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Quantitative Safety Analysis for
Intersections on Washington State
Two-lane Rural Highways
Master’s Thesis Defense
Ngan Ha Nguyen
8/15/2007
Department of Civil Engineering
University of Washington
Overview
Introduction
Study Routes and Data
Methodology
Data Analysis
Accident Risk Modeling
Conclusions and Recommendations
2
Introduction: Traffic Accidents
Traffic accidents are
leading causes of
death
Huge economic loss
to the society
Improving traffic
safety is an Average Comprehensive Cost by Injury Severity
important task Death $3,840,000
Incapacitating injury $193,800
Nonincapacitating evident injury $49,500
Possible injury $23,600
No injury $2,200
3
Leading Causes of U-I Deaths, U.S., 1969-2005
Introduction: National Statistics
Rural fatal accident rate is more than twice as
high as urban fatal accident rate
Total Crashes in 2003, US. Fatal Crashes in 2003, US.
25%
39%
61%
75%
Two-lane rural road
Others
4
Introduction: National Statistics
More than 1 death per hour in accidents at
intersections
Reported Crashes. Fatal Crashes.
28%
45%
55%
72%
Intersection accidents
Others
5
Introduction: Washington State Stats
4.5% increase in total accidents from 2004 to 2005
Total annual VMT. Fatal and Disabling Accidents
25%
44%
56%
75%
Two-lane rural highways
Others
6
Introduction: Objective
Analyze causal factors of intersection
accidents
Identify cost-effective solutions for
intersection safety improvements
7
Overview
Introduction
Study Routes and Data
Methodology
Data Analysis
Accident Risk Modeling
Conclusions and Recommendations
8
Study Routes and Data : Collecting
Three sources:
Highway Safety Information System (HSIS)
WSDOT Office of Information Technology
WSDOT online tool, State Route Web (SRWeb)
Six years data ( 1999 -2004)
Roadway data
Accident data
Traffic data
Intersection data
141 state routes
9
Study Routes and Data : preliminary steps
Focus on 3-legged and 4-legged intersections
Classify manually based on SRWeb.
Link intersection file to roadway files:
Roadway characteristic file,
Curvature file
Gradient file
Complicated process not applicable for all
141 state routes select six representative
study routes
10
Study Routes and Data : six study routes
Two criteria
Route length
Geographic location and spatial alignment
Route Length (mile)
SR-02 237.83
SR-12 268.79
SR-20 366.03
SR-21 188.01
SR-97 234.58
SR-101 317.86
11
Overview
Introduction
Study Routes and Data
Methodology
Data Analysis
Accident Risk Modeling
Conclusions and Recommendations
12
Methodology: Data Organization
Intersection approach section:
Decreasing approach
Increasing approach
Xs Xs
Increasing milepost direction
13
Methodology: Data Organization
Determining “intersection section” by using
“Stopping Sight Distance” (SSD):
V2
XS V t
2d
•V = Approach speed, fps ( feet per
second)
•t = Perception/reaction time ( typically
1 sec)
•d = Constant deceleration rate, fps2
(feet per second square)
•t = 1 sec
•d =10 ft/sec2
14
Methodology: Data Organization
Entity-Relationship
(E/R) Diagram
Microsoft SQL
Server are used to
manage and query
data
15
Methodology: Hypothesis testing
Test whether a variable has a significant
impact on accident rate
T-test testing variable has 2 groups
F-test (ANOVA) testing variable has more than
2 groups
16
Methodology: Modeling
Nature of accident data:
Discrete
Non-negative
Randomly distribute
Poisson model
i EXP ( X i )
•λi is the expected accident frequency
•Xi is a vector of explanatory variables
• β is a vector of estimable coefficient
17
Methodology: Modeling
Over-dispersion problem: mean not equal
variance
Negative binomial model:
i EXP ( X i i )
EXP(εi) is a gamma-distributed error term with mean 1 and variance α2
Over-dispersion parameter : select between
Poisson model and negative binomial model
18
Methodology: Modeling
Parameters estimation using log-likelihood
functions:
Poisson model
m
ln L( ) EXP ( X i ) ni xi ln( ni ! )
i 1
Negative binomial model
m ((1 / ) n ) 1 / 1/ i
ni
L(i ) LN i
(1 / )ni ! (1 / ) i (1 / ) i
i 1
•ni: number of accident happened during 6 consecutive study years
•λi:expected accident frequency in 6 years
•: over-dispersion parameter
19
Methodology: Modeling
Goodness of Fit:
The likelihood ratio test statistic is
X 2 2[ LL ( R LL ( U )]
Sum of model deviances
mi
G 2 2 mi LN ( )
ˆ
i
The ρ-statistic
LL ( U )
2 1
LL ( R )
20
Overview
Introduction
Study Routes and Data
Methodology
Data Analysis
Accident Risk Modeling
Conclusions and Recommendations
21
Data Analysis: Preliminary Analysis
Accident by Type on 6 routes
3%
1%
1%
3%
REAR END
4%
27% STRIKE AT ANGLE
5% STRIKE OTHER OBJECT
OVERTURN
7% ANIMAL/BIRD
STRIKE APPURTENCE
FRONT END
8% ROADWAY DICH
SIDESWIPES
RANOVER EMBANKMENT
8% HEAD ON
23%
OTHER
10%
22
Data Analysis: Statistical Analysis t-test
Significant
Variable Groups N Mean t-value p-value
at α=0.05
No 3648 2.14
Control -4.32 0 YES
Yes 114 6.191
Not consistent 1200 2.46
CurvConsist 1.865 0.062 FAIRLY
Consistent 2521 2.16
Curvy 1513 2.423
CurvStraight 1.862 0.063 FAIRLY
Straight 2208 2.143
Zero 3119 2.166
DiffSW Greater than -2.458 0.014 FAIRLY
643 2.732
zero
Less than or
390 1.807
equal to 5%
SlopedB -2.067 0.039 YES
Greater than
3372 2.315
5%
Less than or
SlopedE 390 1.82 -1.995 0.047 YES
equal to 5%
23
Data Analysis: Statistical Analysis t-test
Significant at
Variable Groups N Mean t-value p-value
α=0.05
No 3560 2.321
SlopeFlat 3.9 0 YES
Yes 202 1.224
No 2848 2.085
SlopeVaried -3.322 0.001 YES
Yes 914 2.817
Less than or
equal to 6 2302 2.377
feet
SWA 2.134 0.033 YES
Greater than
1460 2.082
6 feet
Less than or
equal to 6 2303 2.373
feet
SWB 2.061 0.039 YES
Greater than
1459 2.088
6 feet
24
Data Analysis: Statistical Analysis F-test
Group 1 Group 2 Group 3 Group 4
Variable N DOF
(A) (B) (C) (D)
Greater
0-1000 1000- 1500-
RadCurvA than 3000 3720 3
feet 1500 feet 3000 feet
feet
Greater
0-1000 1000- 1500-
RadCurvB than 3000 3720 3
feet 1500 feet 3000 feet
feet
Greater
0-1000 1000- 1500-
RadCurvE than 3000 3720 3
feet 1500 feet 3000 feet
feet
Less than
From 2%- Greater
SlopeChange or equal 3762 2
4% than 4%
to 2%
Less than Greater
From 30-
Splim or equal than 30 3762 2
50 mph
to 30 mph mph
25
Data Analysis: Statistical Analysis F-test
Least Squares Means Least Squares Means
5 5
4 4
ACCRATE
ACCRATE
3 3
2 2
1 1
Significant
0 0
when A B C D A B C D
Variable Fvalue F-crit p-value α<=0.05 RADCURVA
Least Squares Means
RADCURVE
Least Squares Means
RadCurvA 8.737 2.606 0 YES
RadCurvE 4.818 2.606 0 YES 4 3
SlopeChange 10.067 2.999 0 YES
Splim 17.195 2.999 0 YES
3
2
ACCRATE
ACCRATE
2
1
1
0 0
A B C A B C
SLOPECHANGE SPLIM
26
Overview
Introduction
Study Routes and Data
Methodology
Data Analysis
Accident Risk Modeling
Conclusions and Recommendations
27
All-type Accident Risk Modeling
Negative binomial model applied
Over-dispersion parameter is significant
Model:
i 10 8 (6 365 AADT ) EXP ( X i i )
28
All-type Accident Risk Modeling
Result:
Estimated Standard
Variable Parameter error t-statistic P-value Elasticity
Constant 0.6 0.154 3.902 0.000 -
Control 1.018 0.116 8.745 0.000 0.64
SlopeChange 0.33 0.127 2.602 0.005 0.04
Splim 0.378 0.028 13.272 0.000 1.89
SR12 0.133 0.063 2.115 0.035 0.12
SR20 0.192 0.063 3.026 0.003 0.17
SWA -0.397 0.092 -4.307 0.000 -0.2
DegCurvA 0.367 0.058 6.365 0.000 0.05
T4leg -0.355 0.059 -5.997 0.000 -0.43
Featillum 0.159 0.062 2.538 0.011 0.15
Alpha 1.267 0.084 15.038 0.000 -
29
All-type Accident Risk Modeling
Goodness of fit:
Goodness Of Fit Value
LL(β) -4394.61
LL(0) -4547.75
2
ρ 0.03
X2 306.29
G2 19260.91
30
Strike-At-Angle Accident Risk Modeling
Negative binomial model applied
Over-dispersion parameter is significant
Model:
i 10 8 (6 365 AADT ) EXP ( X i i )
31
Strike-At-Angle Accident Risk Modeling
Result:
Estimated Standard
Variable Parameter error t-statistic P-value Elasticity
Constant -0.392 0.256 -1.531 0.000 -
Control 1.135 0.168 6.769 0.005 0.68
Splim 0.331 0.049 6.763 0.000 1.65
SR2 -0.616 0.119 -5.187 0.035 -0.85
SWA -0.346 0.162 -2.137 0.003 -0.18
T4leg -0.895 0.098 -9.16 0.000 -1.45
DiffSW 0.176 0.114 1.542 0.000 0.16
Featillum 0.722 0.109 6.606 0.000 0.51
WallB 1.119 0.506 2.213 0.000 0.67
ALPHA 0.71 0.09 7.929 0.000 -
32
Strike-At-Angle Accident Risk Modeling
Goodness of fit
Goodness Of Fit Value
LL(β) -1769.94
LL(0) -1893.73
2
ρ 0.07
X2 247.59
G2 4014.95
33
Overview
Introduction
Data Processing
Methodology
Data Analysis
Accident Risk Modeling
Conclusions and Recommendations
34
Conclusions:
1. Reduce speed limit at the intersection
2. Put more signage ahead of the intersections
3. Increase shoulder width (greater than 6 feet)
around the intersection area
4. Keep the shoulder width consistent along the
intersection sections
5. Decrease the degree of curvature at the
intersection locations
6. Decrease the slopes (less than 5%) along the
intersection area
35
Recommendations
Negative binomial model is chosen over
Poisson model for modeling accident
frequency
Before-and-after studies on safety at
intersections that have traffic control device
or feature illumination installed are needed
More data:
Crossing roads
Human activity
Detailed intersection layout
36
Ngan Ha Nguyen
nganhanguyen@gmail.com
37
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