## 3 Establishment of Water Rut Safety Model and Analysis of Braking and Side Deflection
### Simulation Condition Analysis
#### 3.2.2 Correlation Analysis of Indicators  
In order to ensure the accuracy of the proposed model while improving its simplicity and practicality, it is necessary to perform correlation analysis of the indicators; then highly relevant indicators can be selected to establish models for braking and side deflection. Multiple linear regression analysis was performed based on the dangerous braking zone length and side deflection time thresholds of the 19 operating conditions shown in Table 1. At a confidence level of 95%, the \(p-\)values for the \(t\) statistics are given in Figure 11.  
In multiple linear regression analysis, the \(p-\)value is used to evaluate the significance of various influencing factors on driving safety. If \(p<0.05\), it indicates that the factor has a significant impact on the length of the dangerous braking zone or lateral deviation time, and should be included in the model; if \(p\geq 0.05\), the impact is relatively small and can be eliminated. Figure 10 visually displays the \(p\)-value distribution of different factors and indicates the significance level. The results indicate that the rut length, rut width, rainfall intensity, and driving speed significantly affect the length of the dangerous braking zone and should be included in the braking safety evaluation model. The rut width, the difference in depth between the left and right ruts, rainfall intensity, and driving speed significantly affect the lateral deviation time, indicating that vehicle stability is more affected by these factors.The \(\beta\) regression coefficient is used to measure the degree of influence of independent variables on dependent variables. The regression coefficient analysis shows that there is a positive correlation between driving speed and braking zone length (\(\beta>0\)), and a negative correlation between rainfall intensity and lateral deviation time (\(\beta<0\)), indicating that the stronger the rainfall, the more likely the vehicle is to experience lateral deviation. Further analysis shows that the significance of the influencing factors may fluctuate with the change in rainfall intensity, and the influence of rut depth may increase under rainstorm conditions. The analysis results can provide data support for highway safety management and optimize driving speed limit strategies under different rainfall conditions.  
Different working conditions were selected to evaluate the safety of waterlogged rutted vehicle braking, and the results are shown in Figure 12.  
From the Figure 12, it can be seen the hazardous braking zone is affected by rut length, rut depth, rainfall intensity, and traveling speed. The braking hazard zone increases roughly linearly as the rut length is extended; this is mainly due to the expansion of deeper water at the front and rear of the vehicle, which lengthens the braking danger zone. An increased rut depth results in longer braking zones, but the effect diminishes after a certain depth is reached; rainfall intensity also expands the danger zone, but once the ruts are filled, the rate of growth slows. The travel speed has the greatest effect, as higher speeds reduce the coefficient of adhesion, lengthen braking distances, and widen the danger zone due to the fixed distribution of the water film.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Rut Length/\(L_{R}\)**} & \multirow{2}{*}{**Rut Width \(W_{R}\)**} & \multirow{2}{*}{**Rut Depth/\(D_{R}\)**} & \multicolumn{2}{c}{**Depth**} & \multirow{2}{*}{**Rainfall**} & \multirow{2}{*}{**Driving Speed**} \\  & & **(m)** & & **(mm)** & & **Between Left** & **Intensity/I** & **(km/h)** \\  & & & & & **and Right/\(D_{d}\)** & **(mm)** & \\ \hline
15 & 450 & 2 & 18 & 8 & 100 & 100 \\
16 & 450 & 2 & 18 & 8 & 150 & 100 \\
17 & 450 & 2 & 18 & 8 & 150 & 60 \\
18 & 450 & 2 & 18 & 8 & 150 & 80 \\
19 & 450 & 2 & 18 & 8 & 150 & 120 \\ \hline \hline \end{tabular}
\end{table}
Table 1: _Cont._Figure 11: Correlation analysis of influencing factors.