1 Introduction
2 Study sites and datasets
2.1 Study sites
2.2 Segmentation of facility types
Facility type | No. of segments | Total length (km) |
---|---|---|
Basic segment | 38 | 56.6 |
Merge segment | 28 | 20.9 |
Diverge segment | 35 | 25.2 |
Sharp curve | 9 | 2.5 |
3 Methodology
3.1 Data extraction
3.1.1 Detector data
3.1.2 Geometric features
Route no. | Direction* | Kilopost** | h (m) | H (m) | S (m) | ISD (m2) |
---|---|---|---|---|---|---|
1 | SB | 0.0 | −4.63 | 5.49 | 0.78 | 4.30 |
1 | SB | 0.1 | −7.90 | 8.49 | 3.91 | 33.2 |
1 | SB | 0.2 | −10.6 | 11.5 | 6.08 | 69.9 |
1 | SB | 0.21 | −11.5 | 11.8 | 8.88 | 104.7 |
1 | SB | 0.3 | −15.3 | 15.3 | 9.60 | 146.9 |
1 | SB | – | – | – | – | – |
1 | SB | 6.4 | 10.2 | 10.9 | 5.15 | 56.1 |
3.1.3 Ambient conditions
3.1.4 Data matching
Crash ID | Traffic characteristics | Geometric features | Ambient conditions | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
q (veh/5 min) | v (km/h) | MR | DR | Facility typea | h (m) | H (m) | ICF (km3/h2) | ISD (m2) | L
A
b
(m) | L
D
b
(m) | Light | Weather | Pavement | Day type | |
1 | 139 | 88.7 | – | – | B | 1.5 | 1.5 | 0 | 0 | – | – | Day | Sunny | Dry | Holiday |
2 | 96 | 95.0 | – | 0.02 | D | 0.5 | 1.3 | 302 | 45 | – | 220 | Day | Sunny | Dry | Weekday |
3 | 29 | 80.3 | – | – | S | 10.3 | 12.7 | 126 | 249 | – | – | Night | Cloudy | Wet | Holiday |
4 | 154 | 82.9 | 0.07 | – | M | 1.5 | 1.5 | 0 | 0 | 200 | – | Day | Cloudy | Dry | Weekday |
3.2 Classification of traffic conditions
3.3 Calculation of crash rate (CR)
3.4 Principal component analysis (PCA)
4 Crash rate estimation models
4.1 Uncongested flow
Paired | t-Value | df | Sig. |
---|---|---|---|
Pair 1: basic and merge segments | −2.781 | 5 | 0.019 |
Pair 2: basic and diverge segments | −1.070 | 5 | 0.310 |
Pair 3: merge and diverge segments | 2.320 | 5 | 0.043 |
Facility type | Sample size | Modela |
---|---|---|
B | 319 crashes | CR = 6.81 × 10−4k2−3.23 × 10−2k + 0.541, R2 = 0.998, k(CRmin) = 24 |
M | 25 l crashes | CR = 2.55 × 10−3k2−9.29 × 10−2k + 1.01, R2 = 0.983, k(CRmin) = 20 |
D | 204 crashes | CR = 5.68 × 10−4k2−3.34 × 10−2k + 0.747 R2 = 0.849 k(CRmin) = 28 |
S | 513 crashes | CR = 132.2k−0.983, R2 = 0.992 |
4.2 Congested flow
Paired | t-Value | df | Sig. |
---|---|---|---|
Pair 1: basic and merge segments | −2.448 | 4 | 0.092 |
Pair 2: basic and diverge segments | −0.153 | 4 | 0.888 |
Pair 3: merge and diverge segments | 0.325 | 4 | 0.767 |
Facility type | Sample size | Model |
---|---|---|
B + M + D | 513 crashes | CR = 4.87 × 10−1e0.0155k R2 = 0.924 |
5 Effects of influencing factors
5.1 Introduction of variables
Variables | Statisticsa | Description | |
---|---|---|---|
Max. | Min. | ||
k
| 238 | 0 | Traffic density (veh/km) |
v
| 141.0 | 4.7 | Average speed (km/h) |
MR | 0.78 | 0.00 | Merging ratio |
DR | 0.60 | 0.00 | Diverging ratio |
I
CF
| 1997 | 0.1 | Index of centrifugal force (km3/h2) |
h
| 14.8 | 0.1 | Vertical variation (m) |
I
SD
| 1112.7 | 0.0 | Index of space displacement (m2) |
L
A
| 250 | 100 | Length of acceleration lane (m) |
L
D
| 432 | 100 | Length of deceleration lane (m) |
Pave | f(1) = 27.7 % | Equal to 1 if wet pavement, 0 otherwise | |
Light | f(1) = 27.1 % | Equal to 1 if nighttime, 0 otherwise | |
Day | f(1) = 29.4 % | Equal to 1 if holiday, 0 otherwise |
5.2 PCA among various facility types
5.2.1 Low-density uncongested flow
Variables | Component | |||
---|---|---|---|---|
1st | 2nd | 3rd | 4th | |
k
e
| −0.194 | −0.852 | −0.119 | 0.103 |
v
| 0.285 | 0.182 |
0.798
| −0.086 |
I
CF
|
0.953
| 0.005 | 0.053 | −0.122 |
I
SD
|
0.959
| 0.011 | −0.044 | 0.090 |
h
| 0.119 | 0.149 | 0.228 |
0.973
|
Pave | 0.294 | 0.214 |
0.783
| −0.095 |
Day | 0.139 | 0.093 | 0.190 | −0.468 |
Light | −0.164 |
0.838
| −0.130 | 0.143 |
Initial Eigenvalue | 2.12 | 1.54 | 1.37 | 1.12 |
Percent of variance | 30.3 | 20.2 | 18.2 | 15.1 |
Cumulative Percent | 30.3 | 50.5 | 68.7 | 83.8 |
Facility type (number of crash) | Item | Principal component | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
1st | 2nd | 3rd | 4th | 5th | |||||||
F | L | F | L | F | L | F | L | F | L | ||
Basic segment (225) | Component |
I
CF
| 0.953 |
k
| −0.852 |
v
| 0.798 |
h
| 0.973 | ||
I
SD
| 0.959 | Light | 0.838 | Pave | 0.783 | ||||||
Percent of variance | 30.3 | 20.2 | 18.2 | 15.1 | |||||||
Merge segment (140) | Component |
I
CF
| 0.867 |
k
| −0.841 | MR | 0.808 |
v
| 0.721 | Day | 0.874 |
I
SD
| 0.901 | Light | 0.869 |
L
A
| 0.747 | Pave | 0.742 | ||||
Percent of variance | 20.1 | 18.8 | 15.4 | 13.9 | 11.9 | ||||||
Diverge segment (167) | Component | DR | 0.807 |
I
CF
| 0.948 |
k
| −0.807 |
v
| 0.892 |
L
D
| 0.797 |
h
| 0.845 |
I
SD
| 0.746 | Light | 0.860 | Pave | 0.848 | ||||
Percent of variance | 18.9 | 17.6 | 16.2 | 15.3 | 13.3 | ||||||
Sharp curve (319) | Component |
I
SD
| 0.854 |
I
CF
| 0.948 |
k
| −0.820 | Pave | 0.929 | Day | 0.981 |
h
| 0.978 |
v
| 0.753 | Light | 0.794 | ||||||
Percent of variance | 23.7 | 17.5 | 16.4 | 13.6 | 12.7 |
5.2.2 High-density uncongested flow
Facility type (number of crash) | Item | Principal component | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
1st | 2nd | 3rd | 4th | 5th | |||||||
F | L | F | L | F | L | F | L | F | L | ||
Basic segment (94) | Component |
I
CF
| 0.983 |
k
| 0.858 | Day | 0.776 |
h
| 0.925 | ||
I
SD
| 0.974 |
v
| −0.885 | Light | 0.781 | ||||||
Percent of variance | 28.9 | 21.8 | 17.1 | 14.4 | |||||||
Merge segment (112) | Component | MR | 0.818 |
k
| 0.936 |
L
A
| 0.842 | Day | 0.810 | Pave | 0.963 |
I
CF
| 0.923 |
v
| −0.899 | Light | 0.713 | ||||||
I
SD
| 0.960 | ||||||||||
Percent of variance | 28.3 | 18.0 | 13.5 | 12.3 | 10.4 | ||||||
Diverge segment (37) | Component |
I
CF
| 0.970 | DR | 0.904 |
k
| 0.793 |
h
| 0.733 | Pave | 0.913 |
I
SD
| 0.977 |
L
D
| 0.772 |
v
| −0.704 | ||||||
Percent of variance | 21.8 | 19.8 | 16.8 | 13.7 | 13.5 | ||||||
Sharp curve (122) | Component |
I
CF
| 0.723 |
k
| −0.901 | Pave | 0.901 | Day | 0.869 | ||
I
SD
| 0.962 |
v
| 0.872 | ||||||||
h
| 0.908 | ||||||||||
Percent of variance | 33.2 | 21.9 | 15.3 | 13.9 |
5.2.3 Congested flow
Facility type (number of crash) | Item | Principal component | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
1st | 2nd | 3rd | 4th | 5th | |||||||
F | L | F | L | F | L | F | L | F | L | ||
Basic segment (138) | Component |
k
| 0.950 |
I
CF
| 0.842 |
h
| 0.699 | Day | 0.942 | ||
v
| −0.947 |
I
SD
| 0.743 | Pave | 0.814 | ||||||
Percent of variance | 26.0 | 20.3 | 18.9 | 15.4 | |||||||
Merge segment (91) | Component | MR | 0.871 |
k
| 0.883 |
I
CF
| 0.672 |
L
A
| −0.871 | Day | −0.933 |
h
| 0.790 |
v
| −0.884 | Light | 0.745 | Pave | 0.716 | ||||
I
SD
| 0.825 | ||||||||||
Percent of variance | 22.1 | 18.3 | 14.6 | 13.9 | 10.1 | ||||||
Diverge segment (48) | Component |
k
| 0.868 |
I
CF
| 0.849 | DR | 0.854 | Pave | 0.721 | Light | 0.951 |
v
| −0.801 |
I
SD
| 0.879 |
L
D
| −0.783 | Day | −0.716 | ||||
h
| 0.859 | ||||||||||
Percent of variance | 21.9 | 19.6 | 15.4 | 13.8 | 11.6 | ||||||
Sharp curve (27) | Component |
k
| −0.772 |
I
CF
| 0.909 | Pave | 0.799 | Day | 0.912 | ||
v
| 0.950 |
I
SD
| 0.875 | 0.949 | |||||||
h
| 0.971 | Light | |||||||||
Percent of variance | 30.5 | 26.6 | 22.5 | 11.1 |