Department of Civil Engineering

University of Washington

Quantitative Safety Analysis for Intersections on Washington State Two-

lane Rural Highways

Master’s Thesis DefenseNgan Ha Nguyen

8/15/2007

2

Overview

Introduction Study Routes and Data Methodology Data Analysis Accident Risk Modeling Conclusions and Recommendations

3

Death $3,840,000Incapacitating injury $193,800Nonincapacitating evident injury $49,500Possible injury $23,600No injury $2,200

Average Comprehensive Cost by Injury Severity

Improving traffic safety is an important task

Introduction: Traffic Accidents Traffic accidents are

leading causes of death

Huge economic loss to the society

Leading Causes of U-I Deaths, U.S., 1969-2005

4

Total Crashes in 2003, US.

39%

61%

Fatal Crashes in 2003, US.

75%

25%

Two-lane rural road

Others

Introduction: National Statistics

Rural fatal accident rate is more than twice as high as urban fatal accident rate

5

Fatal Crashes.

28%

72%

Reported Crashes.

45%

55%

Intersection accidents

Others

Introduction: National Statistics

More than 1 death per hour in accidents at intersections

6

Introduction: Washington State Stats

4.5% increase in total accidents from 2004 to 2005

Fatal and Disabling Accidents

56%

44%

Total annual VMT.

25%

75%

Two-lane rural highways

Others

7

Introduction: Objective

Analyze causal factors of intersection accidents

Identify cost-effective solutions for intersection safety improvements

8

Overview

Introduction Study Routes and Data Methodology Data Analysis Accident Risk Modeling Conclusions and Recommendations

9

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

10

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

11

Study Routes and Data : six study routes

Two criteria Route length Geographic location and spatial alignment

Route Length (mile)SR-02 237.83SR-12 268.79SR-20 366.03SR-21 188.01SR-97 234.58

SR-101 317.86

12

Overview

Introduction Study Routes and Data Methodology Data Analysis Accident Risk Modeling Conclusions and Recommendations

13

Methodology: Data Organization

Intersection approach section:

Xs Xs

Increasing milepost direction

Increasing approach

Decreasing approach

14

Methodology: Data Organization

Determining “intersection section” by using “Stopping Sight Distance” (SSD):

d

VtVX S 2

2

•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

15

Methodology: Data Organization

Entity-Relationship (E/R) Diagram

Microsoft SQL Server are used to manage and query data

16

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

17

Methodology: Modeling

Nature of accident data: Discrete Non-negative Randomly distribute

Poisson model

)( ii XEXP •λi is the expected accident frequency•Xi is a vector of explanatory variables • β is a vector of estimable coefficient

18

Over-dispersion problem: mean not equal variance

Negative binomial model:

Over-dispersion parameter : select between Poisson model and negative binomial model

Methodology: Modeling

)( iii XEXP EXP(εi) is a gamma-distributed error term with mean 1 and variance α2

19

Methodology: Modeling

Parameters estimation using log-likelihood functions: Poisson model

Negative binomial model

m

iiii nxinXEXPL

1

)!ln()()(ln

m

i

n

i

i

ii

ii

i

n

nLNL

1

/1

)/1()/1(

/1

!)/1(

))/1(()(

•ni: number of accident happened during 6 consecutive study years

•λi:expected accident frequency in 6 years

: over-dispersion parameter

20

Methodology: Modeling

Goodness of Fit: The likelihood ratio test statistic is

Sum of model deviances

The ρ-statistic

)](([22UR LLLLX

)ˆ

(22 i

ii

mLNmG

)(

)(12

R

U

LL

LL

21

Overview

Introduction Study Routes and Data Methodology Data Analysis Accident Risk Modeling Conclusions and Recommendations

22

Data Analysis: Preliminary Analysis

Accident by Type on 6 routes

27%

23%

10%

8%

8%

7%

5%

4%

3%

1%

1%

3%

REAR END

STRIKE AT ANGLE

STRIKE OTHER OBJECT

OVERTURN

ANIMAL/BIRD

STRIKE APPURTENCE

FRONT END

ROADWAY DICH

SIDESWIPES

RANOVER EMBANKMENT

HEAD ON

OTHER

23

Data Analysis: Statistical Analysis t-test

Variable Groups N Mean t-value p-valueSignificant at α=0.05

No 3648 2.14Yes 114 6.191

Not consistent 1200 2.46

Consistent 2521 2.16Curvy 1513 2.423Straight 2208 2.143Zero 3119 2.166Greater than zero

643 2.732

Less than or equal to 5%

390 1.807

Greater than 5%

3372 2.315

SlopedELess than or equal to 5%

390 1.82 -1.995 0.047 YES

SlopedB -2.067 0.039 YES

DiffSW -2.458 0.014 FAIRLY

CurvStraight 1.862 0.063 FAIRLY

CurvConsist 1.865 0.062 FAIRLY

Control -4.32 0 YES

24

Data Analysis: Statistical Analysis t-test

Variable Groups N Mean t-value p-valueSignificant at

α=0.05No 3560 2.321Yes 202 1.224No 2848 2.085Yes 914 2.817Less than or equal to 6 feet

2302 2.377

Greater than 6 feet

1460 2.082

Less than or equal to 6 feet

2303 2.373

Greater than 6 feet

1459 2.088

SWB 2.061 0.039 YES

SWA 2.134 0.033 YES

SlopeVaried -3.322 0.001 YES

SlopeFlat 3.9 0 YES

25

Data Analysis: Statistical Analysis F-test

VariableGroup 1

(A)Group 2

(B)Group 3

(C)Group 4

(D)N DOF

RadCurvA0-1000 feet

1000-1500 feet

1500-3000 feet

Greater than 3000 feet

3720 3

RadCurvB0-1000 feet

1000-1500 feet

1500-3000 feet

Greater than 3000 feet

3720 3

RadCurvE0-1000 feet

1000-1500 feet

1500-3000 feet

Greater than 3000 feet

3720 3

SlopeChangeLess than or equal to 2%

From 2%-4%

Greater than 4%

3762 2

SplimLess than or equal to 30 mph

From 30-50 mph

Greater than 30 mph

3762 2

26

Data Analysis: Statistical Analysis F-test

Least Squares Means

A B CSPLIM

0

1

2

3

AC

CR

AT

E

Least Squares Means

A B C DRADCURVE

0

1

2

3

4

5

AC

CR

AT

E

Least Squares Means

A B CSLOPECHANGE

0

1

2

3

4

AC

CR

AT

E

Least Squares Means

A B C DRADCURVA

0

1

2

3

4

5

AC

CR

AT

E

Variable Fvalue F-crit p-value

Significant when

α<=0.05RadCurvA 8.737 2.606 0 YESRadCurvE 4.818 2.606 0 YESSlopeChange 10.067 2.999 0 YESSplim 17.195 2.999 0 YES

27

Overview

Introduction Study Routes and Data Methodology Data Analysis Accident Risk Modeling Conclusions and Recommendations

28

All-type Accident Risk Modeling

Negative binomial model applied Over-dispersion parameter is significant Model:

)()3656(10 8iii XEXPAADT

29

All-type Accident Risk Modeling

Result:

VariableEstimated Parameter

Standard error t-statistic P-value Elasticity

Constant 0.6 0.154 3.902 0.000 -Control 1.018 0.116 8.745 0.000 0.64SlopeChange 0.33 0.127 2.602 0.005 0.04Splim 0.378 0.028 13.272 0.000 1.89SR12 0.133 0.063 2.115 0.035 0.12SR20 0.192 0.063 3.026 0.003 0.17SWA -0.397 0.092 -4.307 0.000 -0.2DegCurvA 0.367 0.058 6.365 0.000 0.05T4leg -0.355 0.059 -5.997 0.000 -0.43Featillum 0.159 0.062 2.538 0.011 0.15Alpha 1.267 0.084 15.038 0.000 -

30

All-type Accident Risk Modeling

Goodness of fit:

Goodness Of Fit ValueLL(β) -4394.61LL(0) -4547.75

ρ2 0.03

X2 306.29

G2 19260.91

31

Strike-At-Angle Accident Risk Modeling

Negative binomial model applied Over-dispersion parameter is significant Model:

)()3656(10 8iii XEXPAADT

32

Strike-At-Angle Accident Risk Modeling

Result:

VariableEstimated Parameter

Standard error t-statistic P-value Elasticity

Constant -0.392 0.256 -1.531 0.000 -Control 1.135 0.168 6.769 0.005 0.68Splim 0.331 0.049 6.763 0.000 1.65SR2 -0.616 0.119 -5.187 0.035 -0.85SWA -0.346 0.162 -2.137 0.003 -0.18T4leg -0.895 0.098 -9.16 0.000 -1.45DiffSW 0.176 0.114 1.542 0.000 0.16Featillum 0.722 0.109 6.606 0.000 0.51WallB 1.119 0.506 2.213 0.000 0.67ALPHA 0.71 0.09 7.929 0.000 -

33

Strike-At-Angle Accident Risk Modeling

Goodness of fit

Goodness Of Fit ValueLL(β) -1769.94LL(0) -1893.73

ρ2 0.07

X2 247.59

G2 4014.95

34

Overview

Introduction Data Processing Methodology Data Analysis Accident Risk Modeling Conclusions and Recommendations

35

Conclusions:

1. Reduce speed limit at the intersection2. Put more signage ahead of the intersections3. Increase shoulder width (greater than 6 feet)

around the intersection area 4. Keep the shoulder width consistent along the

intersection sections5. Decrease the degree of curvature at the

intersection locations

6. Decrease the slopes (less than 5%) along the intersection area

36

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

37

Ngan Ha Nguyen

nganhanguyen@gmail.com