## 3 Establishment of Water Rut Safety Model and Analysis of Braking and Side Deflection
### Simulation Model Establishment
#### 3.1.2 Selection of Safety Evaluation Indicators  
1. Safety evaluation indicators of braking Further, when combined with the rut waterlogged state of the braking results for in-depth analysis, with different braking starting points for simulation analysis, the braking distance of the the vehicle in relation to the waterlogged rut positional relationship is as shown in Figure 9. From the figure, it can be seen that the braking distance with 180 m as the braking starting point is the smallest; this is due to its braking path and the fact that the rut has no contact, with the rest of the braking starting points of the braking path completely in contact with the rut or partially in contact with the braking path. In the initial braking action, where the braking path is in contact with the thickness of the water film, the larger the vehicle, the longer the braking distance. Therefore, the length and depth of the rutted water is an important factor affecting the safety of vehicle braking on waterlogged rutted pavement. Combining the previous studies and the braking distances at different braking starting points in Figure 9, according to the contact state between the vehicle and the rut, there exists a region between 30 m and 120 m in which the braking distance is greater than the prescribed safety distance. To summarize, on a road with accumulated water, when braking starts at a point and the braking distance is greater than the specified safe distance at the current driving speed, the length along the driving direction is defined as a dangerous braking zone. We select a point on the road as the starting point for car simulation, and define it as the 0 point of coordinate. Then, a point away from the starting point is chosen as the braking point for simulation, and the result curves are shown in Figure 10a. The x-axis is the braking starting point coordinate and the y-axis is the braking distance. We find that the coordinates of the starting  
Figure 8: The flowchart for the establishment of the safety model and the analysis of braking and side deflection. Figure 9: Braking distances for different starting points in waterlogged ruts. point of braking at the braking distance are equal to the safe vehicle distance at the corresponding driving speed, and the length between the two is the length of the dangerous braking zone. For the same rut, under different rainfall intensity and traveling speed, the water accumulation pattern is different, and the length of hazardous braking zone is different; under the same rainfall intensity and traveling speed, the water accumulation pattern is also different for ruts of different lengths, widths, and depths, thus affecting the length of hazardous braking zone. Therefore, this paper selects the length of dangerous braking zone as the safety evaluation index of waterlogged rut braking. 2. Safety evaluation index of side deflection  
The side deflection distance is used as an index for the results of the lateral safety simulation analysis in this paper. The occurrence of the side deviation of a vehicle in a waterlogged rut is mainly due to the different friction states of the left and right wheels in contact with the road surface, resulting in an imbalance of the lateral forces on the wheels, and thus the risk threshold for the amount of side deviation of a rut can be defined as half of the width of the rut waterlogged rut. But for car ruts, if uneven water accumulation occurs, the width of the water area of different ruts is not the same. For the same rut, the width of the accumulated water is not the same for different rainfall intensities and time periods. Therefore, it is impossible to directly characterize the lateral safety of a section with accumulated water. For a rut with accumulated water, the side risk threshold is half the width of the water accumulation, but the time (\(T\)) to reach the risk threshold is not the same under different conditions. If the driver is still unable to respond when the time reaches \(T\), then the vehicle will be in danger (Figure 9(b)).