## 3 Establishment of Water Rut Safety Model and Analysis of Braking and Side Deflection
### Simulation Condition Analysis  
#### 3.2.1 Selection of Simulation Conditions  
This section simulates and analyzes a combination of operating conditions from the three aspects of rut morphology, rainfall intensity, and vehicle speed.  
Figure 10: Schematic diagram of safety evaluation indicators.  
Among them, the rut morphology includes four indicators: rut length, rut width, maximum rut depth, and left-right depth difference. The rut length is the maximum of the left and right half of the rut, and the rut width is the sum of the average of the left and right half of the rut. The maximum rut depth is the average of the maximum depth of the left and right half, and the left-right depth difference is the difference between the maximum depth of the left and right rut. In order to better control the variables, a rutted road section with the actual rut length \(\times\) width \(\times\) depth \(\times\) difference between the left and right depths of 450 m \(\times\) 2 m \(\times\) 18 mm \(\times\) 8 mm was interpolated and transformed in the longitudinal, transverse, and vertical directions, respectively. Based on this, this paper selects different rutting morphology for simulation analysis, in which the rut lengths are 150 m, 300 m, 450 m, and 600 m, the rut widths are 0.8 m, 1.4 m, 2.0 m, and 2.4 m, the maximum rut depth is 6 mm, 12 mm, 18 mm, and 24 mm, and the left-right depth differences are 2 mm, 4 mm, and 8 mm, 12 mm, respectively, in order to comprehensively characterize the impact of different waterlogged ruts on traffic safety.  
The same rutting pattern of the rainy day water distribution pattern is affected by rainfall intensity; in order to facilitate the study in the western region of China, the 5-year 10 min rainfall intensity of 150 mm/h was used for the maximum limit, while the other rainfall intensities of different heavy rainfall levels were converted to a 1-h rainfall intensity value for simulation analysis. Therefore, the rainfall intensity levels selected in this paper are 150 mm/h, 100 mm/h, 50 mm/h, and 10 mm/h for the calculations. At present, the maximum speed on the highway in China is 120 km/h. In order to better analyze the safety of high-speed driving, 120 km/h is used as the maximum braking initial speed and driving speed in the simulations. The driving speed is increased at an interval of 20 km/h, and 100 km/h, 80 km/h, and 60 km/h are used as the simulation speeds.  
This paper analyzes 19 simulation conditions under the rut index values, rainfall intensity, and vehicle speed to perform braking simulation and side deflection simulation. These conditions can comprehensively reflect the impact of waterlogged rutting on driving safety and provide reliable data support for the subsequent evaluation system. The simulation conditions are shown in Table 1.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{3}{*}{**No.**} & **Rut Length/\(L_{R}\)** & **Rut Width \(W_{R}\)** & **Rut Depth/\(D_{R}\)** & **Difference Between Left** & **Rainfall Intensity/I** & **Driving Speed (km/h)** \\  & **(m)** & **(m)** & **(mm)** & **and Right/\(D_{d}\)** & **(mm/h)** & **(mm/h)** \\ \hline
1 & 150 & 2 & 18 & 8 & 50 & 100 \\
2 & 300 & 2 & 18 & 8 & 50 & 100 \\
3 & 450 & 2 & 18 & 8 & 50 & 100 \\
4 & 600 & 2 & 18 & 8 & 50 & 100 \\
5 & 450 & 0.8 & 18 & 8 & 50 & 100 \\
6 & 450 & 1.4 & 18 & 8 & 50 & 100 \\
7 & 450 & 2.4 & 18 & 8 & 50 & 100 \\
8 & 450 & 2 & 6 & 8 & 50 & 100 \\
9 & 450 & 2 & 12 & 8 & 50 & 100 \\
10 & 450 & 2 & 24 & 8 & 50 & 100 \\
11 & 450 & 2 & 18 & 2 & 50 & 100 \\
12 & 450 & 2 & 18 & 4 & 50 & 100 \\
13 & 450 & 2 & 18 & 12 & 50 & 100 \\
14 & 450 & 2 & 18 & 8 & 10 & 100 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation conditions of car rut with accumulated water.