEM Speed environment of the major road

PR ** N *** ***

SRSLM Speed reduction due to a reduction in speed limit (km/h) (Used only if SEM is significant).

EX N - o #

SRCM Speed reduction due to curvature (km/h) (Used only if SEM is significant).

EX * - *** ***

TMINT Visibility to intersection from the major road measured in time

IN N N ** **


EX N N R R


EX N N N N

TTi Major road turn type Factorial variable

- - V TTR

V TTA

WMEDM Median width of LSR, AUR and MNR sites (all other sites set to zero)

EX # - ** **

NLEG Number of legs of the intersection

EX N * # N

TLAUR Minimum length of auxiliary lane each side of the intersection for AUR treatments

PO, EX - N N N

WRS Width of sealed lane plus sealed widening for LSR sites

PO, EX N - N -

WRU Width of sealed lane plus total widening (sealed plus unsealed) for LSR sites

PO, EX N - N -

220

Notes to Table 19.2: (1) Refer to Section 16.3 for the function types shown in the third column. *** = significant at the 0.1% level ** = significant at the 1% level * = significant at the 5% level o = significant at the 10% level # = not significant at the 10% level but explained enough of the variability in the data to be retained







The largest model (LR) is considered the best model to predict Rear-End-Major

vehicle accident rates. This model is comparatively large (compared to the other

accident subcategories) in that it comprises all of the Rear-End-Major accident data.

This is a desirable feature in order to avoid sub-dividing the data into samples that

become too small. In turn, this increases the risk that an inadequate amount of data

exists in each sample to be confident of the result.

An example of the above is for the AUR model, which comprised AUR sites in

mostly high-speed environments. It is difficult to determine relationships between

speed and accident rates for this model because of the lack of range of data. By

selecting the largest model (LR), the effect of speed can be estimated for these AUR

sites.

Although the model is relatively large, it is flexible enough to consider the various

turn types and parameters only relating to these types. It is important that this

flexibility is provided especially for the traffic flow variables relating to each turn

type. This is because of the low number of accidents occurring to left-turning major

road vehicles. The overall conflict model (LR) allows for this by incorporating the

factorial variable ‘major road turn type’.

The ‘LR’ model assumes several interactions between parameters are the same. By

combining the various intersection turn types into the one model, it is assumed that

traffic flow, speed, and visibility terms form the same relationship with Rear-End-

221

Major vehicle accidents for each intersection turn type. This would seem a

reasonable approach given the total amount of data available. To prove otherwise,

collection of much more data would be needed.

Table 19.3 shows that the alternative variable ‘85th percentile through speed’ was a

more significant predictor of Rear-End-Major vehicle accidents than the original

variable ‘speed environment of the major road’. For the reasons given in Section

17.3, it was decided to adopt the alternative variable into the final equation.

Table 19.3 - Alternative Variables for Rear-End-Major Vehicle Accidents for the ‘LR’ Subcategory

Original Variable

Code

Original Variable Description

Alternat. Variable

Code

Alternative Variable Description

Results

SEM Speed environment of the major leg

SMT 85th percentile through speed on the major leg

G

TMINT Sight distance to the intersection

TMINTI Sight distance to the intersection allowing for nearby signalised intersections

L


TES Effective time available to undertake an evasive manoeuvre on a sealed surface at LSR sites

N


TEU Effective time available to undertake an evasive manoeuvre on all surface types (sealed plus unsealed) at LSR sites.

N


WTS Effective total width of sealed lane plus sealed widening for LSR sites

N


WTU Effective total width of sealed lane plus total widening (sealed plus unsealed) for LSR sites

N


222

The results of the regression analysis for the ‘LR’ accident subcategories are shown

in Table 19.4. Also shown in this table are the values of the estimate for the ‘R’

subcategory. These values were included for comparison with the estimates for the

‘LR’ category. The purpose of this was to determine the potential effect of analysing

under-dispersed data on the values of the estimates.

Table 19.4 - Regression Analysis Results for the ‘LR’ Accident Subcategory



(1)

Estimate for the ‘R’

Subcategory (2)

k -29.2 3.62 6.73E-16 100 -29.2 log(QMi) 0.437 0.0874 5.62E-7 100 0.455 log(QMT) 0.943 0.143 4.75E-11 100 0.969 log(SMT) 3.00 0.612 9.15E-7 100 2.91

TMINT 5.02 2.10 0.0171 98 5.13 WMEDM -0.394 0.131 0.00263 100 -0.394

TTA- LSR 3.94 0.516 2.01E-14 - 4.00 TTA - MNR 4.61 0.508 2E-16 - 4.60 TTA - AUR 3.40 0.511 2.99E-11 - 3.45 TTA - LSL 0.0361 0.732 0.961 - - TTA - AUL -0.589 0.834 0.480 - -

Notes: (1) The values in the fifth column are the number of times out of 100 that each variable was selected

by a StepAIC process using 90 percent of the data (refer Section 16.8). (2) The last column shows the values of the estimate for the ‘R’ subcategory for the purposes of

comparison with the estimates for the ‘LR’ category. For the ‘R’ subcategory, the lower bound of the confidence interval for deviance is 217.2 for 260 degrees of freedom at the 2.5% level using a Chi-squared test. As the residual deviance is 189.3, the data is somewhat under-dispersed.

(3) The lower bound of the confidence interval for deviance is 429.6 for 489 degrees of freedom at the 2.5% level using a Chi-squared test. As the residual deviance is 214.7, the data is considerably under-dispersed.

(4) The mean recorded accident rate (number of accidents per year per leg) = 0.0429 The mean predicted accident rate = 0.0425 The mean error in accident rate = 0.0436 (1.02 x average recorded accident rate) Table 19.4 shows that although the ‘LR’ subcategory is under-dispersed to a much

higher degree than the ‘R’ subcategory, the values of the estimates are quite similar.

The greatest difference in these values was only four percent. Part of the difference

was because data for left-turn Rear-End-Major vehicle accidents were included in the

‘LR’ subcategory but not the ‘R’ subcategory. This difference is considered to be

insignificant as compared to the effect of other issues, as discussed in Section 3.

For the above reason, the analysis of under-dispersed data using a Poisson technique

is considered to have no dramatic effect on the results.

223

The selected Rear-End-Major vehicle accident model ‘LR’ is given by Equation

19.1.

ARM = 2.08 x 10-13 x QMR0.437 x QMT

0.943 x SMT3 x exp(5.02 / TMINT - 0.394 x

WMEDM + TTA) Equation 19.1

where ARM = number of Rear-End-Major vehicle accidents per year per major

leg per turn treatment

QMi = turning traffic flow from the major leg for the particular conflict

(veh/d)

QMT = through traffic flow on the major leg (veh/d)

SMT = 85th percentile through major road speed (km/h)

TMINT = visibility for major road vehicles approaching the intersection to a

stationary right-turning vehicle at the intersection measured in

time - refer table C8 of Appendix C - Geometric Variables (s)

WMEDM = width of the major road median (m) - dummy variable (0 for CHR,

LSL and AUL treatments; width of the major road median for LSR,

AUR and MNR treatments)

TTA = type of major road turn treatment - dummy variable (0 for a CHR

treatment, 3.94 for a LSR treatment, 4.61 for a MNR treatment,

3.40 for an AUR treatment, 0.0361 for a LSL treatment and -0.589

for an AUL treatment)


The selected model (LR) gives the following results.

Traffic Flow Parameters

The Rear-End-Major vehicle accident rate is related to the turning traffic flow to a

power of 0.44 and the through traffic flow to a power of 0.95. The larger coefficient

for the through traffic flow is expected to be at least partially a consequence of the

following.

The exposure for traffic turning right at LSR and AUR intersections is not only

related to the number of through vehicles from behind (the flow function used in the

model), but also the number of opposing through vehicles. The higher the number of

opposing through vehicles, the greater the chance that a turning driver has to stop

224

and/or wait for the oncoming vehicle/s to clear. This waiting time increases the

exposure of being hit from behind. The opposing vehicle flow is very strongly

correlated with the through traffic flow from behind.

Through Speed on the Major Road The Rear-End-Major vehicle accident rate is related to the through speed to a power

of three. This result shows that the accident type is strongly related to the through

vehicle speed. Given the same traffic volumes, it indicates that a lower standard turn

treatment, eg an LSR, can be tolerated in a slower speed area (typically urban) more

readily than in a high-speed area (typically rural).

Visibility The model shows that decreased levels of visibility will increase the Rear-End-Major

vehicle accident rate. Figure 19.1 shows a plot of the standardised Rear-End-Major

accident rate (accident rate of one at a sight distance of infinity) versus sight distance

for a speed of 100km/h. The sight distance is measured between an approaching

major road vehicle and a right-turning major road vehicle. Eye and object heights of

1.15m have been used.

Although QDMR (2000) and Austroads (1988) do not check visibility requirements

for this conflict type, Figure 19.1 shows that it is an important predictor of Rear-End-

Major vehicle accidents. The current use of the Safe Intersection Sight Distance

model in QDMR (2000) and Austroads (1988) (which apply the model from minor

road to major road vehicles only) does not consider restrictions to visibility for this

conflict type. Such a case is at intersections on the back of tight horizontal curves

where the amount of visibility can be significantly less for major road drivers

approaching the intersection than for turning drivers from the minor road.

Figure 19.1 shows that the Rear-End-Major vehicle accident rate increases

substantially when the sight distance is less than about 150m. For an 85th percentile

speed of 100km/h and a minimum reaction time of 2 seconds, the safe intersection

sight distance (measured 1.15m eye height to 1.15m eye height) is 240m. This value

would appear to give a reasonably conservative result.

The accident rate at a distance of 500m is 32 percent higher than that at infinity. A

value of close to unity, however, is considered more appropriate. This is because at

sight distances above say 500m, perception of vehicles in conflict situations becomes

225

quite difficult. In addition, by the time the driver travels 500m or more, the original

conflict situation may well be completely different.

As explained previously, the effect of increasing accident rate with decreasing sight

distance from infinity to say 500m is mainly due to the inverse function chosen to

model this variable. Better methods of modelling this variable have not been

considered because of the lack of initial data and the extreme complexity likely in the

development of such methods.

Like other accident types in this study, this model is only based on a limited number

of data points with particularly poor visibility. The 95th percentile confidence limits

in Figure 19.1 have a considerable spread. The cross validation process shown in

Table 18.3, however, shows that a high level of confidence can be placed in this

result.

0

2

4

6

8

10

12


Stan

dard

ised

Rea

r-En

d-M

ajor

Veh

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Acc

iden

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Estimate


Figure 19.1 - Effect of Sight Distance on Rear-End-Major Vehicle Accidents

Major Road Median Width A plot of the standardised Rear-End-Major vehicle accident rate (accident rate of one

at a median width of zero) versus median width is shown in Figure 19.2. This figure

applies for LSR, AUR and MNR turn treatments only.

Figure 19.2 shows that the right-turn Rear-End-Major vehicle accident rate decreases

substantially with median width (raised, painted or depressed median). A 1m median

provides a 33% reduction in accident rates, a 2m median provides a 55% reduction

226

and a 3m median provided a 69% reduction. The expected reason for this

relationship is that right-turning drivers who are waiting for a gap in the oncoming

traffic may position their vehicles further away from the point of conflict in the

through lane. A median width around 2m or more allows drivers to position most or

all of their vehicles off the through carriageway.

The additional median width does not decrease the potential of these drivers being hit

whilst they are decelerating. However, the values above show that removing them

further away from the through lane whilst they are waiting for gaps in the oncoming

traffic stream has a major influence on reducing this accident type. This would seem

consistent with the exposure for waiting vehicles concept discussed under the

previous section titled Traffic Flow Parameters.

It is expected that median widths above say 3m will perform no differently to a

median width of 3m. Figure 19.2 does not reflect this. This result is probably due to a

limited number of data points with a median width greater than 3m. It is

recommended that median widths greater than 3m be input into Equation 19.1 as 3m.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6Median Width of LSR, AUR & MNR Sites (m)

Stan

dard

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Rea

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ajor

Ve

hicl

e A

ccid

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ate


Estimate

Figure 19.2 - Effect of Median Width on Rear-End-Major Vehicle

Accidents at LSR, AUR and MNR Turn Treatments

227

Major Road Turn Type Standardising the Rear-End-Major vehicle accident rate at a CHR turn treatment at a

value of one, the other turn treatments will yield the following accident rates (given

the same traffic volumes, speed and visibility):

• Type LSR - 52

• Type MNR - 100

• Type AUR - 30

• Type LSL - 1

• Type AUL - 0.55

The following conclusions are made from the above results:

• CHR turn treatments record a 98 and a 97 percent lower Rear-End-Major vehicle

accident rate than do LSR and AUR turn treatments respectively. Therefore, CHR

right-turn treatments are much safer for this conflict type than LSR and AUR

treatments.

• AUR treatments record a 42 percent reduction in Rear-End-Major vehicle

accident rates over a LSR treatment.

• MNR treatments record a Rear-End-Major vehicle accident rate almost double

that of a LSR treatment.

• AUL and LSL treatments record a Rear-End-Major vehicle accident rate around

50 times lower than that for AUR and LSR treatments respectively. Therefore,

consideration of appropriate treatments for right-turning vehicles is much more

critical than that for left-turning vehicles.

• AUL treatments record a 47 percent lower Rear-End-Major vehicle accident rate

than do LSL treatments.

Length of Right-turn Slot for CHR Turn Treatments The length of the right-turn slot for CHR turn treatments was not used as a parameter

in the Rear-End-Major vehicle accident analysis. There were only five accidents

recorded at CHR turn treatments, too few to confidently predict the effect of right-

turn slot length.

228

Section 11.5 has shown that a considerable number of CHR turn treatments

comprised short turn slots. Given that the five Rear-End-Major vehicle accidents did

not occur on the shorter length turn slots, there is no evidence that suggests that short

right-turn slots perform any worse than longer slots.

It is likely that this occurs for the same reason as given in the previous section titled

Major Road Median Width. Drivers decelerating in the through traffic stream create

a degree of ‘friction’ which may increase their probability of being involved in a

Rear-End-Major vehicle accident. The probability of them being hit whilst

decelerating appears to be much lower than that for a stationary right-turning vehicle

on the through lane waiting for a gap in the oncoming traffic stream.

Widened Shoulder for LSR Treatments The presence of (or lack of) a widened shoulder at LSR treatments on two lane roads

has no appreciable effect on Rear-End-Major vehicle accident rates. This was found

to be true regardless of whether the widened shoulder is sealed or unsealed. Size of

the widened shoulder (length and width) did not appear to have an effect on Rear-

End-Major vehicle accident rates.

The above finding was surprising as it was felt that a widened shoulder would

provide an emergency escape area and be beneficial in reducing Rear-End-Major

vehicle accident rates. It was originally considered that this might be the result of the

sample comprising only a small number of sites with virtually no shoulders or

shoulder widening.

Table 19.5 shows the total width adjacent the right-turning vehicle (the through lane

width plus the shoulder width plus any additional shoulder widening) for LSR sites

versus the percentage of sites in each range. These values are based on a minimum

length of driver path undertaking an evasive manoeuvre each side of the intersection

equal to two seconds of travel time.

229

Table 19.5 - Percentage of Sites in Each Category of Road Width (Through Lane plus Shoulder Width plus any Additional Shoulder Widening)

at Type LSR Turn Treatments Lane plus Shoulder Percentage of SitesWidth Range (m) (1) in Each Range

3 - 4 154 - 5 145 - 6 296 - 7 247 - 8 108 - 9 5

9 - 10 010 - 15 1

Note: (1) The widths in the first column are based on a minimum available length of driver path

undertaking an evasive manoeuvre each side of the intersection of two seconds of travel time. These widths include the width of sealed and unsealed areas.

It is considered that undertaking an evasive action manoeuvre around a right-turning

vehicle within a total width of 5m or less would be difficult. It can be seen from

Table 19.5 that 29 percent of the sites have a total width of 5m or less. Based on

these values, it is considered that there is an adequate range of sites (those

comprising narrow shoulders to wide shoulders) to be relatively confident of the

result.

230

20 SINGLE-THROUGH VEHICLE ACCIDENTS


described in Chapter 16 to the Single-Through vehicle accident category.


Three subcategories of data have been considered for analysis as follows:

• Major - Single-Through vehicle accidents on the major road per horizontal

geometric element. Sample size 120 accidents and 496 horizontal geometric

elements.

• Minor - Single-Through vehicle accidents on the minor road per horizontal

geometric element (excluding those turning at the intersection which are Low

Frequency Intersection Accidents). Sample size 10 accidents and 282 horizontal

geometric elements.

• Both - A combination of the Major and Minor accident subcategories. Sample

size 130 accidents and 778 geometric elements.

• All - A combination of the Major and Minor accident subcategories and the

accident subcategory ‘Element’ from the low frequency intersection accident type

Single-Minor-Turn. Sample size 152 accidents and 1316 geometric elements.

All the models developed for the above accident subcategories use speed parameters

which are calculated as per Section 6.3. To determine the value of the speed

parameters, the radius and length of the driver path on each horizontal geometric

element are required. These are calculated in accordance with the vehicle path

models in Section 6.4.

The process of selecting appropriate horizontal geometric elements for the Major and

Minor accident subcategories above is discussed below.

Major Accident Subcategory

Horizontal geometric elements on the major road that met the following criteria were

included in the analysis:

• Horizontal geometric elements fully contained within 200m either side of the

intersection excluding short length horizontal straights (<100m long). Curves with

231

transitions were included in the analysis, by considering the full length of the

curve plus half of the transition length as a single radius curve.

• Horizontal elements not fully contained within 200m either side of the

intersection but whose partial length exceeded 200m. This typically included

sections of large radius curves and horizontal straights. The decrease in speed on

such elements was set at zero.

Horizontal geometric elements that did not meet the above criteria were excluded.

Failure to include those elements in the second dot point above would have resulted

in most large radius horizontal curves and horizontal straights being excluded from

the analysis. It would have been preferable for the accident data sample to include

accidents well over 200m from the intersection in order to avoid omitting the

incomplete elements in the second dot point. However, this was not within the

original scope of work for this project.

Single-Through vehicle accidents were located on each horizontal geometric element

from information given in the crash incident reports. Exceptions to this were as

follows:

• 20 accidents were located on a particular geometric element according to the

‘Street/s’ and ‘Landmark’ data entry boxes in the Crash Incident Reports.

However, a review of other data on the Crash Incident Report (especially the

accident description) gave reasonable cause that the accident did not occur at the

location specified. For this reason, these accidents were not coded on the

particular geometric element.

• 24 accidents were located within 10m to 60m past the end of a horizontal curve

according to the ‘Street/s’ and ‘Landmark’ data entry boxes. Sufficient evidence

existed within other parts of the Crash Incident Reports that the drivers lost

control on the horizontal curve. For this reason, these accidents were located on

the horizontal curve.

Minor Accident Subcategory

Only those Single-Through vehicle accidents involving drivers travelling towards the

intersection on the minor road were used. Horizontal geometric elements on the

minor road that meet the following criteria were included in the analysis:

232

• Horizontal geometric elements fully contained within 200m of the intersection for

Departmental roadways, and 50m for Council roads, excluding short length

horizontal straights (<30m long). Curves with transitions were included in the

analysis by considering the full length of the curve and half of the transition

length as a single radius curve.

• Horizontal elements not fully contained within 200m of the intersection for

Departmental roadways, and 50m from the intersection for Council roads, whose

partial length exceeded 30m. This typically included sections of moderate to large

radius curves and horizontal straights. Where 60% or more of the horizontal

geometric element was contained in the sample, the decrease in speed between

successive elements was based on the speed prior to the particular geometric

element. Where this figure was less than 60%, only portions of larger radius

curves and horizontal straights were used. In the latter case, the decrease in speed

between successive elements was set to zero.

Horizontal geometric elements that did not meet the above criteria were excluded.


The variables selected for the Single-Through vehicle accident categories are shown

in Table 20.1, along with the results of applying the regression analysis techniques




Table 20.1 shows that there is reasonable consistency of results across the various

subcategories. The ‘Minor’ accident subcategory comprises only ten accidents. This

small number of accidents produces a relatively consistent result with the other

accident subcategories, which shows that the variables in this model are important

predictors of Single-Through vehicle accidents.

233

Table 20.1 - Variables and Results of the Regression Analysis for Single-Through Vehicle Accident Subcategories


Variable Description Function Types (1) Major Minor Both All

QiT Traffic flow on the geometric element (one direction only)

PR *** QMT

* QST

*** QMT/QST

*** QMT/QST

SiE+∆SiE Through 85th % ile speed on the horizontal element prior to the horizontal element under consideration

PR *** SME+∆

SME

* SSE+ ∆SSE

*** SME+∆SME/ SSE+ ∆SSE

*** SME+∆SME/SSE+ ∆SSE

RCi Road classification EX R C N C Ci

= 1/Ri Vehicle path curvature on the horizontal geometric element

EX, PO *** CME

* CSE

*** CME/ CSE

*** CME/ CSE

AH Horizontal alignment of the minor legs

EX - - - *

MSM Movement type - f (free left-turn), l (non free left-turn), m (major road), s (minor road)

Factorial variable

- - V V







Selected Model

The ‘All’ accident subcategory contained the low frequency accident type Single-

Minor-Turn. It has not been selected as the final equation to predict Single-Through

vehicle accidents for the following reason. It was considered that the behaviour of

drivers involved in Single-Minor-Turn vehicle accidents (those turning from the

minor road onto the major road) might be significantly different to that of through

234

drivers travelling on the major or minor roads.

Through drivers usually approach each horizontal geometric element at speed.

However, drivers turning from the minor road onto the major road may have been

stationary prior to the turn. Therefore, the speed variables may not form the same

relationship for Single-Minor-Turn vehicle accidents as Single-Through vehicle

accidents.

The ‘Major’ accident subcategory comprised a reasonable number of accidents, but

the maximum decrease in speed on the horizontal geometric elements only extended

to 20km/h. The ‘Minor’ accident subcategory comprised a greater range of decreases

in speed but comprised only nine accidents.

The ‘Both’ accident model comprises the Major and Minor accident subcategories

and therefore contains a larger accident sample and a greater range of decrease in

speed between successive element. For this reason, the ‘Both’ accident model is

considered the best model to predict Single-Through vehicle accident rates.

By combining the Single-Through vehicle accidents on the major and minor roads

into the one model, it is assumed that traffic flow, speed, and radius terms form the

same relationship with Single-Through vehicle accidents for the major road as the

minor road. This would seem a reasonable approach given the total amount of data

available. Much more data would be needed to prove otherwise. However, the

accident rate of a horizontal geometric element on the major road with the same

characteristics as one on the minor road will yield a different accident rate because of

the factorial variable ‘Movement Type’.

The results of the regression analysis for the ‘Both’ accident subcategory are shown

in Table 20.2.

The selected Single-Through vehicle accident model ‘Both’ is given by Equation

20.1. The variable ‘Radius’ has been used in this equation in lieu of ‘Curvature’.

AST = 8.03 x 10-9 x QiT0.82 x (SiT + ∆Si)1.91 x exp(106 / Ri + MSM)

Equation 20.1

where AST = number of Single-Through vehicle accidents per year per

horizontal geometric element (one direction only)

QiT = traffic flow on the horizontal geometric element - one way only

235

(veh/d)

SiT+∆Si = 85th percentile speed on the horizontal geometric element plus

the decrease in speed on the element according to the speed

prediction model in Section 6.3 (km/h)

Ri = vehicle path radius on the horizontal geometric element

according to Figure B1 in Appendix B - Vehicle Path Model

(m)

MSM = movement type - dummy variable (0 for a through movement

on the major road, -1.6 for a through movement on the minor

road prior to the intersection)

Table 20.2 - Regression Analysis Results for the ‘Both’ Accident Subcategories



(1) k -18.6 2.78 1.82E-11 100

log(QiT) 0.820 0.111 2.08E-13 100 log(SiT + ∆Si) 1.91 0.494 0.000108 100

Ci 106 10.2 <2E-16 100 MSM - S -1.60 0.500 0.00133 75



the 2.5% level using a Chi-squared test. As the residual deviance is 375.1, the data is considerably under-dispersed.

(3) The mean recorded accident rate (number of accidents per year per element) = 0.0317 The mean predicted accident rate = 0.0313 The mean error in accident rate = 0.0480 (1.51 x average recorded accident rate)


The selected model ‘Both’ gives the following results.

Traffic Flow

The Single-Through vehicle accident rate is a function of the through traffic flow.

This is an expected result.

Speed Prior to the Geometric Element

The Single-Through vehicle accident rate is a function of the 85th percentile speed on

236

the horizontal geometric element prior to the element under consideration to a power

of 1.91. Horizontal geometric elements on high-speed roads potentially record much

higher Single-Through vehicle accident rates than do low-speed roads.

Vehicle Path Radius on the Horizontal Geometric Element

A plot of the standardised Single-Through vehicle accident rate (accident rate of one

at a radius of infinity) versus vehicle path radius is shown in Figure 20.1. This figure

illustrates that Single-Through vehicle accident rates increase substantially as the

radius decreases below about 120m.

0

1

2

3

4

5

6

7

8

9

10

0 100 200 300 400 500Vehicle Path Radius (m)

Stan

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Estimate

Figure 20.1 - Effect of Vehicle Path Radius on Single-Through Vehicle Accidents

Figure 20.1 shows an exponential function. A polynomial function was also used and

was found to be important. The polynomial shape was similar to the exponential

shape except that the accident decreased sharply for radii less than 54m. At radii

around 20m, the accident rate approached zero. It was felt that this was unreasonable

and that the accident rate at 20m should at least be a significant positive value, even

if smaller than the value at a radius of 54m.

It was seen that this was caused by the function itself. A polynomial function will

reach a zero accident rate at a radius of zero (curvature of infinity). This is caused by

the transformation of the polynomial equation back to the original form (refer

Section 16.3). A higher order polynomial could overcome this problem. However,

237

three and four order polynomials were tested in the analysis but were not found to be

significant.

Because the polynomial function did not yield suitable results, the exponential

function was adopted.

Element Type

The Single-Through accident rate on the major road is 5 times higher than that on the

minor road. This is an expected result because an intersection on a minor road can

provide a high level of perception to drivers of the need to reduce speed. This

perception is given by signage, intersection backdrop, the major carriageway and

other features. Conversely, less information is generally provided on the major road

where there is a decrease in speed between successive horizontal elements.

Length of Vehicle Path on the Horizontal Geometric Element

The parameter ‘length of vehicle path on the horizontal geometric element’ was not

used in the regression analysis. As shown in Table 16.2, it was omitted because it

correlated strongly with the primary variable ‘vehicle path radius on the horizontal

geometric element’. This occurred because small radius curves are normally

associated with shorter lengths than larger radius curves.

It is desirable to include this parameter into the analysis in order to account for the

length of the geometric element. This would be particularly useful to account for the

length of larger radii horizontal elements and straights. As the length of these

elements increase, the potential for single vehicle accidents increase due to an

increase in exposure.

Arndt (1998) included this parameter into an analysis of single vehicle accidents at

roundabouts by applying it as an offset variable (a variable having a proportional

function with a power constant of one). Although this has not been done in the final

Single-Through vehicle accident model, it is an option.

Single - Through Vehicle Accident Location

Figure 20.2 shows the location of Single-Through vehicle accidents on horizontal

geometric elements in the ‘Major’ accident subcategory. Twenty percent of the

accidents were located 10m - 60m past the end of the horizontal geometric element.

238

This is a similar finding to that found in Shelton and Arndt (1992) for horizontal

curves on steep downgrades.

0

5

10

15

20

25

30

35

40

0 - 25 25 - 50 50 - 75 75 - 100 >100

Accident Location Along Horizontal Geometric Element (Percentage of the Length of the Element)

Num

ber o

f A

ccid

ents

Figure 20.2 - Location of Single-Through Vehicle Accidents on Horizontal Geometric Elements in the ‘Major’ Accident Subcategory

Comparison with the Formula for Single Vehicle Accidents at Roundabouts

Each of the terms in the ‘Both’ Single-Through vehicle accident model are the same

as those in the single vehicle accident model for roundabouts in Arndt (1998). As

discussed previously, the only exception to this being that Arndt (1998) applied the

parameter ‘length of vehicle path on the horizontal geometric element’, as an offset

variable.

The consistency in results between the studies is a further indication of how

important these terms are in regard to their effect on single vehicle accident rates.

20.4 Alternative Single-Through Vehicle Accident Models

This section shows how selecting alternative variables in the analysis can yield

different results in some instances. The major reason identified for this result is the

high level of correlation between these alternative variables.

Table 20.3 shows alternative accident models using the ‘Both’ accident data sample.

These models were developed using variables that were rejected in Section 16.2 due

to high levels of correlation with primary variables. Where these variables were used,

239

the associated primary variables were not. The alternative models assume different

functional relationships as shown in Table 20.3. These models explained less of the

variability in the data than did the ‘Both’ accident model.

Table 20.3 - Alternative Single-Through Vehicle Accident Models Alternative

Model Number

Variable Code


QiT Traffic flow on the horizontal geometric element (one direction only)

PR

∆Si Decrease in 85th percentile speed on the horizontal geometric element

PO

A1

MSM Movement type, m (major road), s (minor road)

EX


PR

∆Si Decrease in 85th percentile speed on the geometric element

EX

A2


EX


PR

fi Side friction used on the horizontal geometric element

EX

Li Length of vehicle path on the horizontal geometric element

PR

A3


EX

Note: (1) Refer to Section 16.3 for the function types shown in the last column. For the ‘Both’ accident model and the alternative accident models in Table 20.3, the

predicted single vehicle accident rate for a number of cases is given in Table 20.4.

The bottom row of Table 20.4 shows the ratio of the maximum accident rate

predicted by the various models to the minimum for the various cases. These values

show that there can be large differences in the predicted accident rate caused by the

choice of the particular variables and types of functions in each model.

The ratio for case number six particularly highlights the large differential in accident

rates that can occur. Case 6 is an extreme case where a 50m radius curve is used in a

100km/h speed environment. Although this case is extreme, there are a few sites in

the study similar to this. These sites comprise tight curvature on minor legs

immediately before an intersection.

240

The main reason for such a variation in accident rates is a lack of robust data as

discussed in Section 3.1. Correlation between variables is a major reason for this lack

and an example of this correlation problem is given in the following section.

Table 20.4 - Predicted Single-Through Vehicle Accident Rates for Various Cases Variable Case 1 Case 2 Case 3 Case 4 Case 5 Case 6

Speed Environment (km/h)

60 60 60 100 100 100

Radius (m) 500 100 50 500 100 50 Length (m) 250 100 50 250 100 50

Accident Model Standardised Accident Rate (1) Both 1 2.3 6.7 2.7 6.2 18 A1 1.2 3.1 7.5 4.0 28 4.8 A2 1.5 2.6 4.9 3.1 65 610 A3 1.3 3.7 9.9 2.9 18 25 Ratio of the maximum accident rate to the minimum for the particular case.

1.5 1.6 2.0 1.5 11 126

Notes: (1) The accident rate for the ‘Both’ model for Case 1 is standardised at a value of one. (2) Traffic flow = 5000 veh/d, speed environment = speed on the preceding element. The above results show that studies such as this can be particularly ineffective in

predicting absolute values of accident rates. Rather, they have greater benefit

identifying tends between geometric parameters and accident rates.

Comparison of the Alternative Single-Through Vehicle Accident Models

In Table 20.3, alternative Models A2 and A3 use the variables ∆Si (decrease in speed

between successive horizontal elements) and fi (side friction used on the particular

horizontal element) respectively. Both variables are strong predictors of Single-

Through vehicle accidents. However, these variables can yield significantly different

results as described below.

• In the alternative model A2, a large value of ∆Si will yield a high accident rate.

The accident rate on the second curve of two small reverse curves of the same

radius will yield a low accident rate. This is not expected to be a reasonable result

because drivers will be using high degrees of side friction on the second curve if

the curves are in a high-speed environment. The use of high degrees of side

friction is not expected to result in a low accident rate.

241

• In the alternative model A3, a large value of fi will yield a high accident rate. The

accident rate on the second curve of two small reverse curves of the same radius

will be the equal to that for the first curve. This is not expected to be a reasonable

result because a large decrease in speed will occur on the first curve if it follows a

high-speed element. In this case, the accident rate on the second curve is expected

to be lower than for the first curve.

The problems discussed above could be avoided if both the variables ∆Si and fi could

be included in the same model. However, because between these variables were

correlated at a level of 77 percent, this was not possible. Including both variables into

an analysis showed that ∆Si was not significant.

To include both these variables into the one model, the amount of correlation needs

to be decreased substantially. To achieve this, adequate numbers of horizontal

geometric elements comprising the following criteria need to be included in the

study:

• Low values of ∆Si, high values of fi - typically reverse or compound curves where

the radius of the second curve is greater or equal to the first.

• High values of ∆Si, low values of fi - this criterion does not occur simultaneously.

In this study, only 19 elements, 4% of the total traffic and 3 accidents were on

elements that met the criteria in the first dot point. The only way to reduce the

amount of correlation between these variables is to include a greater number of these

elements. A considerable amount of work would be required to obtain an adequate

number of such sites and this is well outside the scope of this study.

The selected accident model ‘Both’ at least partially overcame this correlation

problem by using neither variable in isolation.

242

21 LOW FREQUENCY INTERSECTION ACCIDENTS


described in Chapter 16 to the Low Frequency Intersection accident category.

21.1 Rear-End-Minor

Categorisation of the Data

Two subcategories of data have been considered for analysis as follows:

• Leg - all Rear-End-Minor vehicle accidents per minor leg. Sample size 27

accidents and 269 minor legs.

• Turn - all Rear-End-Minor vehicle accidents per front vehicle movement type.

Sample size 22 accidents and 664 turning movements.

Variables Selected for Analysis

The variables selected for the Rear-End-Minor vehicle accident category are shown

in Table 21.1, along with the results of applying the regression analysis techniques




Table 21.1 shows that the only variable significant across both models is the traffic

flow from the minor leg.


It is recommended that the ‘Turn’ accident subcategory be adopted to predict Rear-

End-Minor vehicle accidents at unsignalised intersections. This model allows for the

various movement types, which are significant predictors of these accidents.

The results of the regression analysis for the Rear-End-Minor vehicle accident

subcategories are shown in Table 21.2.

243

Table 21.1 - Variables and Results of the Regression Analysis for Rear-End-Minor Vehicle Accidents

Accident Subcategory

Variable Code


Leg Turn QSi Traffic flow from the minor leg PR ***

QSA *** QSi

QMA Total traffic flow on the major road (from both major legs)

PR N N

SES Speed environment of the minor road

EX N N

TSAP Approach visibility from the minor road to the intersection measured in time

IN N N

RCS Classification of the minor road

EX N N

LIGHTS Level of lighting on the minor road

EX N N

FOV Field of view EX N N NLS Number of stand-up lanes at

the minor road approach PR N -

DHL Distance from the holding line to the continuity line

EX N -

CONT Level of control EX N - NCONT Number of control signs EX N - NLEG Number of legs at the

intersection EX N -

θRRT Observation angle EX N - FLTLS Presence of a free left-turn lane

from the minor road EX * -

MS1 Movement type from the minor road (free left-turn is the comparative factor)

Factorial variable

- V







244

Table 21.2 - Regression Analysis Results for the ‘Turn’ Accident Subcategory Variable Estimate Standard

Error Pr(>|z|) Cross

Validation (1)

k -9.28 1.60 6.6E-9 100 log(QSi) 0.858 0.216 7.2E-5 100

MS1 - Left -0.711 0.558 0.203 - MS1 - Right -1.55 0.650 0.0172 -

MS1 - Through -1.07 0.862 0.214 - Notes: (1) The values in the last column are the number of times out of 100 that each variable was selected



(3) The mean recorded accident rate (number of accidents per year per movement type) = 0.00617 The mean predicted accident rate = 0.00600 The mean error in accident rate = 0.011 (1.78 x average recorded accident rate) The selected Rear-End-Minor vehicle accident model ‘Turn’ is given by Equation

21.1.

ARS = 9.33 x 10-5 x QSi0.858 x exp(MS1) Equation 21.1

where ARS = number of Rear-End-Minor vehicle accidents per year per minor

leg per movement type

QSi = turning traffic flow from the minor leg for the particular movement

(veh/d)

MS1 = movement type- factorial variable (0 for a free left-turn movement,

-0.711 for a non-free left-turn movement, -1.07 for a through

movement and -1.55 for a right-turn movement)

Discussion of the Regression Analysis Results

The selected accident model ‘Turn’ gives the following results.

Minor Road Traffic Flows The Rear-End-Minor vehicle accident rate is a function of the minor road turning

traffic flows. This is an expected result.

Movement Type

The ‘Turn’ accident subcategory shows that the Rear-End-Minor vehicle accident

rate for a free left-turn movement (for the front vehicle) is as follows:

• 2.0 times that for a non free left-turn movement

245

• 4.7 times higher than for a through movement

• 2.9 times higher than for a right-turn movement

These results cannot be confidently relied upon because there are only a small

number of accidents in each subcategory. However, movement type was a significant

predictor of Rear-End-Minor vehicle accidents and the results suggest that accident

rates may be highest for free left-turning movements. The results also suggest that

accident rates for non-free left-turn movements are higher than for through and right-

turn movements.

The results above are considered reasonable because on-site inspections have

revealed that drivers turning left tend to be travelling faster than did through or right-

turning drivers. For the duration of the turn, drivers turning left appeared to spend a

large amount of time viewing the major leg to the right for oncoming vehicles.

Because of the large observation angle, they looked well away from their direction of

travel. This may increase their chances of not adequately perceiving a vehicle

stopping in front of them. Their higher speed further compounds this situation. This

behaviour was even more pronounced on free left-turn lanes.

It is anticipated that the higher rate for the free left-turn movement may be somewhat

under estimated for the following reason. For non-free left-turn movements, the rear

vehicle may be undertaking a different movement to the front vehicle depending on

the configuration of the stand-up lanes. Therefore, the exposure to this accident type

is greater than the traffic flow for the left-turn movement alone.

For free left-turn movements, it is considered more likely that the rear vehicle is also

taking a left-turn movement. This is because free left-turn lanes only comprise left-

turning traffic, unlike stand-up lanes that allow for multiple turning movements.

Therefore, the exposure for the free left-turn movement is probably related more to

only the left-turn traffic volume. This could only be proven if more data were

available. There are insufficient accidents within this category or sites with the

various stand-up lane configurations (refer Figure 6.2) to perform such an analysis.

Minor Road Approach Speed Arndt (1998) found that rear-end accidents on the approaches to roundabouts

increased with an increase in the speed on the entry curve. It was somewhat

surprising that the approach speed was not a significant predictor of Rear-End-Minor

246

vehicle accidents at unsignalised intersections. This result is possibly due to the small

number of accidents. However, it is anticipated that speed is probably not a major

predictor of these accidents as such an effect would probably have been identified

even with this small data sample.

21.2 Single-Minor-Turn


Three subcategories of data have been considered for analysis as follows:

• Leg - all Single-Minor-Turn vehicle accidents per minor leg. Sample size 23

accidents and 269 minor legs.

• Turn - all Single-Minor-Turn vehicle accidents per minor leg per movement type

(excluding through movements). Sample size 22 accidents and 538 turning

movements.

• Element - all Single-Minor-Turn vehicle accidents per horizontal geometric

element for the particular turning movement. Analysis performed in the same way

as for Single-Through vehicle accidents. Sample size 22 accidents and 538 turning

movements.


The variables selected for the Single-Minor-Turn vehicle accident category are

shown in Table 21.3 along with the results of applying the regression analysis

techniques discussed in Chapter 16. For more information on these variables, refer

Appendix C - Geometric Variables. Table 21.4 shows the significance of alternative

variables used in the analyses.


Table 21.3 shows relatively consistent results across the three accident subcategories.

The variables ‘minor road approach flow’ and ‘road classification’ are significant

across all subcategories. If ‘road classification’ is removed, the approach speed

variable becomes important in each case. Table 21.4 shows this for the ‘Turn’

accident subcategory. The variable ‘horizontal alignment of the minor legs’ was also

significant across all subcategories. The two models that used ‘movement type’ also

gave consistent results for this variable.

247

Table 21.3 - Variables and Results of the Regression Analysis for Single-Minor-Turn Vehicle Accidents


Variable Description Function Types (1) Leg Turn Element

QSi Traffic flow on the minor leg PR * QSA

** QSi

** QSi

QMA Total traffic flow on the major road (from both major legs)

PR N N -

SSAP 85th percentile minor road approach speed

EX N N -

SSE+∆SS 85th percentile speed prior to the turn

PR - - N

TSAP Approach visibility from the minor road to the intersection measured in time

IN N N -


EX *** *** ***

LIGHTS Level of lighting on the minor road

EX R R -

FOV Field of view EX N N - NLS Number of stand-up lanes at

the minor road approach PR N - -

DHL Distance from the holding line to the continuity line

EX N - -

CONT Level of control EX N - - NCONT Number of control signs EX R - -

AH Horizontal layout of the minor legs

EX ** * *

FLTLS Presence of a free left-turn lane from the minor road

EX N - -

RSi Driver path radius on the particular horizontal element

IN,PO - - N

MS1 Movement type from the minor road (free left-turn is the comparative factor)

Factorial variable

- V V







248

Table 21.4 - Alternative Variables for Single-Minor-Turn

Vehicle Accidents for the ‘Turn’ Subcategory Original Variable

Code

Original Variable

Description


Code


Description

Results


SSAP 85th percentile minor road

approach speed

L



It is recommended that the ‘Turn’ accident model be adopted to predict Single-

Minor-Turn vehicle accidents at unsignalised intersections. Unlike the ‘Leg’ accident

subcategory, this model considers the various movement types that are a significant

predictor of Single-Minor-Turn vehicle accidents.

It is considered that the ‘Element’ model does not adequately allow for minor driver

behaviour at intersections. The ‘Element’ model uses the alternative variable ‘85th

percentile speed prior to the turn’ in lieu of ‘road classification’ in order to be

consistent with the Single-Through vehicle accident model. This was the original

purpose of the ‘Element’ model.

The ‘Element’ model utilises a proportional relationship between the variable ‘85th

percentile speed prior to the turn’ and Single-Minor-Turn vehicle accidents. This

relationship yields a zero accident rate at a zero approach speed.

Some drivers involved in Single-Minor-Turn vehicle accidents may well have been

stationary on the minor road prior to the turn (ie zero approach speed). It is possible

for these drivers to accelerate too quickly and be involved in a Single-Minor-Turn

vehicle accident (as evident in the Crash Incident Reports). An exponential

relationship is considered more appropriate for this model because it allows a

positive accident rate at zero approach speed.

This is in contrast to the appropriateness of a proportional relationship for Single-

Through vehicle accidents on the minor road approaches (prior to the intersection)

249

and on the major road. In these cases, drivers usually approach each horizontal

geometric element at speed. There is no evidence in the Crash Incident Reports that

drivers involved in these accidents are losing control due to accelerating from a low

speed.

As discussed previously, the variable ‘minor road approach speed’ was only

significant when the variable ‘road classification’ was removed. These variables

were correlated at the 38% level, close to the value chosen as the cut-off for

maximum correlation allowed. Even at this level, the correlation strongly affects the

results. The stepwise regression analysis did not allow both variables to be included

in the final model. In reality, though, it is considered that both variables would

probably have an effect.

The variable ‘minor road approach speed’ was selected in lieu of the variable ‘road

classification’ for the final equation of the ‘Turn’ accident model. This accident

model was one of the few where road classification was more important than speed.

In most other models, the speed terms only were significant. To provide consistency

across all of the accident types, it was decided to use only speed variables in all of

the final accident models.

It is considered that the variable ‘Minor Road Approach Speed’ may be a more

important predictor of these accidents than ‘Road Classification’. This is because all

of the other single vehicle accident models (excluding Single-Major-Turn accidents)

incorporate speed terms rather than road classification. It is reasonable that the speed

term may be just as important in this case.

The results of the regression analysis for the ‘Turn’ accident subcategory are shown

in Table 21.5.

The selected Single-Minor-Turn vehicle accident model ‘Turn’ is given by Equation

21.2.

ASS = 1.03 x 10-4 x Qsi0.606 x exp(0.0209 x SSAP - 0.642 x AH + MS1)

Equation 21.2

where ASS = number of Single-Minor-Turn vehicle accidents per year per minor


QSi = turning traffic flow from the minor leg for the particular movement

250

(veh/d)

SSAP = 85th percentile minor road approach speed (km/h)

AH = horizontal layout of the minor legs - dummy variable (refer

Table C16 in Appendix C - Geometric Variables)

MS1 = movement type - factorial variable (0 for a free left-turn movement,

-1.07 for a left-turn movement, 0.104 for a right-turn movement)

Table 21.5 - Regression Analysis Results for the ‘Turn’ Accident Subcategory



(1) k -9.18 1.66 3.1E-8 100

log(QSi) 0.606 0.178 0.00068 100 SSAP 0.0209 0.0103 0.0436 87 AH -0.642 0.321 0.0454 98

MS1 - Left -1.07 0.724 0.141 - MS1 - Right 0.104 0.589 0.860 -




(3) The mean recorded accident rate (number of accidents per year per movement type) = 0.00765 The mean predicted accident rate = 0.00764 The mean error in accident rate = 0.0139 (1.82 x average recorded accident rate)


The ‘Turn’ accident subcategory gives the following results.

Minor Road Traffic Flow / Turning Flows The Single-Minor-Turn vehicle accident rate is a function of the minor road turning

traffic flows. This is an expected result.

Road Classification of the Minor Road/ Minor Road Approach Speed The variable ‘Road Classification’ was not used in the final equation of the ‘Turn’

accident model. If it were included, roads with a higher functional classification

would record a higher Single-Minor-Turn vehicle accident rate than would roads of a

lower functional classification. The degree to which this would occur is given in

Table 21.6.

Table 21.6 shows that minor roads with the highest functional level would record a

Single-Minor-Turn vehicle accident rate 30 times higher than would minor roads

251

with the lowest functional level. Roads with higher functional levels usually have

much more through traffic travelling longer distances. Drivers are less likely to be

familiar with the road and are less likely to be anticipating a stop or give way sign at

an intersection on this type of road.

Table 21.6 - Single-Minor-Turn Vehicle Accident Rates for the Various Minor Road Classifications

Minor Road Classification Standardised Single-Minor-Turn Vehicle Accident Rate

(Secondary Road Set at Unity) State Highway, Developmental

Road Urban Arterial or Sub-arterial Road

30

Main Road 5.5 Secondary Road 1

The variable ‘minor road approach speed’ has been used in the final equation in lieu

of ‘road classification’. Figure 21.1 shows the effect of minor road approach speed

on Single-Minor-Turn vehicle accident rates using the results from the ‘Turn’

accident subcategory. This figure shows that the Single-Minor-Turn vehicle accident

rate increases with minor road approach speed. A minor road approach speed of

110km/h has a 2.3 times higher Single-Minor-Turn vehicle accident rate than does a

70km/h approach speed.

0

5

10

15

20

25

0 10 20 30 40 50 60 70 80 90 100 110Minor Road Approach Speed

Stan

dard

ised

Sin

gle-

Min

or-

Turn

Acc

iden

t Rat

e

Estimate95th Percentile Confidence Limits

Figure 21.1 - Effect of Minor Road Approach Speed on Single-Minor-Turn Vehicle Accidents

252

Table 21.5 shows that the minor road approach speed was selected 87 times in the

cross validation process. This value indicates that the model is not as stable as is

desired. The lower 95th percentile confidence limit in Figure 21.1 is almost flat, also

indicating much variability in the data. Part of the reason for this result is that there

was one large outlier in the data, which was a minor leg on a major national highway

in a high-speed environment. This is quite a rare situation. There were no other

minor legs in the data on such a major road.

The choice of the road classification variable ‘RCS’ or the minor road approach

speed variable ‘SSAP’ for the final equation makes a significant difference as to

whether any means of reducing this accident type is possible. The road classification

cannot be changed, whereas the minor road approach speed can potentially be

reduced by devices such as reverse curves, rumble strips, speed limit signage etc.

Horizontal Layout of the Minor Legs T-intersections record a 3.6 times higher Single-Minor-Turn vehicle accident rates

than do cross intersections with completely aligned minor legs. This suggests that

aligned opposite minor legs at a four leg intersection enables drivers not perceiving

the intersection in time to travel at speed through the intersection and onto the

opposite minor leg. The opposite minor road leg therefore acts as a type of ‘escape

area’.

Conversely, at T-intersections (where no opposite minor leg exists), drivers who do

not perceive the intersection in time will potentially collide with signage, roadside

furniture or a cut face or overturn on fill slopes opposite the minor road approach.

This is the only accident type where a cross intersection with aligned minor legs

yields a better safety record than a T-intersection. However, the increased safety

performance of cross intersections for this accident type is more than offset by the

decreased safety record for the other accident types.

This model assumes that cross intersections with the minor road legs significantly

misaligned act in the same way as a T-intersection.

Movement Type The Single-Minor-Turn vehicle accident rate for a free left-turn movement is as

follows:

• 3.4 times that for a non-free left-turn movement

253

• 1.1 times higher than for a right-turn movement

These results cannot be confidently relied upon because there are few accidents in

each subcategory. However, the results suggest that the Single-Minor-Turn vehicle

accident rate may be lower for non-free left-turn movements than for free left-turn

movements and right movements.

The higher accident rate for free left-turn movements (compared to a non-free left-

turn movement) is considered reasonable. As discussed in Section 21.1, on-site

inspections have revealed that left-turning drivers tend to travel faster on free left-

turn lanes than non-free left-turn lanes. This results in drivers using a higher degree

of side friction, which increases their potential for losing control.

Approach Visibility on the Minor Road Approach visibility on the minor road did not significantly affect the Single-Minor-

Turn vehicle accident rate. This variable was measured using the Approach Sight

Distance model in QDMR (2000) and Austroads (1988) in which a 1.15m eye height

and a 0m object height is used. One reason considered for this result is that an

intersection can usually be well perceived from the minor road with values of

approach sight distance far below that listed as the minimum. This is for the same

reasons as given for Angle-Minor vehicle accidents in Section 17.4.

21.3 Single-Major-Turn


Only one category of data has been considered for analysis as follows:

• All Single-Major-Turn vehicle accidents per major leg per movement type.

Sample size 17 accidents and 538 turn movements.


The variables selected for the Single-Major-Turn vehicle accident category are

shown in Table 21.7 along with the results of applying the regression analysis



The final results of the regression analysis for the Single-Major-Turn vehicle

accident category are shown in Table 21.8 and by Equation 21.3. These results were

254

obtained by placing the variable ‘MM1’ (movement type) into the final equation even

though it was not significant. This variable was included because it was desirable to

know the relative accident rates for the three movement types, even though they may

not be significantly different.

Table 21.7 - Variables and Results of the Regression Analysis for Single-Major-Turn Vehicle Accidents

Variable Code


Results

QMi Traffic flow turning from a major leg

PR *

QMMOD Through traffic flow on the opposing major leg (for right-turns only)

EX N


PR N

TMAP Approach visibility from the major road to the intersection measured in time

IN N


EX N

RML/RMR Radius of the vehicle path turning from the major road

EX N


EX N

WMEDM Median width (for right-turns only)

EX N

TTCRLB Major road turn type CHR & AUL or LSR, AUR, MNR, & LSL

EX N

MM1 Movement type from the major road (free left-turn is the comparative factor)

Factorial variable

N







255

Table 21.8 - Final Regression Analysis Results

for the Single-Major-Turn Vehicle Accidents Category Variable Estimate Standard

Error Pr(>|z|) Cross

Validation (1)

k -6.64 1.37 1.35E-6 100 log(QMi) 0.394 0.204 0.0531 96

MM1 - Left -1.17 0.718 0.104 - MM1 - Right -0.702 0.604 0.245 -




(3) The mean recorded accident rate (number of accidents per year per movement type) = 0.00613 The mean predicted accident rate = 0.00589 The mean error in accident rate = 0.0116 (1.89 x average recorded accident rate)

ASM = 1.31 x 10-3 x QMi

0.394 x exp(MM1) Equation 21.3

where ASM = number of Single-Major-Turn vehicle accidents per year per major


QMi = turning traffic flow from the major leg for the particular movement

(veh/d)

MM1 = movement type - factorial variable (0 for a free left-turn, -1.17 for a

non-free left-turn movement, -0.702 for a right-turn movement)


Major Road Turning Flow The Single-Major-Turn vehicle accident rate is a function of the traffic flow turning

from the major road. This is an expected result.

Movement Type This variable was not a significant predictor of Single-Major-Turn vehicle accident

rates. This variable was included because it was desirable to know the relative

accident rates for the three movement types. The Single-Major-Turn vehicle accident

rate is 3.2 times higher on free left-turn lanes than for non-free left-turns. As this

value is only based on a small accident sample, a high level of confidence cannot be

placed in this result.

256

As discussed in Section 21.1, drivers travelling on free left-turns do so with higher

degrees of side friction than drivers undertaking non-free left-turns. This is especially

true for the larger radii free left-turns. It could be expected, therefore, that the

accident rate on a free left-turn would be higher than for a non-free left-turn. A

similar result was found for Single-Minor-Turn vehicle accidents in the previous

section.

The Single-Major-Turn vehicle accident rate for a right-turn is 1.6 times higher than

a non-free left-turn. With the small number of accidents in this sample, a high level

of confidence cannot be placed in this result.

Speed on the Major Road Unlike the other single vehicle accident models in this study, speed was not a

significant parameter in the Single-Major-Turn vehicle accident model. The expected

reason for this is as follows.

Drivers turning from the major road have probably perceived the intersection. For

those wishing to turn but have not adequately perceived the intersection, a potential

consequence is simply overshooting the intersection. These drivers would then have

to undertake a U-turn at some location in order to come back and turn at the

intersection. An increased major road speed may result in a greater number of drivers

overshooting the intersection.

This situation is unlike Single-Minor-Turn vehicle accidents at T-intersections where

the consequence of not adequately perceiving the intersection potentially results in

colliding with the opposite side of the T-intersection eg into a cut batter or

intersection sight board. In this case, higher speeds result in an increased probability

of not stopping in time and an increased level of accident severity.

Approach Visibility on the Major Road It was found that approach visibility on the major road did not significantly affect

Single-Major-Turn vehicle accident rates. This variable was measured using the

Approach Sight Distance model in QDMR (2000) and Austroads (1988) in which a

1.15m eye height and a 0m object height is used.

One reason considered for this result is that in some instances, an intersection can be

well perceived from the major road with values of approach sight distance far below

those listed as the minimum. This is generally the result of good perception of the

257

intersection due to channelisation, pavement marking, a gap between buildings or

vegetation, signage, presence of minor road vehicles, or slope of the minor road.

Another reason considered for this result is that those drivers wishing to turn at the

intersection, but have not adequately perceived the intersection, potentially will

simply overshoot the intersection. This issue has been discussed in the previous

section.

Approach Sight Distance on the major road was found difficult to measure under the

certain conditions. For this reason, an alternative approach sight distance model was

developed as per Angle-Minor vehicle accidents. However, this model was also not a

significant predictor of Single-Major-Turn vehicle accidents.

21.4 Overtaking-Intersection


Only one category of data has been considered for analysis as follows:

• All Overtaking-Intersection vehicle accidents per major leg. Comprises major legs

with right-turn treatments LSR and AUR with no medians. Major legs comprising

type CHR and MNR turn types, and/or major legs with medians were excluded

from this sample because no Overtaking-Intersection accidents were recorded on

these treatments. Sample size 13 accidents and 128 major legs.


The variables selected for the Overtaking-Intersection vehicle accident category are

shown in Table 21.9, along with the results of applying the regression analysis



Table 21.10 shows the significance of alternative variables used in the analysis.

The final results of the regression analysis for the Overtaking-Intersection vehicle

accident category are shown in Table 21.11 and by Equation 21.4. These results were

obtained by placing the variable ‘TTLA’ (right-turn type) into the final equation even

though it was not significant. This variable was included because it was desirable to

know the relative accident rates for the two turn types, even though they may not be

significantly different.

258

The alternative variable ‘SMT’ has been used in the final equation for the reasons

stated in Section 17.3.

Table 21.9 - Variables and Results of the Regression Analysis for Overtaking-Intersection Vehicle Accidents

Variable Code


Results

QMR Traffic flow turning right from a major leg

PR *

QMT Through traffic flow on the major leg (one direction only)

PO N


PR ***

SRSLM Potential reduction in 85th percentile speed on the major leg due to a reduction in speed limit (used if SEM is important)

EX N

SRCM 85th percentile speed reduction on the major road due to curvature (used if SEM is important)

EX N

TMINT Visibility to intersection from the major road measured in time

IN R

RCM Classification of the major road EX N LIGHTM Level of lighting on the major road EX N

CMI Curvature of the major road PO N LINEM Line marking type EX *** TTLA Right-turn type LSR or AUR. LSR

is the comparative factor. Factorial variable

N







259

Table 21.10 - Alternative Variables for Overtaking-Intersection Vehicle Accidents

Original Variable

Code

Original Variable

Description


Code


Description

Results

SEM Speed environment of the major leg

SMT 85th percentile through speed on

the major leg

G


Table 21.11 - Final Regression Analysis Results for the Overtaking-Intersection Vehicle Accident Category



(1) k -60.2 16.6 0.000295 100

log(QMR) 0.877 0.361 0.0151 99 log(SMT) 11.6 3.40 0.000621 100

LINEM - Barrier -3.12 0.787 7.33E-5 100 TTLA - AUR -0.223 0.652 - -




(3) The mean recorded accident rate (number of accidents per year per leg) = 0.0175 The mean predicted accident rate = 0.0155 The mean error in accident rate = 0.0156 (0.891 x average recorded accident rate)

AOI = 7.39 x 10-27 x QMR0.877 x SMI

11.6 x exp(LINEM + TTLA) Equation 21.4

where AOI = number of Overtaking-Intersection vehicle accidents per year per

major leg for Type LSR and AUR turn types

QMR = traffic flow turning right from the major leg (veh/d)

SMi = 85th percentile through speed (km/h)

LINEM = line marking on the major road - factorial variable (0 for a broken

line, -3.12 for a barrier line)

TTLA = right-turn type - factorial variable (0 for a LSR turn type,

-0.223 for an AUR turn type)

260


Right-turn Traffic Flow on the Major Road The Overtaking-Intersection vehicle accident rate is a function of the traffic flow

turning right from the major road. This is an expected result.

Through Traffic Flow on the Major Road The through traffic flow on the major leg is not a significant predictor of Overtaking-

Intersection vehicle accidents. This is an unexpected result because the number of

vehicles overtaking is expected to increase with an increase in traffic volume, up to a

point where overtaking opportunities become limited because of inadequate gaps in

the oncoming traffic. After this point, the accident rate may be expected to decrease

(ie this variable may be expected to form a polynomial relationship with this accident

type). This effect, however, was not found in the data. It may have been caused by

the low number of accidents in the sample.

Through Speed on the Major Road Overtaking-Intersection vehicle accidents are related to the 85th percentile through

speed on the major road to a power of 11.6. This large power constant shows that

these accidents are predominant in high-speed environments with very few occurring

in lower speed areas. It is expected that a larger data sample would show this value to

be smaller.

Visibility to the Intersection on the Major Road The visibility to the intersection (measured in time) was used as an estimate of the

potential for overtaking due to the amount of available sight distance. The results of

the regression analysis showed that these accidents increased in areas of lower

visibility.

It was felt that this is an unreasonable result and that the accident rate should increase

in areas of increased visibility. This is because the amount of overtaking (a measure

of exposure) would increase in areas of increased visibility. This result may have

been caused by an inadequate number of sites with very poor visibility.

Consequently, this variable was removed from the final equation.

Line Marking on the Major Road The Overtaking-Intersection vehicle accident rate for LSR and AUR turn treatments

261

with broken centre line marking is 23 times higher for than these treatments with

barrier line marking. This would suggest that the provision of a barrier line at these

turn treatments would reduce the accident rate by 23 fold.

Many of the Type LSR turn treatments with barrier centre lines may comprise this

marking because of limited visibility for overtaking. This would suggest that the type

of line marking is not the only influence on the accident rate, but also the amount of

visibility. The significance of the variable LINEM may be reflecting the amount of

visibility. For this reason, an analysis of those turn types with only broken centre line

marking was performed. This analysis, however, showed that the visibility TMINT was

not a significant predictor of Overtaking-Intersection vehicle accidents.

Based on the above, it is unknown as to what degree the provision barrier centre line

has on the reduction of the Overtaking-Intersection vehicle accident rate. It is

probably somewhere up to 23 times. The only conclusion that could be reached is

that there are potential benefits in using barrier centre lines at Type LSR and AUR

turn treatments to minimise the Overtaking-Intersection vehicle accident rate. This

finding supports the use of barrier centerlines at all AUR turn treatments as shown in

Figure 13.54 of QDMR (2000).

It is considered that barrier lines should be used on LSR sites with higher traffic

volumes. This includes those sites that meet the warrants for a higher level turn type,

but are not upgraded due to limited funding. This is particularly important for sites in

high-speed environments and those providing good overtaking opportunities.

Turn Type This variable was not a significant predictor of Overtaking-Intersection vehicle

accident rates. This variable was included because it was desirable to know the

relative accident rates for the two turn types. The Overtaking-Intersection vehicle

accident rate for Type LSR turn treatments is 20 percent higher than for Type AUR

turn treatments. A larger value than this was expected because Type AUR treatments

are more prominent and may discourage more drivers from overtaking compared to

Type LSR treatments, which are less easily recognised.

Other Parameters

Of the six sites that recorded Overtaking-Intersection vehicle accidents, four

comprised horizontal straights, had more than sufficient sight distance for

262

overtaking, and were located after a significant section of roadway without

overtaking opportunities. It is probable that Overtaking-Intersection vehicle accident

rates would increase at such intersections with an increase in length of roadway prior

to the intersection that did not provide overtaking opportunities. This would

encourage more drivers to overtake through these intersections because of the

increased amount of time spent following other vehicles.

Measuring a parameter such as ‘length of roadway prior to the intersection that does

not provide overtaking opportunities’ in order to predict Overtaking-Intersection

vehicle accident rates would require much time and resources. This was considered

outside the scope of this study.

21.5 Remaining Intersection Accidents

The following low frequency intersection accident types have not been analysed

separately:

• Incorrect Turn - 17 accidents

• Sideswipe-Major-Auxiliary - 4 accidents

• Other - 8 accidents

These accidents were not analysed for the following reasons:

• Little accident data exists within each accident type; and/or

• Different exposure and propensity terms are applicable to various accident sub-

types within each accident type.

In addition to the ‘Other’ Low Frequency Intersection Accidents above, the

following accidents types have not been included in the final accident equations:

• Angle-Minor - 25 accidents involving minor conflicts or unknown conflicts

• Angle-Major - 5 accidents involving non-through oncoming movements

• Rear-End-Major - 5 accidents involving U-turn or unknown movements

• Rear-End-Minor - 5 accidents involving unknown front vehicle movements

• Single-Minor-Turn - 1 accident with an unknown turning movement

There are a total of 70 accidents that were not analysed, or not included in the final

equations. This represents 8.7 percent of the total intersection accidents data sample.

263

Equation 21.5 has been developed for the ‘Remaining’ intersection accidents by

dividing the 70 accidents by the total number of vehicles approaching all

intersections from all legs over the analysis period.

AOI = 1.45 x 10-5 x ΣQa (Equation 21.5) Where AOI = number of ‘Remaining’ intersection accidents per year per

intersection

Qa = average annual daily traffic flow approaching the intersection from

all legs (veh/d)

Part E

265

22 COMBINED RESULTS

This chapter combines the results obtained across accident types to determine overall

trends in the data.

22.1 Traffic Flow Variables

Table 22.1 shows the power constants of the traffic flow variables for the various

accident types recorded in this study. There are two traffic flow variables in this

table: one for the vehicle at fault and one for the vehicle not at fault. The latter is not

applicable for the single vehicle accident types.

Table 22.1 - Power Constants of the Traffic Flow Variables for the Various Accident Types Recorded in this Study

Power Constant Broad Accident Category

Accident Type QE

QN

Angle-Minor 0.77 0.3 Angle-Major 0.47 0.23

Rear-End-Major 0.94 0.43 Rear-End-Minor N 0.86

Multiple Vehicle

Overtaking-Intersection NS 0.88 Single-Through 0.82 -

Single-Minor-Turn 0.61 - Single

Vehicle Single-Major-Turn 0.39 -

Notes: QE = the traffic flow for the particular movement of the vehicle at fault QN = the traffic flow of the particular movement of the vehicle not at fault N = the traffic flow of the particular movement of the vehicle at fault was not used in the regression

analysis for this case. This was due to the small number of accidents and the complexity of allowing for the various types of conflicts within this accident type.

NS = the traffic flow was not found to be significant in this case. - indicates that a traffic flow is not relevant in this case

Table 22.1 shows that the power constants of all of the traffic flow variables are less

than one. This indicates that higher volume roads record less accidents per number of

vehicles than do low volume roads.

Rural intersections tend to have less traffic and higher speeds than urban

intersections. Many types of studies have shown that accident rates (accidents per

number of vehicles) at rural intersections are higher than those at urban intersections.

In the absence of a regression analysis such as this, one may consider that the

difference would be mostly the result of higher speeds (or longer reaction times) on

rural roads. However, Table 22.1 suggests that it is not solely these issues, but also

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the fact that less traffic uses these roads.

Roadways with lower traffic volumes comprise a greater number of free vehicles.

This probably results in the average speed being higher (as there is less time spent

following). In turn, this indicates that there is an interaction between traffic volume

and average speed. This will vary as traffic volumes change with the time of day.

Such an interaction is too complex to have been considered in this study.

A greater number of free vehicles probably results in a greater number of drivers

taking increased risks (eg travelling too fast for a given situation). Drivers confined

to follow other vehicles probably have less opportunity to take risks. It is expected

that these are some of the reasons why accident rates (accident per number of

vehicles) decrease with an increase in traffic volume.

Table 22.1 also shows the traffic flow for the particular movement of the vehicle at

fault is more important than that for the vehicle not at fault. This was true for all

multiple vehicle accident types except ‘Rear-End-Minor’ and ‘Overtaking-

Intersection’. In the case of Rear-End-Minor vehicle accidents, the traffic flow of the

particular movement of the vehicle at fault was not used in the regression analysis,

due to the small number of accidents and the complexity of the various types of

conflicts within the accident type.

The accident type ‘Overtaking-Intersection’ only consisted of 13 accidents and the

traffic flow of the vehicle at fault is quite complex to determine. For these reasons, it

was hardly surprising that the traffic flow variable used for the vehicle at fault (the

through volume) was not significant.

At many intersections, the highest accident rates are recorded for Angle-Minor

vehicle accidents. The vehicle at fault in these accidents is the minor road vehicle. As

the traffic flow for the particular movement of the vehicle at fault is more important

than that for the vehicle not at fault, the traffic flow on the minor road will have a

large influence on the total accident rate. This is one reason why intersections with

minor road traffic flows higher than the major road flows tended to record very high

total accident rates in this study.

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The fact that the power constants of all the traffic flow variables are less than one

also suggests the following hypothesis. For a particular major roadway, total safety is

increased by providing a smaller number of intersections carrying higher side road

volumes than it is to provide a greater number of intersections carrying lower side

road volumes. This hypothesises supports the notion that the number of intersections

along a roadway should be limited, subject to capacity and delay considerations

22.2 Speed Parameters

Table 22.2 illustrates what speed parameters were significant for the various accident

types recorded in the study. Two speed parameters are included in this table: one for

the vehicle at fault and one for the vehicle not at fault. The latter is not applicable for

the single vehicle accident types.

Table 22.2 - Significance of the Speed Parameters for the Various Accident Types Recorded in this Study

Parameter Significant

Broad Accident Category

Accident Type

SE SN Angle-Minor Y N Angle-Major N N

Rear-End-Major Y N Rear-End-Minor N N

Multiple Vehicle

Overtaking-Intersection Y N Single-Through Y -

Single-Minor-Turn Y - Single

Vehicle Single-Major-Turn N -

Notes: SE = the potential 85th percentile speed of the vehicle at fault SN = the potential 85th percentile speed of the vehicle not at fault Y = the parameter was significant and was included in the final accident model. N = the parameter was not found to be significant and was excluded in the final accident model - indicates that a speed parameter is not relevant in this case

Table 22.2 indicates that the potential speed of vehicles at fault is significant in five

out of the eight accident types. For these five cases, the driver at fault potentially

may not have perceived the intersection or horizontal curve adequately to negotiate

it. For the multiple vehicle accident types, these drivers may not have made a

conscious decision to turn at the intersection.

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For the other three accident types, the ‘speed of the vehicle at fault’ was not

significant. In two out of three of these accident types, the driver at fault has

probably perceived the intersection because there has been a conscious decision to

turn from the major road. The other accident type ‘Rear-End-Minor’ consisted of

only a small data sample and a high level of confidence cannot be placed in the

results.

Table 22.2 shows that the potential speed of vehicles not at fault was not significant

in any case.

Table 22.3 lists the relative accident rate for the accident types where the potential

speed of the vehicle at fault was a significant parameter. The relative accident rate is

the accident rate for a speed of 100km/h divided by the accident rate for a speed of

60km/h. The purpose of this table is to show the relative effect of speed on the

various accident types.

Table 22.3 - Relative Accident Rate for 100 and 60 km/h Speeds for the Accident Types where Speed was a Significant Parameter

Accident Type Relative Accident Rate (Accident Rate for Speed of 100km/h Divided by

Accident Rate for Speed of 60km/h) Angle-Minor 1.6 Rear-End-Major 4.6 Single-Through 2.7 Single-Minor-Turn 2.3 Overtaking-Intersection 374

Table 22.3 shows that Overtaking-Intersection accidents are most affected by an

increase in speed of the vehicle at fault. This number is extremely high (374) because

all 13 accidents in this category occurred in high-speed environments. With more

data, it is probable that this number would be lower. However, it would most likely

tend to be high in comparison to most of the other accident types.

Rear-End-Major vehicle accidents record the next highest relative accident rate (4.6).

It is considered that this result may be because the vehicle stream of the driver at

fault does not normally slow unless there is a turning vehicle. This contrasts with the

remaining accidents types, where most drivers will slow down prior to the

intersection or horizontal geometric element (these record relative accident rates

between 1.6 and 2.7).

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The findings in this section tend to indicate the following:

• The speed of the ‘vehicle at fault’ is important if there is propensity for drivers to

inadequately perceive the intersection or horizontal curve.

• Where the traffic stream of the ‘vehicle at fault’ does not have to slow (under

normal conditions), the speed of the ‘vehicle at fault’ is particularly important.

• The speed of the ‘vehicle at fault’ is relatively unimportant if the driver has made

a conscious effort to turn at the intersection.

• The speed of the ‘vehicle not at fault’ is relatively unimportant.

The above findings can be summarised as ‘the speed of the vehicle at fault is

generally more important than the vehicle not at fault’.

Intersection Design Philosophy

The finding in the previous section is similar to that found for the traffic flow

variables ie aspects of the vehicle at fault (especially the traffic volume and speed)

are more important than those aspects of the vehicle not at fault. This indicates that

safety is improved largely by optimising the aspects of the vehicle at fault, rather

than the vehicle not at fault. For example, introducing measures to reduce the speed

of the vehicle at fault would be more beneficial than measures to reduce the speed of

the vehicle not at fault.

The hypothesis above could be summarised as ‘prevention is better than cure’. It is

better to reduce the likelihood of drivers making errors than to introduce measures to

help drivers not at fault avoid the vehicle at fault.

22.3 Potential Measures to Reduce Vehicle Speed and Accident Rates

Table 22.3 shows that a reduction in accident rate will occur if there is a reduction in

the speed of the traffic stream of the vehicle at fault. This is only possible for the five

accident types listed in this table. Potential measures to reduce vehicle speed in each

of these cases and the practicality of these measures are discussed below.

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Single-Through Vehicle Accidents

For the accident type ‘Single-Through’, accident rates on a particular horizontal

curve (say Curve A for the purposes of this discussion) will be high where the

following occur:

• Curve A is of small radius

• The speed on the previous horizontal geometric element is high

One way to reduce the Single-Through vehicle accident rate on Curve A is to reduce

the speed on the previous horizontal element. This could potentially be achieved

through the use of a local speed limit reduction, but this is unlikely to be a practical

solution.

Another potential solution is to introduce an additional horizontal curve (say Curve P

for the purposes of this discussion) prior to Curve A, such that the two curves form a

reverse curve. The radius of Curve P would be chosen such that the decrease in speed

on both Curve A and Curve P is limited to 10 - 15 km/h in accordance with

Austroads (1989). Unfortunately, the chosen Single-Through vehicle accident model

‘Both’ shows that the total accident rate for this arrangement (the accident rate for

Curve A plus Curve P) can be higher than for Curve A alone. This result was

unexpected.

The alternative Single-Through vehicle accident model ‘A2’ (refer Section 20.4) was

also used to calculate the total accident rate for this reverse curve arrangement. The

result contradicted the ‘Both’ accident model in that the alternative model ‘A2’

showed that there was a significant reduction in total accident rate by the addition of

Curve P.

Because of the conflict in these two models, it can be concluded that there is

insufficient evidence to know the real effect of the introduction of an additional

curve to minimise the decrease in speed between horizontal elements. It is probable

that a much greater range of data is required to build an appropriate single vehicle

accident model. This range would need to minimise the high levels of correlation

between some of the parameters for this accident type.

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The only consistent result between the single vehicle accident models was that a

reduction in single vehicle accident rates would result from increasing the radius of

the tight curve (Curve A).

Single-Minor-Turn Vehicle Accidents

For the multiple vehicle accident types identified in Table 22.3, there is insufficient

evidence in this study to determine which of the two parameters ‘speed environment’

or ‘85th percentile speed’ is the more important predictor of accident rates. For

Single-Minor-Turn vehicle accidents, these two parameters correspond to ‘speed

environment of the minor road’ and ‘85th percentile minor road approach speed’.

The following sections show how the choice of either parameter will affect what

devices will potentially reduce Single-Minor-Turn vehicle accident rates.

Speed Environment of the Minor Road If ‘speed environment of the minor road’ is more important, a reduction in desired

speed over a significant length of road would have to be achieved in order to reduce

the accident rate eg a reduction in speed limit accompanied by a change in roadside

environment over a significant length prior to the intersection. This is not a practical

consideration.

85th Percentile Minor Road Approach Speed If ‘85th percentile minor road approach speed’ is more important, then a local

reduction in this speed can potentially be achieved by introducing devices on the

minor road such as a speed limit reduction, approach curvature, or rumble strips.

For minor road approach curvature to be worthwhile, the reduction in Single-Minor-

Turn vehicle accident rates at the intersection would need to be greater than the

increase in Single-Through vehicle accidents on the approach curves. To test this, the

geometry of several example intersections and approach curve layouts was used in

these accident models. The findings were as follows:

• If the ‘Both’ Single-Through vehicle accident model is used in combination with

the Single-Minor-Turn model, the introduction of approach curves will lead to a

small reduction in total single vehicle accident rates at T-intersections. A

crossroads, approach curves gave an increase in the overall single vehicle accident

rate.

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• If the alternative Single-Through vehicle accident model ‘A2’ is used in

combination with the Single-Minor-Turn model, the introduction of approach

curves will lead to an increase in total single vehicle accident rates at all

intersections.

Based on the above, there appears to be little evidence of any benefit in introducing

approach curves to minimise the Single-Minor-Turn vehicle accident rate, even at T-

intersections.

Rear-End-Major and Overtaking-Intersection Vehicle Accidents

There is insufficient evidence in this study to determine which of the two parameters

‘speed environment of the major road’ or ‘85th percentile through speed on the major

road’ is the more important predictor of the accident types ‘Rear-End-Major’ and

‘Overtaking-Intersection’. If ‘speed environment of the major road’ is more

important, it is unlikely that it can be practically reduced in order to lower the rates

of these accidents.

If ‘85th percentile through speed on the major road’ is more important, a local

reduction in speed can potentially be achieved by a speed limit reduction through

higher speed intersections accompanied by a local change in the roadside

environment (eg by the introduction of medians, signage, lighting etc). Given that

these accident types are generally on lower volume rural roads, this is not likely to be

a practical solution.

Based on the above, there is probably no practical way of reducing the rates of Rear-

End-Major and Overtaking-Intersection vehicles accidents by lowering the speed of

the major road.

Angle-Minor Vehicle Accidents

There is insufficient evidence in this study to determine which of the two parameters

‘speed environment of the minor road’ or ‘85th percentile minor road approach

speed’ is the more important predictor of the accident type ‘Angle-Minor’. If ‘speed

environment of the minor road’ is more important, it is unlikely that it can be

practically reduced in order to lower the rates of these accidents.

If ‘85th percentile minor road approach speed’ is more important, a local reduction in

this speed can potentially be achieved by introducing devices on the minor road such

273

as a speed limit reduction, approach curvature, or rumble strips. For minor road

approach curvature to be worthwhile in this case, the reduction in Angle-Minor

vehicle accident rates at the intersection would need to be greater than the increase in

Single-Through vehicle accidents on the approach curves. To test this, the geometry

of several example intersections and approach curve layouts was used in these

accident models. The findings were as follows:

• If a large proportion of the traffic on the minor road turns left at the intersection,

there is little to no advantage in providing approach curves.

• For all other cases, the reduction in Angle-Minor vehicle accidents considerably

outweigh any increase in single vehicle accident rates.

The findings above show the following:

• If ‘speed environment of the minor road’ is more important, there are no practical

methods of reducing the Angle-Minor vehicle accident rate.

• If ‘85th percentile minor road approach speed’ is more important, there are

potential advantages in introducing devices on the minor road such as a speed

limit reduction, approach curvature, or rumble strips to reduce the Angle-Minor

vehicle accident rate. Approach curvature would be of considerable benefit unless

a large proportion of the traffic on the minor road turns left at the intersection.

In reality, the minor road speed that has the most influence on Angle-Minor vehicle

accidents is probably somewhere between the value of ‘speed environment of the

minor road’ and ‘85th percentile minor road approach speed’. There is insufficient

data in the study to determine this speed. Therefore, the effectiveness of introducing

devices such as a speed limit reduction, approach curvature, or rumble strips remains

unknown.

Although the effectiveness is still unknown, the intent of providing these devices on

the minor road is sound. This study verifies this by showing that a lower minor road

speed produces a lower Angle-Minor vehicle accident rate.

22.4 Intersection Type

This study has shown that the accident rate at a four-leg intersection comprising a

high degree of recognition of the opposite minor leg is significantly higher that for a

four-leg intersection comprising little to no recognition of the opposite minor leg.

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This even applies when there is virtually no through traffic from the minor legs.

An explanation for this result is as follows. Fully aligned minor legs can deceive

drivers as to the presence of the intersection. For drivers not concentrating

adequately, the road can appear to continue straight ahead. This is especially true if

very little of the major road can be seen prior to the intersection due surrounding

development/vegetation or major road crossfall.

Conversely, a four-leg intersection that comprises little to no recognition of the

opposite minor leg can appear to minor road drivers as a T-intersection. This

perception probably helps identify the presence of the intersection.

These results show that cross intersections (with aligned minor legs) are relatively

dangerous compared to other intersection types. These results also show that the

introduction of minor road staggers at all four-leg intersections would be beneficial.

If this is not possible, it is recommended that other devices be provided to warn

minor road drivers that they are approaching a cross intersection. Such devices

include additional signage, pavement markings, introduction of medians etc.

Morrison (1998) found that a kerbed median with keep left and oversized stop signs

on the right side footpath, in addition to the left side, had a major affect in reducing

accident rates.

Example

In order to determine the potential relative safety of four leg intersections to

staggered T-intersections, the accident models developed in this study were applied

to a number of example intersections as follows:

• A cross intersection (four-leg intersection) with fully aligned minor legs (DR4 =

2).

• A four leg intersection with offset minor legs (right-left stagger of greater than the

width of the minor road approach carriageway, DR4 = 0)

• A right-left staggered T-intersection with a relatively large stagger distance

(undertaken by assuming the staggered intersection operates as two completely

independent T-intersections). An AUL turn treatment is provided for the left-turn

from the major road.

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• A left-right staggered T-intersection with a relatively large stagger distance

(undertaken by assuming the staggered intersection operates as two completely

independent T-intersections). A CHR turn treatment is provided for the right-turn

from the major road.

The example intersection layouts comprised the following attributes:

• Through traffic volume from the minor leg is 1000 vehicles per day

• No traffic turns left or right from the minor leg

• Traffic volumes for through movements on the major legs are 2000 vehicles per

day

• There is no queuing through the intersection on the major road

• Two speed environment used on all legs: 70km/h and 110km/h

• All approaches are straight

• Visibility for all relevant conflicts is infinity

• Observation angles for left, through and right-turns from the minor road are 140,

90, and 90 degrees respectively

• Minor roads comprise one lane only (no free left-turn)

Generally, the above attributes limited the intersections to quite simple, standard

arrangements. The analysis of all the example intersection layouts only considered

accidents involving through movements from the minor road. The results of this

analysis are shown in Table 22.4.

Table 22.4 - Relative Accident Rate for Four Leg Intersections versus Staggered T-intersections for Through Movements from the Minor Road

Intersection Type Relative Accident Rate (staggered T-intersection with a left - right stagger standardised at unity)

Cross intersection 7.5 - 10.4 Four leg intersections with offset

minor legs (right-left stagger) 3.5 - 5.2

Staggered T-intersection with a right-left stagger

3.5 - 4.7

Staggered T-intersection with a left-right stagger

1

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Table 22.4 shows that the accident rate for through movements from the minor road

is potentially much less at staggered T-intersections than cross intersections. This is

especially true for staggered T-intersections with a left-right stagger. It is interesting

to note from this table that a small offset of the minor road legs of a four leg

intersection (at least equal to half of the minor road approach carriageway, right-left

stagger only) performs similar to a right-left staggered T-intersection with a large

stagger distance. However, a problem with a small right-left stagger is that right-

turning vehicles on opposing minor road legs may find it difficult to turn

simultaneously, particularly for larger vehicles.

The results for the staggered T-intersections in Table 22.4 assume that the staggered

intersections operate as two completely independent T-intersections. This may not be

the case and the results may be inaccurate for this reason. These results also give a

high relative accident rate for the cross intersection because only through movements

from the minor road are considered. These values would be considerably less if other

turning movements were considered, especially if there was a large proportion of the

minor road traffic turning at the intersection. These results would also be different if

alternative turn treatments were used.

With due consideration to the above issues, the large relative accident rate between

cross intersections and staggered T-intersections for the through movement from the

minor road nevertheless suggest that staggered T-intersections are probably much

safer. Most road design practitioners have always suspected this outcome, as

reflected in road design standards eg Austroads (1988) and QDMR (2000).

The results in Table 22.4 could be summarised as follows:

• Staggered T-intersections potentially perform much better than cross

intersections.

• Staggered T-intersections with a left-right stagger potentially perform better than

staggered T-intersections with a right-left stagger

• Four leg intersections with a small offset of the minor road legs (at least equal to

half of the minor road approach carriageway, right-left stagger only) perform

better than cross intersections. However, right-turning vehicles on opposing minor

road legs may find it difficult to turn simultaneously.

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22.5 Relative Accident Rate of the Various Conflict Types

Failure to Give Way Accidents

Table 22.5 shows accident rates (accidents divided by the square of vehicle volume)

for various Angle-Minor and Angle-Major conflict types. These accident rates are

taken from Table 9.9 and Table 10.8. These conflict types all relate to a driver failing

to give way and colliding with a major road vehicle.

Using the standardised accident rates in Table 22.5, the following may be concluded

about failure to give way accidents:

• Conflicts points with high relative speeds between vehicles tend to record high

accident rates.

• Conflict points for which the driver at error has had to view multiple traffic

streams tend to record high accident rates ie a higher driver workload increases

accident rates.

Table 22.5 - Angle-Minor and Angle-Major Accident Rates for the Various Conflict Types

Accident Type Conflict Type

Accidents / Volume (1)

(A)

Standardised Rate LRT = 1

(A/5.73E-15) LRT 5.73E-15 1 TLT 3.41E-13 60 TRT 2.34E-13 41 RLT 2.16E-14 3.8

Angle-Minor

RRT 1.15E-13 20 Angle-Major RT 4.02E-14 7

Note: (1) The values in the third column equal the number of accidents recorded for the particular conflict

divided by the traffic flow product as per Table 9.9 and Table 10.8.

The conclusions above explain why staggered T-intersections potentially perform

better than crossroads. A crossroad comprises the conflict types TRT and TLT that

involve high relative speeds and high driver workload. A right-left staggered T-

intersection is potentially safer because the TRT and TLT conflicts are converted to

RRT and RLT conflicts (in addition to a very minor left-turn Rear-End-Major

vehicle conflict). The lower relative speed of the RLT conflict is the main reason for

the increased safety performance.

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A right-left staggered intersection is potentially even safer because the TRT and TLT

conflicts are converted to LRT and RT conflicts (in addition to a very minor right-

turn Rear-End-Major vehicle conflict if at a CHR turn treatment). Both the LRT and

RT conflict types involve low driver workload (only one direction to view at a time

unless a free left-turn lane) and the LRT conflict comprises a low relative speed.

Example

The following example has been developed in order to compare rates of the various

accident types and conflicts identified in this study. This example is a four-way

intersection with the following attributes:

• Traffic volumes for each turn from the minor legs (left, through and right-turns)

are 200 vehicles per day.

• Traffic volumes for left and right-turns from the major legs are 200 vehicles per

day.

• Traffic volumes for through movements on the major legs are 1000 vehicles per

day.

• There is no queuing through the intersection on the major road.

• Speed environment on all legs is 110km/h.

• All approaches are straight.

• Visibility for all relevant conflicts is infinity.

• Observation angles for left, through and right-turns from the minor road are 140,

90, and 90 degrees respectively.

• Minor roads comprise one lane only (no free left-turn).

Table 22.6 lists the rates of the various accident types for this example intersection

using the final accident models in this study. These rates are shown for various turn

types and other criterion.

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Table 22.6 - Rates of the Various Accident Types and Conflict Types for the Example Intersection

Accident Conflict Turn Other Accident StandardisedType Type Type Criterion Rate Accident Rate

(acc/y) LRT = 1.0(A) (A / 0.00567)

LRT - - 0.00567 1.0TLT - DR4 = 0 0.116 20.5

Angle-Minor DR4 = 2 0.225 39.7TRT - DR4 = 0 0.083 14.6

DR4 = 2 0.16 28.2RLT - - 0.0175 3.1RRT - - 0.11 19.4

Angle-Major RT - - 0.0271 4.8R LSR - 0.0974 17.2R AUR - 0.0567 10.0

Rear-End-Major R MNR - 0.19 33.5R CHR - 0.0019 0.3L LSL - 0.00196 0.3L AUL - 0.00105 0.2

Rear-End-Minor - - - 0.0092 1.6Single-Minor-Turn - - AH = 0 0.037 6.5

- - AH = 2 0.0103 1.8Single-Major-Turn - - - 0.0085 1.5

- LSR Broken CL 0.358 63.1Overtaking- - Barrier CL 0.0158 2.8Intersection - AUR Broken CL 0.286 50.4

- Barrier CL 0.0126 2.2Remainder - - - 0.0812 14.3

Note: LSR, AUR and MNR turn treatments in this example do not comprise a median.

The following observations have been made from the standardised accident rates in

Table 22.6:

• The two highest rates recorded are for Overtaking-Intersection vehicle accidents

for LSR and AUR turn treatments comprising a broken centreline. Even though

Overtaking-Intersection vehicle accidents were identified as a low frequency

accident type, this example shows that high accident rates can be recorded under

particular circumstances. If the example intersection was in a low speed

environment, a much lower Overtaking-Intersection vehicle accident rate would

be recorded.

280

• Angle-Minor through conflicts (TLT and TRT) record high accident rates,

particularly at cross intersections (comprising aligned minor legs). RRT conflicts

are also quite high. LRT and RLT conflicts, however, record low accident rates.

These findings have already been identified in the study.

• Rear-End-Major right-turn conflicts at MNR sites can record high accident rates.

This result indicates that it is always preferable that intersections on multi-lane

roads comprise a right-turn slot.

• Rear-End-Major right-turn conflicts at LSR sites can also record relatively high

accident rates. If the predominant turning traffic volumes are ‘left from the minor

road’ and ‘right from the major road’ at a T-intersection comprising an LSR turn

treatment from the major road, Rear-End-Major accidents can form the

predominant accident type. This is also true for AUR turn treatments.

• Rear-End-Major conflicts at CHR, LSL, and AUL sites record low accident rates.

These findings have already been identified in the study.

• Rear-End-Minor accident rates are generally low.

• Single-Major-Turn vehicle accident rates are generally low.

22.6 Parameters Relating to Visibility Restrictions

The following parameters relating to visibility restrictions have been found to

increase accident rates:

• Angle-Minor vehicle accidents - decreased levels of visibility between minor

and major road vehicles, increased observation angles, increased number of stand-

up lanes on the minor road, and for TRT conflicts, presence of queuing through

the intersection on a multi-lane major road.

• Angle-Major vehicle accidents - decreased visibility between right-turn and

oncoming major road vehicles and presence of queuing through the intersection

on a multi-lane major road.

• Rear-End-Major vehicle accidents - decreased visibility between approaching

and turning major road vehicles.

It is expected that the parameters listed above are important for the following

reasons:

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• Reduced visibility between vehicles results in less time being available for drivers

to decide whether or not to select an appropriate gap in the traffic stream. In

addition, reduced visibility between vehicles means that drivers not at fault have

less time to react and take the necessary action to avoid a vehicle at fault.

• An increased observation angle makes it more difficult to view other vehicles,

especially for increased angles to the left where various components of a vehicle

(eg vehicle pillars, passengers) can block the line of sight to other vehicles.

• Vehicles in an adjacent stand-up lane on the minor road will block visibility to

major road vehicles in that direction.

• The presence of queuing through the intersection on a multi-lane major road can

block visibility to vehicles in the far lane.

Several of the parameters listed above did not give high levels of validation.

However, the fact that seven parameters relating to visibility restrictions were found

to be significant is reasonable evidence that anything that reduces visibility will

potentially increase accident rates. It highlights the importance of giving drivers the

maximum possible visibility.

There are a number of other variables that can cause visibility restrictions that were

either not found to be important in this study, or were not able to be readily

measured. Some of these are listed below:

• Keep left signage in medians on the major road

• The number of opposing right-turn vehicles on a major road at four way

intersections.

• Presence of parked vehicles on the major road close to the intersection.

The findings above suggest that these parameters may also increase accident rates by

restricting visibility.

Visibility

Figure 22.1 shows a plot of the standardised accident rate (accident rate of one at a

sight distance of infinity) versus sight distance for a speed of 100km/h for the three

major multiple vehicle accident types.

282

0

1

2

3

4

5

6


Stan

dard

ised

Acc

iden

t Rat

e

Angle-Minor

Rear-End-Major

Angle-Major

Figure 22.1 - Effect of Sight Distance on Accident Rates

The current use of the Safe Intersection Sight Distance model in QDMR (2000) and

Austroads (1988) is for Angle-Minor conflicts only. This model does not sufficiently

allow for visibility restrictions for ‘Angle-Major’ and ‘Rear-End-Major’ conflict

types in all cases.

Such a case is at intersections on the back of tight horizontal curves where the

amount of visibility can be significantly less for major road drivers approaching the

intersection than for turning drivers from the minor road. It is therefore

recommended that, for consistency, the Safe Intersection Sight Distance model also

be used to check Angle-Major and Rear-End-Major vehicle conflicts.

The level of validation for these three visibility terms varied between 84 and 98.

Reasons for two of these terms recording a low level of validation are as follows:

• There are few sites in the study with particularly poor visibility

• Sight distance can be a relatively difficult parameter to accurately measure due to

variation in sight distance over time

The fact that visibility was an important predictor of all three multiple vehicle

accident types is quite a good result when considering the above issues. It certainly

confirms the need for sight distance models in road design.

Visibility was not found to be a significant predictor of Angle-Minor and Angle-

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Major vehicle accidents unless an inverse function was used. The inverse function

gave a more logical relationship between visibility and accident rates than the other

functions. This result shows the importance of selecting an appropriate function for

use with each parameter.

Cox (2003) has discussed the use of reduced levels of visibility for existing rural

roads. These levels have been based on using, to advantage, the latitude available

within the sight distance models in QDMR (2000) and Austroads (1988) for the

design of new roads. Less conservative values of a number of parameters have been

chosen based on the results of sight distance related studies from throughout the

world.

The reduced levels of visibility are particularly suitable for checking the geometry of

an existing road where the asset (the road) already exists. It is also used for

upgrading small sections of existing road in constrained situations.

The work of Cox (2003) has been extended to produce reduced values of Safe

Intersection Sight Distance. Values as low as 180m for 100km/h have been used.

Using QDMR (2000) and Austroads (1988), the safe intersection sight distance is

240m for a new 100km/h road and a two second reaction time.

Using the final accident equations in this study, the increase in accident rates by

reducing the visibility from 240m to 180m is given below:

• Angle-Minor: 8%

• Angle-Major: 21%

• Rear-End-Major: 21%

These increases in accident rates are not considered excessive. They may be tolerable

at an existing lower volume rural intersection where the cost of reconstruction is

excessive.

22.7 Free Left-turn Lanes

Table 22.7 shows the effect of providing free left-turn lanes on various types of

accidents recorded in this study. For accident types omitted from this table, presence

of a free left-turn lane was not used as a variable in the analysis. For one of the

accident types shown in Table 22.7, the presence of a free left-turn lane had no effect

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on accident rates. For the remaining three accident types, the provision of a free left-

turn lane yielded an increase in accident rates.

Table 22.7 - Effect of Free Left-turn Lanes on Accident Rates Accident Type Conflict

Type Effect on Accident

Rates of the Provision of a Free

Left-turn Lane

Location of Free Left-Turn Lane

Angle-Minor LRT N From minor road to major road

Rear-End-Minor L I From minor road to major road

Single-Minor-Turn L I From minor road to major road

Single-Major-Turn L I From major road to minor road

Notes: (1) The presence of a free left-turn lane was not used in the analysis of accident types omitted from

this table N = no effect on accident rates I = increases accident rates

These results show that providing free left-turn lanes leads to an overall increase in

accident rates. As discussed previously in this thesis, this increase in accident rates is

expected to result from the higher speed at which drivers on free left-turn lanes

travel.

Although free left-turn lanes record increased accident rates for the various conflict

types shown in Table 22.7, these rates are relatively low as compared to many other

conflict types.

22.8 Warrants for the Various Major Road Turn Types

This study has identified two accident types that are largely influenced by the type of

turn treatment on the major road. These are Rear-End-Major and Overtaking-

Intersection vehicle accidents. It is desirable to use both these accident types to

develop new warrants for major road turn treatments.

This section considers two methods to develop new warrants for the selection of

these turn treatments. Both these methods apply the Rear-End-Major vehicle accident

model but not the Overtaking-Intersection model. The Overtaking-Intersection model

was not used because it is probably very dependent on the likelihood of overtaking

through the intersection. This parameter was not used in the model because of the

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difficulty in measuring it. It is considered that using the model without this parameter

would lead to very inaccurate results in some instances.

This section considers warrants for major road turn treatments on two lane roads

only. Warrants for multi-lane roads were not considered because it is believed that all

intersections on multi-lane roads should comprise CHR treatments. The only

alternative to this (MNR - no special right-turn facility) should not be used because it

produces a very high Rear-End-Major vehicle accident rate, much higher than for a

two-lane road.

The two methods to develop new warrants for turn treatments are ‘By Accident Rate’

and ‘By Benefit Cost Analysis’. These methods and subsequent warrants are

discussed in the following sections.

The units of the traffic flow variables in the Rear-End-Major vehicle accident model

are AADT (vehicles per day). In order to produce new warrants for comparison with

those in QDMR (2000) and Austroads (2003), the units need to be the same. For this

reason, the AADT values have been converted to peak hourly values by multiplying

the AADT values by 0.15. Use of this value is consistent with that used in the

existing warrants in Figure 13.21 of QDMR (2000).

The new warrants developed in this section use the following turn treatment codes:

• BAR (Basic right-turn treatment) as per Figure 13.53 of QDMR (2000), which is

a subset of an LSR treatment. A BAR treatment contains a locally widened,

unsealed shoulder to enable through major road vehicles to pass to the left of

right-turn major road vehicles. A BAR is assumed to perform the same as an LSR

turn treatment. Given that the width, length, and surface type of the widened

shoulder for LSR treatments was not a significant parameter in the Rear-End-

Major vehicle accident model/s, this is considered a logical approach.

• AUR (Auxiliary right-turn treatment) as per Figure 13.54 of QDMR (2000).

• CHR (Channelised right-turn treatment) as per Figure 13.55 of QDMR (2000).

By Accident Rate

This method determines warrants for each turn type based on limiting the estimated

accident rate (accidents per year) to a maximum value for each turn type. An

example of the output of this method is given in Figure 22.2, which shows warrants

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for right-turn treatments for an 85th percentile speed of 110km/h. The new curves

shown in this figure limit the estimated accident rate at all of the right-turn

treatments to one Rear-End-Major right-turn vehicle accident in ten years as follows:

• New BAR/AUR curve - the location at which the Rear-End-Major vehicle

accident rate at a BAR treatment is one accident in ten years

• New AUR/CHR curve - the location at which the Rear-End-Major vehicle

accident rate at an AUR treatment is one accident in ten years

Existing warrants for turn treatments from QDMR (2000) are also shown in Figure

22.2. The new curves in this figure vary considerably from the existing warrants on

the right side of the graph. The existing warrants level out, indicating that the same

intersection turn treatment can be used although the through traffic flow increases.

For example, the BA/AU curve levels out at 10 vehicles per hour.

Various Main Roads’ District offices have considered this inappropriate because of

the high Rear-End-Major vehicle accident rates that have been recorded on particular

intersections meeting this criterion. The new curves overcome this problem by

defining a lower turning volume as through volumes increase.

0

20

40

60

80

0 100 200 300 400 500

Through One-way Volume (Veh/h)

Rig

ht T

urn

Volu

me

(Veh

/h)

BA/AU - QDMR (2000)

NewBAR/AUR

AU/CH - QDMR (2000)

NewAUR/CHR

Figure 22.2 - Potential Warrants for Right-Turn Treatments for an 85th Percentile Speed of 110km/h Using the ‘By Accident Rate’ Method (estimated accident rate

limited to one right-turn Rear-End-Major vehicle accident in ten years)

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Alternative warrants can be quickly generated for different speeds and different

limiting accident rates. As an example, Figure 22.3 shows warrants for right-turn

treatments for an 85th percentile speed of 70km/h. As for Figure 22.2, the new curves

shown limit the estimated accident rate to one Rear-End-Major right-turn vehicle

accident in ten years. Comparing Figure 22.3 with Figure 22.2 shows that the

warrants for the various turn treatments are significantly less stringent for lower

speed areas than for high-speed areas.

The warrants for the various turn types using this method are completely dependent

on the assumed limiting accident rate. If a higher accident rate is assumed, the new

curves will move diagonally up the graph to the right. Conversely, if a lower accident

rate is assumed, the new curves will move diagonally down the graph to the left.

0

20

40

60

80

100

120

140

160

0 200 400 600 800 1000


Rig

ht T

urn

Volu

me

(Veh

/h)

NewBAR/AUR

BA/AU - QDMR (2000)

NewAUR/CHRAU/CH -

QDMR (2000)

Figure 22.3 - Potential Warrants for Right-turn Treatments for an 85th Percentile Speed of 70km/h Using the ‘By Accident Rate’ Method (estimated accident rate

limited to one right-turn Rear-End-Major vehicle accident in ten years)

This method was also used to determine warrants for left-turn treatments.

Unfortunately, using a limiting accident rate of just one accident in one hundred

years, the warrants produced are such that traffic flows, on even the busiest roads,

would never be high enough to justify using an AUL treatment. This is because the

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left-turn Rear-End-Major vehicle accident rate is so low. What this does show,

however, is that using the same warrants for left and right-turn treatments as per

QDMR (2000) and Austroads (2003) is inappropriate. The right-turn warrants should

be much more strict than for the left-turn.

By Benefit Cost Analysis

This method determines warrants for each turn type based on identifying the location

at which the benefits of providing a higher-level treatment (the reduction in

estimated accident costs) are made equal to a proportion of the additional

construction costs. This proportion is the benefit cost ratio (BCR) and applies for an

assumed design life.

The new warrants developed in this section include the following turn treatment

codes:

• CHR(s) (Channelised right-turn treatment with short right-turn slot) as per Figure

13.55 of QDMR (2000). Length of right-turn slot as per minimum dimensions in


• CHR(l) (Channelised right-turn treatment with long right-turn slot) as per Figure

13.55 of QDMR (2000). Length of right-turn slot based on 2.5m/s2 comfortable

deceleration as per Table 13.16 of QDMR (2000).

The reduction in estimated accident rates by the provision of a higher-level turn

treatment is calculated by the Rear-End-Major vehicle accident model. The cost of

each Rear-End-Major vehicle accident is $38, 974, which has been calculated by the

method given in Section 24.1. The construction cost of each turn type is estimated in

Appendix D - Costs of the Various Turn Types.

Two scenarios are possible under this method as follows:

• New Intersection - This is for new roads where the intersection is not yet built. In

this case, the benefits and costs of a higher-level treatment are compared to the

base case (the minimum turn treatment which is a BAR).

• Existing Intersection Upgrade - This is for existing roads where an intersection

already exists. In this case, the benefits of upgrading the intersection are weighed

against the costs of upgrading.

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These two scenarios are discussed below.

New Intersection Figure 22.4 provides an example of applying this method to new intersections. It

shows warrants for right-turn treatments for an 85th percentile speed of 110km/h. The

new curves shown in this figure are for a benefit cost ratio of one and a design life of

20 years.

Each new curve in Figure 22.4 is the location at which the benefits of providing a

higher-level treatment (the savings in estimated right-turn Rear-End-Major vehicle

accidents over a period of twenty years) are equal to the construction costs of the

higher-level treatment minus the construction costs of a BAR treatment as follows:

• New BAR/AUR curve - the location at which the accident cost at a BAR

treatment minus the accident cost at an AUR treatment is equal to the construction

cost of an AUR treatment minus the construction cost of a BAR treatment.

• New AUR/CHR(s) curve - the location at which the accident cost at a BAR

treatment minus the accident cost at a CHR(s) treatment is equal to the

construction cost of a CHR(s) treatment minus the construction cost of a BAR

treatment.

• New CHR(s)/CHR(l) curve - the location at which the accident cost at a BAR

treatment minus the accident cost at a CHR(l) treatment is equal to the

construction cost of a CHR(l) treatment minus the construction cost of a BAR

treatment.

Figure 22.4 shows that the ‘New BAR/AUR’ curve is to the right of the ‘New

AUR/CHR(s)’ curve. This indicates that it is always beneficial to provide a CHR(s)

treatment rather than an AUR treatment. Using other speeds and benefit cost ratios,

the same result was also obtained.

Existing Intersection Figure 22.5 provides an example of applying this method to existing intersections. It

shows warrants for upgrading an AUR intersection for an 85th percentile speed of

70km/h. The new curves shown in this figure are for a benefit cost ratio of one and a

design life of 20 years.

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0

20

40

60

80

0 100 200 300 400 500


Rig

ht T

urn

Volu

me

(Veh

/h)

NewBAR/AUR

BA/AU - QDMR (2000)

AU/CH - QDMR (2000)

NewAUR/CHR(s)

NewCHR(s)/CHR(l)

Figure 22.4 - Potential Warrants for Right-turn Treatments for a New Intersection for an 85th Percentile Speed of 110km/h Using the ‘By Benefit / Cost Analysis’ Method

(based on a benefit / cost ratio of one and an design life of 20 years)

0

20

40

60

80

0 100 200 300 400 500


Rig

ht T

urn

Volu

me

(Veh

/h)

BA/AU - QDMR (2000)

AU/CH - QDMR (2000)

NewAUR/CHR(s)

NewAUR/CHR(l)

Figure 22.5 - Potential Warrants for Upgrading an AUR Intersection for an 85th

Percentile Speed of 70km/h Using the ‘By Benefit / Cost Analysis’ Method (based on a benefit / cost ratio of one and an design life of 20 years)

291

Each new curve in Figure 22.5 is the location at which the benefits of providing a

higher-level treatment (the savings in estimated right-turn Rear-End-Major vehicle

accidents over a period of twenty years) are equal to the construction costs of

upgrading the AUR intersection to the higher-level treatment as follows:

• New AUR/CHR(s) curve - the location at which the accident cost at an AUR


construction cost of upgrading from an AUR treatment to a CHR(s) treatment.

• New CHR(s)/CHR(l) curve - the location at which the accident cost at an AUR


construction cost of upgrading from an AUR treatment to a CHR(l) treatment.

For upgrading an existing BAR intersection, warrants are calculated as follows:

• New BAR/AUR curve - the location at which the accident cost at a BAR

treatment minus the accident cost at an AUR treatment is equal to the construction

cost of upgrading from a BAR treatment to an AUR treatment.

• New AUR/CHR(s) curve - the location at which the accident cost at a BAR


construction cost of upgrading from a BAR treatment to a CHR(s) treatment.

• New CHR(s)/CHR(l) curve - the location at which the accident cost at a BAR


construction cost of upgrading from a BAR treatment to a CHR(l) treatment.

The previous section indicated that it is always beneficial to provide a CHR(s)

treatment rather than an AUR treatment for a new intersection. In a similar way, the

‘by benefit cost analysis’ method shows that it is always beneficial to upgrade an

existing BAR intersection to a CHR(s) treatment, rather than an AUR treatment.

Other Considerations for Using the ‘By Benefit Cost Analysis’ Method The warrants for the various turn types using this method are completely dependent

on the assumed benefit cost ratio and design life. If a higher BCR or a shorter design

life is assumed, the new curves will move diagonally up the graph to the right.

Conversely, if a lower BCR or a longer design life is assumed, the new curves will

move diagonally down the graph to the left.

As per the previous method ‘by accident rate’, the new warrants always define a

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lower turning volume as through volumes increase. This overcomes the problem of

the levelling out of the existing warrants.

This method was also used to determine warrants for left-turn treatments.

Unfortunately, even using BCR values below 0.1 with a design life of 20 years, the

warrants produced are such that traffic flows, on even the busiest roads, would never

be high enough to justify using an AUL treatment. This is the same result as that

obtained using the previous method (by accident rate).

22.9 Variables Found Unimportant in this Study

This section discusses those variables found unimportant across two or more of the

accident types.

Approach Visibility

The amount of approach visibility on the minor and major roads, measured according

the Approach Sight Distance model in QDMR (2000) and Austroads (1988), did not

seem to affect accident rates. One reason for this result may be that many

intersections with less than the minimum Approach Sight Distance can be well

perceived from the minor and major roads.

For minor roads, this is generally the result of the intersection backdrop (eg

buildings, vegetation, cut face), signage and the presence of major road vehicles. For

major roads, this may be the result of channelisation, pavement marking, a gap

between buildings or vegetation, signage, presence of minor road vehicles, or slope

of the minor road.

Another reason for this result on major roads may be that drivers wishing to turn at

the intersection, but have not adequately perceived the intersection, potentially will

simply overshoot the intersection.

Road Classification

Although road classification was found to be mostly unimportant, there were cases

when it was significant. In some cases, this variable was selected in lieu of a speed

variable. In other cases, both variables were selected but the road classification gave

an opposite result to that expected.

It was seen that this result was occurring due to the correlation between road

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classification and speed variables (around 25 percent). Although this level of

correlation was insufficient to warrant rejection of one of the variables in Section

16.2, it did seem to have an effect on the results.

22.10 Variables Yielding Unreasonable or Illogical Results

As discussed in Section 16.6, some variables recorded relationships that were

unreasonable or illogical. One reason for this result was that these variables were

most likely to be upgraded at an existing unsignalised intersection to improve safety.

This outcome is probably reflecting the fact that these measures are often used at the

more dangerous intersections in an attempt to reduce accident rates. These variables

include the following:

• Level of control (replacement of a give way sign by a stop sign)

• Number of control signs (addition of a central median with an additional stop

sign)

• Level of lighting (addition of lighting at the intersection)

Given this scenario, a multi-factor study is not likely to identify appropriate

relationships between such parameters and accident rates. Instead, multi-factor

studies probably give the most reliable result for parameters that are not easily

changed eg angle of the intersection, level of sight distance, number of legs etc.

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23 IMPLICATIONS FOR ROAD DESIGNS STANDARDS

This chapter lists outcomes of this study by referencing relevant sections of this

thesis and discusses the implications of these outcomes on intersections design

standards in QDMR (2000) and Austroads (2003). It is recommended that all these

issues be incorporated into QDMR (2000) and Austroads (2003).

23.1 Intersection Design Philosophy

This study has identified that the following factors will increase accident rates:

• An increase in relative speed between vehicles as discussed in Section 22.5.

• An increase in the number of traffic streams that need to be viewed as discussed

in Section 22.5 ie an increase in driver workload.

• Reduced visibility as discussed in Section 22.6. This includes an increase in the

observation angle.

• A decrease in the levels of perception of an intersection as discussed in Section

22.4.

Based on the above, the safest intersection will be one that minimises the relative

speed between vehicles, decreases the number of traffic streams to be viewed,

provides unrestricted visibility and maximises the perception of the intersection. This

overall design philosophy can explain much about the safety performance of an

intersection. It summarises all the findings of this study.

Sections 22.1 and 22.2 have shown that aspects of the vehicle at fault are more

important than the vehicle not at fault. Safety is improved largely by optimising the

aspects of the vehicle at fault, rather than the vehicle not at fault. This can be

summarised as ‘prevention is better than cure’. It is better to reduce the likelihood of

drivers making errors than to introduce measures to help the drivers not at fault to

avoid the vehicle at fault.

Section 22.1 provides evidence to support the notion that the number of intersections

along a roadway should be limited.

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23.2 Measures to Reduce Vehicle Speed

Speed on the Major Road

Section 22.3 has shown that the speed of the major road is a significant predictor of

Rear-End-Major and Overtaking-Intersection vehicle accidents. Given that these

accident types mostly occur on lower volume rural roads, it is not likely that a speed

reduction on these road types is practical solution. None of the other multiple vehicle

accident types were found to be influenced by the major road speed.

Given the above results, reduction of the major road speed in most instances is either

not a practical solution or will probably do little to reduce accident rates.

Speed on the Minor Road

Section 22.3 has shown that increased minor road speeds result in increased Angle-

Minor and Single-Minor-Turn vehicle accident rates. There is insufficient evidence

in this study to determine which of the two parameters ‘speed environment of the

minor road’ or ‘85th percentile minor road approach speed’ is the more important

predictor of these accidents. In reality, the speed that has the most influence is

probably somewhere between the value of these two speed parameters. Solving this

problem is complex due to the high level of correlation between these two

parameters and with the parameter ‘level of driver alertness’.

Because the relative importance of these two speeds are unknown, the effectiveness

of introducing devices such as a speed limit reduction, approach curvature, or rumble

strips remains unknown. Although the effectiveness is unknown, the intent of

providing these devices on the minor road in high-speed environments is sound.

23.3 Intersection Type

Crossroads

Section 22.4 has shown that cross intersections with fully aligned minor legs record

high accident rates. This geometry potentially deceives drivers as to the presence of

the intersection, even in low speed environments. Assuming staggered T-

intersections operate as two separate T-intersections, the accident rate for through

movements from the minor road at cross intersections is potentially 2 to 10.5 times

higher than that at staggered T-intersections.

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It is preferable to avoid the use of crossroads. If this is not possible, other devices

should be provided to warn minor road drivers that they are approaching a crossroad.

These devices include additional signage, pavement markings, introduction of

medians etc.

Staggered T-Intersections

Section 22.4 has shown that four leg intersections with a small offset of the minor

road legs (at least equal to half of the minor road approach carriageway, right-left

stagger only) are significantly safer than cross intersections. However, right-turning

vehicles on opposing minor road legs may find it difficult to turn simultaneously

under this arrangement.

Staggered T-intersections with a left-right stagger perform better than staggered T-

intersections with a right-left stagger. Assuming staggered T-intersections operate as

two separate T-intersections, the accident rate for through movements from the

minor road at right-left staggered T-intersections is potentially 3.5 to 4.7 times higher

than that at left-right staggered T-intersections (provided Type CHR turn treatments

are used on the major road).

23.4 Parameters Relating to Visibility Restrictions

Section 22.6 has shown that several parameters related to visibility restrictions have

been found important in this study. These are as follows:

Visibility

Visibility was found important in the following instances:

• Between minor road and major road drivers. This result verifies the importance of

using sight distance models for this case.

• Between right-turning major road drivers and oncoming major road drivers.

Current road design guides do not consider this visibility under Safe Intersection

Sight Distance. For consistency, it is recommended that the Safe Intersection

Sight Distance model be extended to cover this case also.

• Between through major road drivers and right-turning major road drivers in front

of them. Current road design guides do not consider this visibility under Safe

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Intersection Sight Distance. For consistency, it is recommended that the Safe

Intersection Sight Distance model be extended to cover this case also.

Values of visibility have to fall significantly below the Safe Intersection Sight

Distance minimums before this parameter has a major influence on accident rates.

This supports the concept of retaining justifiable levels of reduced sight distance on

existing roads. Reduced visibility may be tolerable at existing intersections where the

cost of reconstruction is excessive.

Observation Angle

This study has shown that increased observation angles result in higher accident

rates. This supports the concept of limiting observation angles in the Minimum Gap

Sight Distance model. It also supports the use of using free left-turn lanes as only a

high entry angle or a single radius return with an acceleration lane. It does not

support the use of a single radius return free left-turn lane followed by give way

condition.

Number of Stand-up Lanes on the Minor Road

This study has shown that increasing the number of stand-up lanes on the minor road

from one to two will increase the Angle-Minor vehicle accident rate by 50 percent

for all conflict points other than RRT. The analysis did not consider a free left-turn

lane as an individual stand-up lane.

The reason expected for this result is that vehicles in an adjacent lane can block

visibility to major road vehicle in that direction. It is recommended that only one

stand-up lane be provided on minor road approaches at unsignalised intersections,

particularly at four leg intersections with heavy through movements from the minor

legs. If more than one stand-up lane at an unsignalised intersection is necessary for

reasons of capacity or delay, consideration should be given to signalising the

intersection.

Presence of Queuing Through the Intersection

This study has shown that queuing on a multi-lane major road through an

unsignalised intersection will increase accident rates. The presence of queuing

through the intersection can block visibility for minor road drivers and right-turning

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major road drivers to vehicles in the far lane of the major road.

It is recommended that any coordination and/or re-phasing of traffic signals on multi-

lane roads consider the effect of queuing through adjacent unsignalised intersections.

Other Visibility Related Variables

Seven parameters relating to visibility restrictions have been found to be important in

this study. This is sufficient evidence that anything, which reduces visibility, will

potentially increase accident rates.

There are a number of other variables that can cause visibility restrictions that were

either not found to be important in this study, or were not able to be readily

measured. It is reasonable to assume that these variables can also reduce intersection

safety. Some of these are listed below:

• Keep left signage in medians on the major road.

• The number of opposing right-turn vehicles on a major road at four way

intersections.

• Presence of parked vehicles on the major road close to the intersection.

23.5 Warrants for Turn Types

Section 22.8 has discussed methods of developing new warrants for turn treatments

on the major road. Implications for road design standards are given below.

Warrants for Right-turn Treatments on Single Lane Roads

Two methods of producing new warrants for major road right-turn treatments (for

two lane roads only) have been developed in Section 22.8. It is recommended that

the output of one of these methods be adopted as new warrants for right-turn

treatments.

Both of these methods overcome the problem of levelling out on the right side of the

graph of the existing warrants in QDMR (2000) and Austroads (2003). The new

warrants overcome this problem by continuously defining a lower turning volume as

through volumes increase.

It is debatable as to what traffic flow variable/s should be used on the X-axis of the

existing warrants in QDMR (2000) and Austroads (2003). Currently, one peak hour

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flow variable is used. However, peak hour flows on two separate traffic streams are

relevant. Alternatively, AADT volumes can be used on both axes. It is recommended

that these issues be considered prior to the acceptance of any new warrants.

Use of AUR Treatments

The ‘by benefit cost analysis’ method of developing new warrants for major road

right-turn treatments has shown that it is always more beneficial to provide a CHR

treatment with a short right-turn slot than it is to provide an AUR treatment. The ‘by

accident rate’ method, however, did not give this same result as it is based solely on

the difference in accident rates, not on optimising costs.

Use of CHR Treatments with Short Right-turn Slots

Section 19.3 has shown that CHR turn treatments with short turn slots do not appear

to perform worse than those with longer turn slots. This result is probably due to the

low number of right-turn Rear-End-Major vehicle accidents at CHR treatments in the

study.

What the results do indicate, though, is that CHR turn treatments with short right-

turn slots are much safer than BAR and AUR treatments. There are a sufficient

number of CHR turn treatments with short right-turn slots in the study to be

confident of this result.

Effect of Speed

Section 22.8 has shown that warrants for turn treatments in lower speed

environments are much less strict than for those for high speed environments.

Warrants for Left-turn Treatments

Section 22.8 has shown that the warrants for left-turn treatments should not be the

same as right-turn treatments, as currently exist in QDMR (2000) and Austroads

(2003). This is because left-turn Rear-End-Major vehicle accidents are much less

frequent than for the right-turn accidents.

Practical warrants for left-turn treatments could not be determined using the two

methods discussed above because the left-turn Rear-End-Major vehicle accident rate

is simply too low.

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Warrants for Right-turn Treatments on Multi-lane Roads

Section 19.3 has shown that MNR turn treatments record very high Rear-End-Major

vehicle accident rates. This is probably the main reason why multi-lane undivided

roads tend to record the highest accident rates of all the road types. These findings

support the use of S-lane treatments on multi-lane roads. S-lane treatments ‘drop’ the

outer lane of a multi-lane undivided road. The through lanes then form an ‘S’ shape

in order to achieve room to provide a short right-turn slot.

Warrants for multi-lane roads were not developed because it is believed that all

intersections on multi-lane roads should comprise CHR treatments to avoid the poor

safety performance of MNR treatments.

Through Traffic Volume on the Warrant Graphs

Logically, both of the following traffic flow variables would have an influence on

Rear-End-Major right-turn vehicle accidents:

• The through traffic volume of the vehicle stream of the driver at fault. Higher

volumes increase the probability that a driver will not stop in time to avoid the

turning vehicle.

• The oncoming through traffic volume (the through traffic volume in the opposite

direction). Higher oncoming volumes increase exposure by increasing the time

that a right-turning driver waits for a gap in the oncoming traffic stream.

In the Rear-End-Major vehicle accident model, AADT values were used (one way

volume in vehicles per day). The relative effect of each traffic flow variable above

could not be determined as they were highly correlated. Rather, only the variable in

the first dot point above was used in the model.

The variable on the X-axis of the warrants developed in Section 22.8 is ‘Through

One-way Volume in vehicles per hour’. This is the same as for the warrants in

QDMR (2000) and Austroads (2003). As discussed in Section 22.8, AADT values

have been converted to peak hourly values by multiplying the AADT values by 0.15

in order to produce the graphs shown in these figures.

Peak hourly flows of the two traffic flow variables listed above are likely to be much

less correlated. For a situation where the hourly traffic flows are quite unbalanced,

use of the warrants (either those in QDMR (2000) and Austroads (2003) or those

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developed in this study) will produce a considerably different result depending on

which traffic flow variable is used.

When using the exiting warrants in QDMR (2000), the Department of Main Roads

tends to take the more conservative variable, whilst contractors take the less

conservative variable. This can cause considerable debate between these two parties.

Either of the following approaches can be used to mitigate this problem:

• Use AADT on the X axis and the Y axis of the warrants instead of peak hourly

volumes

• Use the multiplication of the two traffic flow variables on the X-axis of the

warrants (the peak hourly volumes in the dot points above)

Each approaches has advantages and disadvantages. It is recommended that these be

discussed prior to the development of new warrants for the turn treatments.

23.6 Effect of Median Width on BAR, AUR and MNR Turn Treatments

Section 19.3 has shown that the right-turn Rear-End-Major vehicle accident rate

decreases substantially with median width (raised, painted or depressed medians) at

LSR, AUR, and MNR sites. The expected reason for this relationship is that right-

turning drivers waiting for a gap in the oncoming traffic may position their vehicles

further away from the point of conflict in the through lane.

This result shows that there is scope to lower the right-turn Rear-End-Major vehicle

accident rate at existing LSR and MNR turn treatments by introducing a painted

median, even if it is only one to two metres wide. This may be an alternative

treatment to lowering the right-turn Rear-End-Major vehicle accident rate on existing

roads in extremely constrained locations.

23.7 Widened Shoulder for LSR Treatments

Although Section 19.3 showed that wider shoulders at LSR treatments on two lane

roads tended to decrease Rear-End-Major vehicle accident rates, width of the

shoulder (including widening) was not a significant parameter. This suggests that the

provision of the widened shoulder at BAR treatments will not significantly decrease

accident rates.

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Other evidence that loosely supports this was obtained for AUR turn treatments. The

safety performance of Type AUR turn treatments is much closer to that for LSR

treatments, rather than CHR treatments. If there were a strong link between shoulder

width at LSR sites and accident rates, it would be expected that the difference

between accident rates between AUR and LSR sites would be greater.

This result was found to be true regardless of whether the widened shoulder was

sealed or unsealed. For this reason, it is unlikely that the provision of an unsealed

widened shoulder will perform differently to a sealed widened shoulder.

Although the results of this study show that the provision of the widened shoulder at

BAR turn treatments is likely produce minimal improvements in accident rates, it is

recommended that the warrant for this widened shoulder is retained according to

QDMR (2000) and Austroads (2003). It at least provides an emergency escape area

for some drivers to avoid a right-turning vehicle and it minimises delays and driver

frustration.

23.8 Free Left-turn Lanes

Section 22.7 has shown that providing free left-turn lanes (from the major and minor

roads) leads to an overall increase in accident rates. However, relative to many other

conflict types, accident rates on free left-turn lanes (and non-free left-turn lanes) are

low.

The results indicate that there is no advantage in providing free left-turn lanes for

improved safety. Instead, the provision of free left-turn lanes can only be justified

based on operational issues.

23.9 Line Marking

Section 21.4 has shown that Type LSR and AUR turn treatments comprising barrier

centreline marking record far fewer Overtaking-Intersection vehicle accidents. This

finding supports the use of barrier centrelines at all AUR turn treatments as shown in


It is considered that barrier lines should also used on BAR sites with higher traffic

volumes. This includes sites that meet the warrants for a higher level turn type, but

are not upgraded due to limited funding. This is particularly important for sites in

high-speed environments and those sites providing good overtaking opportunities.

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23.10 Approach Visibility

Section 22.9 has shown that the amount of approach visibility generally did not

affect accident rates. A likely reason for this result is that the level of perception of

an intersection from the minor and major roads can be high, even when values of

approach sight distance are far below the minimum.

Given the above, the necessity of obtaining Approach Sight Distance in all situations

is questionable. It does not appear to give a realistic measurement of the potential for

drivers to perceive an intersection. For this reason, it is considered that reduced

values of Approach Sight Distance may be permissible in constrained situations on

existing roads. Where Approach Sight Distance is not provided, devices should be

installed to warn motorists of the intersection ahead eg introducing medians on the

approach, additional signage etc. This will offset against the reduction in sight

distance.

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24 ACCIDENT COSTS AND APPLICATION OF THE RESULTS OF THIS STUDY

This chapter shows the calculated accident costs for each accident type in this study.

It also recommends how the results of this study should be applied to the future

design of unsignalised intersections.

24.1 Accident Costs

Table 24.1 shows calculation of average cost per accident type. The number and

severity of accidents within each accident type was obtained from the Crash Incident

Reports. The average cost of an accident (per severity rating) was obtained from

Queensland Transport. These costs are as follows:

• Fatality - $635,000

• Hospitalised - $118,000

• Treated - $17,000

• Minor - 10,800

• Property Damage - $10,000

Although Queensland Transport has recently updated the above costs, they do not

have widespread use. To be consistent with current use, the original costs have also

been chosen for this study.

The Rear-End-Major vehicle accident costs in Table 24.1 have been used in the

development of warrants for the various right-turn treatments in Section 22.8. The

costs in Table 24.1 may also be used with the regression equations to determine the

benefits in providing or modifying particular geometry at an unsignalised

intersection. This enables determination of whether these benefits outweigh the

additional costs of construction.

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Table 24.1 - Average Cost per Accident for the Various Accident Types Accident Accident Severity and Cost Cost Per

Type Fatality Hospital. Treated Minor Property Total Accident$635,000 $118,000 $17,000 $10,800 $10,000 ($)

Angle-Minor No. Acc. 10 77 124 56 199 466 $43,216Cost ($M) 6.35 9.09 2.11 0.60 1.99 20.14

Angle-Major No. Acc. 1 24 28 12 42 107 $41,987Cost ($M) 0.64 2.83 0.48 0.13 0.42 4.49

Rear-End- No. Acc. 3 13 30 21 54 121 $38,974Major Cost ($M) 1.91 1.53 0.51 0.23 0.54 4.72Single- No. Acc. 8 44 29 19 67 167 $69,702Through Cost ($M) 5.08 5.19 0.49 0.21 0.67 11.64Rear-End- No. Acc. 0 1 10 8 8 27 $16,830Minor Cost ($M) 0.00 0.12 0.17 0.09 0.08 0.45Single-Minor No. Acc. 0 4 5 2 12 23 $30,374-Turn Cost ($M) 0.00 0.47 0.09 0.02 0.12 0.70Single-Major No. Acc. 0 2 1 3 11 17 $23,259-Turn Cost ($M) 0.00 0.24 0.02 0.03 0.11 0.40Overtaking- No. Acc. 1 2 3 2 9 17 $60,800Intersection Cost ($M) 0.64 0.24 0.05 0.02 0.09 1.03Remaining No. Acc. 1 2 4 4 18 29 $40,076

Cost ($M) 0.64 0.24 0.07 0.04 0.18 1.16

24.2 Application of the Results of this Study

Most of the parameters in the final accident models comprise a high level of

significance. A majority of the parameters also comprise moderate to high levels of

stability (calculated by using the second validation method in Section 16.8).

However, the following measures revealed that large amounts of unexplained

variability remained in the final accident models:

• The standard errors and the large spread of the 95th percentile confidence limits

for many of the variables

• The mean error in accident rates (recorded rate minus predicted rate), which

varied between 1.0 and 1.9 times the mean recorded accident rate.

Other authors in the literature review also found that large amounts of unexplained

variability remained in the final accident models.

Due to the large amount of unexplained variability, the results of this study are not

particularly useful in predicting accident rates for a particular intersection. However,

because of the high level of significance obtained for most of the parameters, the

results are useful in identifying the effects of unsignalised intersection geometry on

accident rates. This provides the following applications:

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• Updating road design standards, enabling practitioners to design unsignalised

intersections of optimum safety.

• Using the final accident equations to determine if the additional construction costs

of a particular unsignalised intersection layout warrant the savings in accident

costs.

• Using the final accident equations to determine whether the accident rate at an

existing unsignalised intersection is similar to the average, or whether there are

local factors influencing the accident rates.

Reasons for the large amount of unexplained variability are as follows:

Low Numbers of Accidents

A low number of accidents will produce low levels of accuracy in the value of the

dependent variable ‘accident rate’. The minimum positive number of accidents is

one. For an analysis period of five years, this equates to an accident rate of 0.2

accidents per year. The most accurate result possible will therefore be plus or minus

0.1 accidents per year. When the average accident rate for a particular accident type

is low (eg 0 - 0.5 accidents per year per site), a level of accuracy of 0.1 accidents per

year will produce an amount of variability in the data.

Reasons for the low number of accidents are as follows.

• The amount of accident data obtained. It is difficult to obtain large amounts of

accident data for any particular site because accidents are a relatively infrequent

event. Harwood, Council et al (2000) identifies this fact. Only a very small

proportion of vehicles that travel through an intersection are involved in an

accident. Very long analysis periods are required to obtain a reasonable amount of

accident data. In most cases, however, very long analysis periods cannot be used

because one can never be confident that intersections have not changed over this

period.

• The degree of categorisation of the data. The accident data was categorised into

several accident types according to the principle event/s that gave rise to the

accidents. This has strong advantages in identifying trends in the data. However, it

produces greater variability in each accident type.

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• Low traffic volumes. Some rural intersections in the study comprised quite low

traffic volumes (although intersections with very low volumes were not used in

the study). It was not uncommon for these intersections to record zero accidents.

Variables Used in the Accident Models

The final accident models in this study comprise several variables. However, there

probably are many more variables that affect accident rates. The amount of

variability explained will never be high until other variables are included. Some of

the reasons why these other variables were not included in the final accident models

are as follows:

• They are too difficult to measure. Such variables were listed in Table 6.1.

• Not enough time and resources were available for their measurement. Such

variables were listed in Table 6.1.

• Determining the effect of these variables was not within the scope of this study.

Such variables include non-geometric parameters such as socio-economic area

surrounding the intersection, amount of rainfall in the area, condition of the

vehicle involved in the accident, type of vehicle etc.

• They were rejected based on high levels of correlation with primary variables.

An amount of variability in the data may also result from the relative inaccuracy of

the measurement of some of the variables in the final models. In addition, various

assumptions were made in the measurement of some of the variables. Some

variability in the data may result from inaccuracy in these assumptions.

The Maximised Range of Parameter Values

The range of values for particular variables was maximised in order to help identify

trends in the data. This has an unfortunate effect of increasing the amount of

variability in the data.

As identified in the Literature Review, Golias (1992) selected intersections with

similar road features and operational characteristics. The percentage of variability

explained in the data was high because the range of parameter values was minimised.

Except for traffic flows, this approach was not intended to find trends in the data.

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25 FUTURE WORK

This chapter recommends what future work should be undertaken to obtain

maximum benefits from this study. It also discusses how the findings may be used to

undertake similar research at other forms of intersections and roadways.

25.1 Update of Road Design Standards

It is recommended that the results of this study be incorporated into Austroads (1988;

QDMR (2000) and Austroads (2003). Implications for current road design standards

in these documents have been discussed in Chapter 23.

25.2 Implications for Further Analysis of Unsignalised Intersections Using the Techniques Developed in this Study

As discussed in Section 3.4, it is considered that this type of study forms part of an

evolutionary or iterative process to obtain better results. The results of this study can

identify where more data is required to overcome the problems associated with

multi-factor studies as discussed in Section 3.1. This data can then be collected and

added to the existing data in the study.

However, the data collection and compilation phase of this study alone involved

approximately 2,000 person hours of work, which equates to a cost in the order of

A$175,000. The next step of such an evolutionary process to obtain better results

would also involve similar amounts of time and cost. It would likely be beyond the

scope of what most road authorities are prepared to fund.

If funding was found to undertake the next phase of this evolutionary process, it is

probable that additional analysis techniques would also be identified.

25.3 Reanalyse the Data in Arndt (1998)

Several new techniques for the analysis of multi-factor studies have been developed

in this study as documented in Chapter 3. It is recommended that these techniques be

used to re-analyse the roundabout data in Arndt (1998). It is expected that the

application of these techniques will produce improved and more accurate results than

those previously obtained.

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25.4 Combine the Results of this Study with the Updated Results of Arndt (1998)

The results of this study could be combined with the updated results of the

roundabout study discussed above. This would enable practitioners to compare

potential accident rates of unsignalised intersections with roundabouts. Practitioners

would then be able to determine the optimum type of intersection for a particular

location given specific traffic flows and speed environment/s.

Some issues with combining these results are as follows:

• The databases used in this study and Arndt (1998) were different.

• The analysis period in Arndt (1998) started about nine years before the

unsignalised intersection study. The accidents recorded are for different periods of

time.

• The method of reporting ‘property damage only’ accidents has changed since the

roundabout study. For the duration of the analysis period of the roundabout study,

the cost of a property damage accident had to exceed $1000 before it was

classified as a major accident. This cost was increased to $2500 before the start of

the analysis period of the unsignalised intersection study.

The above issues would need to be addressed prior to the combination of these

results. One way of combining these results would be to place the final models of the

unsignalised study into the software package ‘ARNDT’. In this way, one software

program can analyse both roundabouts and unsignalised intersections.

25.5 Analysis of All Forms of Roadways and Intersections

When the results of the roundabout study (discussed above) are updated, studies of

the effect of geometry on accident rates at roundabouts and unsignalised intersections

will be complete. The next logical step would be to apply the techniques used in this

study to signalised intersections. In this way, all forms of at-grade intersections

would be analysed.

Studies into the effect of geometry on accident rates for all forms of roadways and

interchanges could also be undertaken. This could include a more detailed analysis of

single vehicle accidents to overcome the correlation problems with the Single-

Through vehicle accident model developed in this study.

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At the completion of these studies, one computer program could be developed that

analyses all forms of roadways and intersections.

It is considered that this type of study forms part of an evolutionary or iterative

process to obtain better results. The results of this study can identify where more data

is required to overcome the problems associated with multi-factor studies as

discussed in Section 3.1. This data can then be collected and added to the existing

data in the study.

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26 CONCLUSIONS

The aim of this study has been to determine the effect of unsignalised intersection

geometry on the rates of the various types of accidents occurring at unsignalised

intersections.

26.1 Results of the Literature Review

A literature review has identified that there is little consistency between the results of

previous studies. The only results found consistent across two or more independent

studies are as follows:

• T-intersections are safer than cross-intersections, when taking into account traffic

volumes.

• Lit intersections record lower accident rates than do unlit intersections

• Larger stop signs on the minor legs result in a lower accident rate

If a particular study did identify an important parameter (other than traffic volume),

it was often not considered by other studies, was not found to be important or was

found to have the opposite effect.

26.2 Approaches Taken in this Study

This study sought to determine reasons for the above results by investigating

potential problems of undertaking multi-factor studies. Multi-factor studies consider

simultaneously the effects of many factors on the incidence of accidents using a

sample of collected data.

It was concluded that ‘multi-factor studies’ would potentially yield many highly

significant parameters and explain much of the variability in the data only if the data

sample comprised the following:

• An adequate amount of accident data

• A wide range of values for each variable

• Accurate measurements of each variable

• Sites that cover every possible combination of variables

It is highly unlikely that any multi-factor study could ever meet all the criteria listed

in the four dot points above. As a result, the collected data is likely to be insufficient

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for determining all relationships between variables and accident rates.

It was concluded that the above criteria need to be addressed in order to mitigate

some of the problems associated with multi-factor studies, thus obtaining better

results. For this reason, the following approaches were developed in this study:

• Maximise the efficiency of data collection

Obtain a wide range of values of each variable

Exclude very low volume intersections

• Develop techniques for analysing less than perfect data

Categorise the accident data

Select variables that are expected to relate to accident rates

Develop driver behavioural models

Determine suitable methods of measuring variables

Determine suitable methods of dealing with correlation between variables

Identify appropriate relationships between variables and accident rates

Develop suitable methods of dealing with interactions between variables

Identify suitable regression analysis techniques

Determine methods of accepting/rejecting parameters in the regression analysis

Develop suitable methods of validating the models

Some of these approaches make assumptions based on the results of previous

research, observation of driver behaviour on-site, experience, and logical/reasonable

outcomes and relationships. These form the framework on which the results were

based.

The results of this study will only be as good as these assumptions and the suitability

of the collected data. Regardless of the amount of data collected (even when

adopting the techniques listed under dot point number one above - ‘maximise the

efficiency of data collection’), it will usually be inadequate to obtain even results that

yield many highly significant variables and explain much of the variability in the

data. For this reason, the framework on which the results are based needs to be rigid

enough to avoid results that do not make sense. Conversely, the framework cannot be

so rigid that very few results could ever be obtained.

These approaches seek to identify the important variables affecting accident rates and

produce a logical result. Relationships for variables having only a small effect on

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accident rates are unlikely to be determined. In the same way, only strong

interactions between variables are likely to be identified using these approaches.

Unreasonable results were obtained for parameters that are readily changed at

intersections to improve safety eg replace a give way sign with a stop sign, increase

number of stop signs and install lighting. It was suspected that these results were

reflecting the fact that these measures are often used at the more dangerous

intersections in an attempt to reduce accident rates.

It was identified that multi-factor studies are not likely to identify appropriate

relationships between such parameters and accident rates. Instead, multi-factor

studies probably give the most reliable result for parameters that are not easily

changed eg angle of the intersection, level of sight distance, number of legs etc.

26.3 Analysis Results

The above approaches were used to analyse accident data, traffic volume data and

geometric data for 206 unsignalised intersection sites from throughout Queensland.

The accident data was categorised into accident types as given in Table 5.6 and in

Figures 5.1 to 5.3. The accident types used in the regression analysis were Angle-

Minor, Angle-Major, Rear-End-Major, Single-Through, Rear-End-Minor, Single-

Minor-Turn, Single-Major-Turn, and Overtaking-Intersection.

The intersection turn treatment codes in QDMR (2000) and Austroads (2003) were

found to be insufficient in covering all cases of turn types in this study. For this

reason, additional codes were developed as shown in Figures 4.1 to 4.3 and in

Appendix E - Turn Types Used in this Study. The codes used are LSR, AUR, CHR,

MNR, LSL and AUL.

Applying the approaches given in the previous section to this data, the following

results were obtained.

Intersection Design Philosophy

This study has identified that the following factors will increase accident rates:

• An increase in relative speed between vehicles

• An increase in the number of traffic streams that need to be viewed ie an increase

in driver workload.

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• An increase in restrictions to visibility. This includes an increase in the

observation angle.

• A decrease in the levels of perception of an intersection.

Based on the above, the safest intersection will be one that minimises the relative

speed between vehicles, decreases the number of traffic streams to be viewed,

provides unrestricted visibility and maximises the perception of the intersection.

Aspects of the vehicle at fault are more important than the vehicle not at fault. Safety

is improved largely by optimising the aspects of the vehicle at fault, rather than the

vehicle not at fault. This can be summarised as ‘prevention is better than cure’. It is

better to reduce the likelihood of drivers making errors than to introduce measures to

help the drivers not at fault to avoid the vehicle at fault.

This study has provided evidence to support the notion that the number of

intersections along a roadway should be limited.

Measures to Reduce Vehicle Speed

In most instances, reduction of the major road speed was found to either not be a

practical solution, or would probably do little in reducing accident rates.

Increased minor road speeds result in increased Angle-Minor and Single-Minor-Turn

vehicle accident rates. There is insufficient evidence in this study to determine which

of the two parameters ‘speed environment of the minor road’ or ‘85th percentile

minor road approach speed’ is the more important predictor of these accidents.

Because the relative importance of these two speeds is unknown, the effectiveness of

introducing devices such as a speed limit reduction, approach curvature, or rumble

strips remains unknown. Although the effectiveness is unknown, the intent of

providing these devices on the minor road in high-speed environments is sound.

Intersection Type

Cross intersections (comprising fully aligned minor legs) record high accident rates.

Assuming staggered T-intersections operate as two separate T-intersections, the

potential accident rate for through movements from the minor road at cross

intersections is 2 to 10.5 times higher than that at staggered T-intersections.

Four leg intersections with a small offset of the minor road legs (at least equal to half

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of the minor road approach carriageway, right-left stagger only) are significantly

safer than cross intersections. However, right-turning vehicles on opposing minor

road legs may find it difficult to turn simultaneously under this arrangement.

Staggered T-intersections with a left-right stagger potentially perform better than

staggered T-intersections with a right-left stagger. Assuming staggered T-

intersections operate as two separate T-intersections, the accident rate for through

movements from the minor road at right-left staggered T-intersections is potentially

3.5 to 4.7 times higher than that at left-right staggered T-intersections (provided that

Type CHR turn treatments are used on the major road).

Parameters Relating to Restrictions to Visibility

The following parameters relating to restrictions to visibility have been found to

increase accident rates:

• Angle-Minor vehicle accidents - decreased visibility between minor road and

major road vehicles, increased observation angles, increased number of stand-up

lanes on the minor road, and for conflicts involving a through minor road vehicle

colliding with a major road vehicle from the right (TLT conflict), presence of

queuing through the intersection on a multi-lane major road.

• Angle-Major vehicle accidents - decreased visibility between right-turning and

oncoming major road vehicles and presence of queuing through the intersection

on a multi-lane major road.

• Rear-End-Major vehicle accidents - decreased visibility between approaching

and turning major road vehicles.

Major Road Turn Type

The following results have been obtained for the various major road turn types:

• CHR turn treatments record a 98 and a 97 percent lower Rear-End-Major vehicle

accident rate than do LSR and AUR turn treatments respectively.

• AUR treatments record a 42 percent reduction in Rear-End-Major vehicle

accident rates over a LSR treatment.

• MNR treatments record a Rear-End-Major vehicle accident rate almost double

that of a LSR treatment.

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• AUL and LSL treatments record a Rear-End-Major vehicle accident rate around

50 times lower than that for AUR and LSR treatments respectively. Therefore,

consideration of appropriate treatments for right-turning vehicles is much more

critical than that for left-turning vehicles.

• AUL treatments record a 47 percent lower Rear-End-Major vehicle accident rate

than do LSL treatments.

There was no evidence that CHR turn treatments with short right-turn slots perform

worse than CHR turn treatments with longer slots.

The presence of (or lack of) a widened shoulder at LSR treatments on two lane roads

has no appreciable effect on Rear-End-Major vehicle accident rates. This was found

to be true regardless of whether the widened shoulder is sealed or unsealed.

The right-turn Rear-End-Major vehicle accident rate decreases substantially with

median width (raised, painted or depressed medians) at LSR, AUR, and MNR sites.

Horizontal Curve Radius

Single-Through vehicle accident rates are highest on the smallest radii horizontal

curves in any given speed environment.

Free Left-Turn Lanes

Providing free left-turn lanes (from the major and minor roads) leads to an overall

increase in accident rates. However, relative to many other conflict types, accident

rates on free left-turn lanes (and non-free left-turn lanes) are low.

Line Marking

Type LSR and AUR turn treatments comprising barrier centreline marking record far

fewer Overtaking-Intersection vehicle accidents.

Approach Visibility

The amount of approach visibility on the minor and major roads generally did not

affect accident rates.

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27 RECOMMENDATIONS

27.1 Implications for Road Design Standards

It is recommended that the following issues identified in Section 23 be considered for

incorporation into QDMR (2000) and Austroads (2003):

• Include a discussion on intersection design philosophy.

• Discuss the influence of speed of the minor and major roads on accident rates.

• Discuss the relative safety of the various intersection types including cross and

staggered T-intersections.

• Expand the existing Safe Intersection Sight Distance model to cover the following

cases:

Right-turning major road drivers and oncoming major road drivers.

Approaching major road drivers and turning major road drivers.

• Discuss the use of reduced values of sight distance at existing intersections in

constrained situations subject to a number of other considerations.

• Limit the number of stand-up lanes on the minor road to one, particularly for four-

leg intersections with heavy through movements from the minor legs (a free left-

turn lane is not considered to be an individual stand-up lane).

• Limit the amount of amount of queuing on the multi-lane major roads through

intersections.

• Adopt new warrants for major road right-turn treatments (for two lane roads only)

based on one of two methods developed in this study. Include warrants for low-

speed in addition to high-speed environments.

• Consider what appropriate variables should be used on the axes of the warrants

for major road right-turn treatments.

• Consider the future use and benefits of using Type AUR turn treatments as

opposed to Type CHR turn treatments with short right-turn slots.

• Use a reduced set of warrants for major road left-turn treatments.

• Include a discussion on the poor safety record of Type MNR right-turn treatments

and the need to always provide CHR turn treatments on multi-lane roads.

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• Include a discussion on the benefits of including medians (even if only one to two

metres wide) at BAR, AUR and MNR major road turn treatments.

• Indicate that the provision of either a sealed or unsealed area at BAR turn

treatments makes no significant difference to accident rates.

• Indicate that there is no advantage in providing free left-turn lanes for improved

safety.

• Discuss the advantage of using barrier lines at major road BAR turn treatments.

This is particularly important for sites in high-speed environments, sites providing

good overtaking opportunities and sites with higher traffic volumes.

• Discuss the necessity of obtaining Approach Sight Distance in all situations.

Consider the use of reduced values of Approach Sight Distance in constrained

situations on existing roads.

27.2 Future Work

It is recommended that the following future work be undertaken as discussed in

Section 25:

• Use the techniques developed in this study to obtain additional unsignalised

intersection data and reanalyse the data to obtain better results. This will be

subject to greater funding levels becoming available.

• Re-analyse the roundabout data in Arndt (1998) according to the approach used in

this study. The aim of this is to produce improved and more accurate results than

those previously obtained.

• Combine the results of this study with the updated results of the roundabout study

to enable practitioners to compare potential accident rates of unsignalised

intersections with roundabouts. One way of combining these results would be to

place the final models of the unsignalised study into the software package

‘ARNDT’.

• Undertake multi-factor studies of all other forms of roadways and intersections.

Use all of the techniques developed in Chapter 3 to mitigate the problems

associated with undertaking multi-factor studies. Incorporate all the results into

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one computer package that can check the potential safety performance of any road

design.

Appendices

APPENDIX A - ACCIDENT CATEGORIES

The coding system used for the initial accident classification is shown in Table A1.

The final major accident categories developed in this study are shown in Table A2

and Figure A1. The types and numbers of sub-accident categories, recorded for each

final major accident category, are given in Tables A3 to A6. The codes given in the

second column of Tables A3 to A6 are those identified during the initial accident

classification (as listed in Table A1).

Table A1 - Coding System for the Initial Accident Classification Location in Code Code Description

A Angle R Rear-end S Single vehicle H Head-on D Sideswipe P Pedestrian

First Letter (Nature of collision)

C Cyclist M On major road Second Letter

(Original direction of vehicle at fault)

S On minor road

Third Letter/s

(Specific accident details)

Varies - dependent on specific circumstances (refer column 2 of Tables A3 to A6)

Varies - dependent on specific circumstances (refer column 2 of Tables A3 to A6)

Table A2 - Major Accident Categories Broad

Accident Category

Major Accident Type



466




107

694


27

Single-Minor-Turn


23

Single-Major-Turn


17


17



13



4


Other 8

109


Single-Through


167

167


39

U-turn Hit whilst undertaking a U-turn at mid-block

33



Other 10

121

Total 1091


100%

High Frequency


64%

Low Frequency


10%


Accidents 167 acc.

15%


Accidents 121 acc.

11%

Pedestrian: 39 acc. U-Turn: 33 acc. Changed Lanes: 16 acc. Single-Object: 16 acc. Overtaking: 7 acc. Other: 10 acc.

Single-Through: 167 acc.

Angle-Minor: 466 acc.Rear-End-Major: 121 acc.Angle-Major: 107 acc.

Rear-End-Minor: 27 acc. Single-Minor-Turn: 23 acc. Single-Major-Turn: 17 acc. Incorrect Turn: 17 acc. Overtaking Intersection: 13 acc. Sideswipe-Major-Auxiliary: 4 acc. Other: 8 acc.

Figure A1 - Major Accident Categories

Table A3 - High Frequency Intersection Accidents Major

Accident Category

Accident Types

Included

Accident Description

No. Total

A/S/Z A minor and a major road vehicle collided (unknown movement)

1

A/S/ZLT A minor road vehicle (unknown movement) collided with a through major road vehicle from the left

2

A/S/ZRT A minor road vehicle (unknown movement) collided with a through major road vehicle from the right

5

A/S/LRT A left-turning minor road vehicle collided with a through major road vehicle from the right

12

A/S/TZ A through minor road vehicle collided with a major road vehicle, movement unknown

1

A/S/TLT A through minor road vehicle collided with a through major road vehicle from the left

121

A/S/TLO A through minor road vehicle collided with a through vehicle from the left which was overtaking.

1

A/S/TRT A through minor road vehicle collided with a through major road vehicle from the right

83

A/S/RZ A right-turning minor road vehicle collided with a major road vehicle, movement unknown

1

A/S/RLT A right-turning minor road vehicle collided with a through major road vehicle from the left

35

A/S/RLR A right-turning minor road vehicle collided with a right-turning major road vehicle from the left

3

A/S/ROT A right-turning minor road vehicle collided with a opposing minor road vehicle travelling through

5

A/S/ROR A right-turning minor road vehicle collided with a opposing minor road vehicle turning right

1

A/S/RRT A right-turning minor road vehicle collided with a through major road vehicle from the right

188

A/S/RRR A right-turning minor road vehicle collided with a right-turning major road vehicle from the right

1

A/S/RRO A right-turning minor road vehicle collided with a through vehicle from the right which was overtaking a left-turning vehicle

1

Angle-Minor (Principally failure to give way by a minor road vehicle)

A/S/TLO A through minor road vehicle collided with a through vehicle from the left which was overtaking another through vehicle.

1

466

Table A3 - High Frequency Intersection Accidents (Continued) Major

Accident Category

Accident Types

Included


No. Total

R/S/TE A major road vehicle ran into another vehicle that braked for a minor road vehicle that failed to give way.

1

S/S/ZZT A major road vehicle lost control after avoiding a minor road vehicle failing to give way.

1

S/S/ZRT A major road vehicle lost control after avoiding a minor road vehicle failing to give way on the left

1

S/S/LRT A major road vehicle lost control after avoiding a left-turning minor road vehicle on the left

1

Angle-Minor (continued) (Principally failure to give way by a minor road vehicle)

S/S/RRT A major road vehicle lost control after avoiding a right-turning minor road vehicle on the left

1

A/M/RT A right-turning major road vehicle collided with an oncoming through vehicle

102

A/M/RL A right-turning major road vehicle collided with an oncoming left-turning vehicle

2

Angle-Major (Principally failure to give way by a major road vehicle)

A/M/UT A major road vehicle undertook a U-turn and collided with an oncoming through vehicle

3

107

R/M/Z A major road vehicle ran into a vehicle turning at intersection, turning movement unknown

1

R/M/L A major road vehicle ran into a vehicle turning left or ran into another through vehicle slowing for a left-turning vehicle.

3

R/M/R A major road vehicle ran into a vehicle turning right or ran into another through vehicle slowing or stopped for a right-turning vehicle.

104

R/M/U A major road vehicle ran into a vehicle undertaking a U-turn at the intersection

3

S/M/AZ A major road vehicle lost control after avoiding another major road vehicle turning at intersection

1

S/M/AL A major road vehicle lost control after avoiding another major road vehicle turning left at the intersection

1

S/M/AR A major road vehicle lost control after avoiding another major road vehicle turning right at the intersection

4

Rear-End-Major (Principally not adequately negotiating a slowed or stopped turning major road vehicle)

S/M/RH A major road vehicle’s load fell onto an oncoming vehicle after avoiding another major road vehicle turning right at the intersection

1

121

Table A3 - High Frequency Intersection Accidents (Continued) Major

Accident Category

Accident Types

Included


No. Total

H/M/AL A major road vehicle collided with an oncoming vehicle after avoiding another major road vehicle turning left at the intersection

1

H/M/AR A major road vehicle collided with an oncoming vehicle after avoiding another major road vehicle turning right at the intersection

1

Rear-End-Major (continued) (Principally not adequately negotiating a slowed or stopped turning major road vehicle)

D/M/CA A major road vehicle changed lanes to avoid a major road vehicle turning right at the intersection and collided with another vehicle travelling in the same direction

1

Total 694

Table A4 - Low Frequency Intersection Accidents Major

Accident Category

Accident Types

Included


No. Total

R/S/Z A minor road vehicle ran into a vehicle turning at intersection, turning movement unknown

5

R/S/L A minor road vehicle ran into a vehicle turning left or ran into another vehicle slowing or stopped for a left-turning vehicle.

15

R/S/R A minor road vehicle ran into a vehicle turning right or ran into another vehicle slowing or stopped for a right-turning vehicle.

4

Rear-End-Minor (Principally not adequately negotiating a slowed or stopped minor road vehicle)

R/S/T A minor road vehicle ran into a vehicle travelling through

3

27

S/S/Z A minor road vehicle lost control at the intersection - turning movement unknown

1

S/S/L A minor road vehicle lost control whilst turning left from minor road at the intersection

8 Single-Minor-Turn (Principally lose of control whilst turning from minor leg)

S/S/R A minor road vehicle lost control whilst turning right from minor road at the intersection

14

23

S/M/L A vehicle lost control whilst turning left from the major road at the intersection

8 Single-Major-Turn (Principally lose of control whilst turning from major leg)

S/M/R A vehicle lost control whilst turning right from the major road at the intersection

9 17

R/M/D A major road vehicle ran into a vehicle in the deceleration lane which was attempting to change lanes

1

S/M/CA A major road vehicle lost control after avoiding a vehicle changing lanes on an auxiliary lane of the intersection

1

Sideswipe-Major-Auxiliary (Principally hit another vehicle by moving from deceleration lane)

D/M/D A driver in a deceleration lane attempted to change lanes and collided with another vehicle travelling in the same direction

2

4


D/M/OR An overtaking vehicle hits a vehicle turning right at the intersection

13 13

Table A4 - Low Frequency Intersection Accidents (Continued) Major

Accident Category

Accident Types

Included


No. Total

A/S/ZLW A minor road vehicle (movement unknown) collided with a right-turning major road vehicle from the left that was on the wrong side of the carriageway.

1

H/M/Z A vehicle turned from the major road onto the wrong side of minor road and collided with an oncoming vehicle - movement unknown

1

H/M/L A vehicle turned left from the major road onto the wrong side of minor road and collided with an oncoming vehicle

2

H/S/L A vehicle turned left from the minor road onto the wrong side of major road and collided with an oncoming vehicle

5

D/M/CC A major road driver, about to turn right, changed into left lane instead and collided with another vehicle travelling in the same direction

2

D/M/CL A major road driver attempted to turn left from the right of another vehicle

2

D/M/CR A major road driver attempted to turn right from left of another vehicle

2

D/S/L Two vehicles sideswipe each other whilst turning left from the minor road

1

Incorrect Turn (Principally undertaking an incorrect turning manoeuvre)

D/M/LO A vehicle turning left from the major road sideswipes an oncoming vehicle on the minor road

1

17

R/M/EV A major road vehicle ran into a vehicle stopped for a turning emergency vehicle at the intersection

1

R/M/TA A major road vehicle ran into another vehicle that was slowing and anticipating that a minor road vehicle was pulling out.

1

R/M/RV A major road vehicle ran into a vehicle reversing back to intersection

1

R/S/RV A minor road vehicle ran into a vehicle reversing back from intersection.

1

A/M/AA A major road vehicle collided with a vehicle involved in an earlier accident at the intersection

1

R/M/RN A major road vehicle ran into right-turning vehicle after a series of figure 8 manoeuvres

1

H/S/LW A minor road vehicle turned left and hit a cyclist travelling on wrong side of carriageway

1

Other

S/M/LL A major road vehicle turning left at the intersection lost control after avoiding another major road vehicles turning left at the intersection.

1

8

Total 109

Table A5 - High Frequency Through Accidents Major

Accident Category

Accident Types

Included


No. Total

S/S/T A minor road vehicle lost control on the minor leg prior to or after intersection

11

H/S/T A minor road vehicle lost control on minor leg prior to intersection and veered onto opposite carriageway into an oncoming vehicle

2

S/M/FV A rider fell from the vehicle 1 S/M/T A major road vehicle lost control 113 H/M/T A major road vehicle lost control and

veered onto opposite carriageway into an oncoming vehicle

38

Single-Through (Principally loss of control whilst travelling through on a major or minor leg)

D/M/LC A major road vehicle lost control and collided into another vehicle travelling in the same direction in an adjacent lane

2

167

Table A6 - Low Frequency Through Accidents Major

Accident Category

Accident Types

Included


No. Total

P/M/T A pedestrian was hit whilst crossing the road (not at a pedestrian crossing)

33

C/M/T A cyclist was hit whilst crossing road (not at a pedestrian crossing)

3

P/M/O A pedestrian walking parallel to the road was hit by an overtaking vehicle.

1

Pedestrian (Principally hit a pedestrian or cyclist crossing road) P/S/T A pedestrian was hit whilst crossing road

prior to the intersection (not at a pedestrian crossing)

2

39

A/M/UB A major road vehicle undertaking a U-turn collided with a vehicle from behind

25

A/M/UO A major road vehicle undertaking a U-turn collided with an oncoming through vehicle

6

A/S/UB A minor road vehicle undertaking a U-turn collided with a vehicle from behind

1

U-Turn (Principally hit whilst undertaking a U-turn at mid-block) A/S/UO A minor road vehicle undertaking a U-turn

collided with an oncoming through vehicle.

1

33

R/M/C A major road vehicle ran into another vehicle whilst changing lanes

3

S/M/C A major road vehicle lost control after avoiding a vehicle that was changing lanes

6

D/M/C One or more major road vehicles changed lanes and collided with another vehicle travelling in the same direction

6 Changed Lanes (Principally changed lanes when unsafe) H/M/AT A major road vehicle avoided a vehicle in

an adjacent lane then lost control and veered onto the opposite carriageway into an oncoming vehicle

1

16

Table A6 - Low Frequency Through Accidents (Continued) Major

Accident Category

Accident Types

Included


No. Total

S/M/A A major road vehicle lost control after avoiding an object or animal

6 Single-Object (Principally hit or avoid object)

S/M/H A major road vehicle hit an object or animal on the carriageway

10 16

S/M/AO A major road vehicle lost control after avoiding an overtaking vehicle from the opposite direction

2

S/M/O A major road vehicle lost control whilst overtaking

1

H/M/O A major road vehicle collides with an oncoming vehicle whilst overtaking

3

Overtaking-Through (Principally unsafe overtaking)

D/M/OD An overtaking vehicle hits the vehicle being overtaken.

1

7

S/M/AT A major road vehicle lost control after avoiding a vehicle travelling in same direction

3

S/M/NA An unattended vehicle rolled down an embankment

1

S/S/TA A minor road vehicle lost control on minor leg after negotiating the intersection

2

S/M/RV A vehicle reversing at high speed lost control

1

S/M/OH An overtaking vehicle hit debris from the vehicle being overtaken.

1

D/M/CT A major road vehicle sideswiped a cyclist

1

Other

D/M/LF A load from a truck fell on cyclist 1

10

Total 121

APPENDIX B - VEHICLE PATH MODEL

Figures B1 to B13 show the methods used to construct vehicle paths at unsignalised

intersections. These methods are sufficient to construct paths for most situations.

However, some intersection layouts have quite complex geometry and additional

subjective decisions are required in order to draw the vehicle paths.

The following considerations are relevant to the construction of vehicle paths in

Figures B1 to B13.

• The symbols used in the figures have the following meaning:

D - The vehicle path at this location is parallel to the geometric element at the

relevant distance ‘DE’ (listed below). Draw these paths first along with ‘M’.

DCUR - The vehicle path at this location is the largest single radius curve that

can be drawn such that the relevant distance ‘DE’ occurs at the closest point of

the applicable geometric element.

DMIN - The vehicle path at this location is the largest single radius curve that

can be drawn such that the relevant distance ‘DE’ occurs at point shown on the

applicable geometric element.

M - The vehicle path at this location is in the centre of the lane and parallel to

the lane edge. Draw these paths first along with ‘D’.

DE - 1.0m for an edge line or adjacent lane edge, 1.5m for kerbing or a

centerline

• For reverse or compound curves, construct the curve labelled by the number ‘1’

first.

• If no holding line is provided, assume the holding line is at the same location as

the give way line.

• If no centre linemarking is provided on the minor road, draw linemarking at the

centre of the minor road.

• Where the vehicle path models in these figures produce a radius smaller than 8m,

adopt 8m as a minimum and draw it as such. Where this occurs, draw the holding

line at the start of the turn.

• Medians shown in these figures can be depressed, raised or painted.

Vehicle Paths on the Major and Minor Roads (Excluding Intersection Turn Movements)

Vehicles paths on horizontal straights and large radii curves were drawn parallel to

the edge line or centre line of the roadway. Vehicle paths on smaller radii curves

were drawn in accordance with Figure B1. For four lane roads, construct vehicle

paths in the right most through lane. For six lane roads, construct vehicle paths in the

centre lane.

Vehicle Paths for Left-turns from the Minor Road

Figures B2 to B4 show construction of vehicle paths for left-turns from the minor

road. For minor roads with greater than one stand-up lane, construct vehicle paths for

left-turning drivers in the left most lane.

Vehicle Paths for Through Movements from the Minor Road

Figures B5 to B7 show construction of vehicle paths for through movements from

the minor road. For minor roads with greater than one stand-up lane, construct

vehicle paths for through movements in the right most through lane.

Vehicle Paths for Right-turns from the Minor Road

Figures B8 to B10 show construction of vehicle paths for right-turns from the minor

road. For minor roads with greater than one stand-up lane, construct vehicle paths for

right-turn movements in the right most lane.

Vehicle Paths for Right-turns from the Major Road

Figures B11 to B13 show construction of vehicle paths for right-turns from the major

road.

Figure B1 - Major and Minor Road Vehicle Paths (excluding intersection movements)

Note: * Construct smaller radius curve (labelled as ‘T1’) first. Draw it tangential to the dashed curve that

represents the centreline of the roadway. The larger radius curve is made tangential to the smaller radius curve.

Figure B2 - Left-Turn Movements from Minor Road Note: * If a single radius curve cannot be drawn within the lane according to these criteria, construct

vehicle paths parallel to the left edge of lane.

Figure B3 - Left-Turn Movements from Minor Road

Figure B4 - Left-Turn Movements from Minor Road

Note: * If a single radius curve cannot be drawn within the lane according to these criteria, construct

vehicle paths parallel to the left edge of lane.

Figure B5 - Through Movements from Minor Road



Figure B8 - Right-Turn Movements from Minor Road


Note: * If a single radius curve cannot be drawn within the lane according to these criteria, construct

vehicle paths on approach curve as per a straight approach as shown in Figure B8 - Straight Minor Road Approaches


Figure B11 - Right-Turn Movements from Major Road



APPENDIX C - GEOMETRIC VARIABLES

Tables C1 to C16 detail all measured or calculated variables identified by the method

given in Section 6.1.

Table C1 - Exposure and Queuing Variables Variable

Code Variable Description Measurement of the Variable

QSi Traffic flow from the minor leg (veh/d)

i = L for the left-turn traffic flow i = T for the through movement traffic flow i = R for the right-turn traffic flow i = A for the traffic flow for all movements L, T and R (the total approaching traffic volume)

QSM Traffic flow from the minor leg for the particular conflict (veh/d)

QSL for a LRT conflict QST + m x (QSL+QSR) for TLT and TRT conflicts where m = a constant. (The QSL and QSR terms are included because four leg intersections can record accidents for TLT and TRT conflicts even if the through traffic count is zero). QSR for RLT and RRT conflicts

QMi Traffic flow from a major leg (veh/d)

i = L for the left-turn traffic flow i = T for the through movement traffic flow i = R for the right-turn traffic flow i = A for the traffic flow for all movements L, T and R (the approaching traffic volume) i = O for the opposing through movement traffic flow i = OR for the opposing right-turn traffic flow

QiT Traffic flow on a horizontal geometric element (veh/d)

i = S for a minor road horizontal geometric element i = M for a major road horizontal geometric element

QMMOD Through traffic flow on the opposing major road leg (veh/d) - dummy variable

0 - left-turn QMO - for right-turns

QUEi Presence of queuing through the intersection from a downstream set of traffic signals on a multi-lane road only - dummy variable i = N for the near carriageway of a multi-lane major road relative to the minor road i = F for the far carriageway of a multi-lane major road relative to the minor road i = O for the opposing carriageway of a multi-lane major road

The value of this variable has been subjectively chosen according to the following system: 0 - no queuing through the intersection from an upstream set of traffic signals in peak hour. A value of zero applies to all two-lane roads. 1 - some queuing through the intersection from an upstream set of traffic signals in peak hour. Queues mostly dissipate on each change of signals. 2 - extended queuing through the intersection from an upstream set of traffic signals in peak hour. Queues do not dissipate for at least five changes of signals.

Table C2 - Road Classification Variables Variable


RCS Classification of the minor road using the Department of Main Road’s road classes - dummy variable

1 - State highways (no’s 10 - 49), urban arterial roads (no’s U10 - U49), developmental roads (no’s 50 - 99) and urban sub-arterial roads (no’s U50 - U99) 2 - Main roads (no’s 100 - 999), secondary roads (no’s 1000 - 9999) and higher volume Local Authority roads 3 - Lower to moderate volume Local Authority roads.

RCM Classification of the major road using the Department of Main Road’s road classes - dummy variable

As per previous row excluding number 3.

Table C3 - Driver Alertness Variables Variable

Code Variable

Description Measurement of the Variable

DAS Driver alertness on the minor road - dummy variable

DAM Driver alertness on the major road - dummy variable

The value of this variable has been subjectively chosen according to the following system: 1 - Local streets and roads (including local roads in rural residential areas of short to moderate length), arterials through commercial / industrial areas, roads with a high frequency of side streets, roads with a high frequency of roadside parking, roads in mountainous terrain 2 - Rural roads in hilly terrain with winding alignments, rural roads of short to moderate length joining other major roads, longer length urban arterials with few intersections, local rural roads of moderate to long length 3. Rural roads with moderate distances of rural environment before the intersection. 4. Rural roads with very long distances of rural environment before the intersection eg national highways Other methods of measuring this variable that were considered but not used are as follows. Distance since last potential stop condition is not an appropriate measurement because not all vehicles travel over this distance. In addition, the intersection could be in an urban area a large distance since the last potential stop condition.

Table C4 - Speed Limit Variables Variable

Code Variable Description Measurement of the Variables

SLSP Speed limit on the minor road prior to the intersection

SLMP Speed limit on a major leg prior to the intersection

This value excludes changes in speed limits immediately prior to the intersection

SLSI Speed limit on the minor road immediately before the intersection

SLMI Speed limit on a major leg immediately before the intersection

Same as the previous row unless the speed limit changes immediately before intersection. In the latter case, it is the changed speed limit.

SLRS Speed limit reduction on the minor road immediately before the intersection (km/h)

This value equals SLSP minus SLSI

SLRM Speed limit reduction on the major leg immediately before the intersection (km/h)

This value equals SLMP minus SLMI

SLSZS Speed limit on the minor road through school zones or school bus zones (zero if not applicable)

SLSZM Speed limit on the major road leg through school zones or school bus zones (zero if not applicable)

Speed limit through school or school bus zones on the intersection approaches or through the intersection during the posted school times.

Notes: (1) For most sites, a posted speed limit was identified and this value was used as the speed limit.

Where a posted speed limit was not provided and the roadway was continually lit, a value of 60km/h was used. Alternatively, where a posted speed limit was not provided and the roadway was not lit, a value of 100km/h was used.

Table C5 - Minor Road Speed Variables Variable


SES Speed environment of the minor road (km/h)

Refer Notes 1 and 2. Minimum speed environment used was 40km/h.

SROS Potential reduction in speed from the speed environment due to various devices on the minor leg before the intersection (km/h).

This value equals the speed environment minus the estimated 85th percentile approach speed due to these devices. If no devices exist, this value equals the speed environment. These various devices include stop or give way signs at previous intersections or railway level crossings, short roads or major traffic generators. Refer Note 2.

SRSLS Potential reduction in speed from the speed environment due to a reduction in speed limit on the minor leg (km/h).

This value equals the speed environment minus the estimated 85th percentile approach speed due to the reduction in speed limit. If no reduced speed limit exists, this value equals the speed environment

SRCS Potential reduction in speed from the speed environment due to approach curvature on the minor leg (km/h).

This value equals the speed environment minus the estimated 85th percentile approach speed due to the approach curvature. If no approach curvature exists, this value equals the speed environment. The approach speed is calculated based on the speed prediction model in Section 6.3 and the vehicle path model in Section 6.4 using the minimum approach curve radius and the speed environment.

SSAP 85th percentile minor road approach speed (km/h)

This value is the minimum approach speed estimated from the previous three rows.

SSi 85th percentile speed on a minor road horizontal geometric element (km/h) i = L for left-turn from the minor road i = R for right-turn from the minor road i = E for approach element on the minor road

The 85th percentile speed is calculated based on the speed prediction model in Section 6.3 and the vehicle path model in Section 6.4 using the minimum curve radius and the speed environment.

∆SSE Decrease in 85th percentile speed on the minor road horizontal geometric element (m)

This value equals the 85th percentile speed on the previous horizontal element minus the 85th percentile speed on the horizontal element under consideration.

Notes: (1) Speed environment is defined in Austroads (1989). For this study, speed environment was taken

as the estimated 85th percentile speed of free passenger cars on the longer sections of roadway before the intersection that comprised horizontal straights or large radius horizontal curves. The speed environment was measured in multiples of 10km/h. This speed was estimated by driving the particular section of roadway whilst unhindered by other vehicles. The speed environment selected was often 10km/h over the speed limit although in some cases (eg where local conditions dictated or there was no speed limit), this did not apply. The same driver was used for all measurements. This was a quite subjective method of measuring the speed environment. Given the enormous time and resources needed to measure it accurately, this was the only known practical way. The accuracy in most cases was expected to be plus or minus 10km/h. Arndt (1998) used this process and found the estimated speed parameters to be amongst the most important predictors of accidents.

(2) Speeds were estimated for the following conditions: a) Where sample intersections comprised the following devices on the minor leg: a railway level crossing or another intersection with stop or give way signs. The speed environment was taken prior to the device and the approach speed was estimated allowing for the device. b) Where there was a major traffic generator or major intersection in close proximity to a particular sample intersection ie where vehicles were approaching from different paths. In these cases, the speed environment and the expected approach speed were estimated for the predominant vehicle stream. c) Where a minor road was a short dead-end road. In this case, the speed environment was selected as 40km/h (the minimum) and the approach speed was based on a vehicle starting at a point midway along the minor road.

Table C6 - Other Speed Variables

Variable Code

Variable Description Measurement of the Variable

SEM Speed environment of a major leg (km/h)

Refer Notes 1 and 2 of Table C5. Minimum speed environment used was 40km/h.

SRSLM Potential reduction in speed from the speed environment due to a reduction in speed limit on a major leg (km/h).

This value equals the speed environment minus the estimated 85th percentile speed due to the reduction in speed limit. If no reduced speed limit exists, this value equals the speed environment

SRCM Potential reduction in speed from the speed environment due to curvature on the major leg (km/h).

This value equals the speed environment minus the estimated 85th percentile speed due to curvature. If no curvature exists, this value equals the speed environment. The 85th percentile speed is calculated based on the speed prediction model in Section 6.3 and the vehicle path model in Section 6.4 using the minimum curve radius and the speed environment.

SMi 85th percentile through speed on a major leg (km/h) i = T for the through movement speed i = O for the opposing through movement speed

This value is the minimum 85th percentile speed estimated from the previous two rows.

SRi Relative speed between minor and major road vehicles for various conflict types (km/h)

i = LRT, TLT, TRT, RLT or RRT vehicle conflicts (refer to Figure 9.7 for these conflict types). This value is calculated based on the values of SES, RSi, SMT, and the angle between vehicle paths.

SME 85th percentile speed on the major road horizontal geometric element (km/h)

The 85th percentile speed is calculated based on the speed prediction model in Section 6.3 and the vehicle path model in Section 6.4 using the minimum curve radius and the speed environment.

∆SME Decrease in 85th percentile speed on the major road horizontal geometric element (m)

This value equals the 85th percentile speed on the previous horizontal element minus the 85th percentile speed on the horizontal element under consideration

Table C7 - Lighting Variables Variable


LIGHTS Level of lighting on the minor road - dummy variable

LIGHTM Level of lighting on the major road - dummy variable

The value of this variable has been subjectively chosen according to the following system: 1 - High level of lighting at the intersection but not prior to the intersection. 2 - Continuous route lighting 3 - Low level of lighting at the intersection conflict area only. 4 - No lighting

LIGHT Average level of lighting at the intersection.

Average of LIGHTS and LIGHTM

Table C8 - Visibility Variables

Variable Code

Variable Description Measurement of the Variable

TiAP Approach visibility measured in time (s). Measured according to the Approach Sight Distance model in QDMR (2000) ie 1.15m eye height to 0m object height. This variable equals the sight distance divided by the 85th percentile approach speed. i = S for visibility on the minor road. 0m object height measured at the giveway line. i = M for visibility on the major road. 0m object height taken to the following points: - For right turns with no median and for left turns, the crossing point of the giveway line and an extension of the minor road centreline. - For right turns with a median, crossing point of the edgeline adjacent the median and an extension of the minor road centreline.

Ti Visibility between a minor road vehicle 5m behind the give way line and approaching vehicles on a major leg measured in time (s). Measured according to the safe Intersection Sight Distance model in QDMR (2000) ie 1.15m eye height and 1.15m object height. This variable equals the sight distance divided by the 85th percentile major road through speed. i = L for visibility to the left major leg i = R for visibility to the right major leg

TiI Same as for Ti above except if a signalised intersection exists within the extent of Ti (s). In the later case, it is the distance to the signalised intersection divided by the 85th percentile major road through speed.

TMOPP Visibility between a stationary right-turning major road vehicle at the intersection and oncoming major road vehicles measured in time (s). Measured 1.15m eye height and 1.15m object height. This variable equals the sight distance divided by the 85th percentile major road through speed.

TMOPPI Same as TMOPP above except if a signalised intersection exists within the extent of TMOPP (s). In the later case, it is the distance from the signalised intersection divided by the 85th percentile major road through speed.

TMINT Visibility between major road vehicles approaching the intersection and stationary right-turning vehicle at the intersection measured in time (s). Measured 1.15m eye height and 1.15m object height. This variable equals the sight distance divided by the 85th percentile major road through speed.

TMINTI Same as TINT above except if a signalised intersection exists within the extent of TINT.(s) In the later case, it is the distance to the signalised intersection divided by the 85th percentile major road through speed.

Assumptions made to overcome problems with measuring these variables are given below: At intersections where there was parked vehicles obscuring visibility for a proportionally short amount of time, it was assumed these vehicles did not restrict visibility. At intersections where there was parked vehicles obscuring visibility for proportionally long amounts of time, visibility was measured based on a permanent presence of the parked vehicles. Sight distance across agricultural land can vary significantly depending on crop type and height of crop. Subjectively allowed for the most common case. At intersections with wide medians, TL was measured from the median rather than from 5m behind the continuity line. Not all sight distances were similar if there was a major traffic generator or major intersection in close proximity to the particular sample intersection ie where vehicles were approaching from different paths. In these cases, sight distances were based on the predominant vehicle stream. Not all approach sight distances were similar if the side road was a single dead-end road of short length. In this case, the visibility was measured from a point midway along the side road. The approach sight distance measurement of 1.15m eye height to 0m object height did not necessarily give a good indication of how well a driver may have recognised the intersection. For this reason, values of 1.15m and 0.2m respectively were also measured.

Table C9 - Signage Variables and Level of Control Variable

Code Variable

Description General Sign

Type Measurement of the Variable Value

Advance direction sign 2 Advance direction sign and warning sign

2

Warning Sign 1

Advance warning

None 0 Intersection direction sign 2 Fingerboard sign 1

Intersection direction

None 0 Stop 2 Give way 2

SIGNS Level of signage on the minor road - dummy variable (the value of this variable is the addition of the applicable values given for each of the three cases of general sign type) Control

None 0 Advance direction sign 2 Advance direction sign and warning sign

2

Fingerboard sign 1 Warning sign 1

Advance warning

None 0 Intersection direction sign 2 Fingerboard sign 1

SIGNM Level of signage on the major road - dummy variable (the value of this variable is the addition of the applicable values given for each of the two cases of general sign type)

Intersection direction

None 0

Stop 2 Give way 1

CONT Level of control on the minor road

None 0 Two control signs 2 One control sign 1

NCONT Number of control signs (stop or give way signs)

No control signs 0

Table C10 - Number of Legs / Number of Lanes Variables Variable


NLEG Number of legs at the intersection Use the values of 3 or 4. NLS Number of stand-up lanes on the

minor leg Use the values of 1 or 2.

NLSi Number of adjacent stand-up lanes on the minor leg in the direction of the major leg relevant to the particular conflict.

A value of one (one stand-up lane) is given to the following (refer to Figure 6.2 for the type of stand-up lane arrangements): L-TR, LT-TR, LT-R, and L-R stand-up lane arrangements for an LRT conflict. L-TR and LT-TR stand-up lane arrangements for a TLT conflict. LT-TR, LT-R, F-T-R, and F-T-TR stand-up lane arrangements for a TRT conflict. L-TR, LT-TR, LT-R, F-T-R, F-T-TR and L-R stand-up lane arrangements for a RLT conflict. A value of zero (no stand-up lanes) is given for all other situations not listed above.

NLM Number of lanes on the major road

Table C11 - Turn and Movement Type Variables Variable


FLTLS Presence of a free left-turn lane from the minor road - dummy variable

FLTLM Presence of a free left-turn lane from the major road - dummy variable

The value of this variable has been subjectively chosen according to the following system: 0 - no free left-turn lane 1 - free left-turn lane

TTi Turn type from the major road - factorial variable i = L for left-turn types only i = R for right-turn types only i = A for all turn types - L and R i = LA for right-turn types LSR and AUR only

This factorial variable has been given the following codes: LSR - Low standard right-turn treatment on two lane, two way roads. AUR - Auxiliary right-turn treatment on 2 lane, 2 way roads CHR - Channelised right-turn. MNR - Multi-lane road with no specific right-turn facility LSL - Low standard left-turn treatment AUR - Auxiliary left-turn treatment (These turn types are discussed in Section 4.3)

TTCRLB Turn type from the major road -dummy variable

1 - CHR or AUL turn 2 - LSR, AUR, MNR or LSL turn

MS1 Movement type from the minor road - factorial variable

F - free left-turn L - non free left-turn T - through movement R - right-turn

MM1 Movement type from the major road - factorial variable

F - free left-turn L - left-turn R - right-turn

MSM Movement type - factorial variable

F - free left-turn from minor road L - non free left-turn from minor road S - through movement on the minor road prior to the intersection M - through movement on the major road

CONF Major conflict type - factorial variable

LRT, TLT, TRT, TLT or RRT (refer to Figure 9.7 for these conflict types).

Table C12 - Length Variables Variable


WS Entry width of the minor road (m) This variable is measured perpendicular to the left edge line or kerb edge to a point where an extension of the centreline of the minor road meets the give way line

WM Width of the major road traffic lanes (m)

WMED Width of the median on the major road (m)

WMEDM Width of the median on the major road for LSR AUR, and MNR sites only (m) - dummy variable

0 - CHR, LSL and AUL sites WMED - for LSR, AUR and MNR sites

DHL Distance from the holding line to the continuity line (m)

Distance of zero if no holding line

RSi Radius of the vehicle path on the minor road horizontal geometric element (m)

LSi Length of the vehicle path on the minor road horizontal geometric element (m)

i = L for the radius of the left-turn movement from the minor road i = R for the radius of the right-turn movement from the minor road i = E for the radius of a horizontal geometric element on the minor road approach These variables are measured according to the vehicle path model in Section 6.4.

RMi Radius of the vehicle path on the major road horizontal geometric element (m)

LMi Length of the vehicle path on the major road horizontal geometric element (m)

i = L for the radius of the left-turn movement from the major road i = R for the radius of the right-turn movement from the major road i = E for the radius of a horizontal geometric element on the major road These variables are measured according to the vehicle path model in Section 6.4.

TLAUR Minimum length of Type AUR auxiliary lane either side of the intersection (m)

Table C13 - Shoulder Width Variables Variable


WRS Width of sealed lane plus sealed widening for LSR sites. Measured adjacent the tangent point for the right-turn from the major road (m).

WRU Width of sealed lane plus total widening (sealed plus unsealed) for LSR sites. Measured adjacent the tangent point for the right-turn from the major road (m).

WTS Effective total width of sealed lane plus sealed widening for LSR sites. Measured adjacent the tangent point for the right-turn from the major road (m). Based on a given length of driver path ‘TEi’ either side of the intersection (measured in seconds).

WTU Effective total width of sealed lane plus total widening (sealed plus unsealed) for LSR sites. Measured adjacent the tangent point for the right-turn from the major road (m). Based on a given length of driver path ‘TEi’ either side of the intersection (measured in seconds).

TES Effective time available to undertake an evasive manoeuvre on a sealed surface at LSR sites. Measured for each side of the intersection adjacent the tangent point for the right-turn from the major road (s). Based on a given width of sealed lane plus sealed shoulder of ‘WTi’.

TEU Effective time available to undertake an evasive manoeuvre on all surface types (sealed plus unsealed) at LSR sites. Measured for each side of the intersection adjacent the tangent point for the right-turn from the major road (s). Based on a given width of sealed lane plus total widening (sealed plus unsealed) of ‘WTi’.

Refer to Figure C4 for calculation of these variables. These variables were developed as a measure of the degree that through drivers on the major road could undertake an evasive manoeuvre around a stationary right-turning vehicle. They were developed because it proved very difficult to separately account for the following variables that can affect the ability of these drivers to evade. - sealed shoulder width - unsealed shoulder width - width of sealed additional widening - width of unsealed additional widening - length of additional sealed widening prior to and after right-turn vehicle - length of additional unsealed widening prior to and after right-turn vehicle - lane width The developed variables consider various combinations of the above variables.

Table C14 - Observation Angle Variable Variable


θi Observation angle (degrees) This angle is measured between a line representing the instantaneous direction of travel of minor road drivers 4m behind the give way line and a line tangential to the major road (refer Figure C1). i = LRT, TLT, TRT, RLT or RRT vehicle conflicts.

The driver observation point is taken from 4m behind the give way line. A value of 4m was chosen as an approximate average where drivers would view other vehicles. Actual values largely varied as discussed below. On-site inspections were undertaken with the aim of determining a typical location where drivers would stop and view major road vehicles. Observations revealed, however, that not all drivers stop on minor road approaches. This was especially true if no major road vehicles were present. A greater number of drivers tended to stop at stop conditions but not all did. Drivers not stopping were observed to view major road vehicles at various locations along their turning path. Thus, the viewing angle changed throughout the turn. This was especially true for the left-turn. For drivers that did stop on the minor road, the location varied considerably depending on the following: Turn type - drivers turning left tended to stop closer to the give way line Position of holding line - drivers tended to stop further from the give way line if the holding line was further away from the give way line Presence of right-turn vehicles from the major road - drivers tended to stop further from the give way line if there were major road vehicle turning right. Visibility - drivers tended to stop closer to the give way line in areas of reduced visibility. Vehicle type - the size of larger vehicles meant that drivers of these vehicles were positioned further from the give way line Driver behaviour - drivers that were more aggressive positioned themselves closer to the give way line than did drivers that are more conservative. Time - once stopped, drivers tended to move slowly forward whilst waiting for a gap. If the vehicle path is on a radius over this distance, the viewing angles changed. This was especially true for the left-turn. Major road width - drivers tended to stop closer to the give way line on wider major roads.

Table C15 - Intersection Perception Variables Variable


DRS Driver recognition of the intersection from the minor road approach - dummy variable

The value of this variable has been subjectively chosen according to the following system: 1 - A significant portion of the major road can be seen at the approach sight distance. Intersection is completely channelised. Roadway does not continue through other side of intersection 2 to 4 - Subjectively rate for conditions between a value of 1 and 5. 5 - Cannot see intersection at the approach sight distance. Includes crossroads where minor roads are aligned and where the major road outside of the limits of the minor road cannot be seen from the minor road.

DR4 Driver recognition of an opposite minor leg - dummy variable

For TLT and TRT conflicts, chose value according to Figure C2. For all other conflicts, the value is made equal to zero.

BACK Level of perception of the backdrop of a T-intersection - dummy variable

The value of this variable has been subjectively chosen according to the following system. It is measured at the minimum approach sight distance on the minor road. 0 - Low levels of backdrop perception. Includes cases where the intersection was not visible, the backdrop was sky, and/or the backdrop was not close to the intersection 1 - Mediums levels of backdrop perception. Includes cases where the backdrop was formed by seasonal crops, grassed paddocks, and/or partially visible intersections 2 - High levels of backdrop perception. Includes cases where the backdrop immediately on the opposite side of the intersection is a cutting, buildings, or a solid phalanx of tall trees.

FOV Field of view - dummy variable. This variable is a measure of the amount of the major road that can be seen from the minor road.

The value of this variable has been subjectively chosen according to the following system. It is measured at the minimum approach sight distance on the minor road. 0 - Could not see the major road carriageway or the amount of the major road carriageway that could be seen was less 20m. 1 - The amount of the major road carriageway that could be seen was approximately equal to 20m. 2 - The amount of the major road carriageway that could be seen was greater than 20m.

Table C16 - Other Variables Variable


AH Horizontal layout of the minor legs - dummy variable

Subjectively chose according to Figure C3.

LINEM Type of line marking - dummy variable

0 = broken line 1 = barrier line

CSE Curvature of the vehicle path on the particular horizontal geometric element of the minor road (1/m). Equals 1 / RSE

CMi Curvature of the vehicle path on the particular horizontal geometric element of the major road (1/m). Equals 1 / RMi

i = SL for the curvature of the major road to the left of the minor leg. i = SR for the curvature of the major road to the right of the minor leg. i = SA for the average curvature of the major road relative to the minor leg. Equals the average of CMSL and CMSR. The curvature is negative for minor leg on the inside of a major road curve The curvature is positive for a minor leg on the outside of a major road curve i = O for the curvature of the major road immediately past the intersection. i = I for the curvature of the major road immediately prior to the intersection. The curvature is negative for a left major road curve The curvature is positive for a right major road curve i = E for the curvature of

fS Side friction used on the minor road horizontal geometric element

This value equals the square of the 85th percentile minor road speed ‘SSE’ divided by the radius of the vehicle path ‘RSE’.

fM Side friction used on the major road horizontal element

This value equals the square of the 85th percentile major road speed ‘SME’ divided by the radius of the vehicle path ‘RME’.

Figure C1 - Observation Angle ‘θi’ Notes: (1) Vehicle paths shown in this diagram are determined using the process in Appendix B - Vehicle

Path Model (2) Driver observation is taken from a point 4m behind the give way line. A value of 4m was chosen

as an approximate average where drivers would view other vehicles. (3) If the major road is on a horizontal curve, the angle is measured tangential to the major road at a

point closest to the observation point.

Figure C2 -Driver Recognition of an Opposite Minor Leg Notes: (1) This category covers situations where there is little to no recognition of an opposite minor leg

until immediately before the intersection. (2) This category covers cases where the minor legs of a four-leg intersection with a right-left

stagger are horizontally offset by a width equal to or greater than the width of the minor road approach carriageway.

(3) This category covers all other four-leg intersections not meeting the conditions for a score of zero or two. Typical examples are shown. Use this category if any one of the conditions occurs as shown.

(4) This category covers four leg intersections where the opposite minor leg appears as an extension of the roadway. This category is appropriate if the following occur: a) Minor legs are horizontally aligned and are straight or are on a continuous large radius horizontal curve for at least 50m prior to the intersection; and b) Minor legs are on the same constant grade for at least 50m prior to the intersection or minor legs are on a continuous sag curve.

(5) The values in the figure apply to TLT and TRT conflicts only. For all other conflicts, a value of zero is used.

Figure C3 - Horizontal Layout of the Minor Legs Notes: (1) This category covers situations where there is no directly opposite minor leg (2) Use this category if the minor legs of a four-leg intersection are horizontally offset by a width

equal to or greater than the full width of the minor road approach. (3) This category covers all other four-leg intersections not meeting the conditions for a score of

zero or two. Typical examples are shown. Use this category if any one of the conditions occur as shown.

(4) This category covers four leg intersections where there is a directly opposite minor leg.

Figure C4 - Parameters for the Calculation of TLS, TLU, WTS, and WTU for LSR Turn Treatments

The following codes apply to Figure C4:

A = the evasive manoeuvre prior to the right-turning vehicle

B = the evasive manoeuvre after to the right-turning vehicle

VPi = outer edge of the vehicle path of the particular evasive manoeuvre

WSi = width of the shoulder for the particular manoeuvre (m)

WW = width of the widened shoulder (m)

WL = lane width (m)

TP = tangent point of the right-turn vehicle path (refer Appendix B - Vehicle Path

Model)

TLWi = length from the start of the widened area to the right-turn vehicle for the

particular movement (m)

Calculation of WTS and WTU

TLi = (SMT x TEi)/3.6 Equation C1

Where TLi = the selected minimum evasive manoeuvre distance (m)

SMT = 85th percentile through speed (km/h)

TEi = the selected minimum evasive manoeuvre time (s)

TLa and TLb are made equal to TLi.

WTi = the maximum total width of lane plus widening available to perform the

required evasive manoeuvre (m). This is calculated according to the coding

below (in the order shown):

- If WW = 0, WTi = WL + WSi

- If TLi ≤ TLWi, WTi=WL + WW

- If TLi> TLWi, WTi= minimum of (WL + WW) and

(((WL + WSi - 3)TLi)/(TLi-TLWi)+3)

WTi = minimum of WTa and WTb

WTS is calculated according to the above formulae based on the width of seal for all

relevant parameters in Figure C4.

WTU is calculated according to the above formulae based on the total width (seal

plus unsealed width) for all relevant parameters in Figure C4.

Calculation of TES and TEU

WTi = the selected total width of the lane plus widening. WTa + WTb are made equal

to this width (m)

TLi = the maximum length of vehicle path available in order to perform the required

evasive manoeuvre (m). This is calculated according to the coding below (in

the order shown):

- If (WTi.> WL + WW), TLi = 0

- If (WTi ≤ WL + WSi), TLi = 99999

- If (WTi ≤ WL + WW), TLi = TLWi (WTi-3)/(WTi-WL-WSi)

TL = minimum of TLa and TLb

TEi = 3.6 x TL / SMT Equation C2

Where TEi = the maximum time available in order to perform the needed evasive

manoeuvre (s)

SMT = 85th percentile through speed (km/h)

TES is calculated according to the above formulae based on the width of seal for all

relevant parameters in Figure C4.

TEU is calculated according to the above formulae based on the total width (seal plus

unsealed width) for all relevant parameters in Figure C4.

APPENDIX D - COSTS OF THE VARIOUS TURN TYPES

The ‘By Benefit Cost Analysis’ method for determining new warrants in Section

22.8 has used the following turn types:

• BAR (Basic Right-Turn Treatment) as per Figure 13.53 of QDMR (2000), which

is a subset of an LSR treatment. A BAR treatment contains a locally widened,

unsealed shoulder to enable through major road vehicles to pass to the left of

right-turn major road vehicles. A BAR is assumed to perform the same as an LSR

turn treatment.

• AUR (Auxiliary Right-Turn Treatment) as per Figure 13.54 of QDMR (2000).

• CHR(s) (Channelised Right-Turn Treatment with short right-turn slot) as per

Figure 13.55 of QDMR (2000). Length of right-turn slot as per minimum

dimensions in Figure 13.40 of QDMR (2000).

• CHR(l) (Channelised Right-Turn Treatment with long right-turn slot) as per

Figure 13.55 of QDMR (2000). Length of right-turn slot based on 2.5m/s2

comfortable deceleration as per Table 13.16 of QDMR (2000).

• BAL (Basic Left-Turn Treatment) as per Figure 13.65 of QDMR (2000), which is

a subset of an LSL treatment. A BAL treatment contains a minimum of a 2m

shoulder to enable left-turning vehicles to pull at least partially off the through

lane whilst decelerating. A BAL is assumed to perform the same as an LSL turn

treatment.

• AUL (Auxiliary Left-Turn Treatment). Length of auxiliary lane based on 2.5m/s2

comfortable deceleration as per Table 13.16 of QDMR (2000).

The following assumptions have been made for each turn type:

• Pavement depth = 0.4m

• Normal shoulder width = 1.5m

• Normal lane width = 3.5m

• Depth of earthworks = 1.0m

• Shoulder width adjacent to additional lane excluding BAR = 1.5m

• Shoulder is not sealed

• Angle of side road = 90 degrees

• Subgrade CBR = 5

• Dimensions used allow for a 19 metre semi-trailer

• Auxiliary lane width allowance (where applicable) = 3.5 metres

• Medians at CHR treatments comprise linemarking only ie no raised or depressed

medians

• No allowance has been made for drainage, resumptions, service relocations or

street lighting

Unit rates used for calculating the costs for each turn type as shown in Table D1.

Table D1 - Unit Rates Work Item Unit New Upgrade

ConstructionPreparation of Natural Surface m2 4.00 5.00Earthworks m3 10.00 20.00Base, unbound pavement, Type 2 m3 60.00 80.00Sprayed bituminous surfacing incl all materials m2 4.00 8.00Excavation of existing shoulder material m3 - 20.00Pavement marking m 1.00 1.20Overheads allowed on Costs % 20.00 20.00

Costs of the various turn types are given in Table D2.

Table D2 - Costs of the Various Turn Types Construction Type Turn Total Cost ($)

Type 70 km/h 90 km/h 110 km/hNew Intersection BAR 2964 3192 3420New Intersection AUR 18696 21378 24060New Intersection CHR(s) 26918 35308 50040New Intersection CHR(l) 30513 46093 66218New Intersection BAL 4032 4032 4032New Intersection AUL 18732 27612 55656Existing Intersection Upgrade BAR to AUR 29173 34158 39143Existing Intersection Upgrade BAR to CHR(s) 37259 49902 72288Existing Intersection Upgrade BAR to CHR(l) 42794 66507 97195Existing Intersection Upgrade AUR to CHR(s) 27513 43745 74944Existing Intersection Upgrade AUR to CHR(l) 35137 66618 109253Existing Intersection Upgrade BAL to AUL 35300 51492 70900

APPENDIX E - TURN TYPES USED IN THIS STUDY

Figure E1 - Types of Turn Treatments Used in this Study

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