## 2 Literature Review  
### Studies on Vehicle Skidding Based on the Model-Driven Method  
The existing design policy for horizontal curves is based on a mathematical model that represents a vehicle as a mass point. According to this model, when a vehicle traverses a horizontal curve, it experiences centripetal acceleration that is balanced by superelevation and tire-pavement interface friction [13]. However, recent research has highlighted safety concerns associated with this model. [PERSON]'s studies [31; 32] have shown that when vehicles, especially trucks, traverse horizontal curves with longitudinal slopes, the application of braking and traction forces on a slope can result in dynamic variations in both vertical tire load and tire-pavement side friction. These variations may cause the vehicle to skid at lateral accelerations lower than predicted by the point mass model. To address these concerns, [PERSON] et al. [33] proposed an improved bicycle model that incorporates various factors such as slope, superelevation, front- and rear-wheel drive, and aerodynamic resistance. The bicycle model offers advantages over the point mass model as it allows for analysis of both force and torque balance of the vehicle. Furthermore, it enables the examination of individual axle skid [17]. However, the research lacks a comprehensive consideration of driver braking maneuvers. In [PERSON]'s study [34], an enhanced bicycle model was presented, and slight braking scenarios for two-axle vehicles were analyzed. The findings indicated potential safety problems for roads with combined horizontal and vertical components. NCHRP Rep. [PERSON] proposed superelevation criteria for sharp horizontal curves on steep grades based on the findings of [PERSON] et al., using bicycle and multibody dynamics models [19]. Although the multibody model offers high accuracy and minimal errors, it incorporates the force analysis of various vehicle components, leading to complex influencing factors and solving procedures. The impact of braking on vehicle skidding is related to the redistribution of braking force and lateral force [5; 35; 36]. Several studies have analyzed the relationship between tire braking force and lateral force during braking. [PERSON] [37] was the first to theoretically analyze the skidding characteristics during tire braking and designed an expression for the lateral force function, considering the braking force as a variable. [PERSON] [38] proposed that, under specific conditions, the longitudinal and side friction relationship of tires follows a friction ellipse, with boundaries determined by the peak braking force (driving force) and peak lateral force. [PERSON] and [PERSON] [39] simulated and analyzed vehicle skidding using a simulation model, and the study identified that factors such as water film thickness and driving speed significantly influence the peak friction coefficient of the vehicle. [PERSON] et al. [40] used simulation models to calculate the peak friction under different operating conditions and analyzed three possible modes of skidding when vehicles travel on a horizontal curve. The safety concerns arising from braking maneuvers pose significant challenges to researchers studying human driving behavior. They are also a critical focus of research for emerging autonomous driving and driver-assistance systems [5; 10; 30]. Automotive companies have proposed active braking collision avoidance algorithms that employ similar models. These algorithms utilize three key indicators--relative distance, relative velocity, and driving speed--to define the critical distance function for warning and active collision avoidance control. The brake control information is then computed by onboard computer systems and conveyed to the driver. This research primarily focuses on longitudinal collisions and pays insufficient attention to the lateral safety issues during braking on horizontal curves.