## 4 Case Analysis of Driving Safety Evaluation of Water-Filled Ruts
### Driving Safety Evaluation on Roads with Water-Filled Ruts  
Based on the calculation results of the multi-dimensional rut index above, it is possible to evaluate the braking and side deflection safety on any road section using models established in this paper. For the water-filled rut, its safety evaluation model is shown in Table 3.  
As can be seen from the table, under different rainfall intensities, it is possible to control the dangerous braking length and critical side deflection time of the water-filled \begin{table}
\begin{tabular}{c c c c c c} \hline  & **df** & **SS** & **MS** & **F** & **Significance-F** \\ \hline Regression analysis & 4 & 203.5507 & 50.88768 & 41.46921 & \(2.16\times 10^{-5}\) \\ Residual & 8 & 9.816958 & 1.22712 & & \\ Total & 12 & 213.3677 & & & \\ \hline \end{tabular}
\end{table} 
Table 2: Analysis of variance of the factors affecting traveling side deviation. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**No.**} & **Braking Safety Evaluation Model** & **Side Deflection Safety Evaluation Model** \\ \hline Rut 1 \# & \(S=-538.619+1.576I+4.303v\) & \(T=25.718-0.082I-0.171v\) \\ Rut 2 \# & \(S=-307.9+1.576I+4.303v\) & T=\(24.87-0.082I-0.171v\) \\ Rut 3 \# & \(S=-110.987+1.576I+4.303v\) & \(T=22.13-0.082I-0.171v\) \\ \hline \end{tabular}
\end{table} 
Table 3: Safety and side deflection evaluation models on different road sections. rut by controlling the driving speed. Using the braking safety evaluation model and side deflection safety evaluation model in Table 2, the length of the dangerous braking area and critical side deflection time under different rainfall intensities and different driving speeds are calculated. For Rut 1#, Rut 2#, and Rut 3#, the changes in the length of the dangerous braking zone and the critical deflection time are shown in Figure 14.  
As far as braking is concerned, for Rut 1#, when the driving speed is 120 km/h or less, there are no dangerous braking zones. When the rainfall intensity is 30 mm/h and 60 mm/h, there are no dangerous braking zones at driving speeds below 100 km/h. When the rainfall intensity is 90 mm/h and 120 mm/h, there are no dangerous braking zones at driving speeds below 80 km/h. For Rut 2#, when the rainfall intensity is 10 mm/h and 30 mm/h, there are no dangerous braking zones at driving speeds below 60 km/h. When the rainfall intensity is 60 mm/h, there will be no dangerous braking zone at driving speeds below 40 km/h. When the rainfall intensity is 90 mm/h and 120 mm/h, there will be no dangerous braking zone at driving speeds below 40 km/h. When the rainfall intensity is 90 mm/h and 120 mm/h, there will be no dangerous braking zone when the driving  
In this paper, the length of the dangerous braking zone is 0, as the safety limit of the braking zone length, and the time to reach the critical side deviation is 5 s, as the safety threshold of the side deviation time. The results of calculating the critical safe vehicle speed based on the braking hazard length and side deflection time are shown in Table 4.  
The results of the analysis in this section can be directly used for rainy day traffic management and road safety optimization. By calculating the critical safe speeds under different rainfall conditions, recommendations for rainy day travel speed management are provided. From the figure, it can be seen the safe driving limits within different ruted sections are different. For example, for the road section K1244+250 K1245+250, when the rainfall intensity exceeds 80 mm/hour in one hour, it is no longer possible to ensure safe driving by controlling the speed. Speed control is critical for safety on slippery roads, but extreme rainfall conditions may render speed control ineffective, and additional road design measures may be required to prevent accidents. In addition, increased rut depth can significantly reduce the coefficient of adhesion, so it is recommended that rut depth be reduced and drainage design be optimized through proper road maintenance.