- Email: [email protected]
Multi-scale traffic safety and operational performance study of large trucks on mountainous interstate highway
Accident Analysis and Prevention 43 (2011) 429–438
Contents lists available at ScienceDirect
Accident Analysis and Prevention journal homepage: www.elsevier.com/locate/aap
Multi-scale traffic safety and operational performance study of large trucks on mountainous interstate highway Suren Chen ∗ , Feng Chen, Jun Wu Dept. of Civil & Environmental Eng., Colorado State University, Fort Collins, CO 80523, United States
a r t i c l e
i n f o
Article history: Received 26 January 2010 Received in revised form 8 September 2010 Accepted 27 September 2010 Keywords: Mountainous highway Large trucks Single-vehicle accident Multi-vehicle accident Multi-scale
a b s t r a c t In addition to multi-vehicle accidents, large trucks are also prone to single-vehicle accidents on the mountainous interstate highways due to the complex terrain and fast-changing weather. By integrating both historical data analysis and simulations, a multi-scale approach is developed to evaluate the traffic safety and operational performance of large trucks on mountainous interstate highways in both scales of individual vehicle as well as traffic on the whole highway. A typical mountainous highway in Colorado is studied for demonstration purposes. Firstly, the ten-year historical accident records are analyzed to identify the accident-vulnerable-locations (AVLs) and site-specific critical adverse driving conditions. Secondly, simulation-based single-vehicle assessment is performed for different driving conditions at those AVLs along the whole corridor. Finally, the cellular-automaton (CA)-based simulation is carried out to evaluate the multi-vehicle traffic safety as well as the operational performance of the traffic by considering the actual speed limits, including the differential speed limits (DSL) at some locations. It is found that the multi-scale approach can provide insightful and comprehensive observations of the highway performance, which is especially important for mountainous highways. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction Extensive works have been conducted on the traffic safety and injury prevention related to multi-vehicle accidents of large trucks in past decades (e.g. Braver et al., 1997; Chang and Mannering, 1999; Lyman and Braver, 2003). Different from most passenger vehicles which are dominantly vulnerable to multi-vehicle traffic conflicts, large trucks are also prone to single-vehicle accidents on the mountainous interstate highways due to the complex terrain and fast-changing weather (USDOT, 2005; Baker, 1991). Although the absolute number of single-vehicle accidents is typically smaller than that of multi-vehicle accidents, single-vehicle accidents have caused serious injury and casualty (The National Academies, 2006). For example, single-vehicle accidents were responsible for 57.8% of the total fatalities of traffic accidents in 2005 (USDOT, 2005). This is especially true when complex terrain couples with inclement weather conditions, such as snow, ice or strong wind. Each year in the United States, adverse weather alone is associated with more than 1.5 million vehicular accidents, which result in 800,000 injuries and 7000 fatalities (The National Academies, 2006).
∗ Corresponding author. Tel.: +1 970 491 7722; fax: +1 970 491 7727. E-mail address: [email protected] (S. Chen). 0001-4575/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.aap.2010.09.013
The primary causes of accidents involving large trucks on rural highways were found to be excessive speed and adverse driving conditions (The Road Information Program, 2005). Different from passenger vehicles, it is known that the safety performance of large trucks in adverse driving conditions greatly depends on the specific terrain and local weather condition (USDOT, 2005; Baker, 1991). To accommodate the considerable difference on safety performance of large trucks and common passenger vehicles, differential speed limits (DSL) have been applied in many highways for large trucks at locations where the driving conditions are not ideal. There are, however, mixed opinions on the benefits of DSL to the traffic safety and operational performance, which highly depend on the specific geometric, traffic and environmental conditions (FHWA, 2004). As a matter of fact, there is not yet compelling evidence to support more widespread applications of DSL instead of universal speed limits (USL), and neither is strong evidence that DSL should be eliminated (Garber et al., 2006; Awadallah, 2007; Harkey et al., 1990). On one hand, the lower speed limits for large trucks may reduce the risk of single-vehicle accidents. On the other hand, the differential driving speeds for trucks and other vehicles, if not reasonable, may also cause additional risks of traffic conflicts between large trucks and other vehicles and/or traffic congestions. Therefore, it is necessary to comprehensively evaluate the safety and operational performance of large trucks on a mountainous highway by looking into not only the safety of individual trucks, but also the impacts to the whole traffic on the highway.
430
S. Chen et al. / Accident Analysis and Prevention 43 (2011) 429–438
In the present study, an attempt is made to integrally evaluate the safety and operational performance of large trucks on mountainous highways at both scales of individual vehicle and whole traffic flow. The I-70 corridor in Colorado is chosen to demonstrate the methodology because of its typical mountainous terrain and adverse weather conditions. Firstly, ten-year historical accident records will be analyzed to identify the accidentvulnerable-locations (AVLs) and critical adverse driving conditions specific to I-70. Secondly, simulation-based single-vehicle assessment will be performed for different inclement weather conditions at these AVLs along the whole corridor. The advisory critical vehicle speeds (CVS) will be compared to the corresponding speed limits along the highway to give some insights about single-vehicle safety performance of large trucks. Finally, the cellular-automaton (CA)based multi-vehicle accident simulation (Nagel and Schreckenberg, 1992; Moussa, 2005) will be carried out to evaluate the impacts on traffic safety and operational performance of the whole highway by considering the actual speed limits, including DSL at some locations. 2. Simulation-based analytical models Extensive works have been carried out on both multi- (USDOT, 2005) and single-vehicle accidents (Young and Liesman, 2007a,b; Summerfield and Kosior, 2001; Edwards, 1998) with a focus on data analyses of historical accidents. In addition to analyses based on historical data, there were also studies using various simulation models on multi-vehicle traffic conflicts (Moussa, 2005; Zhang et al., 2006) as well as single-vehicle accidents (Baker, 1991; Chen and Cai, 2004; Guo and Xu, 2006). Compared to data-based accident analyses, simulation-based analyses of multivehicle or single-vehicle accidents have the advantage of exploring more comprehensive collections of possible scenarios, which may not be covered by the historical accident data (Baker, 1991; Snaebjornsson et al., 2007; Chen et al., 2009). In this section, the simulation-based evaluation models of single-vehicle safety and multi-vehicle safety as well as operational performance which will be used in the present study are briefly introduced in the following. 2.1. Simulation-based assessment model of single-vehicle accidents The single-vehicle simulation model recently developed by the writers (Chen and Chen, 2010, 2009) will be used to evaluate the vehicle safety at the selected vulnerable locations. In order to provide essential background information, the simulation model is briefly introduced below (Chen and Chen, 2010). For a typical vehicle, the sprung mass rotates about the roll center which is dependent on the kinematical properties of the suspensions. The unsprung masses can rotate with the vertical compliance of the tires. Five force and moment equilibrium equations of vehicle motions of sprung mass, unsprung masses and suspensions in y and z directions are defined in Eqs. (1)–(5) (Chen and Chen, 2010). ¨ = mV (ˇ˙ + ˙ ) − Fy,f − Fy,r + Fw,y − mg + may ms h
(1)
¨ + Iz z ¨ = Fy,f af + Fy,r ar + Mz −Ix z
(2)
¨ − Ix z ¨ = ms gh + ms Vh(ˇ˙ + ˙ ) + Mx − ms gh + ms gay Ix x + Fw,y hw − kf ( − t,f ) − lf (˙ − ˙ t,f ) + uf − kr ( − t,r ) − lr (˙ − ˙ t,r ) + ur
(3)
rFy,f = −mu,f V (hu,f − r)(ˇ˙ + ˙ ) + mu,f g(hu,f − r)t,f + mu,f g(hu,f − r) −
aroll Ix x mf m
− mu,f ay (hu,f − r) + kt,f t,f
− kf ( − t,f ) − lf (˙ − ˙ t,f ) + uf
(4)
rFy,r = −mu,r V (hu,r − r)(ˇ˙ + ˙ ) + mu,r g(hu,r − r)t,r + mu,r g(hu,r − r) −
aroll Ix x mr − mu,r ay (hu,r − r) m
+ kt,r t,r − kr ( − t,r ) − lr (˙ − ˙ t,r ) + ur
(5)
where the subscripts r and f refer to the rear and front axles, respectively. Fw,y , Mx , Mz are lateral wind force, wind-induced roll moment and yaw moment, respectively. is road superelevation. ay and aroll are accelerations in the lateral (y) direction and the rolling direction of the supporting infrastructures (e.g. pavement or bridge), respectively. m, ms , mu are the total mass, sprung mass and unsprung mass, respectively. h is the height of the center of sprung mass. r and hu are the heights of rolling center and unsprung mass center. Fy,f and Fy,r are lateral forces of front and rear tires, respectively. Ix x , Ix z , Iz z are the roll moment, yaw-roll product and yaw moment of inertia of sprung mass, respectively. k, kt , l are roll stiffness of suspension, roll stiffness of tire and roll damping rate of suspension, respectively. and t are absolute roll angle of sprung mass and unsprung mass, respectively. ˇ and are sideslip angle and heading angle, respectively. u is active roll torque. The dynamic models as introduced in Eqs. (1)–(5) are used when the wheels are not lifted up or sideslip. The dynamic simulation of the whole process of an accident involves series of vehicle dynamic simulation models for different stages of the accident, such as before/after wheels being lifted up, before/after wheels starting to slide (Chen and Chen, 2010). At any time step of the simulation, the corresponding criterion will be checked to decide whether the wheels have been lifted up or sideslip has occurred. When any of these scenarios is identified to occur, the corresponding new set of dynamic equations, which consider the specific dynamic nature and restraints, will be adopted to continue the simulation (Chen and Chen, 2010). As a result, the transient process of the overturn and sideswipe accidents can be simulated in a more rational way and more details can be found in Ref. Chen and Chen, 2010. For any given driving condition as well as specific vehicle conditions, the occurrence of single-vehicle accidents will be evaluated at each driving speed. The simulation process continues by gradually increasing driving speeds until any single-vehicle accident occurs. As a result, the advisory critical vehicle speed (CVS) for a specific combination of environmental and vehicular conditions is the highest allowable driving speed under which no single-vehicle accident is likely to happen (Chen and Chen, 2010). 2.2. Multi-vehicle accident risk assessment using cellular automaton model The Cellular Automaton (CA) model proposed by Nagel and Schreckenberg (1992) is an efficient tool to study the operational performance of traffic flow and traffic safety in a microscopic scale (Moussa, 2005; Zhang et al., 2006). The major strength of the CA model is the robustness for different intricate features of traffic flow (Nagel and Schreckenberg, 1992). As a probabilistic microscopicscale traffic flow simulation tool, the CA-model can provide detailed time-variant information of individual vehicles. The basic features of the CA model are as follows (Nagel and Schreckenberg, 1992): (1) each lane is divided into cells with an equal length; (2) each cell is empty or occupied by one vehicle at
S. Chen et al. / Accident Analysis and Prevention 43 (2011) 429–438
a time; (3) the instantaneous speed of a vehicle can be decided by the number of cells the vehicle can move in each time step; (4) the maximum velocity a vehicle can reach is defined by the actual speed limit of that particular stretch of the highway. At each time step, a vehicle moves, accelerates, decelerates or changes lanes based on specific rules established according to the actual traffic rules and some reasonable assumptions of the driver behavior (Nagel and Schreckenberg, 1992; Wu and Chen, 2009). For example, a driver is typically believed to have the intention to achieve the maximum driving speed without violating traffic rules (Nagel and Schreckenberg, 1992). When the conditions presented below are satisfied, the multilane CA model is implemented (Rickert et al., 1996; Li et al., 2006): (1) the distance between Vehicle i and the vehicle ahead on the same lane is smaller than v + 1, where v is the vehicle velocity; (2) the distance between Vehicle i and the vehicle ahead on the target lane is more than v + 1; (3) the distance between Vehicle i and the back vehicle on the target lane is more than vmax , which is the maximum velocity a vehicle is allowed to achieve; (4) with the probability of pch, Vehicle i changes the lane if all the three above conditions are satisfied. If Vehicle i changes lane, its location and the velocity will be updated through two sub-steps: (1) Vehicle i moves to the target lane transversely without advancing; (2) Vehicle i moving forward to the target lane obeys the single-lane rule (Nagel and Schreckenberg, 1992). In the multi-lane CA accident model, two types of accidents are considered. Type I is that caused by the rear-end collision between two successive vehicles moving on the same lane; Type II is that caused by lane-changing of the successive vehicles. Two parameters are introduced to define the accident-prone conditions: the delayed reaction time () of the following vehicle and the deceleration limit (vd ) of the ahead vehicle. The prerequisites of Type I accident can be expressed as follows (Moussa, 2005): 1) The vehicle ahead of Vehicle k decelerates abruptly:
vk+1 (t + 1) − vk+1 (t) ≥ vd
(6)
2) Vehicle k cannot brake during the delayed reaction time period () to avoid a crash: vk (t) − vk+1 (t + 1) > gk (t)
(7)
where gk (t) is the distance between Vehicle k and Vehicle k + 1 at time step t. For Type II accidents, it is assumed that all the drivers obey the traffic rules when they change lanes, for example, keeping the safe distance. When two successive vehicles change to the same target lane simultaneously, the crash may occur as the front vehicle automatically ignores the gap behind because it just focuses on the gap with the vehicles on the target lane (Moussa, 2005). 3. Historical accident data analysis of I-70 in Colorado 3.1. I-70 interstate corridor The Interstate I-70 Mountain Corridor within the State of Colorado, from Denver to Grand Junction is a typical mountainous highway in rural areas as it is a gateway to recreation, commerce and everyday necessities for Colorado residents and visitors. At some locations along the corridor, very steep grades which are coupled with extreme weather conditions have been blamed for many accidents involving large trucks. Differential speed limits have been adopted at several locations where the terrains are complicated on the I-70 mountain corridor. Ten-year (1996–2005) historical accident data of I-70 in Colorado from Vail to Golden (Mile Post
431
179.90–258.60) were studied. The percentage of trucks in traffic is 5.7–13% on this corridor in Year 2005. Average daily traffic (ADT) on I-70 in Colorado is 32,962. During the ten-year period, there were totally 1565 accidents reported, out of which 762 and 639 accidents involved large trucks/bus as the first vehicle (Vehicle 1) and the second vehicle (Vehicle 2), respectively. 3.2. Data analysis and accident vulnerable locations (AVLs) Based on the comprehensive analysis of the historical accident data on I-70 corridor between 1996 and 2005, some accident vulnerable locations (AVLs) experiencing a considerable number of past accidents are summarized in Table 1. AVLs are selected based on the number of accidents occurring on each segment (typically 0.1 mile long), which is identified with the beginning and ending mileposts (MP) (e.g. MP 184.4–185.4). Due to the limit of the space, Table 1 only gives detailed information for several selected AVLs, including the mileposts (MP), the numbers of accidents associated with different vehicle types, accident types, geometric conditions, speed limits and adverse weather conditions. Most differential speed limits on I-70 are applied in the westbound direction, as shown in column 4 in Table 1. “No. of truck-initiated accidents (% of all accidents)” (column 5) is the number (and percentage) of accidents with large trucks (more than 10k lbs) as the first vehicle (Vehicle 1). Column 6 shows the number of accidents occurring at different adverse road surface conditions (e.g. wet, icy or snowy). Column 7 gives the number of the accidents by accident type: single-vehicle accidents, including overturn and sideswipe accidents, and typical multi-vehicle accidents (rear-end accidents). By comparing the actual driving speeds reported in the accident record with the corresponding speed limits, the percentage of those trucks with the driving speeds at least 10 mph over the speed limits in the truck-initiated accidents was given in Column 8. Some general observations from the accident data analysis of I70 AVLs include: (1) trucks were more vulnerable to accidents than other vehicles (around 50–70% of all accidents were initiated by trucks); (2) for multiple-vehicle accidents, rear-end collisions were dominant (over 80%); (3) adverse road surface conditions were found to have significant impacts on traffic safety (associated with up to 70% accidents); and (4) dominant accident types at different locations were sideswipe or overturn accidents (single-vehicle), rear-end accidents (multi-vehicle) or both. Based on these observations, the need and significance of the present study focusing on trucks and adverse driving conditions are well justified. 3.3. Accident analysis under adverse driving conditions Historical accidents are firstly studied for different adverse driving conditions, such as windy, snowy, icy conditions of road surface and different terrains. Among all the adverse driving conditions, Figs. 1–3 give the statistics of historical accidents involving trucks under several most significant adverse driving conditions on I-70, including strong wind, snow-covered, ice-covered road surface and on grades, respectively. Different sizes of the dots on the maps represent different numbers of similar accidents happening at the same locations during the past ten years, as defined in the legend. It is found in Fig. 1 that there are about 30 accidents identified as wind-induced ones in the accident records during the ten-year period. It is noted that the actual number may be higher since it is possible that some accidents were not identified as windinduced ones on the accident report despite the fact that wind may also contribute to the accidents along with other reported factors. According to Fig. 1, except for some scattered locations along I-70, most of the wind-induced accidents happened in the east portion of the corridor. Repetitive accidents happened at several locations along I-70, such as MP 229, 244, and 250–252.
432
S. Chen et al. / Accident Analysis and Prevention 43 (2011) 429–438
Table 1 Selected accident vulnerable locations (AVLs) on I-70 (1996–2005). (1) Milepost range
(2) Terrain features
(3) Grade
(4) Speed limit (mph)
(5) No. of truck-initiated accidents (% of all accidents)
(6) No. of accidents under adverse road surface conditions
(7) Accident types
184.4–185.4
Curve R = 1250 ft
6%
Truck 45 Others 65
24 (64.9%) EB3, WB21
Wet 2 Icy 13 Snowy 7 Wet 3 Icy 4 Snowy 2 Wet 1 Icy 2 Snowy 5 Wet 3 Icy 3 Snowy 12 Wet 3 Icy 5 Snowy 1 Wet 6 Icy 5 Snowy 1 Wet 2 Icy 3 Snowy 2
Overturn 0 Sideswipe 11 Rear-end 7 Overturn 0 Sideswipe 5 Rear-end 4 Overturn 8 Sideswipe 8 Rear-end 12 Overturn 0 Sideswipe 12 Rear-end 10 Overturn 8 Sideswipe 5 Rear-end 2 Overturn 15 Sideswipe 11 Rear-end 7 Overturn 1 Sideswipe 4 Rear-end 2
204.8–205.14
208.0–209.3
213.0–214.0
242.5–242.92
243.4–244.7
250.8–251.2
Curve R = 2130 ft
Straight
Straight
Curve R = 690 ft
Curve R = 850 ft
Curve R = 1540 ft
8%
8%
8%
4%
4%
3%
Truck 30 Others 60
Truck 30 Others 60
Truck 30 Others 60
All 55
All 55
All 65
13 (56.5%) EB6, WB7 36 (69.2%) EB2, WB34 19 (48.7%) EB7, WB12 18 (69.3%) EB12, WB6 44 (70.3%) EB28, WB16 7 (58.3%) EB0, WB7
(8) Percentage of trucks over speed limits by 10 mph or more
8.3%
38.5%
86.1%
0%
33.3%
22.2%
0%
Note: EB = east bound vehicles; WB = west bound vehicles; R = curve radius.
Fig. 2 shows the historical accidents happening on snowcovered roads. A large number of repetitive accidents happened frequently along the whole stretch between MP 182 and 228. The accidents happening on curves with grades are also studied (Fig. 3).
It can be found that the most vulnerable locations identified in Fig. 2 (snowy road) are similar to those shown in Fig. 3 (on grades). It is understandable since both scenarios cause challenges for the truck drivers to stop efficiently.
Fig. 1. Historical wind-induced accidents (1996–2005).
S. Chen et al. / Accident Analysis and Prevention 43 (2011) 429–438
433
Fig. 2. Historical accidents on snow-covered road surface (1996–2005).
As shown in Fig. 3, MP 242–248 suffered from frequent accidents because of the well-known steep grades (6%) which are coupled with sharp curves. Based on the observations from Figs. 2 and 3, it is obvious that both the road surface condition and the road geometric condition (e.g. grade and curves) have large impacts on the accident risk for trucks. The similarities between the observations in Figs. 2 and 3 suggest that such two critical conditions (i.e. roadsurface and geometric) work interactively to pose threats on the safety of trucks under adverse driving environments. Given the fact that the complex terrain is common throughout the I-70 corridor in Colorado, the historical accidents on snow-covered road surface and grade curves were found to occur in nearly all the portions of the whole corridor with a comparatively higher number of accidents on the western part.
4. Single-vehicle traffic safety under adverse weather The data analyses of the historical accidents in the last section identified several AVLs and the critical adverse driving conditions. In this section, with the single-vehicle accident simulation model introduced earlier, more comprehensive simulations of singlevehicle accidents under different adverse driving conditions are conducted along the whole I-70 corridor including those identified AVLs. As a result, different advisory critical vehicle speeds (CVS) are obtained under various weather and road surface conditions such as: (1) windy conditions (U = 30 mph (13.4 m/s)); (2) snow storm (U = 30 mph and snow-covered road); or (3) icy storm (U = 30 mph and icy road). The results from the simulation will be compared with the observations from the data analysis of historical accidents.
In the following Figs. 4–6, the x-axis shows different milepost numbers along I-70. The y-axis is the dimensionless variable—the ratio between the critical vehicle speed (CVS) identified from the simulation and the corresponding posted speed limit at the same spot. The ratio of the “critical vehicle speed/speed limit” (called “speed ratio” for brevity purpose hereafter) as shown in Figs. 4–6 is not a variable intended to rigorously quantify the effectiveness or rationality of the posted speed limits for the adverse driving conditions. Rather, the speed ratio is only used to provide qualitative information about (1) the relationship between the CVS and the corresponding speed limit at the same location, and (2) the relative risk of single-vehicle accidents at different locations along the I-70. It is made possible by comparing the speed ratio and unit at one location, and the speed ratios at different locations. The CVS in windy conditions (U = 30 mph) for a typical truck along the I-70 is identified considering the corresponding geometric condition for each segment along I-70 and the results are displayed in Fig. 4. It is known that 30 mph wind speed is pretty common for mountainous highways, especially during winter and spring seasons. As shown in Fig. 4, there are several locations with relatively low speed ratios, such as MP 244, MP 250–252. As compared to the historical accident results, these locations with lower speed ratios were also identified as AVLs in Table 1 as well as in Fig. 1. Pretty good correlations between the simulation results and the historical accident records can be found for most of the locations studied as displayed in Fig. 1. There is, however, one location (MP 198) which seems pretty vulnerable to single-vehicle accidents according to the simulation results in Fig. 4, while this observation is not well supported by the historical accident records (Table 1 and Fig. 1). It is possibly because that the unique terrain or sur-
434
S. Chen et al. / Accident Analysis and Prevention 43 (2011) 429–438
Fig. 3. Historical accidents on grade curves (1996–2005).
rounding near MP 198 may improve the actual wind condition from the theoretical one. This observation underscores the importance of collecting site-specific wind and other environmental data for those locations with complex terrain or surroundings (Chen et al., 2010). One possible option is to use the mobile mapping technology to collect the site-specific wind and environmental data (Chen et al., 2010). A detailed investigation of this particular location involves significant data collection, which is beyond the scope of the present study.
Fig. 5 gives the CVS results on I-70 under snow storms (i.e. the road surface is covered by snow and the wind speed equals to 30 mph). It can be found that there are several locations with the speed ratios considerably lower than 1, such as MP 182–184, MP 250–252. Such a phenomenon observed from the simulation results is generally consistent with the historical accident records as shown in Table 1 and Fig. 2, except for MP 205–213. In Fig. 5, the speed ratios are all above 1 between MP 205–213, which seem to contradict with the fact as shown in Fig. 2 that there were many
Fig. 4. Critical vehicle speed ratio of different mileposts in windy conditions (U = 30 mph).
Fig. 5. Critical vehicle speed ratio of different mileposts in snowstorm (U = 30 mph and snow).
S. Chen et al. / Accident Analysis and Prevention 43 (2011) 429–438
435
Table 2 Parameters of CA traffic model. Parameters
Value
Description
Lc dt pb pch
7.5 m 1s 0.5 0.8 1s 2 cell 20%
Length of each cell The period of every time step The probability of braking The probability of changing lane The delayed reaction time Deceleration limit The percentage of heavy vehicle among all the types of vehicles
vd Ch
fore, it is not straightforward to tell which situation (i.e. fully loaded or partially loaded) is more vulnerable to single-vehicle accidents without a specific and detailed analysis. The single-vehicle simulation model (Chen and Chen, 2010) can be used to conduct a detailed analysis on a case-by-case basis. Fig. 6. Critical vehicle speed ratio of different mileposts in cold winter season (U = 30 mph and icy road).
5. Traffic safety and operational performance of whole traffic with DSL
accidents happening during snowy conditions in that region. It is known that MP 208–213 involves very steep grades with the speed limits of 30 mph for trucks and 60 mph for other vehicles. A closer look of Table 1 discloses that for MP 204–209, 38.5–86.1% of those trucks which were involved in the accidents were actually driven at speeds at least 10 mph (16.1 km/h) higher than the speed limits according to the accident records. With the assumption that most large trucks were driven in speeds close to the posted speed limits, the speed ratios used in the present study were usually found to provide pretty accurate information about single-vehicle accident risks for most of locations (Fig. 5). However, the results of MP 204–213 in Fig. 5 also suggest the need of using the actual operational speeds of trucks instead of the posted speed limits in the study for those special regions where the actual driving speeds of the large trucks are considerably different from those of the posted speed limits. The results of trucks under ice storm during winter seasons were reported in Fig. 6. The wind speed is assumed to be 30 mph and the road surface is covered with ice. For most locations of the whole corridor, the speed ratios are around 0.3–0.4 which suggests very large difference between the advisory CVS and the speed limits. It is thus found that during a severe snow storm, the closure of traffic to large trucks is probably the best solution. Most speed limits, primarily decided based on normal driving conditions, provide little information to the drivers about the appropriate driving speeds that the large trucks should maintain at a specific adverse driving condition. Therefore, adaptive (variable) speed limits for trucks which can automatically adjust with different extreme weather conditions at those critical locations will be helpful on improving truck safety on mountainous highways. The information gathered from the present study and the simulation methodology may help on developing the algorithm for the adaptive (variable) speed limit with ITS technology in the future. In Figs. 4–6, the results for both fully loaded and partially loaded trucks (50% loaded) were plotted together. Although the results in Figs. 4–6 show relatively larger risk (lower speed ratio values) for partially loaded trucks as compared to fully loaded vehicles, it is premature to make a general conclusion about which one between a partially loaded truck and a fully loaded truck is more vulnerable. Compared to a partially loaded truck, a fully loaded truck has a higher center of gravity (C.G.) and also larger weight. A partially loaded truck is lighter, but usually also has a lower C.G. than a fully loaded truck. It is effortless to find out from the simulation model or even common sense that vehicles with larger weights or lower C.G. are less prone to overturn accidents. For a particular truck, there-
Like many mountainous highways around the country, differential speed limits (DSL) are currently applied at several locations on the I-70 corridor. The lower speed limits for large trucks are primarily for avoiding serious overturn, sideswipe or losing controls at some sharp turns and steep grades. As a tradeoff, it is also known that larger velocity difference may possibly introduce higher risks of multi-vehicle conflicts or congestion. In this section, the multivehicle safety and operational performance for the whole highway are studied for those sections where DSL is applied. The CA-based traffic safety model which was briefly introduced in Section 2.2 will be adopted to evaluate the accident probability of multi-vehicle accidents as well as the traffic operational performance on the whole I-70 corridor in Colorado. The road is divided into cells each of which has a length of 7.5 m (24.6 ft). 7.5 m is defined as the typical distance between the mass centers of two consecutive vehicles when the road is in complete congestion (Nagel and Schreckenberg, 1992). The speed limits used in the simulation at different sections remain same as the corresponding actual speed limits along I-70. For example, when the speed limit is 65 mph (104 km/h), the vmax in the CA model can be computed as follows: 1000 m/km 104 km/h × = 3.85 cell/s ≈ 4 cell/s 3600 s/h 7.5 m/cell
(8)
The initial velocities of all vehicles are set to be zero. The observation of the traffic flow starts after 1 h of the simulation being made when the traffic flow is believed to become steady (Wu and Chen, 2009). With the assumption that the traffic occupancy does not fluctuate significantly during a short period of time (i.e. 5 min), the occupancy (unit: vehicle/cell) or the vehicle density (unit: vehicle/mile/lane) in this system keeps constant. All the parameters used in the CA traffic model are summarized in Table 2. On I-70, there are several places that differential speed limits (DSL) are applied to trucks and other vehicles. In order to compare the DSL and the uniform speed limit (USL) setups, the safety and operational performance studies are conducted for both DSL (actual) and USL (assumed) situations. To get the overall performance of safety and operation throughout the whole corridor in Colorado, the CA model in a coarse scale of 1:20 is applied to evaluate the overall performance of the whole corridor. Fig. 7(a) and (b) shows the overall accident probability of Type I (rear-end) and II (change-lane) with different traffic densities, respectively. “DSL” means the results using actual differential speed limits at some sections along the corridor. “USL” denotes the “what if” scenario using the same uniform speed limits for both trucks and other vehicles
S. Chen et al. / Accident Analysis and Prevention 43 (2011) 429–438
DSL
2.0E-03
USL
1.5E-03 1.0E-03 5.0E-04 0.0E+00 0
20
40
60
80
60
80
Probability of accidents
Vehicle/mile/lane (a) Accident type I 1.4E-05 1.2E-05
DSL
1.0E-05
USL
8.0E-06 6.0E-06 4.0E-06 2.0E-06 0.0E+00 0
20
40
Vehicle/mile/lane (b) Accident type II Fig. 7. Accident probability of the whole corridor.
for the comparison purpose. As shown in Fig. 7(a), the probability of Type I accidents varies with traffic density in a nonlinear way. When the vehicle density is less than 32 veh/mile/lane, the USL scenario causes lower accident probability than the DSL scenario does. However, when vehicles are more densely distributed (>32 veh/mile/lane), the DSL scenario can lead to smaller accident probability. For both cases, the peak accident rate occurs when the vehicle density is about 51 veh/mile/lane. As shown in Fig. 7(b), the accident probability of Type II varies with the traffic density randomly. As compared to that of Type I, it is found that the accident probability of Type II is about 100 times smaller. This is consistent with the observation from the historical accident data analysis that rear-end accidents usually dominate the multi-vehicle accidents. Because of the relative insignificance of the accident probability for Type II as compared to Type I, only the rear-end accident probability (i.e. Type I accidents) will be studied in the following sections, which is approximated to represent the total probability of multi-vehicle accidents. In addition to investigating the accident probability, the traffic operational performance along I-70 is also evaluated for different scenarios. It is found from Fig. 8(a) that the mean velocity generally decreases with the increase of the vehicle density and the mean velocity of the DSL case is lower than that of the USL case. This is because the USL setup usually allows more convenient acceleration of vehicles than the DSL setup due to the smaller speed deferential among the vehicles. With the increase of the vehicle density, the difference between the two cases becomes smaller. As shown in Fig. 8(b), the COV of velocity of all vehicles for both cases are close and all gradually increase with the vehicle density. The overall assessment of the I-70 corridor as shown in Figs. 7 and 8 can give the general trend about the traffic safety and operational performance on the I-70 corridor by considering the actual DSL scenarios. In order to look into the impacts on the performance of local segments of the corridor, the refined assessment
of local traffic characteristics is also conducted by investigating individual portions of the corridor with a smaller scale (1:1). The whole corridor is separated into eight segments, each of which has a length between 5 and 10 miles. The CA-model is applied to each segment to study the traffic safety and operational performance in the same way as the overall study introduced above except for using the refined scale. Similar to the overall analysis, for each segment, the actual speed limits, including DSL in some locations, are applied. It is found that most segments show similar phenomena in the refined analysis as the overall assessment. For example, Fig. 9 gives the results of accident probability and operational performance of MP 249–253. With the increase of vehicle density, the DSL case usually has lower accident probability than that of the USL case (Fig. 9(a)). Traffic operational performance as shown in Fig. 9(b) shows similar results as those of the overall assessment in Fig. 8. It is found that the current DSL setup on I-70 is generally more beneficial than the assumed USL setup when traffic is heavy (i.e. higher traffic density). When traffic is light, the DSL case may not have obvious benefits compared to the USL case. There is one section (MP 208–214) demonstrating unique characteristics which are different from other sections. As shown in Fig. 10(a), the accident probability for DSL case is much higher than the USL situation. According to Table 1, the actual speed limits for MP 208–214 are 60 mph (96.6 km/h) for other vehicles and 30 mph (48.3 km/h) for heavy trucks. The historical accident data analysis in Section 3 also shows that a high percentage (>86%) of accidents involving trucks which were speeding at least 10 mph (16.1 km/h) above the posted speed limits. Therefore, some further studies of speed limits at this portion of I-70 may be needed to optimize traffic safety and operational performance. One possible optimization is to narrow the gap of the current differential speed limits for trucks and other vehicles at that particular location. 100
Mean velocity (mph)
2.5E-03
DSL
80
USL
60 40 20 0 0
20
40
60
80
60
80
Vehicle/mile/lane (a) Mean velocity 2.0 DSL
COV of velocity
Probability of accidents
436
USL
1.5 1.0 0.5 0.0 0
20
40
Vehicle/mile/lane (b) COV of velocity Fig. 8. Traffic operational performance evaluation of the whole corridor.
S. Chen et al. / Accident Analysis and Prevention 43 (2011) 429–438
Probability of accidents
2.5E-03
6. Conclusions DSL
2.0E-03
USL
1.5E-03 1.0E-03 5.0E-04 0.0E+00 0
20
40
60
80
Vehicle/mile/lane (a) Accident probability
Mean velocity (mph)
100
DSL
80
USL
40 20
0
20
40
60
80
Vehicle/mile/lane (b) Mean velocity Fig. 9. Safety and operational performance evaluation of MP 249–253.
2.5E-02
DSL USL
2.0E-02 1.5E-02 1.0E-02 5.0E-03 0.0E+00 0
20
40
60
80
60
80
Vehicle/mile/lane (a) Accident probability Mean velocity (mph)
An integrated study was conducted to evaluate the traffic safety and operational performance of large trucks at two different scales: individual vehicles for single-vehicle accident risk assessment and the whole traffic on the highway for multi-vehicle accident risk assessment and operational performance evaluation. It includes investigating the advisory critical vehicle speeds of large trucks under site-specific adverse driving conditions as compared to the actual driving speed limits, as well as impacts on the overall traffic safety and operational performance of the whole corridor. Such a methodology, integrating historical accident data analysis and simulations with both single-vehicle accident and CA-based traffic safety and operational performance models, can be used on any mountainous highway experiencing complex driving conditions and high traffic volumes. The I-70 corridor in Colorado was chosen to demonstrate the methodology. The simulation results showed good correlations with the historical accident data. The specific findings are summarized in the following.
60
0
Probability of accidents
437
100
DSL USL
80 60 40 20 0 0
20
40
(1) It was found from the 10-year historical accident data analysis that snowy and icy road surfaces, windy weather and graded curves are the major critical adverse conditions for I-70. (2) With the simulation model of single-vehicle accidents considering site-specific topographic conditions along the highway, the advisory critical vehicle speeds (CVS) were obtained for those critical adverse driving conditions identified from the data analysis. The ratios between the CVS and the corresponding posted speed limits can be used to qualitatively evaluate the accident risk as long as the actual operational speeds of large trucks are close to the posted speed limits. (3) Although the general wind information can lead to reasonable predictions of the traffic safety performance for most of the locations on I-70, it is possible that the unique terrain or surrounding for some location may require site-specific wind and environmental data. The site-specific data may be obtained through the field data collection such as using the mobile mapping technology. (4) For those special locations where the actual operational speeds of large trucks are significantly different from those of the posted speed limits, a specific analysis using the actual operational driving speeds rather than the posted speed limits is needed. (5) For a particular truck, it is not straightforward to tell which situation (i.e. fully loaded or partially loaded) is more vulnerable to single-vehicle accidents without a specific analysis. The simulation study with the model introduced in the present study on a case-by-case basis is needed. (6) Adaptive (variable) driving speed limits for trucks which can automatically adjust with different extreme weather conditions at those critical locations will be helpful on improving the truck safety on mountainous highways. The information gathered from the present study and the multi-scale study methodology may help on the decisions about adopting advanced transportation management and ITS technology. (7) DSL was found to be more beneficial to the traffic safety and operational performance when the traffic density is high. When traffic is light, the DSL case may not have obvious benefits compared to the USL case.
Vehicle/mile/lane (b) Mean Velocity Fig. 10. Safety and operational performance evaluation of MP 208–214.
Acknowledgements The present study was partially supported by Colorado Department of Transportation (CDOT) and the United States Department of Transportation through the Mountain Plains Consortium (MPC).
438
S. Chen et al. / Accident Analysis and Prevention 43 (2011) 429–438
The data and technical advices provided by the study group of CDOT Region One are highly appreciated. The opinions in this study are solely the responsibility of the authors and do not necessarily represent the official views of CDOT, USDOT or MPC. References Awadallah, F., 2007. Differential speed limit analysis and regulations on rural expressways. Road and Transport Research 16 (4), 16–25, December. Baker, C.J., 1991. Ground vehicles in high cross winds. 3. The interaction of aerodynamic forces and the vehicle system. Journal of Fluids and Structures 5, 221–241. Braver, E., Zador, P., Thum, D., Mitter, E., Baum, H., Vilardo, F., 1997. Tractor-trailer crashes in Indiana: a case–control study of the role of truck configuration. Accident Analysis and Prevention 29 (1), 79–96. Chang, L.-Y., Mannering, F., 1999. Analysis of injury severity and vehicle occupancy in truck- and non-truck-involved accidents. Accident Analysis and Prevention 31 (5), 579–592. Chen, S.R., Cai, C.S., 2004. Accident assessment of vehicles on long-span bridges in windy environments. Journal of Wind Engineering and Industrial Aerodynamics 92 (12), 991–1024. Chen, S.R., Cai, C.S., Wolshon, B., 2009. From normal operation to evacuation: singlevehicle safety under adverse weather, topographic and operational conditions. Natural Hazards Review, ASCE 10 (2), 68–76. Chen, S.R., Chen, F., 2010. Simulation-based assessment of vehicle safety behavior under hazardous driving conditions. Journal of Transportation Engineering, ASCE 136 (4), 304–315. Chen, S.R., Chen, F., Liu, J., Bienkiewicz, B., 2010. Mobile mapping technology of wind velocity data along highway for traffic safety evaluation. Transportation Research Part C 18, 507–518. Chen, F., Chen, S.R., 2009. Assessment of vehicle safety behavior under adverse driving conditions. In: 11th American Conference of Wind Engineering, June 22–26 2009, Puerto Rico. Edwards, J.B., 1998. The relationship between road accident severity and recorded weather. Journal of Safety Research 29 (4), 249–262. FHWA (2004). The safety impacts of differential speed limits on rural interstate highways, Tech Brief. FHWA-HRT-04-156. Garber, N.J., Miller, J.S., Sun, X., Yuan, Bo., 2006. Safety impacts of differential speed limits for trucks and passenger cars on rural interstate highways: a modified empirical Bayes approach. Journal of Transportation Engineering 132 (January (1)), 19–29.
Guo, W.H., Xu, Y.L., 2006. Safety analysis of moving road vehicles on a long bridge under crosswind. Journal of Engineering Mechanics 132 (4), 438–446. Harkey, D.L., Robertson, H.D., Davis, S.E., 1990. Assessment of current speed zoning criteria. In: Transportation Research Record 1281. Transportation Research Board, National Research Council, Washington, D.C, pp. 40–51. Lyman, S., Braver, E.R., 2003. Occupant deaths in large truck crashes in the United States: 25 years of experience. Accident Analysis and Prevention 35 (5), 731–739. Li, X.G., Jia, B., Gao, Z.Y., Jiang, R., 2006. A realistic two-lane cellular automata traffic model considering aggressive lane-changing behavior of fast vehicle. Physica A 367, 479–486. Moussa, N., 2005. Dangerous situations in two-lane traffic flow models. International Journal of Modern Physics C 16 (7), 1133–1148. Nagel, K., Schreckenberg, M., 1992. A cellular automaton model for freeway traffic. Journal of Physics I 2 (12), 2221–2229, France. Rickert, M., Nagel, K., Schreckenberg, M., Latour, A., 1996. Two lane traffic simulations using cellular automata. Physica A 231, 534–550. Snaebjornsson, J.T., Baker, C.J., Sigbjornsson, R., 2007. Probabilistic assessment of road vehicle safety in windy environments. Journal of Wind Engineering and Industrial Aerodynamics 95, 1445–1462. Summerfield, S., Kosior, J., 2001. Simulation of heavy trucks in inclement weather. Canadian Transportation Research Forum. The national Academies, 2006. Where the weather meets the road—a research agenda for improving road weather system. In: Report in Brief. The National Academies. The Road Information Program, 2005. Growing Traffic in Rural America: Safety, Mobility and Economic Challenges in America’s Heartland (last accessed May 17, 2008) http://www.tripnet.org/RuralRoads2005Report.pdf. U.S. Department of Transportation (USDOT), 2005. Report to Congress on the Large Truck Crash Causation Study. Federal Motor Carrier Safety Administration, U.S. Department of Transportation. Wu, J., Chen, S., 2009. Traffic flow simulation on bridge with cellular automaton technique. In: 88th Annual meeting of the Transportation Research Board, Washington, D.C. Young, R., Liesman, J., 2007a. Intelligent transportation systems for operation of roadway segments in high-wind conditions, 2000. Journal of Transportation Research Record, 1–7. Young, R, Liesman, J., 2007b. Estimating the relationship between measured wind speed and overturning truck crashes using binary logit model. Accident Analysis and Prevention 39 (3), 574–580. Zhang, W., Yang, X.Q., Sun, D.P., Qiu, K., Xia, H., 2006. Traffic accidents in a cellular automaton model with a speed limit zone. Journal of Physics A: Mathematical and General 39, 9127–9137.
Contents lists available at ScienceDirect
Accident Analysis and Prevention journal homepage: www.elsevier.com/locate/aap
Multi-scale traffic safety and operational performance study of large trucks on mountainous interstate highway Suren Chen ∗ , Feng Chen, Jun Wu Dept. of Civil & Environmental Eng., Colorado State University, Fort Collins, CO 80523, United States
a r t i c l e
i n f o
Article history: Received 26 January 2010 Received in revised form 8 September 2010 Accepted 27 September 2010 Keywords: Mountainous highway Large trucks Single-vehicle accident Multi-vehicle accident Multi-scale
a b s t r a c t In addition to multi-vehicle accidents, large trucks are also prone to single-vehicle accidents on the mountainous interstate highways due to the complex terrain and fast-changing weather. By integrating both historical data analysis and simulations, a multi-scale approach is developed to evaluate the traffic safety and operational performance of large trucks on mountainous interstate highways in both scales of individual vehicle as well as traffic on the whole highway. A typical mountainous highway in Colorado is studied for demonstration purposes. Firstly, the ten-year historical accident records are analyzed to identify the accident-vulnerable-locations (AVLs) and site-specific critical adverse driving conditions. Secondly, simulation-based single-vehicle assessment is performed for different driving conditions at those AVLs along the whole corridor. Finally, the cellular-automaton (CA)-based simulation is carried out to evaluate the multi-vehicle traffic safety as well as the operational performance of the traffic by considering the actual speed limits, including the differential speed limits (DSL) at some locations. It is found that the multi-scale approach can provide insightful and comprehensive observations of the highway performance, which is especially important for mountainous highways. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction Extensive works have been conducted on the traffic safety and injury prevention related to multi-vehicle accidents of large trucks in past decades (e.g. Braver et al., 1997; Chang and Mannering, 1999; Lyman and Braver, 2003). Different from most passenger vehicles which are dominantly vulnerable to multi-vehicle traffic conflicts, large trucks are also prone to single-vehicle accidents on the mountainous interstate highways due to the complex terrain and fast-changing weather (USDOT, 2005; Baker, 1991). Although the absolute number of single-vehicle accidents is typically smaller than that of multi-vehicle accidents, single-vehicle accidents have caused serious injury and casualty (The National Academies, 2006). For example, single-vehicle accidents were responsible for 57.8% of the total fatalities of traffic accidents in 2005 (USDOT, 2005). This is especially true when complex terrain couples with inclement weather conditions, such as snow, ice or strong wind. Each year in the United States, adverse weather alone is associated with more than 1.5 million vehicular accidents, which result in 800,000 injuries and 7000 fatalities (The National Academies, 2006).
∗ Corresponding author. Tel.: +1 970 491 7722; fax: +1 970 491 7727. E-mail address: [email protected] (S. Chen). 0001-4575/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.aap.2010.09.013
The primary causes of accidents involving large trucks on rural highways were found to be excessive speed and adverse driving conditions (The Road Information Program, 2005). Different from passenger vehicles, it is known that the safety performance of large trucks in adverse driving conditions greatly depends on the specific terrain and local weather condition (USDOT, 2005; Baker, 1991). To accommodate the considerable difference on safety performance of large trucks and common passenger vehicles, differential speed limits (DSL) have been applied in many highways for large trucks at locations where the driving conditions are not ideal. There are, however, mixed opinions on the benefits of DSL to the traffic safety and operational performance, which highly depend on the specific geometric, traffic and environmental conditions (FHWA, 2004). As a matter of fact, there is not yet compelling evidence to support more widespread applications of DSL instead of universal speed limits (USL), and neither is strong evidence that DSL should be eliminated (Garber et al., 2006; Awadallah, 2007; Harkey et al., 1990). On one hand, the lower speed limits for large trucks may reduce the risk of single-vehicle accidents. On the other hand, the differential driving speeds for trucks and other vehicles, if not reasonable, may also cause additional risks of traffic conflicts between large trucks and other vehicles and/or traffic congestions. Therefore, it is necessary to comprehensively evaluate the safety and operational performance of large trucks on a mountainous highway by looking into not only the safety of individual trucks, but also the impacts to the whole traffic on the highway.
430
S. Chen et al. / Accident Analysis and Prevention 43 (2011) 429–438
In the present study, an attempt is made to integrally evaluate the safety and operational performance of large trucks on mountainous highways at both scales of individual vehicle and whole traffic flow. The I-70 corridor in Colorado is chosen to demonstrate the methodology because of its typical mountainous terrain and adverse weather conditions. Firstly, ten-year historical accident records will be analyzed to identify the accidentvulnerable-locations (AVLs) and critical adverse driving conditions specific to I-70. Secondly, simulation-based single-vehicle assessment will be performed for different inclement weather conditions at these AVLs along the whole corridor. The advisory critical vehicle speeds (CVS) will be compared to the corresponding speed limits along the highway to give some insights about single-vehicle safety performance of large trucks. Finally, the cellular-automaton (CA)based multi-vehicle accident simulation (Nagel and Schreckenberg, 1992; Moussa, 2005) will be carried out to evaluate the impacts on traffic safety and operational performance of the whole highway by considering the actual speed limits, including DSL at some locations. 2. Simulation-based analytical models Extensive works have been carried out on both multi- (USDOT, 2005) and single-vehicle accidents (Young and Liesman, 2007a,b; Summerfield and Kosior, 2001; Edwards, 1998) with a focus on data analyses of historical accidents. In addition to analyses based on historical data, there were also studies using various simulation models on multi-vehicle traffic conflicts (Moussa, 2005; Zhang et al., 2006) as well as single-vehicle accidents (Baker, 1991; Chen and Cai, 2004; Guo and Xu, 2006). Compared to data-based accident analyses, simulation-based analyses of multivehicle or single-vehicle accidents have the advantage of exploring more comprehensive collections of possible scenarios, which may not be covered by the historical accident data (Baker, 1991; Snaebjornsson et al., 2007; Chen et al., 2009). In this section, the simulation-based evaluation models of single-vehicle safety and multi-vehicle safety as well as operational performance which will be used in the present study are briefly introduced in the following. 2.1. Simulation-based assessment model of single-vehicle accidents The single-vehicle simulation model recently developed by the writers (Chen and Chen, 2010, 2009) will be used to evaluate the vehicle safety at the selected vulnerable locations. In order to provide essential background information, the simulation model is briefly introduced below (Chen and Chen, 2010). For a typical vehicle, the sprung mass rotates about the roll center which is dependent on the kinematical properties of the suspensions. The unsprung masses can rotate with the vertical compliance of the tires. Five force and moment equilibrium equations of vehicle motions of sprung mass, unsprung masses and suspensions in y and z directions are defined in Eqs. (1)–(5) (Chen and Chen, 2010). ¨ = mV (ˇ˙ + ˙ ) − Fy,f − Fy,r + Fw,y − mg + may ms h
(1)
¨ + Iz z ¨ = Fy,f af + Fy,r ar + Mz −Ix z
(2)
¨ − Ix z ¨ = ms gh + ms Vh(ˇ˙ + ˙ ) + Mx − ms gh + ms gay Ix x + Fw,y hw − kf ( − t,f ) − lf (˙ − ˙ t,f ) + uf − kr ( − t,r ) − lr (˙ − ˙ t,r ) + ur
(3)
rFy,f = −mu,f V (hu,f − r)(ˇ˙ + ˙ ) + mu,f g(hu,f − r)t,f + mu,f g(hu,f − r) −
aroll Ix x mf m
− mu,f ay (hu,f − r) + kt,f t,f
− kf ( − t,f ) − lf (˙ − ˙ t,f ) + uf
(4)
rFy,r = −mu,r V (hu,r − r)(ˇ˙ + ˙ ) + mu,r g(hu,r − r)t,r + mu,r g(hu,r − r) −
aroll Ix x mr − mu,r ay (hu,r − r) m
+ kt,r t,r − kr ( − t,r ) − lr (˙ − ˙ t,r ) + ur
(5)
where the subscripts r and f refer to the rear and front axles, respectively. Fw,y , Mx , Mz are lateral wind force, wind-induced roll moment and yaw moment, respectively. is road superelevation. ay and aroll are accelerations in the lateral (y) direction and the rolling direction of the supporting infrastructures (e.g. pavement or bridge), respectively. m, ms , mu are the total mass, sprung mass and unsprung mass, respectively. h is the height of the center of sprung mass. r and hu are the heights of rolling center and unsprung mass center. Fy,f and Fy,r are lateral forces of front and rear tires, respectively. Ix x , Ix z , Iz z are the roll moment, yaw-roll product and yaw moment of inertia of sprung mass, respectively. k, kt , l are roll stiffness of suspension, roll stiffness of tire and roll damping rate of suspension, respectively. and t are absolute roll angle of sprung mass and unsprung mass, respectively. ˇ and are sideslip angle and heading angle, respectively. u is active roll torque. The dynamic models as introduced in Eqs. (1)–(5) are used when the wheels are not lifted up or sideslip. The dynamic simulation of the whole process of an accident involves series of vehicle dynamic simulation models for different stages of the accident, such as before/after wheels being lifted up, before/after wheels starting to slide (Chen and Chen, 2010). At any time step of the simulation, the corresponding criterion will be checked to decide whether the wheels have been lifted up or sideslip has occurred. When any of these scenarios is identified to occur, the corresponding new set of dynamic equations, which consider the specific dynamic nature and restraints, will be adopted to continue the simulation (Chen and Chen, 2010). As a result, the transient process of the overturn and sideswipe accidents can be simulated in a more rational way and more details can be found in Ref. Chen and Chen, 2010. For any given driving condition as well as specific vehicle conditions, the occurrence of single-vehicle accidents will be evaluated at each driving speed. The simulation process continues by gradually increasing driving speeds until any single-vehicle accident occurs. As a result, the advisory critical vehicle speed (CVS) for a specific combination of environmental and vehicular conditions is the highest allowable driving speed under which no single-vehicle accident is likely to happen (Chen and Chen, 2010). 2.2. Multi-vehicle accident risk assessment using cellular automaton model The Cellular Automaton (CA) model proposed by Nagel and Schreckenberg (1992) is an efficient tool to study the operational performance of traffic flow and traffic safety in a microscopic scale (Moussa, 2005; Zhang et al., 2006). The major strength of the CA model is the robustness for different intricate features of traffic flow (Nagel and Schreckenberg, 1992). As a probabilistic microscopicscale traffic flow simulation tool, the CA-model can provide detailed time-variant information of individual vehicles. The basic features of the CA model are as follows (Nagel and Schreckenberg, 1992): (1) each lane is divided into cells with an equal length; (2) each cell is empty or occupied by one vehicle at
S. Chen et al. / Accident Analysis and Prevention 43 (2011) 429–438
a time; (3) the instantaneous speed of a vehicle can be decided by the number of cells the vehicle can move in each time step; (4) the maximum velocity a vehicle can reach is defined by the actual speed limit of that particular stretch of the highway. At each time step, a vehicle moves, accelerates, decelerates or changes lanes based on specific rules established according to the actual traffic rules and some reasonable assumptions of the driver behavior (Nagel and Schreckenberg, 1992; Wu and Chen, 2009). For example, a driver is typically believed to have the intention to achieve the maximum driving speed without violating traffic rules (Nagel and Schreckenberg, 1992). When the conditions presented below are satisfied, the multilane CA model is implemented (Rickert et al., 1996; Li et al., 2006): (1) the distance between Vehicle i and the vehicle ahead on the same lane is smaller than v + 1, where v is the vehicle velocity; (2) the distance between Vehicle i and the vehicle ahead on the target lane is more than v + 1; (3) the distance between Vehicle i and the back vehicle on the target lane is more than vmax , which is the maximum velocity a vehicle is allowed to achieve; (4) with the probability of pch, Vehicle i changes the lane if all the three above conditions are satisfied. If Vehicle i changes lane, its location and the velocity will be updated through two sub-steps: (1) Vehicle i moves to the target lane transversely without advancing; (2) Vehicle i moving forward to the target lane obeys the single-lane rule (Nagel and Schreckenberg, 1992). In the multi-lane CA accident model, two types of accidents are considered. Type I is that caused by the rear-end collision between two successive vehicles moving on the same lane; Type II is that caused by lane-changing of the successive vehicles. Two parameters are introduced to define the accident-prone conditions: the delayed reaction time () of the following vehicle and the deceleration limit (vd ) of the ahead vehicle. The prerequisites of Type I accident can be expressed as follows (Moussa, 2005): 1) The vehicle ahead of Vehicle k decelerates abruptly:
vk+1 (t + 1) − vk+1 (t) ≥ vd
(6)
2) Vehicle k cannot brake during the delayed reaction time period () to avoid a crash: vk (t) − vk+1 (t + 1) > gk (t)
(7)
where gk (t) is the distance between Vehicle k and Vehicle k + 1 at time step t. For Type II accidents, it is assumed that all the drivers obey the traffic rules when they change lanes, for example, keeping the safe distance. When two successive vehicles change to the same target lane simultaneously, the crash may occur as the front vehicle automatically ignores the gap behind because it just focuses on the gap with the vehicles on the target lane (Moussa, 2005). 3. Historical accident data analysis of I-70 in Colorado 3.1. I-70 interstate corridor The Interstate I-70 Mountain Corridor within the State of Colorado, from Denver to Grand Junction is a typical mountainous highway in rural areas as it is a gateway to recreation, commerce and everyday necessities for Colorado residents and visitors. At some locations along the corridor, very steep grades which are coupled with extreme weather conditions have been blamed for many accidents involving large trucks. Differential speed limits have been adopted at several locations where the terrains are complicated on the I-70 mountain corridor. Ten-year (1996–2005) historical accident data of I-70 in Colorado from Vail to Golden (Mile Post
431
179.90–258.60) were studied. The percentage of trucks in traffic is 5.7–13% on this corridor in Year 2005. Average daily traffic (ADT) on I-70 in Colorado is 32,962. During the ten-year period, there were totally 1565 accidents reported, out of which 762 and 639 accidents involved large trucks/bus as the first vehicle (Vehicle 1) and the second vehicle (Vehicle 2), respectively. 3.2. Data analysis and accident vulnerable locations (AVLs) Based on the comprehensive analysis of the historical accident data on I-70 corridor between 1996 and 2005, some accident vulnerable locations (AVLs) experiencing a considerable number of past accidents are summarized in Table 1. AVLs are selected based on the number of accidents occurring on each segment (typically 0.1 mile long), which is identified with the beginning and ending mileposts (MP) (e.g. MP 184.4–185.4). Due to the limit of the space, Table 1 only gives detailed information for several selected AVLs, including the mileposts (MP), the numbers of accidents associated with different vehicle types, accident types, geometric conditions, speed limits and adverse weather conditions. Most differential speed limits on I-70 are applied in the westbound direction, as shown in column 4 in Table 1. “No. of truck-initiated accidents (% of all accidents)” (column 5) is the number (and percentage) of accidents with large trucks (more than 10k lbs) as the first vehicle (Vehicle 1). Column 6 shows the number of accidents occurring at different adverse road surface conditions (e.g. wet, icy or snowy). Column 7 gives the number of the accidents by accident type: single-vehicle accidents, including overturn and sideswipe accidents, and typical multi-vehicle accidents (rear-end accidents). By comparing the actual driving speeds reported in the accident record with the corresponding speed limits, the percentage of those trucks with the driving speeds at least 10 mph over the speed limits in the truck-initiated accidents was given in Column 8. Some general observations from the accident data analysis of I70 AVLs include: (1) trucks were more vulnerable to accidents than other vehicles (around 50–70% of all accidents were initiated by trucks); (2) for multiple-vehicle accidents, rear-end collisions were dominant (over 80%); (3) adverse road surface conditions were found to have significant impacts on traffic safety (associated with up to 70% accidents); and (4) dominant accident types at different locations were sideswipe or overturn accidents (single-vehicle), rear-end accidents (multi-vehicle) or both. Based on these observations, the need and significance of the present study focusing on trucks and adverse driving conditions are well justified. 3.3. Accident analysis under adverse driving conditions Historical accidents are firstly studied for different adverse driving conditions, such as windy, snowy, icy conditions of road surface and different terrains. Among all the adverse driving conditions, Figs. 1–3 give the statistics of historical accidents involving trucks under several most significant adverse driving conditions on I-70, including strong wind, snow-covered, ice-covered road surface and on grades, respectively. Different sizes of the dots on the maps represent different numbers of similar accidents happening at the same locations during the past ten years, as defined in the legend. It is found in Fig. 1 that there are about 30 accidents identified as wind-induced ones in the accident records during the ten-year period. It is noted that the actual number may be higher since it is possible that some accidents were not identified as windinduced ones on the accident report despite the fact that wind may also contribute to the accidents along with other reported factors. According to Fig. 1, except for some scattered locations along I-70, most of the wind-induced accidents happened in the east portion of the corridor. Repetitive accidents happened at several locations along I-70, such as MP 229, 244, and 250–252.
432
S. Chen et al. / Accident Analysis and Prevention 43 (2011) 429–438
Table 1 Selected accident vulnerable locations (AVLs) on I-70 (1996–2005). (1) Milepost range
(2) Terrain features
(3) Grade
(4) Speed limit (mph)
(5) No. of truck-initiated accidents (% of all accidents)
(6) No. of accidents under adverse road surface conditions
(7) Accident types
184.4–185.4
Curve R = 1250 ft
6%
Truck 45 Others 65
24 (64.9%) EB3, WB21
Wet 2 Icy 13 Snowy 7 Wet 3 Icy 4 Snowy 2 Wet 1 Icy 2 Snowy 5 Wet 3 Icy 3 Snowy 12 Wet 3 Icy 5 Snowy 1 Wet 6 Icy 5 Snowy 1 Wet 2 Icy 3 Snowy 2
Overturn 0 Sideswipe 11 Rear-end 7 Overturn 0 Sideswipe 5 Rear-end 4 Overturn 8 Sideswipe 8 Rear-end 12 Overturn 0 Sideswipe 12 Rear-end 10 Overturn 8 Sideswipe 5 Rear-end 2 Overturn 15 Sideswipe 11 Rear-end 7 Overturn 1 Sideswipe 4 Rear-end 2
204.8–205.14
208.0–209.3
213.0–214.0
242.5–242.92
243.4–244.7
250.8–251.2
Curve R = 2130 ft
Straight
Straight
Curve R = 690 ft
Curve R = 850 ft
Curve R = 1540 ft
8%
8%
8%
4%
4%
3%
Truck 30 Others 60
Truck 30 Others 60
Truck 30 Others 60
All 55
All 55
All 65
13 (56.5%) EB6, WB7 36 (69.2%) EB2, WB34 19 (48.7%) EB7, WB12 18 (69.3%) EB12, WB6 44 (70.3%) EB28, WB16 7 (58.3%) EB0, WB7
(8) Percentage of trucks over speed limits by 10 mph or more
8.3%
38.5%
86.1%
0%
33.3%
22.2%
0%
Note: EB = east bound vehicles; WB = west bound vehicles; R = curve radius.
Fig. 2 shows the historical accidents happening on snowcovered roads. A large number of repetitive accidents happened frequently along the whole stretch between MP 182 and 228. The accidents happening on curves with grades are also studied (Fig. 3).
It can be found that the most vulnerable locations identified in Fig. 2 (snowy road) are similar to those shown in Fig. 3 (on grades). It is understandable since both scenarios cause challenges for the truck drivers to stop efficiently.
Fig. 1. Historical wind-induced accidents (1996–2005).
S. Chen et al. / Accident Analysis and Prevention 43 (2011) 429–438
433
Fig. 2. Historical accidents on snow-covered road surface (1996–2005).
As shown in Fig. 3, MP 242–248 suffered from frequent accidents because of the well-known steep grades (6%) which are coupled with sharp curves. Based on the observations from Figs. 2 and 3, it is obvious that both the road surface condition and the road geometric condition (e.g. grade and curves) have large impacts on the accident risk for trucks. The similarities between the observations in Figs. 2 and 3 suggest that such two critical conditions (i.e. roadsurface and geometric) work interactively to pose threats on the safety of trucks under adverse driving environments. Given the fact that the complex terrain is common throughout the I-70 corridor in Colorado, the historical accidents on snow-covered road surface and grade curves were found to occur in nearly all the portions of the whole corridor with a comparatively higher number of accidents on the western part.
4. Single-vehicle traffic safety under adverse weather The data analyses of the historical accidents in the last section identified several AVLs and the critical adverse driving conditions. In this section, with the single-vehicle accident simulation model introduced earlier, more comprehensive simulations of singlevehicle accidents under different adverse driving conditions are conducted along the whole I-70 corridor including those identified AVLs. As a result, different advisory critical vehicle speeds (CVS) are obtained under various weather and road surface conditions such as: (1) windy conditions (U = 30 mph (13.4 m/s)); (2) snow storm (U = 30 mph and snow-covered road); or (3) icy storm (U = 30 mph and icy road). The results from the simulation will be compared with the observations from the data analysis of historical accidents.
In the following Figs. 4–6, the x-axis shows different milepost numbers along I-70. The y-axis is the dimensionless variable—the ratio between the critical vehicle speed (CVS) identified from the simulation and the corresponding posted speed limit at the same spot. The ratio of the “critical vehicle speed/speed limit” (called “speed ratio” for brevity purpose hereafter) as shown in Figs. 4–6 is not a variable intended to rigorously quantify the effectiveness or rationality of the posted speed limits for the adverse driving conditions. Rather, the speed ratio is only used to provide qualitative information about (1) the relationship between the CVS and the corresponding speed limit at the same location, and (2) the relative risk of single-vehicle accidents at different locations along the I-70. It is made possible by comparing the speed ratio and unit at one location, and the speed ratios at different locations. The CVS in windy conditions (U = 30 mph) for a typical truck along the I-70 is identified considering the corresponding geometric condition for each segment along I-70 and the results are displayed in Fig. 4. It is known that 30 mph wind speed is pretty common for mountainous highways, especially during winter and spring seasons. As shown in Fig. 4, there are several locations with relatively low speed ratios, such as MP 244, MP 250–252. As compared to the historical accident results, these locations with lower speed ratios were also identified as AVLs in Table 1 as well as in Fig. 1. Pretty good correlations between the simulation results and the historical accident records can be found for most of the locations studied as displayed in Fig. 1. There is, however, one location (MP 198) which seems pretty vulnerable to single-vehicle accidents according to the simulation results in Fig. 4, while this observation is not well supported by the historical accident records (Table 1 and Fig. 1). It is possibly because that the unique terrain or sur-
434
S. Chen et al. / Accident Analysis and Prevention 43 (2011) 429–438
Fig. 3. Historical accidents on grade curves (1996–2005).
rounding near MP 198 may improve the actual wind condition from the theoretical one. This observation underscores the importance of collecting site-specific wind and other environmental data for those locations with complex terrain or surroundings (Chen et al., 2010). One possible option is to use the mobile mapping technology to collect the site-specific wind and environmental data (Chen et al., 2010). A detailed investigation of this particular location involves significant data collection, which is beyond the scope of the present study.
Fig. 5 gives the CVS results on I-70 under snow storms (i.e. the road surface is covered by snow and the wind speed equals to 30 mph). It can be found that there are several locations with the speed ratios considerably lower than 1, such as MP 182–184, MP 250–252. Such a phenomenon observed from the simulation results is generally consistent with the historical accident records as shown in Table 1 and Fig. 2, except for MP 205–213. In Fig. 5, the speed ratios are all above 1 between MP 205–213, which seem to contradict with the fact as shown in Fig. 2 that there were many
Fig. 4. Critical vehicle speed ratio of different mileposts in windy conditions (U = 30 mph).
Fig. 5. Critical vehicle speed ratio of different mileposts in snowstorm (U = 30 mph and snow).
S. Chen et al. / Accident Analysis and Prevention 43 (2011) 429–438
435
Table 2 Parameters of CA traffic model. Parameters
Value
Description
Lc dt pb pch
7.5 m 1s 0.5 0.8 1s 2 cell 20%
Length of each cell The period of every time step The probability of braking The probability of changing lane The delayed reaction time Deceleration limit The percentage of heavy vehicle among all the types of vehicles
vd Ch
fore, it is not straightforward to tell which situation (i.e. fully loaded or partially loaded) is more vulnerable to single-vehicle accidents without a specific and detailed analysis. The single-vehicle simulation model (Chen and Chen, 2010) can be used to conduct a detailed analysis on a case-by-case basis. Fig. 6. Critical vehicle speed ratio of different mileposts in cold winter season (U = 30 mph and icy road).
5. Traffic safety and operational performance of whole traffic with DSL
accidents happening during snowy conditions in that region. It is known that MP 208–213 involves very steep grades with the speed limits of 30 mph for trucks and 60 mph for other vehicles. A closer look of Table 1 discloses that for MP 204–209, 38.5–86.1% of those trucks which were involved in the accidents were actually driven at speeds at least 10 mph (16.1 km/h) higher than the speed limits according to the accident records. With the assumption that most large trucks were driven in speeds close to the posted speed limits, the speed ratios used in the present study were usually found to provide pretty accurate information about single-vehicle accident risks for most of locations (Fig. 5). However, the results of MP 204–213 in Fig. 5 also suggest the need of using the actual operational speeds of trucks instead of the posted speed limits in the study for those special regions where the actual driving speeds of the large trucks are considerably different from those of the posted speed limits. The results of trucks under ice storm during winter seasons were reported in Fig. 6. The wind speed is assumed to be 30 mph and the road surface is covered with ice. For most locations of the whole corridor, the speed ratios are around 0.3–0.4 which suggests very large difference between the advisory CVS and the speed limits. It is thus found that during a severe snow storm, the closure of traffic to large trucks is probably the best solution. Most speed limits, primarily decided based on normal driving conditions, provide little information to the drivers about the appropriate driving speeds that the large trucks should maintain at a specific adverse driving condition. Therefore, adaptive (variable) speed limits for trucks which can automatically adjust with different extreme weather conditions at those critical locations will be helpful on improving truck safety on mountainous highways. The information gathered from the present study and the simulation methodology may help on developing the algorithm for the adaptive (variable) speed limit with ITS technology in the future. In Figs. 4–6, the results for both fully loaded and partially loaded trucks (50% loaded) were plotted together. Although the results in Figs. 4–6 show relatively larger risk (lower speed ratio values) for partially loaded trucks as compared to fully loaded vehicles, it is premature to make a general conclusion about which one between a partially loaded truck and a fully loaded truck is more vulnerable. Compared to a partially loaded truck, a fully loaded truck has a higher center of gravity (C.G.) and also larger weight. A partially loaded truck is lighter, but usually also has a lower C.G. than a fully loaded truck. It is effortless to find out from the simulation model or even common sense that vehicles with larger weights or lower C.G. are less prone to overturn accidents. For a particular truck, there-
Like many mountainous highways around the country, differential speed limits (DSL) are currently applied at several locations on the I-70 corridor. The lower speed limits for large trucks are primarily for avoiding serious overturn, sideswipe or losing controls at some sharp turns and steep grades. As a tradeoff, it is also known that larger velocity difference may possibly introduce higher risks of multi-vehicle conflicts or congestion. In this section, the multivehicle safety and operational performance for the whole highway are studied for those sections where DSL is applied. The CA-based traffic safety model which was briefly introduced in Section 2.2 will be adopted to evaluate the accident probability of multi-vehicle accidents as well as the traffic operational performance on the whole I-70 corridor in Colorado. The road is divided into cells each of which has a length of 7.5 m (24.6 ft). 7.5 m is defined as the typical distance between the mass centers of two consecutive vehicles when the road is in complete congestion (Nagel and Schreckenberg, 1992). The speed limits used in the simulation at different sections remain same as the corresponding actual speed limits along I-70. For example, when the speed limit is 65 mph (104 km/h), the vmax in the CA model can be computed as follows: 1000 m/km 104 km/h × = 3.85 cell/s ≈ 4 cell/s 3600 s/h 7.5 m/cell
(8)
The initial velocities of all vehicles are set to be zero. The observation of the traffic flow starts after 1 h of the simulation being made when the traffic flow is believed to become steady (Wu and Chen, 2009). With the assumption that the traffic occupancy does not fluctuate significantly during a short period of time (i.e. 5 min), the occupancy (unit: vehicle/cell) or the vehicle density (unit: vehicle/mile/lane) in this system keeps constant. All the parameters used in the CA traffic model are summarized in Table 2. On I-70, there are several places that differential speed limits (DSL) are applied to trucks and other vehicles. In order to compare the DSL and the uniform speed limit (USL) setups, the safety and operational performance studies are conducted for both DSL (actual) and USL (assumed) situations. To get the overall performance of safety and operation throughout the whole corridor in Colorado, the CA model in a coarse scale of 1:20 is applied to evaluate the overall performance of the whole corridor. Fig. 7(a) and (b) shows the overall accident probability of Type I (rear-end) and II (change-lane) with different traffic densities, respectively. “DSL” means the results using actual differential speed limits at some sections along the corridor. “USL” denotes the “what if” scenario using the same uniform speed limits for both trucks and other vehicles
S. Chen et al. / Accident Analysis and Prevention 43 (2011) 429–438
DSL
2.0E-03
USL
1.5E-03 1.0E-03 5.0E-04 0.0E+00 0
20
40
60
80
60
80
Probability of accidents
Vehicle/mile/lane (a) Accident type I 1.4E-05 1.2E-05
DSL
1.0E-05
USL
8.0E-06 6.0E-06 4.0E-06 2.0E-06 0.0E+00 0
20
40
Vehicle/mile/lane (b) Accident type II Fig. 7. Accident probability of the whole corridor.
for the comparison purpose. As shown in Fig. 7(a), the probability of Type I accidents varies with traffic density in a nonlinear way. When the vehicle density is less than 32 veh/mile/lane, the USL scenario causes lower accident probability than the DSL scenario does. However, when vehicles are more densely distributed (>32 veh/mile/lane), the DSL scenario can lead to smaller accident probability. For both cases, the peak accident rate occurs when the vehicle density is about 51 veh/mile/lane. As shown in Fig. 7(b), the accident probability of Type II varies with the traffic density randomly. As compared to that of Type I, it is found that the accident probability of Type II is about 100 times smaller. This is consistent with the observation from the historical accident data analysis that rear-end accidents usually dominate the multi-vehicle accidents. Because of the relative insignificance of the accident probability for Type II as compared to Type I, only the rear-end accident probability (i.e. Type I accidents) will be studied in the following sections, which is approximated to represent the total probability of multi-vehicle accidents. In addition to investigating the accident probability, the traffic operational performance along I-70 is also evaluated for different scenarios. It is found from Fig. 8(a) that the mean velocity generally decreases with the increase of the vehicle density and the mean velocity of the DSL case is lower than that of the USL case. This is because the USL setup usually allows more convenient acceleration of vehicles than the DSL setup due to the smaller speed deferential among the vehicles. With the increase of the vehicle density, the difference between the two cases becomes smaller. As shown in Fig. 8(b), the COV of velocity of all vehicles for both cases are close and all gradually increase with the vehicle density. The overall assessment of the I-70 corridor as shown in Figs. 7 and 8 can give the general trend about the traffic safety and operational performance on the I-70 corridor by considering the actual DSL scenarios. In order to look into the impacts on the performance of local segments of the corridor, the refined assessment
of local traffic characteristics is also conducted by investigating individual portions of the corridor with a smaller scale (1:1). The whole corridor is separated into eight segments, each of which has a length between 5 and 10 miles. The CA-model is applied to each segment to study the traffic safety and operational performance in the same way as the overall study introduced above except for using the refined scale. Similar to the overall analysis, for each segment, the actual speed limits, including DSL in some locations, are applied. It is found that most segments show similar phenomena in the refined analysis as the overall assessment. For example, Fig. 9 gives the results of accident probability and operational performance of MP 249–253. With the increase of vehicle density, the DSL case usually has lower accident probability than that of the USL case (Fig. 9(a)). Traffic operational performance as shown in Fig. 9(b) shows similar results as those of the overall assessment in Fig. 8. It is found that the current DSL setup on I-70 is generally more beneficial than the assumed USL setup when traffic is heavy (i.e. higher traffic density). When traffic is light, the DSL case may not have obvious benefits compared to the USL case. There is one section (MP 208–214) demonstrating unique characteristics which are different from other sections. As shown in Fig. 10(a), the accident probability for DSL case is much higher than the USL situation. According to Table 1, the actual speed limits for MP 208–214 are 60 mph (96.6 km/h) for other vehicles and 30 mph (48.3 km/h) for heavy trucks. The historical accident data analysis in Section 3 also shows that a high percentage (>86%) of accidents involving trucks which were speeding at least 10 mph (16.1 km/h) above the posted speed limits. Therefore, some further studies of speed limits at this portion of I-70 may be needed to optimize traffic safety and operational performance. One possible optimization is to narrow the gap of the current differential speed limits for trucks and other vehicles at that particular location. 100
Mean velocity (mph)
2.5E-03
DSL
80
USL
60 40 20 0 0
20
40
60
80
60
80
Vehicle/mile/lane (a) Mean velocity 2.0 DSL
COV of velocity
Probability of accidents
436
USL
1.5 1.0 0.5 0.0 0
20
40
Vehicle/mile/lane (b) COV of velocity Fig. 8. Traffic operational performance evaluation of the whole corridor.
S. Chen et al. / Accident Analysis and Prevention 43 (2011) 429–438
Probability of accidents
2.5E-03
6. Conclusions DSL
2.0E-03
USL
1.5E-03 1.0E-03 5.0E-04 0.0E+00 0
20
40
60
80
Vehicle/mile/lane (a) Accident probability
Mean velocity (mph)
100
DSL
80
USL
40 20
0
20
40
60
80
Vehicle/mile/lane (b) Mean velocity Fig. 9. Safety and operational performance evaluation of MP 249–253.
2.5E-02
DSL USL
2.0E-02 1.5E-02 1.0E-02 5.0E-03 0.0E+00 0
20
40
60
80
60
80
Vehicle/mile/lane (a) Accident probability Mean velocity (mph)
An integrated study was conducted to evaluate the traffic safety and operational performance of large trucks at two different scales: individual vehicles for single-vehicle accident risk assessment and the whole traffic on the highway for multi-vehicle accident risk assessment and operational performance evaluation. It includes investigating the advisory critical vehicle speeds of large trucks under site-specific adverse driving conditions as compared to the actual driving speed limits, as well as impacts on the overall traffic safety and operational performance of the whole corridor. Such a methodology, integrating historical accident data analysis and simulations with both single-vehicle accident and CA-based traffic safety and operational performance models, can be used on any mountainous highway experiencing complex driving conditions and high traffic volumes. The I-70 corridor in Colorado was chosen to demonstrate the methodology. The simulation results showed good correlations with the historical accident data. The specific findings are summarized in the following.
60
0
Probability of accidents
437
100
DSL USL
80 60 40 20 0 0
20
40
(1) It was found from the 10-year historical accident data analysis that snowy and icy road surfaces, windy weather and graded curves are the major critical adverse conditions for I-70. (2) With the simulation model of single-vehicle accidents considering site-specific topographic conditions along the highway, the advisory critical vehicle speeds (CVS) were obtained for those critical adverse driving conditions identified from the data analysis. The ratios between the CVS and the corresponding posted speed limits can be used to qualitatively evaluate the accident risk as long as the actual operational speeds of large trucks are close to the posted speed limits. (3) Although the general wind information can lead to reasonable predictions of the traffic safety performance for most of the locations on I-70, it is possible that the unique terrain or surrounding for some location may require site-specific wind and environmental data. The site-specific data may be obtained through the field data collection such as using the mobile mapping technology. (4) For those special locations where the actual operational speeds of large trucks are significantly different from those of the posted speed limits, a specific analysis using the actual operational driving speeds rather than the posted speed limits is needed. (5) For a particular truck, it is not straightforward to tell which situation (i.e. fully loaded or partially loaded) is more vulnerable to single-vehicle accidents without a specific analysis. The simulation study with the model introduced in the present study on a case-by-case basis is needed. (6) Adaptive (variable) driving speed limits for trucks which can automatically adjust with different extreme weather conditions at those critical locations will be helpful on improving the truck safety on mountainous highways. The information gathered from the present study and the multi-scale study methodology may help on the decisions about adopting advanced transportation management and ITS technology. (7) DSL was found to be more beneficial to the traffic safety and operational performance when the traffic density is high. When traffic is light, the DSL case may not have obvious benefits compared to the USL case.
Vehicle/mile/lane (b) Mean Velocity Fig. 10. Safety and operational performance evaluation of MP 208–214.
Acknowledgements The present study was partially supported by Colorado Department of Transportation (CDOT) and the United States Department of Transportation through the Mountain Plains Consortium (MPC).
438
S. Chen et al. / Accident Analysis and Prevention 43 (2011) 429–438
The data and technical advices provided by the study group of CDOT Region One are highly appreciated. The opinions in this study are solely the responsibility of the authors and do not necessarily represent the official views of CDOT, USDOT or MPC. References Awadallah, F., 2007. Differential speed limit analysis and regulations on rural expressways. Road and Transport Research 16 (4), 16–25, December. Baker, C.J., 1991. Ground vehicles in high cross winds. 3. The interaction of aerodynamic forces and the vehicle system. Journal of Fluids and Structures 5, 221–241. Braver, E., Zador, P., Thum, D., Mitter, E., Baum, H., Vilardo, F., 1997. Tractor-trailer crashes in Indiana: a case–control study of the role of truck configuration. Accident Analysis and Prevention 29 (1), 79–96. Chang, L.-Y., Mannering, F., 1999. Analysis of injury severity and vehicle occupancy in truck- and non-truck-involved accidents. Accident Analysis and Prevention 31 (5), 579–592. Chen, S.R., Cai, C.S., 2004. Accident assessment of vehicles on long-span bridges in windy environments. Journal of Wind Engineering and Industrial Aerodynamics 92 (12), 991–1024. Chen, S.R., Cai, C.S., Wolshon, B., 2009. From normal operation to evacuation: singlevehicle safety under adverse weather, topographic and operational conditions. Natural Hazards Review, ASCE 10 (2), 68–76. Chen, S.R., Chen, F., 2010. Simulation-based assessment of vehicle safety behavior under hazardous driving conditions. Journal of Transportation Engineering, ASCE 136 (4), 304–315. Chen, S.R., Chen, F., Liu, J., Bienkiewicz, B., 2010. Mobile mapping technology of wind velocity data along highway for traffic safety evaluation. Transportation Research Part C 18, 507–518. Chen, F., Chen, S.R., 2009. Assessment of vehicle safety behavior under adverse driving conditions. In: 11th American Conference of Wind Engineering, June 22–26 2009, Puerto Rico. Edwards, J.B., 1998. The relationship between road accident severity and recorded weather. Journal of Safety Research 29 (4), 249–262. FHWA (2004). The safety impacts of differential speed limits on rural interstate highways, Tech Brief. FHWA-HRT-04-156. Garber, N.J., Miller, J.S., Sun, X., Yuan, Bo., 2006. Safety impacts of differential speed limits for trucks and passenger cars on rural interstate highways: a modified empirical Bayes approach. Journal of Transportation Engineering 132 (January (1)), 19–29.
Guo, W.H., Xu, Y.L., 2006. Safety analysis of moving road vehicles on a long bridge under crosswind. Journal of Engineering Mechanics 132 (4), 438–446. Harkey, D.L., Robertson, H.D., Davis, S.E., 1990. Assessment of current speed zoning criteria. In: Transportation Research Record 1281. Transportation Research Board, National Research Council, Washington, D.C, pp. 40–51. Lyman, S., Braver, E.R., 2003. Occupant deaths in large truck crashes in the United States: 25 years of experience. Accident Analysis and Prevention 35 (5), 731–739. Li, X.G., Jia, B., Gao, Z.Y., Jiang, R., 2006. A realistic two-lane cellular automata traffic model considering aggressive lane-changing behavior of fast vehicle. Physica A 367, 479–486. Moussa, N., 2005. Dangerous situations in two-lane traffic flow models. International Journal of Modern Physics C 16 (7), 1133–1148. Nagel, K., Schreckenberg, M., 1992. A cellular automaton model for freeway traffic. Journal of Physics I 2 (12), 2221–2229, France. Rickert, M., Nagel, K., Schreckenberg, M., Latour, A., 1996. Two lane traffic simulations using cellular automata. Physica A 231, 534–550. Snaebjornsson, J.T., Baker, C.J., Sigbjornsson, R., 2007. Probabilistic assessment of road vehicle safety in windy environments. Journal of Wind Engineering and Industrial Aerodynamics 95, 1445–1462. Summerfield, S., Kosior, J., 2001. Simulation of heavy trucks in inclement weather. Canadian Transportation Research Forum. The national Academies, 2006. Where the weather meets the road—a research agenda for improving road weather system. In: Report in Brief. The National Academies. The Road Information Program, 2005. Growing Traffic in Rural America: Safety, Mobility and Economic Challenges in America’s Heartland (last accessed May 17, 2008) http://www.tripnet.org/RuralRoads2005Report.pdf. U.S. Department of Transportation (USDOT), 2005. Report to Congress on the Large Truck Crash Causation Study. Federal Motor Carrier Safety Administration, U.S. Department of Transportation. Wu, J., Chen, S., 2009. Traffic flow simulation on bridge with cellular automaton technique. In: 88th Annual meeting of the Transportation Research Board, Washington, D.C. Young, R., Liesman, J., 2007a. Intelligent transportation systems for operation of roadway segments in high-wind conditions, 2000. Journal of Transportation Research Record, 1–7. Young, R, Liesman, J., 2007b. Estimating the relationship between measured wind speed and overturning truck crashes using binary logit model. Accident Analysis and Prevention 39 (3), 574–580. Zhang, W., Yang, X.Q., Sun, D.P., Qiu, K., Xia, H., 2006. Traffic accidents in a cellular automaton model with a speed limit zone. Journal of Physics A: Mathematical and General 39, 9127–9137.