Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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Caldwell and Wilson (1999)
1. Determine primary rating factor for a road section based on traffic volume and user types
2. Primary rating factor is then modified by an adjustment factor accounting for speed, terrain, and heavy vehicles
3. Adjusted rating factors used to prioritize the sections for further safety analysis
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
2
Caldwell and Wilson (1999)
• Primary rating factor determined by:
Traffic Volume (based on subjective evaluation)
User Types
(Users mainly consist of) Low Average High Local A B C
Local + Recreational B C D Local + Recreational +
Tourist C D E
Caldwell and Wilson (1999)
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
3
Caldwell and Wilson (1999)
• Adjusted rating factor determined by:Element Levels of Ranking
(based on subjective evaluation) Rating Adjustment
Factor Operating
Speed High and/or Large Variation in Speed Average Low
Move down 1 Class Neutral Move up 1 Class
Heavy Vehicles
High (Logging, Mining, Agriculture, etc.) Average Low
Move down 1 Class Neutral Move up 1 Class
Terrain Mountainous Rolling Level
Move down 1 Class Neutral Move up 1 Class
Caldwell and Wilson (1999)
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
4
Severity Indices• Severity indices serve as indicators of the
expected injury consequences of a crash• Many express low confidence in their validity
• Two definitions:(1) proportion of severe injuries experienced in crashes
with fixed objects
(2) injury cost for the entire distribution of injuries experienced ~ like an expected value
Hall et al. (1994)
Council and Stewart (1996)
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
5
Cost-Effectiveness Approaches• Cost-effectiveness utilized as means of
comparison• Benefits:
– Reduction in the frequency of accidents, or– Reduction in the severity of accidents
• Costs:– Societal - injuries and fatalities– Direct - initial, maintenance, repair of accidents
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
6
4. Calculate:
total present worth or
costs incurred by the highway department
AASHTO Roadside Design Guide (1989)1. Determine:
lateral placement, length, and width of obstacle
encroachment and collision frequency
2. Assign a severity index to the hazard
3. Determine:
initial, average damage, and average maintenance costs as well as other factors for the obstacle
average occupant injury and vehicle damage cost per accident
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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AASHTO Roadside Design Guide (1989)
(1) Determine the following:
A = lateral placement of the roadside obstacle from EOP (feet)
L = horizontal length of the roadside obstacle (feet)
W = width of the roadside obstacle (feet)
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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AASHTO Roadside Design Guide (1989)
(2) Determine the ADT (vehicle per day)
(3) Determine the encroachment frequency (Ef) (vehicle encroachments per mile per year) using the following figure (other available data may be used in place of figure):
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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Predicting Encroachments
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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AASHTO Roadside Design Guide (1989)
(4) Determine the collision frequency, Cf, from appropriate nomographs:
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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Estimating Collision Frequency
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
12
Estimating Collision Frequency
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
13
AASHTO Roadside Design Guide (1989)
(5) Assign a severity index to the obstacle of concern (an extensive list of severity indexes is provided)
(6) Determine the:
initial cost, CI
average damage cost to obstacle per accident, CD (present dollars)
average maintenance cost per year, CM (present dollars)
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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AASHTO Roadside Design Guide (1989)
(7) Determine the:
average occupant injury and vehicle damage cost per accident, COVD (present dollars)
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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Estimating Injury and Vehicle Damage Cost
DO
LL
AR
VA
LU
E O
F A
N
AC
CID
EN
T ($ x 1000)
SEVERITY INDEX
Figure VII-C-6. Average Occupant Injury and Vehicle Damage Costs
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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AASHTO Roadside Design Guide (1989)
(8) Determine the useful life (T) of the obstacle
(9) Determine the economic present worth factors, KT and KJ, for the useful life
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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Present Worth Factors
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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Present Worth Factors (cont.)
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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AASHTO Roadside Design Guide (1989)
(10) Estimate expected salvage, CS value at the end of obstacle’s useful life (future dollars)
(11) Calculate total present worth:
(12) or, costs incurred by the highway department:
)())(()())(( JSTfOVDTMTfDIT KCKCCKCCCCCC
)()())(( JSTMTfDITD KCKCKCCCC
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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Mak (1995)
• Benefit - cost ratio of alternative 2 compared to alternative 1
• B1, C1 = Benefits and cost of alternative 1
• B2, C2 = Benefits and cost of alternative 2
)/()( 121212 CCBBBC
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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Predicting Accident Frequency
• Accident data-based model– Historical data from reported accidents– Develop multiple-regression models– Input parameters:
• Roadway characteristics
• Roadside characteristics
– Output:• Accident frequency
Mak (1995)
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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Predicting Accident Frequency• Encroachment probability model:
– Assumes that accident frequency can be related to encroachment frequency
– Assumptions made about the distribution of lateral encroachment distances, speeds and angles, and vehicle sizes
– Advantages• Applicable to a wide variety of roadside features
• Allows evaluation of multiple performance levels
Mak (1995)
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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Encroachment Probability
ModelSicking and Hayes (1986)
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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Encroachment Probability Model (cont.)
Probability that a vehicle of size W will encroach at speed V and angle into encroachment range 2, given that an encroachment has occurred
probability that an encroaching vehicle will be of size W
Probability that an encroaching vehicle will be traveling at speed V
Effective vehicle width ( ½ vehicle width + ½ vehicle length) in feet
280,5/)sin/)(|()()|( ,2,
, eVWV WEEPWPEEP
)|( 2,, EEP W
V
)(WP
)|( , EEP V
eWSicking and Hayes (1986)
Center for Risk Management of Engineering Systems University of Virginia, Charlottesville
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Encroachment Probability Model (cont.)
Probability that a vehicle of size W encroaching at speed V and angle will strike hazard within range 2, given that an encroachment has occurred
Distance from travelway to fixed object (ft)
Probability that the lateral extent of encroachment is greater than or equal to (a + …)
We* cos (ft)
N
jV
WV jaLEPEPWPECP
1,
2,, )]}2/1([csc{sec280,5/1)()()|(
)|( 2,, ECP W
V
a
...)]([ aLEP
N
Sicking and Hayes (1986)
