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Contract Report Use of Pavement Strength Information in Network Asset Management by Tim Martin and Simon Crank for Austroads Austroads Project No: BS.A.C.025 RC1702 October 2001
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Page 1: Austroads Project No BS a C 025

Contract Report

Use of Pavement Strength Information in Network Asset Management

by Tim Martin and Simon Crank

for Austroads

Austroads Project No: BS.A.C.025 RC1702 October 2001

Page 2: Austroads Project No BS a C 025

Use of Pavement Strength Information in Network Asset Management

for Austroads

Reviewed

Project Leader

Quality Manager

Austroads Project No: BS.A.C.025 RC1702 October 2001

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Use of Pavement Strength Information in Network Asset Management

Executive Summary

Scope:

The aim of this Report is to review the current state of knowledge on the use of pavement strength data at a road network planning level. This review includes an overview of the following:

1. the collection of network pavement strength data;

2. the conversion of network pavement strength data into useful network parameters; and,

3. the prediction of the deterioration of network pavement strength.

This Report also outlines and discusses the current state of knowledge on the following aspects of network pavement strength: (1) how parameters representing the pavement/subgrade system may be applied to network asset management; (2) the usefulness and relevance of methods of collecting network pavement strength data; and, (3) the prediction of the deterioration of pavement strength through existing and proposed models. These aspects will allow identification of the limitations to using strength as an input to an asset management system.

This Report is one of four outputs of the Austroads Project BS.A.C.025 that is ultimately directed to producing Austroads Guidelines on the use of pavement strength data in road network analysis.

Summary:

The Need for Network Strength Data

The need for an overview of the structural condition of the whole network for future strategic planning reasons is driven by the following issues:

� increased axle mass limits for heavy vehicles;

� increased heavy vehicle traffic growth on strategic freight routes; and,

� some road agencies have decided to include the structural condition of pavements as a network performance indicator.

The first two issues above can potentially reduce the remaining life of the pavements in the network which means that earlier than expected rehabilitation treatments are needed. These treatments are relatively costly and have a major impact on annual road agency budgets.

The third issue above is often chosen as a contractual requirement for the contractor managing a road network on behalf of the road agency. This does not necessarily mean that the network level structural condition of the pavements becomes an input into managing the network mainly on a structural basis.

The Collection of Pavement Strength Data at a Network Level

Despite the historic lack of use of pavement strength data at a network level, there is now more focus on its use in asset management systems for timely structural intervention due to the above reasons. Monitoring of strength at appropriate time and space intervals at a network level is expected to produce major benefits through lower life-cycle costs achieved by timely structural intervention.

Although the Report is believed to be correct at the time of publication, ARRB Transport research Ltd, to the extent lawful, excludes all liability for loss (whether arising under contract, tort, statute or otherwise) arising from the contents of the Report or from its use. Where such liability cannot be excluded, it is reduced to the full extent lawful. Without limiting the foregoing, people should apply their own skill and judgement when using the information contained in the Report.

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Use of Pavement Strength Information in Network Asset Management

The increased use of network condition survey methods may provide the structural condition data that allows a review of pavement deterioration trends in combination with other structural condition indicators. There are the following two distinct approaches to a network structural condition survey:

1. Continuous Deflectograph sampling, at 3.5 metre intervals every three to five years as used in the UK, for a comprehensive network assessment of pavement strength. Project level structural condition surveys, typically using an FWD, are initiated based on this network survey for the future design and implementation of structural intervention works.

2. Relatively wide spaced sampling using the FWD, varying from 100 metres to 800 metres intervals every year, are used for network pavement strength assessment in Western Australia and New Zealand. Follow up detailed structural condition surveys currently use the FWD at intervals from 10 to 100 metres, depending on the Project length.

Approach (1) is an almost continuously sampling device that provides some information, while approach (2) relies on a device that provides relatively reliable information that is sampled at a relatively wide interval.

Conversion of Pavement Strength Data into Strength Parameters

In conjunction with the increased availability of network data there has also been changes in the way the pavement strength data is quantified. This development began with the SN1 pavement parameter, which was enhanced by the creation of the SNC2 and SNP3 parameters. Other parameters, such as the SAI4, also provide a numerical tool for comparing pavements mainly based on their deflection data regardless of their initial structure or degree of deterioration. Simple relationships, such as the RPS5, are useful guides to preliminary intervention and testing.

Relationships between remaining strength and traffic levels, such as the SNP with traffic load capacity, CAP, have been developed to predict the structural condition of pavements. These predictions are the basis of the analysis for decisions regarding the remaining life of the pavement and the necessity and timing of structural intervention through rehabilitation.

Prediction of the Deterioration of Network Pavement Strength

Pavement performance models, such as the deterioration of roughness, rutting, cracking, etc., often include the pavement strength as an independent variable. Pavement strength is also treated as a dependent variable and performance indicator in a separate structural deterioration model, such as that found in HDM-4. The appropriateness of structural models in predicting network level structural deterioration has not been confirmed with actual Australian deterioration data, so these models cannot yet be used with confidence at a network level. The models could be simplified by using only the variables that are appropriate at a strategic network level. Prediction of pavement performance, in terms of surface and structural condition, allows asset managers to perform life-cycle costing analyses at a pavement network level.

1 Structural Number for pavement. 2 Modified Structural Number for pavement/subgrade. 3 Adjusted Structural Number for pavement/subgrade (weighted). 4 Structural Adequacy Indicator. 5 Relative Pavement Strength.

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Use of Pavement Strength Information in Network Asset Management

Contents

1. INTRODUCTION.....................................................................................................1

1.1 SCOPE......................................................................................................................1 2.2 THE NEED FOR STRENGTH DATA .............................................................................1

2. STRENGTH DATA AT A NETWORK LEVEL ...................................................2

2.1 THE NEED FOR NETWORK STRENGTH DATA ............................................................2 2.2 REMAINING LIFE......................................................................................................2 2.3 STRUCTURAL INTERVENTION...................................................................................3 2.4 PAVEMENT PERFORMANCE, PAVEMENT LIFE AND LIFE CYCLE COSTING................4 2.5 SHORTCOMINGS OF PAVEMENT STRENGTH..............................................................5

3. COLLECTION OF PAVEMENT STRENGTH DATA ........................................5

3.1 GENERAL.................................................................................................................5 3.2 BENKELMAN BEAM SURVEYS FOR STRTENGTH.......................................................6 3.3 DEFLECTOGRAPH SURVEYS FOR STRENGTH ............................................................6 3.4 FWD SURVEYS FOR STRENGTH...............................................................................7

4. ESTIMATION OF PAVEMENT STRENGTH PARAMETERS.........................8

4.1 LABORATORY ESTIMATION OF STRENGTH PARAMETERS.........................................8 4.2 NON-LABORATORY ESTIMATION OF STRENGTH PARAMETERS................................9

5. PREDICTION OF NETWORK PAVEMENT STRENGTH..............................12

5.1 GENERAL CONSIDERATIONS..................................................................................12 5.2 PAVEMENT STRENGTH DETERIORATION................................................................12

6. SUMMARY .............................................................................................................13

6.1 THE COLLECTION OF PAVEMENT STRENGTH DATA AT A NETWORK LEVEL ..........13 6.2 CONVERSION OF PAVEMENT STRENGTH DATA INTO STRENGTH PARAMETERS......14 6.3 PREDICTION OF THE DETERIORATION OF NETWORK PAVEMENT STRENGTH..........14

7. REFERENCES........................................................................................................14

APPENDIX A: DETAILS OF HDM-4 PAVEMENT STRENGTH DETERIORATION MODEL .........................................................................................18

A.1 ADJUSTED STRUCTURAL NUMBER, SNP 18 A.2 ADJUSTED STRUCTURAL NUMBER, SNP, VARIATION WITH CRACKING 19

APPENDIX B: DETAILS OF ALTERNATIVE PAVEMENT STRENGTH DETERIORATION MODEL .........................................................................................20

B.1 ADJUSTED STRUCTURAL NUMBER, SNP 21

APPENDIX C: DETAILS OF THE STRUCTURAL ADEQUACY INDICATOR, SAI ..............................................................................................................................20

C.1 STRUCTURAL ADEQUACY INDICATOR, SAI 21

APPENDIX D: STRENGTH PARAMETERS FROM DEFLECTION DATA .........20

D.1 FWD DEFLECTION DATA ......................................................................................13

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1. Introduction

1.1 Scope

The aim of this Report is to review the current state of knowledge on the use of pavement strength data at a road network planning level. This review includes an overview of the following:

1. the collection of network pavement strength data;

2. the conversion of network pavement strength data into useful network parameters; and,

3. the prediction of the deterioration of network pavement strength.

Item (1) has been reviewed elsewhere (Robinson 1999, 2000, 2001) covering current practices of Member Authorities (MAs) at both a network and a project level. This Report will refer to this work mainly in a network level context.

In Item (2) the current state of knowledge should also include the relationships that currently exist between the strength data collected by several devices and the conversion of this potentially common data in useful network parameter(s).

In reference to Item (3), the prediction of pavement strength deterioration at a project level is undertaken within the HDM-4 suite of models (ISOHDM 2000). These models now supersede the HDM-III models (Watanatada et al. 1987). The enhancement of the HDM-4 models for sealed granular pavements in Australia has been undertaken to some extent (Roberts and Crank 2000c), including the structural deterioration of these pavements at a project level.

This Report also outlines and discusses the current state of knowledge on the following aspects of network pavement strength: (1) how parameters representing the pavement/subgrade system may be applied to network asset management; (2) the usefulness and relevance of methods of collecting network pavement strength data; and, (3) the prediction of the deterioration of pavement strength through existing and proposed models. These aspects will allow identification of the limitations to using strength as an input to an asset management system.

This Report is one of four outputs of the Austroads Project BS.A.C.025 that is ultimately directed to producing Austroads Guidelines on the use of pavement strength data in road network analysis.

1.2 The Need for Strength Data

A range of characteristics are used to define the quality of a pavement. Traditionally, however, the characteristics and associated defects that were used to assess pavements were those visible and measurable on the surface. This approach was used because of the prevailing economics of consistent data collection practice.

For example cracking is a commonly used measure of pavement condition, but it has significant limitations as an indication of pavement strength. This is due to the many types of cracks that can exist and the limited methods for clearly identifying them. Most cracks are identified by a visual inspection of the pavement surface so that cracks on the surface are indistinguishable from full depth structural cracks, while sub-surface cracks can not be identified at all (Eijbersen and Zwieten 1998). This is a major issue as deep cracks have a profound effect on structural adequacy. Similar criticisms can also be made about other distress measures, such as roughness and rutting, as they are detected only by surface measurements and can only be related loosely to the structural condition of the pavement.

Since 1975 pavement/subgrade deflection data has been used to define the structural condition, in some form or other, of parts of the road network (Sheldon 1988). A recent example of a parameter used to define the structural condition of the pavement/subgrade system is the International Study of Highway Development Tools’ (ISOHDM 2000) Adjusted Structural Number (SNP). This parameter, and others similar to it, may be used to assess pavement

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structural condition and manage the rehabilitation of pavements, at both a network and project level. Some determination needs to be made of how parameters such as these are an accurate measure of pavement structural condition. The structural condition of pavements is particularly critical when they are approaching the end of their structural lives.

2. Strength Data at a Network Level

2.1 The Need for Network Strength Data

Many pavement performance characteristics (roughness, cracking, rutting, etc.) do not give an accurate assessment of the structural condition of a pavement, as noted above. These measures, however, are inexpensive to collect and have traditionally been used to identify suspect areas of the network for detailed structural testing and assessment at a project level.

The need for an overview of the structural condition of the whole network for future strategic planning reasons is driven by the following expectations:

� increased axle mass limits for heavy vehicles (NRTC 1996);

� increased heavy vehicle traffic growth on strategic freight routes (Gargett and Perry 1998); and,

� some road agencies have decided to include the structural condition of pavements as a network performance indicator.

The first two issues above can potentially reduce the remaining life of the pavements in the network which means that earlier than expected rehabilitation treatments are needed. These treatments are relatively costly and have a major impact on annual road agency budgets.

The third issue above is often chosen as a contractual requirement for the contractor managing a road network on behalf of the road agency. This does not necessarily mean that the network level structural condition of the pavements is an input for managing the network mainly on a structural basis.

2.2 Remaining Life

To determine the expected life of a pavement, there are many factors that must be considered including traffic load, pavement material size and properties, pavement construction quality, climate, subgrade strength, surface and sub-surface drainage and the past maintenance regimes (Zhu 1998). Some form of assessment of pavement/subgrade strength is a direct indication of structural adequacy and probably is the most important determinant of pavement life (Robinson 2000). Discussed below are different ways in which an assessment of the strength of a pavement can be used at the network level.

Pavement strength data can be used to estimate the remaining life of a pavement based on its current structural condition, but this only takes into account traffic loading and does not consider the other factors noted above.

Using the Adjusted Structural Number (SNP) approach, pavement sections with the same value of SNP may have very different remaining lives if the traffic loading is significantly different. For example, an SNP value of 3 may be adequate for low traffic roads, but is insufficient for highly trafficked highways (Roberts 2000b). Therefore the calculation of the remaining pavement life must consider the future traffic loading (Paine 1998), including the anticipated growth.

A quantitative example of how strength relates to the remaining life of a pavement is given in Roberts (2000a). Figure 1 shows the relationship between the remaining traffic load capacity of a pavement, CAP, in terms of millions of equivalent standard axles (MESAs), and its estimated Adjusted Structural Number, SNP. The Figure 1 relationship is logarithmic with the characteristic that even a slight increase in the value of SNP can have significant benefits on remaining pavement capacity. For example, a remaining capacity of 7 MESAs is achieved with

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a SNP value of 4.01. This remaining capacity is more than doubled to 15 MESAs with a relatively small increase in the value of SNP to 4.44.

SNP-CAP-SNP Relationship

1

2

3

4

5

6

7

8

0.001 0.010 0.100 1.000 10.000 100.000 1000.000Remaining Capacity (MESAs)

SN

P

Figure 1: Strength to Traffic Load Capacity Relationship (Roberts 2000a)

This estimated remaining life and capacity can then be used in conjunction with the predicted traffic load (MESAs per year) to estimate the time (years) to reach the expected structural failure of the pavement.

2.3 Structural Intervention

2.3.1 General approach to structural intervention

The estimation of remaining pavement life and capacity can be refined with the estimation of pavement strength deterioration using either prediction models or regular in situ pavement testing. This information will allow the more precise determination of the timing and nature of the required structural intervention works for asset managers. These structural intervention works include rehabilitation overlays (asphalt pavements), granular resheet rehabilitation (chip sealed pavements) and even full pavement reconstruction.

Paine (1998) has argued that pavement sections, even at the network level, can have a design rehabilitation intervention option based on an estimation of remaining pavement life. This allows selection of an appropriate rehabilitation treatment for intervention at the most appropriate time.

In addition, there can be a distinction between structural intervention levels based on estimated remaining structural capacity. In this case the remaining structural capacity can be used to set the timing for further in situ pavement testing or as the basis for design of the rehabilitation treatment. Two examples of how this has been performed are shown below.

2.3.2 Use of the approach

One example of pavement strength being used in a large scale asset management system was reported by Zaghloul et al. (1998) with a follow up by Zaghloul and Kerr (1999). This involved the development and implementation of a network level rehabilitation program in New Jersey, USA. Pavement strength was assessed on a cost effective basis using falling weight deflection (FWD) survey results at 100 metre intervals to develop a rehabilitation program for the network. The deflection data was used to estimate the Adjusted Structural Number (SNP) values, as further discussed in Section 4.

This approach allowed several structural intervention treatment options to be selected based on the subgrade strength or the pavement/subgrade strength. The pavement sections were then grouped according to four classifications of their estimated remaining life based on structural condition (subgrade strength, SNsb, or the pavement/subgrade strength, SNP). Each of these groups was then assigned the rehabilitation treatment appropriate to the estimated remaining life.

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These four classifications (and their associated works) were defined as follows for the pavement sections:

� serviceable (no structural works);

� unserviceable (rehabilitation overlay);

� below minimum SNP (partial reconstruction); and,

� below minimum SNsb (full pavement reconstruction).

SNsb is defined as the subgrade contribution to the structural number.

For the New Jersey case two pavement strength values were estimated to check the suitability of the rehabilitation overlays and determine their thicknesses. The first pavement strength value involved FWD data to estimate the Effective Structural Number (SNeff). The second pavement strength value, the Required Structural Number (SNreq), was estimated based on future traffic predictions. The difference between these two strength values determined the required thickness of the overlays. These overlay thicknesses were then compared with those required for roughness and rutting reasons.

2.3.3 Relative Pavement Strength (RPS) Indicator

Another asset management tool which uses pavement strength data for assigning the timing of structural intervention was developed by Roberts (2000b). This approach uses an indicator known as Relative Pavement Strength (RPS). The RPS is a dimensionless unit that estimates the current structural adequacy of a pavement. The RPS is defined as the percentage of remaining life due to traffic load relative to the user defined analysis period.

Consequently, a pavement with adequate structural strength for the analysis period (and only the analysis period) has an RPS value of 100%. To use this indicator each pavement is assigned an RPS value, generally based on a 20 year analysis period, however, the analysis period can be revised as required.

Assuming the 20 year analysis period, a pavement with only two years of remaining life has an RPS of 10%, while a pavement with 50 years remaining life has an RPS of 250%. The timing of investigative and structural intervention works are assigned according to the outcomes of this simple analysis. For instance an RPS of less than 10% requires immediate site investigation for pavement strengthening, while an RPS ranging from 10% to 40% may need a future strengthening and a more focussed monitoring of strength within one to two years, and an RPS ranging from 40% to 80% does not require any detailed attention in the short to medium term other than some strength monitoring within the next two to three years.

2.4 Pavement Performance, Pavement Life and Life Cycle Costing

Asset management has two goals (Prabhu 2000). The first goal is to provide an acceptable level of service to the community on the road network in the short to medium term. The second goal is to minimise the cost of maintaining the road network over its entire life. This is a long term goal consistent with sound economic and financial practice. Life-cycle costing (LCC) analysis is a direct means of achieving the second goal. The first goal can be achieved by some form of community assessment of acceptable levels of service, the maintenance cost consequences of which can be assessed by LCC analysis.

The design of pavements is based on them having at least adequate structural capacity to withstand traffic loading over their nominated design life (Paine 1998). Therefore estimation of the expected pavement life is a major input to LCC analysis.

LCC analysis is used in asset management at a network level to allocate annual budgets and develop maintenance strategies. LCC analysis at a project level is used to detail and program treatments that achieve budgets and services levels throughout pavement life (Martin and Roberts 1998). LCC analysis needs inputs such as cost rates, current road conditions, and constraints (such as budgets and road condition limits), while the actual analysis should be based on the sound prediction of future pavement performance (Steel and Hallett 1998) under

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various scenario options. Performance models of the loss of pavement strength at a network level ideally would be a useful refinement of LCC analysis to ensure that some form of intervention occurs before the structural failure of pavements. These performance models are the predictors of the structural life of a pavement.

2.5 Shortcomings of Pavement Strength

Despite the benefits of using pavement strength data in an asset management system there are the following limitations:

� Seasonal variation of pavement strength data. In a recent strength survey of the Western Australian road network (Sapkota et al. 2001) there was a significant difference between annual survey results undertaken in different seasons. This limitation can be overcome, only to some extent, by conducting the survey at the same time of each year. In the Western Australian case this survey is now undertaken at the end of the wet season in order to give an estimation of network pavement strength when it is expected to be at its lowest.

� The relatively high cost of gaining reliable, appropriate and representative pavement strength data at a road network level; and,

� The variability and lack of consistency of network level pavement strength data over time. This data characteristic makes it difficult to develop sound statistically based strength deterioration prediction models with meaningful independent variables.

Fortunately pavement strength data is not the only distress indicator needed for pavement maintenance or rehabilitation intervention based on LCC analysis. Generally strength data is used as an aid in determining the extent of pavement rehabilitation works in conjunction with surfacing treatments. However, pavement strength data needs to be used in conjunction with surface distress data to give the full picture of what is happening to a pavement. Using the two sets of data allows the possibilities of reseals and shape correction to be considered, rather than limiting works to a rehabilitation overlay or a pavement reconstruction as is the case with FWD data only (Roberts 2000b). In the New Jersey case if the program shows no overlay is required in the design period then other distress measures are used to determine further works (Zaghloul and Kerr 1999).

3. Collection of Pavement Strength Data

3.1 General

At present most pavement management systems (PMS) do not use an indicator of the current state of the structural capacity of pavements at a network level as an input. A reason for this is that historically there has not been a continuous and robust monitoring system that assessed pavement strength (Paine 1998) at a network level in either Australia or elsewhere (Tyson and Diaz 1995). The existence of such a device would also be expected to reduce the current cost of network level surveys for pavement strength.

Some Australian States and Territories with smaller networks have used some form of network strength assessment with one of the usual devices (see below). These assessments were made at relatively close sampling intervals at a moderate testing cost because of these States’ smaller scale networks. The data collection methods currently used at the project level are a high cost and time consuming at the network level, particularly for large scale networks. This is because the data is collected at low speed which can reduce the availability of structural data (Robinson 2000) for a given program and budget.

Under the current limitations of existing strength assessment devices, strength surveys proceed only where other performance indicators, such as cracking and rutting, suggest potential or existing loss of structural strength. These surveys are aimed at achieving full representation of pavement strength over the selected road section lengths.

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To reduce costs and speed up the analysis process, deflection data is currently the most commonly used method for assessing pavement strength. There are three main methods for collecting deflection data: (1) Deflectograph; (2) Benkelman Beam; and, (3) FWD. In many instances the availability of the deflection device may govern the choice of the device used. In addition, an agreed standard test procedure does not always exist for each device.

The use of the FWD, which collects similar data to a Deflectograph, is increasing at a network level in Western Australia and New Zealand because in low trafficked rural areas it is believed to be capable of collecting more deflection readings per day (Sapkota et al. 2001). The assessment of pavement strength by some form of high speed collection process is seen as an ideal goal and may be feasible (Tyson and Diaz 1995).

All forms of deflection testing require strict compliance with Occupation, Health and Safety (OH&S) requirements. Consequently, most forms of testing require lane closures around the test area and immediately beyond it. Adequate traffic controls are also needed to protect the operators and equipment when they are stationary. Because deflection surveys are either of a stop-start nature or they proceed slowly, it is often only possible to conduct testing on some sections, particularly those in urban areas, at non-peak traffic periods incorporating both lane closures and traffic controls.

3.2 Benkelman Beam Surveys for Strength

3.2.1 Benkelman Beam Sampling of Strength

The Benkelman Beam measures relative deflection of a pivot beam to a base beam at one point on the pavement as the test wheel load moves slowly along the pavement. Full bowl deflections are possible if required and this is unique to this device. The testing process is relatively slow compared with the Deflectograph (Robinson 1999, 2000).

Improvements such as the electronic measurement of deflections have been made to improve testing speed. The Benkelman Beam provides highly reliable deflection data at a point.

The Benkelman Beam has been used for network surveys of the arterial roads in Tasmania, but it is more likely to be used in other states (Western Australia, Queensland, New South Wales and Victoria) as a project level strength assessment tool. Nevertheless, data from the Benkelman Beam may be useful for network level assessments of strength.

Benkelman Beam surveys in Tasmania ceased in 1994/95 mainly due to the higher costs associated with this device. The higher costs were due to higher manning levels and the lower rates of testing relative to other deflection devices.

3.3 Deflectograph Surveys for Strength

3.3.1 Deflectograph Sampling of Strength

Three versions of this device are in common use: the Lacroix Deflectograph; a Queensland Mains Roads (QMR) version of the Lacroix Deflectograph; and, the PaSE Deflectograph. The Deflectograph is similar to a pair of Benkelman Beams, measuring the deflection in each wheel path. Normally a half deflection bowl (up to D900) is measured when sampling continuously at intervals between 3 to 7 metres. The continuous sampling speed is around 3 to 4 kph, making the rate of sampling greater than that of the Benkelman Beam (Robinson 1999, 2000).

The main difference between the Lacroix and PaSE Deflectographs is that the PaSE Deflectograph has a higher test axle load than standard axle load (8.2 tonne) used in the Lacroix Deflectograph. Other versions of the Deflectograph may also exist, such as the QMR Deflectograph, using different axle weights, wheel bases, tyre pressures and configurations. These variations on the same device make comparisons of the deflections obtained from these devices difficult.

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The Deflectograph is in wide use in most States, except Western Australia, because of its relatively higher sampling speed, although it is not used for whole network surveys. In Tasmania the Deflectograph was used in 1997 for a survey at the network level (Lang 2001) to obtain a benchmark assessment of pavement strength for maintenance contracts. This survey adopted a minimum sampling interval of 100 metres to gain an adequate level of confidence in the strength assessment. A network survey using the Deflectograph is planned in Tasmania at the conclusion of the current maintenance contracts.

The Deflectograph is routinely used in England for a comprehensive assessment of network level pavement strength every three to five years (Ferne 1997). This sampling is done continuously at a 3.5 metre interval for the 10,000 kilometres of major roads in England, with characteristic measurements (85th percentile) in both wheel paths reported every 100 metres. The sampling process is used to establish maintenance budgets and define areas of the network for further detailed investigation.

This survey approach relies on a possibly less reliable device (half deflection bowl rapidly tested), but sampling almost continuously.

3.4 FWD Surveys for Strength

3.4.1 FWD Strength Testing

The FWD surveys measure reliably a half deflection bowl at the pavement surface by measuring surface deflection distances from the centre of the test load, ranging from 0 mm to 1500 mm. The test load applied to the pavement is at a nominal surface stress of 700 kPa, however, this is not always achievable so all actual test loads are normalised to a surface stress value of 700 kPa. This value represents the load applied to the pavement by a standard truck tyre.

It is also necessary to vary the applied test loads in order to assess the stiffness of the pavement. Typically 560 kPa is used as the test stress value which is the same test load stress used in a Deflectograph survey. The FWD survey can also incorporate a Differentially Corrected Global Positioning System (DGPS) receiver that locates the survey test point to within 5 metres of its actual location. The DGPS could also be applied to other forms of deflection measuring devices.

In some instances where future test checks and repeatability studies are to be carried out the actual test point is marked for reference. This is achieved by spraying a paint mark onto the pavement, 700 mm left of the actual test point, after the test has been performed at each specified location. This pavement marking can be undertaken under all traffic conditions provided there is appropriate traffic control.

3.4.2 Network Sampling of Strength

Generally FWD data for pavement management at a network level is collected between 50 to 500 metre spacings along a pavement, depending on the nature of the assessment survey (Robinson 1999, 2000, Roberts 2000b). Data collected at spacings greater than 100 metres is often not regarded as a representative sample of structural conditions. However, FWD data can be collected at spacings greater than 100 metres provided this sampling captures the variability of the particular pavement. Consequently, wider sampling intervals mean that only a relatively small sample of any given pavement section is tested for a road network. Despite this drawback the FWD is may still be preferable to destructive sampling techniques even if they are taken at even greater spacings between samples.

Until 1998 Main Roads Western Australia (MRWA) based its network level asset management intervention on pavement roughness limits. Strength data was collected with Benkelman Beam surveys, but it was limited and costly and not used to manage either rehabilitation intervention or pavement reconstruction at a network level. Since 1998 MRWA has surveyed its network annually with the FWD to verify the structural condition of the pavement network being managed under Term Network Contracts (TNC). This survey involves of some 17,000 km of the Western Australian state highway network (Sapkota et al. 2001).

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To comfortably complete the MRWA network surveys within a short time frame (8 months) using one FWD testing unit, the test location points were placed at a nominal 800 metre interval, with some test points specified at 400 metre or 600 metre intervals. This time frame generally required both a driver and an operator to be used at all times. However, a single person operator can perform both the testing and driving. This results in a reduced rate of testing to comply with OH&S requirements.

In New Zealand FWD surveys were commenced in 1998 on 800 lane km of road under contract management (Robertson 2001). The FWD testing was undertaken at 100 metre intervals in alternative lanes. Following on from this further FWD network surveys were undertaken annually from 1999 to 2001.

The FWD survey approach relies on a device providing reasonably reliable information (half deflection bowl) sampling at a relatively wide interval. Ideally the spacing of the sampling interval should be such that it captures the variability of the pavement at the time of testing. Generally increasing the sampling interval will increase the likelihood of not capturing all the variability of the pavement, unless the pavement is relatively uniform.

3.4.3 Design Considerations for Pavement Rehabilitation

There are a few other issues that needed to be considered using a FWD survey at both a network and project level. The overlay design procedure used in most Australian road agency’s Asset Management system is based on the AUSTROADS (1992) procedures. This method requires the input from the Benklemen Beam, which although similar to FWD, does not give the same results. Therefore an initial investigation was required to correlate the results between the two survey types. From this investigation it was found that the FWD deflection at a surface pressure of 550 kPa was equivalent to that from a Benklemen Beam, while curvature based on FWD deflections required a factor of 0.7 to be applied to them (Goh and Begg 2000).

4. Estimation of Pavement Strength Parameters

4.1 Laboratory Estimation of Strength Parameters

4.1.1 Structural Number, SN

The concept of the Structural Number, SN, was first introduced by AASHTO in the 1960’s (Paine 1998). It was determined as follows:

n

SN = Σ ai × hI (1)

i = 1

where;

ai = material strength coefficient for the ith layer of the pavement

hi = height of the ith layer in inches.

The SN value for a pavement only applied to layers above the pavement subgrade and had to be determined under laboratory conditions. This approach did not recognise the influence of the subgrade on the structural performance of the pavement.

4.1.2 Modified Structural Number, SNC

In the 1970’s TRL developed the Modified Structural Number, SNC (Hodges et al. 1975) for flexible pavements. The main difference between the Structural Number, SN, and SNC parameter was that the subgrade was included as an input to the estimation of pavement strength for SNC. The Modified Structural Number, SNC, is defined as follows:

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SNC = SN + SNsg (2)

where;

SN = Calculated as shown in equation (1)

SNsg = 3.51 × Log10 × CBR − [ 0.85 × ( Log10 × CBR )2 ] − 1.43

= Subgrade contribution to SNC

CBR = Subgrade Californian Bearing Ratio.

4.1.3 Adjusted Structural Number, SNP

The final step of developing the SNP parameter for pavement/subgrade strength was also undertaken by TRL. The difference between the SNC and SNP parameters is the application of a weighting factor (Parkman and Rolt 1997, Parkman 1998). This factor reduces the contribution to pavement strength of the sub-base and subgrade with their increasing depth. The strength contribution from surface (only applicable to asphalt and similar surfacings) and base layers is estimated as in the SN calculations, however, the sub-base and subgrade strength contributions are reduced according to the thickness of the upper layers. This approach eliminates the overestimation of overall pavement strength, particularly in the case of thick pavements. This is especially the case with pavements having a thickness greater than 700 mm (Roberts 2000b).

The SNP pavement/subgrade strength parameter can be estimated in one of two ways. It can either be determined by summation of layer thickness and material coefficients or by a back analysis of deflection data (Roberts 2000b). However, summation from layer thicknesses requires a great deal of information about the pavement, normally derived from destructive testing and laboratory analysis, making this a very slow and costly exercise.

Appendix A provides details of the estimation of the SNP parameter used in the HDM-4 model for pavement strength deterioration.

4.2 Non-laboratory Estimation of Strength Parameters

Measuring the pavement surface, base, sub-base and subgrade layer thicknesses and estimating their respective material coefficients can be done by at least two different methods. A Ground Penetrating Radar (GPR) device can measure layer thicknesses, but requires informed interpretation combined with sampling of materials for the calibration of this method to each particular site. Other direct sampling methods (such as coring) also require some material to be removed from the pavement to laboratory. Both of these methods have two significant draw backs. Firstly, they are varying forms of destructive testing and add extra local strain to the test pavement section. Secondly, the laboratory estimation of material coefficients tends to underestimate pavement strength. This underestimation of strength is due the difference between material moisture levels and layer interconnectivity under in situ and laboratory conditions (Roberts 2000b). These moisture and layer differences occur with the removal of material from the pavement.

4.2.1 Strength Parameters from Deflection Data

Modified Structural Number, SNC

Because laboratory conditions do not match in situ conditions, it was necessary to develop other methods for estimating pavement strength. Pavement strength can be defined as the ability of the pavement to resist deformation from traffic loading (Robinson 2000). Consequently, the concept of using surface deflection data to calculate either an SNC or SNP parameter has a sound basis if a strong statistical relationship can be established between SNC or SNP and surface deflection data. Appendix D details some relationships available for both SNC and SNP based on FWD deflections.

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Currently pavement strength estimation data is often based on deflection data, which includes maximum deflection and deflection bowl data (Jameson 1993, Paine 1998). The deflection bowl data usually includes the surface deflection 900 mm from the test load, D900, the surface deflection 200 mm from the test load, D200, and the surface deflection 1500 mm from the test load, D1500. In fact collection of deflection data via the Deflectograph or FWD is one of the accepted practices in Australia, due to its non-destructive nature and its speed in collecting full or half deflection bowl data.

There are many means of calculating a Modified Structural Number, or strength parameter, from deflection data. The use of peak deflection, D0, deflection and curvature, (D0 − D200), back analysis of deflection bowl and structural capacity indices are all common. However, these approaches require additional information, such as pavement thickness or layer depth, that most road authorities don’t often have on a large scale network (Paine 1998).

Adjusted Structural Number, SNP

Some models also derive SNP from deflection data only, but often are limited to particular pavement structures and materials. One of these models (Salt 1999) requires three points of the deflection bowl data. This model was adjusted by Roberts (2000a) to account for the differing test plate pressures (see Appendix D).

Radius of Curvature

Appendix B (equation B.10) defines how the FWD deflection values are combined to give a radius of curvature (ROC). ROC can be used to determine the stiffness of the upper pavement layers.

4.2.2 Relationships between Deflections from FWD, Benkelman Beam and Deflectograph

It is useful to be able to relate deflection data from different deflection devices so that the above strength parameters can be estimated from various forms of deflection data. Preliminary evaluation of the relationships between the FWD and Benkelman Beam deflections was undertaken in Australia by Smith (1985). These relationships appeared to vary with the pavement type and structure and have not been widely used.

More recently relationships between the deflection data from FWD, Benkelman Beam and Deflectograph devices were investigated in Victoria (Clayton and Jameson 2001) and Western Australia (Goh and Begg 2000). In summary, these relationships also appeared to vary with pavement type and structure and other factors such as differing ranges of accuracy for different devices make the conversion of deflection from one device to another problematic. The development of these deflection relationships may be limited to specific pavement types and structures and ranges of deflection.

4.2.3 Some Limitations with Parameters from Deflection Data

There are two further considerations that must be taken into account in order to estimate SNP from FWD (Zaghloul et al. 1998). Firstly, all deflection data must be normalised, as noted above, for the applied test load. The initial recorded deflections are generally not precise as the load applied by an FWD can vary from drop to drop and the surface stress is not always the required value. Secondly, the deflections must be adjusted according to local climatic factors. Both the pavement and the air temperature at the time of testing can effect the deflection results. Therefore both the pavement and the air temperature must be recorded and may be factored into final SNP calculations, particularly for asphalt pavements.

Despite these shortcomings the strength parameter SNP is a measure of structural condition and a useful input to asset management systems, mainly through its use in asset management analysis software packages such as HDM-4. The pavement strength is an important factor for assessing pavement performance, in terms of deterioration, as it can effect other distresses such as cracking, rutting, etc. (Robinson 2000).

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However, it should be noted that there are still some shortcomings with using SNP that need to be taken into account in asset management systems. One such shortcoming is that the most precise collection and analysis of FWD data, or any other deflection data, at a network level may not necessarily be always possible due to its high collection cost (Paine 1998). Therefore before collection of deflection data commences it is necessary to determine how much data and what type of data is required in order to effectively meet the needs of the network assessment of pavement strength.

In Australia the high cost of deflection data collection has resulted in sampling only of suspect structurally deficient pavements, as signalled by short term increases in performance indicators such as roughness, rutting and cracking. Historically broad network level surveys have not been used for large road networks, as noted earlier.

4.2.4 Other Pavement Strength Parameters from Deflection Data

Structural Adequacy Indicator (SAI)

SNP is not the only parameter used to estimate the structural capacity of a pavement. A Structural Adequacy Indicator (SAI) was developed by Eijbersen and Zwieten (1998). Within this model the following three parameters were considered necessary to characterise a pavement: the strain on the bottom of asphalt layer; traffic level; and, generic pavement type. However, the time and effort required to model strain on the underside of the asphalt layer was found to be too difficult.

Therefore an alternative parameter using deflections was sought. It was found that the Surface Curvature Index, SCI, produced very good results. The goodness of fit of this index to strain at the bottom of the layer was very good for full depth asphalt (r2 = 0.98), with similar results for granular pavements (r2 = 0.91) when compared to the actual measured strains. This difference in correlation for given pavement types furthered the argument that pavement type was a necessary input. The final input, traffic, was indicated as the number of trucks per lane per day (Trucks).

The use of the Structural Adequacy Indicator, SAI, is described in Appendix C.

Other Strength Parameters

There are many other methods for analysing deflection data, to describe all of them in detail is beyond the scope of this document. However, a brief list of some techniques is provided here (European Commission 2001, Austroads 1992):

• Maximum deflection, D0, produced by an FWD is used in several countries to produce a measure of pavement performance with respect to traffic loads.

• Bearing Capacity Ratio is the main factor derived in Finland, amongst others. It is determined as D0/160 and a target value depending on design standards and cumulative axles. This value is only useful at a network level, however, it should be noted that seasonal correction factors are required.

• Residual life from E-Moduli can be produced by back calculated in a simplified manner, using equivalent thickness.

• The deflection data can be used to calculate pavement moduli and then determine the required overlay or resheet thickness. The estimated overlay/resheet costs can then be estimated and used as

• Overlay Requirements, as discussed in Section 2.

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5. Prediction of Network Pavement Strength

5.1 General Considerations

Asset management is not limited to the initial condition of the pavement and its deterioration due to cumulative traffic loading and environmental effects. Determination of residual structural capacity at any point during pavement life, allows decisions regarding the intervention or non-intervention of structural rehabilitation works.

For instance, pavement sections can have a comparison of their measured indicators of structural condition, such as rutting or structural cracking, with the objectively defined limits to the condition indicators for these sections. When these condition indicator limits are close to being exceeded or are exceeded some form of structural intervention may need to be implemented.

Pavement sections are often combined to represent a network link where these defined limits for the condition indicators are set on a strategic basis. Any significant variation of the measured condition indicators from the defined limits for these indicators determines if the structural conditions on these sections are deficient (Hellmuth 1998). The degree of structural deficiency then determines the possible type of intervention needed.

The remaining life of these deficient sections, based on the condition indicators, can then be used to establish the required structural intervention works such as overlays and pavement reconstruction to restore a pavement to its expected structural condition (Paine 1998). Pavement strength, or indicators of it, is fundamental to these decision making processes.

5.2 Pavement Strength Deterioration

5.2.1 HDM-4 Deterioration Model

The model for strength deterioration currently found in HDM-4 uses the SNP parameter, as noted earlier (see Appendix A). This deterioration model relates pavement moisture content (from rainfall and drain deterioration) and surface deterioration (cracking and potholes) to the proportion of the pavement strength remaining. The model reduces pavement strength according to the degree of defects on the pavement surface. However, the extent of this reduction is related heavily to the moisture in the pavement. Therefore a pavement that is 20% cracked will have lost a great deal more strength if it is a in wet climate, as opposed to being in a dry climate. This approach is based on the strength loss due to cracking on bound pavements, so it may not be appropriate for unbound pavements.

Other HDM-4 models for pavement performance indicators, such as the deterioration of roughness, rutting, cracking, etc. (ISOHDM 2000), use the strength deterioration model for the SNP parameter as an independent variable in these models.

There are three main issues with this model that need to be addressed. Firstly, there is no correlation in this model between strength and traffic. Therefore two roads with the same strength and climate, but completely different traffic loads will show exactly the same value of strength, SNP, for a given cracking level. The only variation here is that roads with heavier traffic will crack quicker and therefore the strength loss is earlier.

Secondly, if all the cracks and potholes are repaired all of the original pavement strength is predicted to be fully restored as a consequence. Experience suggests that this an optimistic prediction as surface repairs are more likely to reduce the rate of deterioration in strength rather than fully restore it. The model predicts there is no loss in original strength if the pre-performed works are routine maintenance (patching surface defects) and 100% of defects are fixed annually.

Thirdly, this model needs verification and/or calibration with actual Australian deterioration data before it can be used with confidence at a network level. The model may need some simplification, using only the variables that are appropriate at a strategic network level.

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5.2.2 Alternative Pavement Strength Deterioration Model

Roberts (2000a) has developed an alternative strength prediction model, based on the HDM-4 model. This model also incorporates traffic as an input and has a four step process that is repeated on an annual basis. Appendix B provides details of this alternative pavement strength deterioration model. Similar to the HDM-4 model, the appropriateness of this model at a network level has yet to be proven against actual deterioration data.

The first step in the estimation of SNP is to adjust the SNPd (dry weather Adjusted Structural Number) to be representative of the SNP for the climate in which the pavement is situated. This process incorporates information on seasons, allowing multiple seasons to influence the result, rather than just the wet and dry seasons as under the HDM-4 model. However, in view of the difficulty of gaining representative pavement strength at a network level for a particular season, this refinement for strength variation in response to multiple seasons is difficult to substantiate.

The second step is to reduce the pavement strength due to moisture, as in HDM-4. The third step then reduces the structural number by subtracting the annual cumulative traffic load from the pavement capacity. The general relationship between pavement traffic load capacity, CAP, and SNP is shown in Figure 1. Finally the SNP is converted back to SNPd for use in the other pavement distress deterioration models.

Under this model simply patching cracks will not return the pavement to its original strength. This is because this model assumes that the strength loss to traffic is not fully recoverable by simply patching. The model arbitrarily restricts the regain of strength lost by moisture to 50% of that lost since the last rehabilitation works. There is currently no experimental evidence to support this arbitrary assumption, although it has some anecdotal support.

Consequently, this alternative model also needs confirmation about its capacity to accurately reflect the varying structural condition of pavements. This model confirmation should be based on an extensive time series of either pavement strength data or specific experimental data. For use at the network level, this model may be simplified by using only variables that are statistically significant from this data.

6. Summary

6.1 The Need for Network Strength Data

The need for an overview of the structural condition of the whole network for future strategic planning reasons is driven by the following expectations:

� increased axle mass limits for heavy vehicles (NRTC 1996);

� increased heavy vehicle traffic growth on strategic freight routes (Gargett and Perry 1998); and,

� some road agencies have decided to include the structural condition of pavements as a network performance indicator.

The first two issues above can potentially reduce the remaining life of the pavements in the network which means that earlier than expected rehabilitation treatments are needed. These treatments are relatively costly and have a major impact on annual road agency budgets.

The third issue above is often chosen as a contractual requirement for the contractor managing a road network on behalf of the road agency.

6.2 The Collection of Pavement Strength Data at a Network Level

Despite the historical lack of use of pavement strength data at a network level, there is now more focus on its use in asset management systems for timely structural intervention due to the above reasons. Routine monitoring of strength at a network level is expected to produce major

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benefits through lower life-cycle costs achieved by timely structural intervention when it is warranted.

The increased use of network structural condition survey methods provides the structural condition data that allows a review of pavement deterioration trends in combination with other structural condition indicators. There appears to be the following two quite distinct approaches to a network structural condition survey:

1. Continuous Deflectograph sampling, at 3.5 metre intervals every three to five years, is used in the UK for a comprehensive network assessment of pavement strength. Project level structural condition surveys, typically using an FWD, are initiated based on this network survey for the future design and implementation of structural intervention works.

2. Wide spaced sampling using the FWD, at a nominal 800 metre interval every year, is currently used for network pavement strength assessment in Western Australia only. Follow up detailed structural condition surveys currently use the FWD at intervals from 10 to 100 metres, depending on the Project length.

Approach (1) uses an almost continuously sampling device that provides limited information, while approach (2) relies on a device that provides extensive and relatively reliable information that is sampled at a relatively wide interval.

6.3 Conversion of Pavement Strength Data into Strength Parameters

In conjunction with the increased availability of network data there has also been changes in the way the pavement strength data is quantified. This development began with the SN pavement parameter, which was enhanced by the creation of the SNC and SNP parameters. Other parameters, such as the SAI, also provide a numerical tool for comparing pavements mainly based on their deflection data regardless of their initial structure or degree of deterioration. Simple relationships, such as the Relative Pavement Strength indicator, RPS, are useful guides to preliminary intervention and testing.

Relationships between remaining strength and traffic levels, such as the SNP with traffic load capacity, CAP, have been developed to predict the structural condition of pavements. These predictions are the basis of the analysis for informed decisions regarding the remaining life of the pavement and the necessity and timing of structural intervention through rehabilitation.

6.4 Prediction of the Deterioration of Network Pavement Strength

Pavement performance models (deterioration of roughness, rutting, cracking, etc.) are often based on the predictions from pavement strength models, such as those found in HDM-4. The appropriateness of the structural models in predicting network level structural deterioration has not been confirmed with actual Australian deterioration data, so these models cannot yet be used with confidence at a network level. The models could be simplified by using only the variables that are appropriate at a strategic network level. Prediction of pavement performance, in terms of surface and structural condition, allows asset managers to perform life-cycle costing analyses at a pavement network level.

7. References AUSTROADS (1992). Pavement Design – A Guide to the Structural Design of Road Pavements, Sydney.

CLAYTON, B. and JAMESON, G. (2001). Correlation between Benkelman Beam, PaSE Deflectograph and FWD, ARRB Transport Research Contract Report RC2007, ARRB TR, Vermont South, Victoria.

EIJBERSEN, M.J. and VAN ZWIETEN, J. (1998). Application of FWD-measurements at the network level, 4th International Conference on Managing Pavements, Durban, South Africa.

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EUROPEAN COMMISSION (2001). Cost 336 – Falling Weight Deflectometer, Chapter 5, Directorate General Transport, Paris, France.

FERNE, B.W. (1997). Use of deflections at network level in England for programming and other purposes, Cost 336 Workshop, 4-5 June at LNEC, Lisbon.

GARGETT, D. and PERRY, R. (1998). Interstate non-bulk freight, Proc. 22nd Australian Transport Research Forum, Vol.22 pp 19-28, Transport Data Centre of New South Wales Department of Transport: Sydney.

GOH, A.L. and BEGG, S. (2000). Development of a relationship between Falling Weight Deflectometer and Benkelman Beam Deflection, Goh and Begg Consultants, MWRA Panel Contract 1035C98.

HELLMUTH, M. (1998). Asset management – an Emerald perspective, Road and Bridge Asset Management in Queensland, Conference, Brisbane.

HODGES, J.W., ROLT, J. and JONES, T.E. (1975). The Kenya Road Transport Cost Study: Research on Road Deterioration. TRRL Laboratory Report 673, Transport and Road Research Laboratory: Crowthorne, United Kingdom.

ISOHDM (International Study of Highway Development Management Tools) (2000). HDM4, Volume 4 – Analytical Framework and Model Descriptions: Part C, Version 1, University of Birmingham, UK.

JAMESON, G.W. (1993). Development of procedures to predict structural number and subgrade strength from falling weight deflectometer deflections, ARRB TR, Vermont South, Victoria.

LANG, J. (2001). Personal Communication, October 2001, Department of Infrastructure, Energy and Resources, Tasmania.

MARTIN, T. and ROBERTS, J. (1996). Recommendations for monitoring Pavement Performance, ARRB Transport Research Report ARR 293, ARRB TR, Vermont South, Victoria.

MARTIN, T.C. and ROBERTS, J.D. (1998). Network and project level pavement life-cycle costing modelling for asset management, 9th Road Engineering Association of Asia and Australasia (REAAA) Conference, Wellington, New Zealand.

MARTIN, T., GLEESON, B., JOHNSON-CLARKE, J., TREDREA, P., LUKE, R. and FOSSEY, D. (2001). The Effect of Maintenance on Pavement Performance: Accelerated Load Testing in 2000/01, ARRB Transport Research Contract Report RC1739, ARRB TR, Vermont South, Victoria.

NRTC (National Road Transport Commission) (1996). Mass Limits Review: Report and Recommendations, July 1996, pp 64, NRTC, Melbourne.

PAINE, D. (1998). The incorporation of structural data in a pavement management system, International Conference on Managing Pavements, 4th, Durban, South Africa.

PARKMAN, C.C. (1998). Personal Communication E-Mail, 10 November 1998, Transport Research Laboratory, Crowthorne, Berkshire, UK.

PARKMAN, C.C. and ROLT, J. (1997). Characterisation of pavement strength in HDM-III and possible changes for HDM-4, Transport Research Laboratory Unpublished Report, PR/ORC/587/97, Crowthorne, Berkshire, UK.

PATERSON, W.D.O. (1987). Road Deterioration and Maintenance Effects: Models for Planning and Management. The Highway Design and Maintenance Standards Series, John Hopkins University Press, Baltimore, USA.

PRABHU, A, and Fortune, P. (2000). Life Cycle Costing: Case Study of a City’s Pavement Network, Australian Asphalt Pavement Association, Victoria.

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ROBERTS, J.D. (2000a). A Pavement Structural Deterioration Model for HDM-4, Proceedings First European Conference on Pavement Management Systems, Budapest, Hungary.

ROBERTS, J.D. (2000b). Project level pavement performance modelling, Road and Transport Research, 9(4), pp. 29-47, ARRB Transport Research Ltd, Vermont South, Victoria.

ROBERTS, J.D. and CRANK, S. (2000c). Enhancement of HDM-4 (Version 1) Road Deterioration Models for Chip Sealed Granular Pavements, Contract Report RC91007-4, ARRB Transport Research Ltd, Vermont South, Victoria.

ROBERTSON, D. (2001). Personal Communication, July 2001, Asset Systems Engineer, Transit New Zealand.

ROBINSON, P. (1999). Progress Report – Pavement Strength: A Brief Review of Current Practice (Update Incorporating Member Authority Comments), Contract Report, RC1729, ARRB Transport Research Ltd, Vermont South, Victoria.

ROBINSON, P. (2000). Guidelines for Pavement Condition Monitoring Part 3 – Pavement Strength, Contract Report, RC91082-2, ARRB Transport Research Ltd, Vermont South, Victoria.

ROBINSON, P. (2001). Guidelines for Pavement Condition Monitoring Part 3 – Pavement Strength, Contract Report, RC1635-3, ARRB Transport Research Ltd, Vermont South, Victoria.

SALT. G. (1999). Determining the Structural Capacity of Unbound Pavements in New Zealand using Deflection Testing, Report for Transfund New Zealand, Tonkin and Taylor, New Zealand.

SAPKOTA, B., BUTKUS, F., NORRIS, B. and GOH, A.L. (2001). Main Roads Western Australia’s experience in the use of the falling weight deflectometer for network pavement strength assessment, 20th ARRB TR Conference, Melbourne, ARRB TR Vermont South, Victoria.

SHELDON, G.N. (1988). New adjunct to deflection measurement - Deflecdas captures deflection bowl curvature automatically. Proceedings of the 14th ARRB Conference, Canberra 1988. Australian Road Research Board, Vermont South, Victoria.

SMITH, R.B. (1985). Preliminary Evaluation of the Dynatest 8000 Falling Weight Deflectometer, Australian Road Research, 15(4), pp. 229-238. Australian Road Research Board, Vermont South, Victoria.

STEEL, R. and HALLETT, J. (1998). Road asset management: the use of pavement performance prediction models, 9th Road Engineering Association of Asia and Australasia (REAAA) Conference, New Zealand.

TYSON, G. and DIAZ, E. (1995). Continuous automated pavement deflection measurement. ARRB Transport Research Ltd., Working Document WD95/004, July 1995, ARRB TR, Vermont South, Victoria.

WATANATADA, T, HARRAL, C,G., PATERSON, W.D.O., DHARESHWAR, A.M., BHANDARI, A. and TSUNOKAWA, K. (1987). The Highway Design and Maintenance Standards Model: Volume 1: Description of the HDM-III Model, John Hopkins University Press, Baltimore, USA.

ZAGHLOUL, S., HE, Z., VITILLO, N. and KERR, J.B. (1998). Project scoping using falling weight deflectometer testing: New Jersey experience, Transport Research Record, No. 1643, pp. 34-43, Washington, DC., USA.

ZAGHLOUL, S.M. and KERR, J.B. (1999). Reduced Rehabilitation Cost from use of Falling Weight Deflectometer, Transport Research Record, No. 1655, Washington, DC., USA.

ZHU, D. (1998). Chip seal performance prediction models, 9th Road Engineering Association of Asia and Australasia (REAAA), Conference, Wellington, New Zealand.

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Appendix A: Details of HDM-4 Pavement Strength Deterioration Model

A.1 Adjusted Structural Number, SNP The HDM-III approach to estimating pavement strength in terms of the modified structural number, SNC, (Paterson 1987, Watanatada et al. 1987) was significantly modified by using the Adjusted Structural Number, SNP, in HDM-4. The aim of this modification was to develop pavement sub-base layer coefficients that are dependent upon their depth from the pavement surface so that the lower layers do not have an undue influence on the overall pavement strength (Parkman and Rolt 1997). Theoretically pavement strength coefficients depend upon the inherent strength and stresses and strains to which each layer is subjected, so this modification has a sound theoretical basis.

The HDM-4 adjusted structural number for season ‘s’, SNPs, is defined as follows (ISOHDM 2000):

SNPs = SNBASUs + SNSUBAs + SNSUBGs (A.1)

where;

SNBASUs = 0.0394

i

n

=∑

1

ais hi

= Contribution of surfacing and base layers for season ‘s’

SNSUBAs = 0.0394 ab b z

b

b b b z

b bjsj

m0 3

3

1 2 3

2 31

exp( ) exp( ( ) )

( )

−−

+− +

+

=∑

z z

z z

j

j

=

=

−1

= Contribution of the sub-base or selected fill layers for season ‘s’

SNSUBGs = (b0 - b1exp(-b2zm)) (exp(- b3zm)) × [3.51 log10CBRs – 0.85(log10CBRs)2 - 1.43]

= Contribution of the subgrade for season ‘s’

n = Number of base and surfacing layers (i = 1, n)

ais = layer coefficient for base or surfacing layer i for season ‘s’ (ranging from 0 to 0.45)

hi = Thickness of base or surfacing layer, i, in mm

m = Number of sub-base and selected fill layers (j = 1, m)

ajs = layer coefficient for sub-base or selected fill layer j for season ‘s’ (≤ 0.14)

b0, b1, b2,

and b3 =

model coefficients, b0 =1.6; b1 = 0.6; b2 = 0.008; b3 = 0.00207

z = depth parameter measured from the top of the sub-base (underside of base), in mm

zj = depth to the underside of the jth layer (z0 = 0), in mm

CBRs = in situ subgrade CBR for season ‘s’.

HDM-4 allows for seasonal variation of SNP, by using the SNP for a wet season, SNPw, and the SNP for a dry season, SNPd, in estimating an average annual SNP as input into the deterioration models. The seasonal variation in SNP depends upon drainage factors, monthly rainfall and the amount of cracking as defined below:

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(1 − exp(a0 MMP)) f = K f { 1 −

a1

(1 − a2 DFa) (1 + a3 ACRAa + a4 APOTa)} (A.2)

where;

f = SNPw / SNPd ratio

SNPw = wet season SNP

SNPd = dry season SNP

MMP = mean monthly precipitation in mm/month

DFa = Drainage factor at start of analysis year (= 1 (excellent) to = 5 (poor))

ACRAa = total area of cracking at start of analysis year, in per cent

APOTa = total area of potholes at start of analysis year, in per cent

K f = Calibration factor (default value = 1)

a0, a1, a2, a3,

and a4 =

model coefficients, a0 = − 0.01; a1 = 10; a2 = 0.25; a3 = 0.02; a4 = 0.05.

The average annual SNP is derived as follows:

SNP = fs SNPd (A.3)

where;

f fs =

[(1 − d) + d(fp)]1/p

SNP = Average annual adjusted structural number

SNPd = dry season SNP

f = SNPw / SNPd ratio

d = length of dry season as a fraction of the year

p = Exponent of SNP specific to the appropriate deterioration model

= 2 for structural cracking.

The SNBASUs term in equation (A.1) is the same as that used in HDM-III (Watanatada et al. 1987). The SNSUBAs term is similar to SNBASUs, but been modified by the new model coefficients. The SNSUBGs term is similar to the SNSG term used in HDM-III, but it also has been modified by the new model coefficients.

The SNSUBAs term is defined somewhat cryptically above as it has several possible interpretations. Clarification was necessary (Parkman 1998) to confirm precisely how SNSUBAs was calculated.

A.2 Adjusted Structural Number, SNP, variation with Cracking HDM-4 in similar manner to HDM-III predicts that the adjusted pavement strength, SNP, reduces due to cracking. The term SNPKb is the adjusted SNP due to cracking, at the end of the analysis year, and it is estimated as follows:

SNPKb = max [(SNPa − dSNPK), 1.5] (A.2)

where;

dSNPK = a0 [min (a1, ACXa) HSNEW + max (min (ACXa − PACX, a2), 0) HSOLD]

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dSNPK = Reduction in adjusted structural number due to cracking

SNPa = Adjusted structural number at start of analysis year

ACXa = area of indexed cracking at start of analysis year, in per cent

PACX = area of previous indexed cracking in old surfacing, in per cent

ie. 0.62 (PCRA) + 0.39 (PCRW)

PCRA = area of all cracking before lastest reseal or overlay, in per cent

PCRW = area of all wide cracking before lastest reseal or overlay, in per cent

HSNEW = Thickness of the most recent surfacing, in mm

HSOLD = total thickness of previous underlying surfacing layers, in mm ( = 0 when not resealed and > 0 when resealed)

a0, a1, and

a2 = model coefficients;, a0 = 0.0000758; a1 = 63; a2 = 40.

The estimation of cracking initiation and progression is evaluated by HDM-4 models. The cracking is defined as ‘all’ structural cracking (crack width ≥ 1mm) and ‘wide’ structural cracking (crack width ≥ 3mm).

Cracking initiation and progression is considered in terms of structural cracking. Cracking due to environmental effects, such as that occurring in sealed granular pavements is not considered by these models.

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Appendix B: Details of Alternative Pavement Strength Deterioration Model

B.1 Adjusted Structural Number, SNP

B.1.1 Introduction

The modelling of pavement structural performance is important for PMS, as it is a primary determinant of many other pavement performance condition indicators. HDM-4 recognises this need through the use of the Adjusted Structural Number (SNP). However, there is scope for enhancement of the HDM-4 modelling for flexible pavements as noted below:

• structural deterioration modelling using the variations of strength with four seasons;

• explicit modelling of pavement structural adequacy;

• layer by layer modelling for generic pavement type differentiation, particularly the difference between bound and unbound pavements; and,

• integration of all the above, that is, the integration of climatic, condition and traffic induced structural degradation.

B.1.1.1 Multi Season Modelling of Strength

Long term modelling requires a representative annual value of SNP. The current HDM-4 model takes a weighted average SNP between an assumed two season yearly scenario of a bone dry period and one in which all rain falls. The revised model extends the HDM-4 modelling to multi season scenarios (from 4 up to 12), with any rainfall value in any season (Roberts 2000a).

For example, SNP variation from season to season can be estimated based on the HDM-4 relationship (Appendix A, equation A.2) using the following seasonal correctional factors:

(1 − exp(a0 0.5 MMPsu)) SEsu = Ksu { 1 −

a1

(1 − a2 DFa) (1 + a3 ACRAa + a4 APOTa)} (B.1)

(1 − exp(a0 0.5 MMPau)) SEau = Kau { 1 −

a1

(1 − a2 DFa) (1 + a3 ACRAa + a4 APOTa)} (B.2)

(1 − exp(a0 0.5 MMPsp)) SEsp = Ksp { 1 −

a1

(1 − a2 DFa) (1 + a3 ACRAa + a4 APOTa)} (B.3)

(1 − exp(a0 0.5 MMPsp)) SEwi = Kwi { 1 −

a1

(1 − a2 DFa) (1 + a3 ACRAa + a4 APOTa)} (B.4)

where;

SEsu, SEsp, SEau,

and SEwi = seasonal correction factors for summer, spring, autumn and winter, respectively

MMPsu, MMPsp, MMPau,

and MMPwi = mean monthly precipitation in mm/month for summer, spring, autumn and winter, respectively

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DFa = drainage factor at start of analysis year (= 1 (excellent) to = 5 (very poor))

ACRAa = total area of cracking at start of analysis year, in per cent

APOTa = total area of potholes at start of analysis year, in per cent

Ksu, Ksp, Kau, Kwi = respective calibration factors for summer, spring, autumn and winter (default value = 1)

a0, a1, a2, a3,

and a4 =

model coefficients, a0 = − 0.06; a1 = 2.7; a2 = 0.25; a3 = 0.02; a4 = 0.05.

If the value for SNP is known for one season, say SNPsu for a summer measurement, any other season value for SNP can be estimated using the above correction factors as follows:

SNPau = SEau SNPsu (B.5) SEsu

SNPsp = SEsp SNPsu (B.6) SEsu

SNPwi = SEwi SNPsu (B.7) SEsu

where;

SNPsu, SNPsp, SNPau,

and SNPwi = seasonal value for SNP in summer, spring, autumn and winter, respectively.

The average annual value of SNPaa is derived as a weighted average of all the seasonal values as follows:

SNPaa = SNPsu 1/su + SNPau 1/au + SNPsp 1/sp + SNPwi 1/wi (B.8) where;

1/su, 1/au, 1/sp, and 1/wi = portion of the year that is the summer, autumn, spring and winter season, respectively.

B.1.1.2 Explicit Structural Adequacy

In the prediction of structural adequacy it is essential to include the degradation effects of condition, climate and traffic on pavement strength and structural capacity. A structural adequacy relationship is proposed between SNP and residual structural capacity, CAP (in terms of MESAs), that is capable of calibration to allow the following aspects of structural performance to be predicted (see Figure 1 and Figure B1 below):

• realistic prediction of other dependent pavement performance condition indicators;

• load sensitivity, for the investigation of increased axle mass options;

• structural penalties of maintenance neglect; and,

• triggering of structural treatments for structural reasons.

The relationship for structural capacity, CAP (in MESAs per lane), as a function of SNP is as follows (Roberts 2000a):

CAP = 10^{1.662661933 + −10.61663029 (SNP) + 16.842724182 (SNP)^2 + −10.18882876 (SNP)^3 + 3.504417685 (SNP)^4 + −0.753642325 (SNP)^5 + 0.103534412 (SNP)^6 + −0.008851876 (SNP)^7 + 0.000429867 (SNP)^8

(B.9)

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+ (−9.06736/1000000) (SNP)^9}/1000000 where;

SNP = Adjusted Structural Number (can use the average annual value of SNPaa) for the particular year.

SNP-C apacity -SN P R elat ion ship

1

2

3

4

5

6

7

8

0.001 0.010 0.100 1.000 10.000 100.000 1000.000

R emain ing C apacity (MESAs)

Cu

rre

nt

SN

P

Figure B1: Strength to Capacity Relationship

B.1.1.3 Pavement Type Differentiation

Pavement type differentiation is achieved by a layer by layer modelling of the four main layers of surfacing, base, sub-base and subgrade for a given reference season. Layer performance under condition, moisture and traffic loading depends on layer location and material type (Figure B2). The HDM-4 relationships for seasonal corrections (equations B.1 to B.4) can be used to model the pavement layer differences when water ingress into the base and lower layers is possible. The HDM-4 (equations B.1 to B.2) model coefficients, a0, a1, a2, a3, and a4, are used to reflect the pavement layer location and material.

The initial value of SNP measured for a given season can be subsequently adjusted using this approach with the observed changes in surface conditions from the initial measured condition. This means that the seasonal correction factors are calculated for the initial measured condition for the four main pavement layers and then subsequent changes in the factors due to changed conditions are used to readjust the initial value of SNP. The other season values of SNP are estimated as shown above (equations B.5 to B.7) which are then used to estimate the average annual value of SNPaa by means of equation B.8.

The above process is expected to model the deterioration of SNP with time in accordance with observed surface conditions.

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Surfacing

Base

Sub-Base

Subgrade

Primary water

ingress into Sub-Base & Subgrade

from Drains

Primary water ingress into Base through surface cracks

Base water susceptible if unbound, not if bound

Sub-Base water susceptible if unbound, not if bound

Figure B2: Modelling of Pavement

B.1.1.4 Integration: Climatic, Condition and Traffic Degradation

The primary cause of strength (SNP) degradation (and capacity consumption) is traffic loading. The rate of SNP reduction depends on SNP magnitude (available residual capacity). SNP (and structural capacity) can also be degraded directly by moisture induced weakening (wet climates), and condition (structural cracking or moisture ingress). If equation (B.9) is used with an annually changing value of SNPaa, based on the observed changes in surface and seasonal conditions as noted above, the deteriorating structural capacity of the pavement can be predicted.

B.1.2 Data Input Requirements

The input requirements are relatively light, in keeping with a PMS scope:

• generic pavement type (surfacing material and thickness, base and sub-base material types, estimated subgrade strength, CBR);

• deflection data (full bowl FWD, or just D0 and D200);

• mean monthly precipitation (MMP, mm per month) for each month of the year in the area of the survey; and,

• projection of annual traffic loading.

B.1.2.1 Initial Data Processing

Preliminary data processing includes the following:

• SNP for the month of survey is calculated from a previously derived relationship between SNP and deflection (for example, see equation (3)).

• an estimate is made of the Radius of Curvature (ROC) of the seat of the deflection bowl by consideration of D0 and D200. ROC is a measure of bowl shape (see Figures B3 and B4) and is proposed for use to indicate the relative strength (or weakness) contributions from the upper and lower pavement layers. It is estimated as follows (Roberts 2000a):

ROC = 2002 (B.10)

2(D0 − D200)

where;

D0 = FWD deflection (micron) under centre of test plate load

D200 = FWD deflection (micron) 200 mm from centre of test plate load

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• a representative annual value of SNP, SNPaa, is derived by the seasonal distribution of rainfall through the year, and its relationship with SNP value, as noted in B.1.1.4.

Small ROC : Low StiffnessDo = 727 microns,

Pavement Strength SNP = 4.3

Fitted ROC can be shown to be : as plotted x vertical exagerration

(=150mm x 500 = 75m )Calculated ROC from Do & D200 = 75m

-1000

-800

-600

-400

-200

0

-2000 -1800 -1600 -1400 -1200 -1000 -800 -600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000

Offset from Do (mm )

De

fle

cti

on

(m

icro

ns

)

Figure B3: Relatively Small Radius of Curvature (ROC)

Large ROC : High StiffnessDo = 814 microns,

Pavement Strength SNP = 4.3

Fitted ROC can be shown to be : as plotted x vertical exagerration

(=700mm x 500 = 350m )Calculated R OC from Do & D200 = 360m

-1000

-800

-600

-400

-200

0

-2000 -1800 -1600 -1400 -1200 -1000 -800 -600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000

O ffset from Do (m m )

De

fle

cti

on

(mic

ron

s)

Figure B4: Relatively Large Radius of Curvature (ROC)

B.1.2.2 Modelling of Structural Deterioration

• The initial annual value of SNP is input, and loaded with traffic.

• SNP is reduced in accordance with the relationship in Figure B2.

• SNP at start of each year is reviewed for condition induced reductions prior to application of traffic.

Typical plots for a maintained pavement are shown in Figure B5.

Annual MESAs = 0.26 with 2% growth, for varying strength. Humid Climate, fully maintained surface

1

2

3

4

5

6

0 5 10 15 20 25 30 35 40 45 50Elapsed Time (Years)

SN

P

Figure B5: Predicted Deterioration of SNP

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B.1.2.3 Depth Effects

These effects allow for differential degradation at different levels in the pavement structure and for the protective effect of structural overlays.

The traffic loading effect on each pavement layer is dependent on the pressure of the load on the upper surface of the layer after its distribution and reduction due to the protective effect of layers above it. This effect applies both to the layers in an existing pavement, and to the modelling of the technical benefits of a structural overlay in the reduction of the rate of degradation of the layers it is protecting. The load distribution rate takes account of:

• the depth of the top of the loaded layer below the existing (or new, after overlay) pavement surface.

• the thickness of the asphaltic surfacing layer, with allowance for variation from chip seals to 75mm AC and above.

• the effect of the structural degradation of the asphaltic surfacing layer on its protective load dispersal capability.

The stress distribution model was implemented as the mathematical description of a three dimensional surface defined according to four separate curves for granular pavements with a chip seal, and 35mm AC, 50mm AC and 75mm AC pavements, are nominally bound by the curves shown in Figures B6 and B7.

Figure B6: Chip Sealed Granular Pavement

Figure B7: 75 mm AC Pavement

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B.1.2.4 Outcomes

The main outcome from this work is a structural deterioration model for forward prediction of pavement condition within HDM-4 and a PMS in general. Other outcomes of the work are summarised as follows:

• a means for estimating the remaining structural capacity of a pavement, which with projected traffic loading allows an estimate of residual structural life in years;

• a simple means of using bowl shape, (D0 − D200), for diagnosing the location within the pavement of strength (or weakness); and,

• a means of estimating the SNP (or deflection) value at a site in any season, based on data from a survey in only one season.

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Appendix C: Details of the Structural Adequacy Indicator, SAI

C.1 Structural Adequacy Indicator, SAI

C.1.1 Introduction

The use of the Structural Adequacy Factor, SAI, developed by Eijberson and Zwieten (1998) is described below.

To apply this model in practice three levels were developed as follows:

� Level 1 = SCI600 below lower level;

� Level 3 = SCI600 above highest level; and,

� Level 2 = SCI600 between highest and lowest level.

The parameter, SCI600, at the lower level is defined as follows:

SCI600 = a2 + a1 (C.1)

( 1 + a3 × Trucks )

where;

Trucks = Number of trucks per day per lane

a1, a2 and a3 = Constants defined in tabulation below.

Constant Full Depth Construction

Granular Base Construction

a1 53.9 60.52

a2 134.1 269.6

a3 0.002576 0.003841

The parameters, SCI600, lower level and highest level are defined as follows:

• SCI600 = D0 − D600

• lower level = see equation (C.1)

• higher level = 1.8 × lower level

If the Surface Curvature Index, SCI600, is above the highest level then the pavement is regarded as being structurally inadequate (SAI at level 3) and if SCI600 is below the lower level then the pavement is regarded as being structurally sound (SAI at level 1) . When SCI600 falls between the higher and lower levels, the structural condition of the pavement is uncertain (SAI at level 2).

The above was further refined by developing a Structural Distress Indicator matrix which, included the following parameters:

1. the SAI level (1, 2 or 3);

2. the parameter, Diff. SCI, defined below in equation (C.2); and,

3. the amount of visible cracking (percentage of surface area cracked) in the pavement (%cracking).

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Diff. SCI = ( SCI600,traffic − SCI600,untraffic ) × 100% (C.2)

SCI600,untraffic

where;

SCI600,traffic = SCI measured on trafficked area of pavement

SCI600,untraffic = SCI measured on untrafficked area of pavement.

The three parameters were then combined to develop the Structural Distress Indicator matrix of values from 1 to 10, where 1 indicates a poor structural condition and 10 is a very good structural condition. Below is the layout of this matrix.

SAI Level 1 SAI Level 2 SAI Level 3

Visible Cracking

Diff.SCI <1%

Diff.SCI 10-

20%

Diff.SCI 20-

40%

Diff.SCI >40%

Diff.SCI <1%

Diff.SCI 10-

20%

Diff.SCI 20-

40%

Diff.SCI >40%

Diff.SCI <1%

Diff.SCI 10-

20%

Diff.SCI 20-

40%

Diff.SCI >40%

<1% 10

1-10%

10-30%

>30% 1

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Appendix D: Strength Parameters from Deflection Data

D.1 FWD Deflection Data

D.1.1 Modified Structural Number, SNC

The Modified Structural Number, SNC, used by HDM-III (Paterson 1987) was the first major use of deflection data for strength estimation, although it was based only on the peak deflection immediately under the test load, D0, from a Benkelman Beam and/or FWD. The relationship below for SNC with deflection is that developed by Peterson (1987):

SNC = ao × ( D0 )- 0.63 (D.1)

where;

SNC = Modified Structural Number for pavement/subgrade strength

D0 = Maximum deflection (mm) determined from either Benkelmanz Beam or FWD

ao = Model coefficient = 3.2 (uncemented base), = 2.2 (cemented base).

D.1.2 Adjusted Structural Number, SNP

A model proposed by Salt (1999) uses the D0, D900 and D1500 FWD deflection measurements to determine the Adjusted Structural Number, SNP, for the pavement/subgrade system. This model was adjusted by Roberts (2000a) to account for the differing test plate pressures. The adjusted Salt (1999) relationship for pavements with unbound granular bases is defined as follows:

SNP = 112 × ( 0.809 × D0 )- 0.5 + 47 × ( 0.809 × ( D0 – D900 ) )

- 0.5 – 56 × ( 0.809 × ( D0 – D1500 ) )

- 0.5 – 0.4 (D.2)

where;

SNP = Adjusted Structural Number for pavement/subgrade strength

D0 = FWD deflection (micron) under centre of test plate load

D900 = FWD deflection (micron) 900 mm from centre of test plate load

D1500 = FWD deflection (micron) 1500 mm from centre of test plate load.

The above FWD deflection values, D0, D900, and D1500 are normalised to a surface distress of 700kPa.

A check on the utility of equation (D.2) for estimating SNP compared with equation (D.1) for estimating SNC was made by plotting the predictions of SNP against SNC as shown in Figure D1. Figure D1 shows that the equation (D.2) estimate of SNP closely approximates to the equation (D.1) estimate of SNC. This outcomes suggests that the additional FWD deflection values, D900, and D1500, make no contribution to the estimate of SNP in equation (D.2). In this case equation (D.2) does not appear to be significantly different to equation (D.1) in terms of its predictions.

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3

4

5

6

7

3 4 5 6 7

SNC (Paterson 1987)

SN

P (

Sal

t 19

99)

Plot based on 71 data points from Martin et al . 2001

Figure D1: Comparison of Estimations SNP and SNC


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