# Quantitative Safety Analysis for Intersections on Washington State

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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
death
 Huge economic loss
to the society
   Improving traffic
safety is an                                Average Comprehensive Cost by Injury Severity

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%

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)
   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.
   Curvature 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
SIDESWIPES
RANOVER EMBANKMENT
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-
feet      1500 feet 3000 feet
feet
Greater
0-1000    1000-     1500-
feet      1500 feet 3000 feet
feet
Greater
0-1000    1000-     1500-
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
Least Squares Means
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:
   Human activity
   Detailed intersection layout

36
Ngan Ha Nguyen
nganhanguyen@gmail.com

37

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