1. Introduction
Rutting is a common distress of asphalt pavements, which adversely impacts the serviceability of the pavement and driving stability of the vehicle [
1,
2]. When a vehicle drives through a rut, it will produce a phenomenon known as wandering, and the vehicle may show potentially unstable, oscillatory lateral, or yaw motions with a low frequency. Drivers may feel discomfort, due to bumps, while negotiating the rutting or even cause serious traffic accidents due to operational faults. The number of accidents per 100 million vehicle-miles of highways in the states of Arizona, North Carolina, and Maryland significantly increases when the rut depth approaches 10 mm [
3]. It has been identified that the presence of rutting would cause lateral instability in vehicles and impact driving safety when the rutting depth exceeds 20 mm [
4]. So, driving safety is remarkably influenced by pavement rutting.
Exactly as the findings about the threats of rutting to driving safety, rutting distress is more crucial for influencing driving safety than roughness or cracking, due to the large height differences and features of easy ponding and frozen in rutting. In order to improve the rutting maintenance from the perspective of driving safety, quite a few investigators have studied the effects of different rutting shape indicators on driving comfort or the safety of vehicles and obtained their allowable values. Zheng et al. [
5] possessed the view that the rut depth and rut side angle obviously affected the maximum vertical acceleration of the vehicle, while the rut average width had small effects. A mathematical model regarding the interaction between automobiles, wheels, and road surfaces with ruts was developed by Vansauskas et al. [
6]. They found that the vehicle became unstable if the rut is over 5cm and the width over 50 cm, when driving at a speed of 60 km/h. Guo et al. [
7] suggested lateral offset and lateral acceleration as rutting indicators for evaluating the influence of rutting length. Jia et al. [
8] found that driving across rutting had a greater influence than driving on the rutting sidewall and stated that rutting depth should be less than 20 mm to ensure driving quality when across a rut on dry pavement. Kuznetsov et al. [
9] determined the maximum allowable rutting depth via a computer program and accordingly defined 14 mm as the allowable value of rutting depth to ensure safety when driving over 160 km/h.
In recent years, in addition to the road safety affected by pavement rutting, unfavorable conditions with adverse weather have been frequent events and constantly cause serious impacts on traffic safety. Approximately 300 traffic accidents happened due to adverse weather in Germany in January 2016 [
10]. More than 60% of traffic accidents caused by fierce winds and other adverse weather were accounted for in the south-eastern coast of China [
11]. Adverse weather mainly includes strong winds, heavy rain, ice, and snow [
12], and even their simultaneous occurrence. On the one hand, the influence of adverse weather can be considered as a kind of action subject to the vehicle and, thus, affecting its driving stability. On the other hand, the driving risk possibly intensifies, due to the coupling effect of adverse weather and rutting distress. The ponding formed in the rutting under adverse weather may decrease the friction coefficient of road surface and change the mechanical characteristics of the vehicle, resulting in losing lateral stability [
13], while driving in heavy rains, snows, and strong winds. Moreover, a water film on the pavement surface will generate a hydroplaning phenomenon on the rolling tire, as a result of the joint impact of rutting and ponding. Due to the hydroplaning phenomenon, the water pressure in the front of the tire pushes the water under the tire, and then the water film is formed and separates the tire from the pavement, thus resulting in a loss of road friction coefficient [
14,
15]. Confronting such adverse circumstances, smart tires, a promising technology, are highlighted in detecting distressed rutting sections and road friction, then interacting with follow-up vehicles to avoid unfavorable positions, in order to ensure driving stability [
14,
16].
In addition to adverse weather, traffic accidents more frequently happen in horizontal curve segments than tangent segments of the road [
17,
18]. Fatal accidents commonly suddenly occur due to loss of lateral sideslip stability or roll-over stability as a result of unfavorable external factors. Exceeding the limit value of side friction is a key reason for lateral instability in curve segment [
19,
20], but it connects closer relationship with weather and pavement material. The instability of the vehicle is generally induced by inappropriate geometry parameters of curve segments. The relevant studies have demonstrated that the accident frequency dramatically increases as the radius of the curve decreases [
21]. In addition, the vehicle on the curve segment is prone to occur kidding and roll-over with the increase of road slope and the decrease of superelevation [
22]. However, the sideslip risk is not remarkably affected by superelevation of the road [
23]. As a result, driving stability analysis is a complex and comprehensive topic, which shall follow the integrated consideration of adverse weather, road, alignment, and rutting in need.
As a result, recent studies have highlighted the significance of researching driving stability under adverse weather, as well as focusing on adverse effects caused by alignment of curve segment. It is generally accepted that strong winds and heavy rains lead to low lateral stability [
24,
25,
26,
27], which is susceptible to resulting in sideslip, yawing, and roll-over instability. The evaluations of these instabilities under unfavorable situations were performed by means of analyzing the dynamic indicators of vehicles [
28], including lateral displacement, lateral acceleration, load transfer rate, yaw angle rate, and roll-over angle [
29,
30,
31,
32,
33,
34]. Chen et al. [
35,
36] found that the car is more likely to sideslip and the cargo truck has higher roll-over risks under crosswind. Wang et al. [
37] simulated driving experiments under snowy weather in a bridge and tunnel connection segment, and finally found that the large lateral offset can be prevented by increasing the friction coefficient of pavement and radius of circular curve. Yin et al. [
38] investigated the skidding, roll-over, and lateral slip of the vehicle by accounting radius of circular curve and superelevation and found that the safety margin of the vehicle’s skidding, roll-over, and lateral slip increased when the radius of the circular curve and superelevation increases. Alrejjal et al. [
39] focused on the roll-over propensity influenced by horizontal and vertical alignments under different weather conditions, thus revealing that the lateral acceleration was amplified due to a tight degree of curvature and steep downgrades.
The previous findings mainly investigated the effect of single adverse weather or road alignment on driving stability, but neglected rutting conditions accordingly, or solely analyzed the unfavorable conditions of vehicle stability due to rutting distress, with only a few research on the composite effects of rutting and wet condition. However, the dynamic response process of the vehicle driving across rutting coupled in curve segments with adverse weather is a crucial issue that determines driving safety. So, relevant evaluation remains to be proposed, so as to implement the management and control of adverse situations, as well as make pavement maintenance decisions.
Given the research shortcomings and gaps above, this study intends to figure out the dynamic responses of the vehicle driving across rutting on the curve segment under adverse weather and further evaluate the effects of various driving conditions on the lateral stability of the vehicle. So, a framework for evaluating lateral stability of the vehicle was developed to efficiently describe the impacts of different factors. The Carsim software was utilized to simulate the process of driving across rutting, considering various road alignments and adverse weather. The vehicle’s dynamic responses that represent lateral stability were analyzed via indicator lateral acceleration (LA), slip angle (SA), load transfer ratio (LTR), and roll-over angle (RA). Considering the likelihood of poor correlation between LA, SA, LTR, and RA, the integrated lateral stability caused by various factors was compared with entropy-weighted grey relational analysis (GRA), based on orthogonal tests. The outcomes of this study will contribute to establishing criteria for controlling key adverse conditions and making decisions on pavement maintenance.
5. Conclusions and Prospects
In this study, a novel framework was established to implement a systematic evaluation of the lateral stability of the vehicle by considering various impact factors. The software Carsim was utilized to perform simulations. Targeted indicators were adopted to evaluate the effects of seven factors on the lateral stability of the vehicle, including LA, SA, LTR, and RA, as well as the comprehensive relation grade (CRG). The most important findings of the present study are concluded below:
- (1)
Four targeted indicators generally experienced several stages, due to the composite effect of lateral wind, rutting, and curve driving, including a stable increasing stage, sharp increase, sharp decrease, and fluctuation. The sharp fluctuation, up and down, of four indicators was due to the process of the wheel driving into a rut and then out of a rut during the lane change. Lateral wind created a relatively weak influence on the indicators’ tendencies during the stable increasing stage.
- (2)
LTRs were generally within the threshold, while the maximum RA far exceeded the threshold in the results of single-factor analysis, despite the fact that they both characterized the roll-over stability of the vehicle. Consequently, the application of a single indicator showed limitations in evaluating the lateral stability of the vehicle, so a comprehensive indicator was expected to enhance this defect.
- (3)
The targeted indicators suddenly changed in a short time, due to the wandering behavior caused by rutting. Especially, this sudden change phenomenon was greatly enlarged in the case of WHR = 5. The indicator RA exceeded the threshold after driving across the rutting immediately, i.e., behaving with high driving risks. So, the instantaneous state of crossing severe rutting could be defined as a dangerous moment, which shall be cautiously prevented from the perspectives of both pavement and vehicle.
- (4)
The vehicle was out of control, due to the joint adverse conditions with severe rutting, poor road alignment, strong wind, and low skid resistance, obviously presenting high roll-over risks. Controlling a single factor was unable to ensure driving safety, due to the notable significance of the other factors. The combined requirement of WHR > 10 and f > 0.4 was recommended to control the pavement condition for ensuring driving safety in this study.
- (5)
LA and SA had a strong correlation to jointly evaluate the sideslip stability of the vehicle. However, the Pearson’s correlation between LTR and RA was small, so a single indicator is weak in performing good efficiency on the roll-over stability of the vehicle. A comprehensive indicator remains to be proposed to enhance evaluation efficiency.
- (6)
A comprehensive relational grade (CRG) was, thus, proposed in the developed framework to improve evaluation performance, and it revealed that vehicle speed and the WHR of rutting had leading effects on driving safety, followed by radius of circular curve, superelevation, crosswind angle, crosswind speed, and friction coefficient, respectively.
The findings of this study revealed that the established framework performs well on evaluating the effect of different impact factors on the lateral stability of the vehicle, while driving across rutting, and particularly provides guidance to control pavement conditions from the perspective of driving safety. Despite the aforementioned contributions, a few shortcomings of this study remain to be optimized and enhanced. The major limitations lie in the quality and accuracy of the simulation, due to lack of real-world data. The consideration of factors is relative comprehensive, but in modeling the road, due to the uncertainty and variability of the hydroplaning potential, influenced by complex multi-factors, there is a case of simplified modeling. Further, only small-size passenger cars are discussed, on account of the limitation of the length of the article. Therefore, extensive in-depth investigations on the optimization of the developed framework, based on practical measured data, are envisaged in the follow-up studies. Moreover, the comparative study on the lateral stability of different vehicle types will be systematically performed, in conjunction with road maintenance recommendations for future consideration.