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Project supported by the National Natural Science Foundation of China (Grant No. 50478088) and the Natural Science Foundation of Hebei Province, China (Grant No. E2015202266)
The aim of this work is to investigate the influence of rainy weather on traffic accidents of a freeway. The micro-scale driving behaviors in rainy weather and possible vehicle rear-end and sideslip accidents are analyzed. An improved CA model of two lanes one-way freeway is presented, where some vehicle accidents will occur when the necessary conditions are simultaneously satisfied. The characteristics of traffic flow under different rainfall intensities are discussed and the accident probabilities are analyzed via the simulation experiments by using variable speed limit (VSL) and incoming flow control. The results indicate that the measures are effective especially during heavy rainstorms or short-time heavy rainfall. According to different rainfall intensities, an appropriate strategy should be adopted in order to reduce the probability of vehicle accidents and enhance traffic flux as well.
Driving on a highway in rainy weather can become unsafe.[1–3] It may become difficult to control the vehicle when a pavement with a layer of water fails to offer the required amount of friction, especially at high speed even for a highly skilled and alert driver.[4,5] At the same time low visibility may not guarantee enough safe sight distance when the rainfall intensity is large. This increases the safety risks, e.g., resulting in single or multiple rear-end accidents, or a sideslip accident. It means that the road flux will drop. As is well known, there are many influencing factors on traffic safety, such as road geometric condition, driver character and state, vehicle type, weather, and other traffic states. All these factors interact in complicated ways, making the traffic accident size, e.g., the occurrence of accident and accident rate, have a nonlinear relationship with the factors.[6–10] Now, the point is how to describe the complex dynamic process microscopically by using a model and then providing the effect of rainy weather on road safety?
On the whole, the approaches of road traffic safety in rainy weather can be classified as three categories. Firstly, a number of previous studies were devoted to the effect of rainy weather on road traffic safety by using macro data and statistical methods.[1,4,6,8–13] Some analytic equations or models were used to map the relationships among the rainfall intensity, other variables, and traffic accident size.[6,8,9,11] For example, Keay and Simmonds investigated the effect of weather variables on traffic flow at a site in Melbourne, Australia,in the period 1989–1996.[6] Rainfall was the strongest correlated weather parameter and it had the greatest influence in winter and spring, when traffic volume decreased on wet days. A novel and rigorous approach was presented to analyze the influence of rainfall on road traffic accidents in urban areas by Jaroszweski and McNamara.[8] Cai et al. developed a quantitative model to analyze driving risks under rainy weather conditions and built a multi-ordered discrete choice model to analyze those risk factors and their influence degrees.[9] Those studies show that the road factors, driver factors and environment factors are strongly related to the accident size, and some control advice, e.g., variable speed limit (VSL), is provided for the traffic management department. But the complex dynamic process of traffic flow, e.g., the micro-scale driver behavior and the occurrence of traffic accident, are not described. Secondly, some are devoted to the estimation of vehicle sideslip from the angle of vehicle engineering caused by tire force, wheel cornering stiffness, road friction coefficient, etc.[14,15] Traffic flow and its nonlinear evolution in rainy weather have not been discussed. Thirdly, some research focused on the traffic accident avoidance and road safety improvement in adverse weather conditions by using the microscopic simulation models of traffic flow.[3,5,7] Using the car-following model, Wang et al. estimated the emergency braking distance of passenger vehicles with respect to the following interval that should be kept as a “gap” between two consecutive vehicles moving in the same lane.[7] The theoretical models for lane change and operational risk are used to study the multi-lane freeway at a microscopic level in disaster weather. Wan et al. discussed a dynamic speed control strategy to reduce collision risks on freeways by using a car-following model to simulate the traffic operation in adverse weather.[5] An indicator, chosen risk index (CRI), was defined for describing the chosen risk level for drivers in a car-following case by Hjelkrem and Ryeng[3] Obviously, only a car-following model was used to describe the traffic flow process, and the complex time-space evolution in rainy weather has not been discussed.
As an excellent tool, cellular automata (CA) models have been used widely to investigate the traffic flow behaviors. In particular, many researchers have studied the occurrence of car accidents by using the extended CA models,[16–26] e.g., the deterministic NS model proposed firstly by Boccara et al.[20] Only the traffic influences of low visibility weather, e.g., foggy weather, on a freeway including the fraction of real vehicle rear-end accidents and road traffic capacity were studied by using the established CA model. The traffic flow model in rainy weather has not been established and the possible traffic accident has not been discussed. In the present work, according to those and symmetric two-lane Nagel–Schreckenberg (STNS) model, we analyze the micro-scale driving behaviors in rainy weather and possible vehicle rear-end and sideslip accidents. An improved CA model of two lanes one-way freeway is presented. The characteristics of traffic flow under different rainfall intensities and traffic demand are discussed and the different effects are analyzed via the simulation experiments by using VSL and incoming flow control. The optimal strategies are provided under different conditions.
After it rains for some time, the road surface will be covered with rain water. This makes the tyre surface become smooth, for the tire tread gaps are also filled with rain water. There is not enough time to squeeze out the water from the smooth wheel tires especially in a heavy rainstorm or short-time heavy rainfall. The water film will gather in the rotating wheel and form a wedge. For a concrete road, the relationship between the depth of surface water (water film) and rainfall intensity is described as follows:[27]
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![](cpb_26_10_108901/cpb_26_10_108901_ieqn001.gif)
The water film leads to the decreasing of contact area between tire and road surface and makes the adhesion coefficient decrease with the increase of wedge length. The reduced friction coefficient (φ) can be fitted by a linear formula as follows:[2]
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The decreasing of adhesion coefficient makes the braking distance lengthen, which may occur in single or multiple rear-end accidents. So the the safety distance Ssafe between a vehicle and its preceding vehicle should increase. By using the classical vehicle safety braking model, Ssafe can be calculated from formula (
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Obviously, some rear-end accidents will happen if the distance between a vehicle and its predecessor is not larger than Ssafe, meaning that the safety distances are not met and the drivers cannot brake in time.
In the driving course, the influence of many forces on the vehicle, e.g., side wind, braking imbalance between left and right wheels of automobile, and steering brake, can cause its lateral displacement even sideslip, which makes the vehicle deviate from the right direction. Considering the fact that the vehicle sideslip in rainy weather is mainly caused by lateral gravity component due to the decrease of friction coefficient, we only study the case of a transverse slope. As shown in Fig.
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Fy denotes the lateral force acting on the center of mass and is calculated from
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According to Fig.
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If the above formula is integrated, we can derive vehicle yaw rate model as shown in formula (
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If r in formula (
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For a vehicle driving at speed v, lateral gravity component leads to its steering angle θ due to the decrease of friction coefficient. At the same time, the driver makes the vehicle return to normal driving conditions by braking and adjusting the direction after the reaction time T0. But the longitudinal displacement and lateral displacement will appear.
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If Sy is large enough to make the vehicle deviate from the original lane, a sideslip motion occurs and part of sideslip motions form a traffic accident. For only one mainline on a freeway with no ramp as shown in Fig. Sy for a left lane vehicle with the left sideslip direction is larger than the sum of the width of marginal strip and the width between its left front corner and the lane left line; Sy for a right lane vehicle with the right sideslip direction is larger than the sum of the shoulder width and the width between its right front corner and the lane right line; Sy for a left lane vehicle with the right sideslip direction is larger than the distance between its right and the left of right lane vehicle if the position is occupied with a vehicle. Sy for a right lane vehicle with the left sideslip direction is larger than the distance between its left and the right of left lane vehicle if the position is occupied with a vehicle.
As shown in Fig.
Each cell may be either empty or occupied by one vehicle with an integer velocity v between zero and the maximal speed limit vmax, where we use vmax1 in place of vmax for a car and vmax2 in place of vmax for a truck and Pcar denotes the proportion of car. The vmax is a stable value when no VSL signal is inputted and a variable value when a VSL signal is inputted. Two speed limit values are set for car and truck, respectively. In order to describe the traffic flow processing of the studied object, we establish an extended CA model based on symmetric Nagel–Schreckenberg (NS) model with the occurrence of vehicle accidents in rainy weather. The x(i, t) denotes the position of vehicle i at discrete time step t. The first vehicle is marked as 1, and the following vehicles are marked as 2, 3,...,i. The d(i, t) denotes the empty cells between vehicle i and its predecessor at time t, d(i, t)front and d(i, t)back refer to the empty cells between vehicle i and its preceding vehicle and between vehicle i and its successor on the adjacent road, respectively. The a denotes the acceleration if it is greater than zero or denotes the deceleration if it is smaller than zero.
Under normal circumstances, the vehicle evolution rules are as follows.
The lane-changing rules of mainline vehicle are as follows.
In rainy weather, the driver sight distance is affected when the rainfall intensity reaches 0.206 mm/min.[28] At the same time, the driver will open the fog lamps in order to find the preceding vehicle, which makes his actual sight distance longer than that for visibility. The actual sight distance is set to be 1.1 times that for visibility in the present study for describing the actual reaction of driver.[24] For each vehicle, Ssafe in each simulation step is calculated by using formula (
In a basic model, the rule is designed to decelerate to any value immediately for a vehicle in order to keep the safety distance. So a vehicle rear-end accident will not occur. As discussed in Subsection
If one of the above conditions is met, a rear-end accident occurs once during or after time T0. The number of the rear-end accident occurrences N1ac is increased by 1 under the assumption of neglecting time correlations proposed by Boccara et al.[20] The vehicle rear-end accident does not really occur in the simulation. These dangerous situations are calculated and considered to be the signal of the occurrence of accidents. The rear-end accident probability P1ac is defined as N1ac/N, where N is the total number of vehicles.
As discussed in Subsection
The total number of vehicles Nac is equal to N1ac plus N2ac. The total accident probability Pac is defined as Nac/N and also equal to P1ac plus P2ac.
The boundary conditions are open. In each time step, when the update of vehicles on the freeway is finished, the position xlast of the last vehicle on each lane is checked. If xlast > vmax, a vehicle with velocity vmax is injected with the entering probability Pe at the cell min{vmax, xlast − vmax}. If rand2 > Pcar, the injected vehicle is a truck, otherwise it is a car. The leading vehicle on each lane is removed, if its position xfirst > L0 and its following vehicle becomes the new leader.
The freeway section described in Section
According to actual statistics in traffic engineering, the values of accident rate AH under different rainfall intensities are in a range from 0.76 to 160 number/billion vehicle·km.[32] It means that comparable accident rate AH1 is transformed due to unity of units varies from 0.0532 to 11.2 (‰) number/vehicle· 5 km·7000 s. The simulated accident probabilities in rainy weather is in a range from 0.5 to 8.5 (‰) number/vehicle· 5 km·7000 s. Obviously the accident probability of the simulated CA model is in a range of the actual statistics. The validity is preliminarily proved.
Figure
Figure
![]() | Fig. 12. Comparison among speed-density plots. In Figs. |
Figure
Figure
Figure
The micro-scale driving behaviors in rainy weather and possible vehicle rear-end and sideslip accidents are analyzed. The influences of traffic accident in rainy weather and the management strategies are studied by using an improved CA model for a two-lane freeway mainline. The simulation results indicate that controlling the incoming flow and inputting VSL signal are effective especially when there is a heavy rainstorm or short-time heavy rainfall. According to different rainfall and traffic demand, the appropriate control strategies should be adopted in order to reduce the probability of vehicle accidents and enhance traffic flux as well. These findings may provide reference values for freeway management and control.
The formula for the micro-scale driving behaviors in rainy weather is still relatively simple and realistic. Vehicle accidents do not really occur in the simulation and these dangerous situations are only calculated and considered to be the signal of the occurrence of accidents. These problems will be further studied in future.
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