## 3 Establishment of Water Rut Safety Model and Analysis of Braking and Side Deflection
### Driving Safety Evaluation Model for Water Rut  
#### 3.3.1 Braking Safety Evaluation Model  
By analyzing the impact of the above factors on the length of the dangerous braking zone of water rut, it can be seen that rut length, rut depth, rainfall intensity, and driving speed all have a good linear correlation with the length of the dangerous braking zone. Therefore, it is possible to establish multiple linear regression models of dangerous braking zone length, rut length, rut depth, rainfall intensity, and driving speed based on the calculation results of 13 operating conditions (1, 2, 3, 4, 8, 9, 10, 14, 15, 16, 17, 18, and 19). We assume the model relationship between the length of the dangerous braking zone and these four indicators is as follows:  
\[S=\beta_{0}+\beta_{1}L_{R}+\beta_{2}D_{R}+\beta_{3}I+\beta_{4}V\]  
If we set the confidence level to be 95% and perform multiple linear regression analysis with a significance level of 0.05 on the selected operating conditions and results, the obtained regression coefficients are as follows:  
\[\{\beta_{0},\beta_{1},\beta_{2},\beta_{3},\beta_{4}\}=\{-899.845,0.997,15.549, 1.576,4.303\}\]  
Then, we obtain a regression equation as shown in Equation (14) for the driving safety evaluation model based on dangerous braking length.  
\[S=-899.545+0.997L_{R}+15.54D_{R}+1.576I+4.303V \tag{14}\]  
where \(S\) is the dangerous braking zone length (m), \(L_{R}\) is the rut length (m), \(D_{R}\) is the rut depth (m), \(I\) is the rainfall intensity (mm/h), and \(V\) is the driving speed (km/h).  
Different working conditions were selected to evaluate the safety of the side deflection of the waterlogged rut, and the results are shown in Figure 13.  
According to the results of conditions 3, 5, 6, and 7, increasing the rut width prolongs the lateral deviation time and improves safety. This is because as the width increases, both wheels will contact the water film more evenly, thus reducing the risk of deviation; according to the results of Case 3, 11, 12, and 13, the greater the difference in rut depth between the left and right wheels, the shorter the lateral deviation time and the higher the safety risk. This is because the depth difference will cause an uneven thickness of water film, resulting in unbalanced tire adhesion and increased lateral instability. Through the simulation results of Case 3, 14, 15, and 16, the higher the rainfall intensity, the shorter the lateral deviation time, but the effect will be stabilized after exceeding a certain critical value. By analyzing the results of Case 3, 17, 18, and 19, the higher the vehicle speed, the shorter the lateral deviation time, and the more abrupt and dangerous the deviation is. Increased vehicle speed reduces traction, increases the likelihood of skidding, and makes it more difficult to maintain control.  
Differences in rut width and depth are key structural factors affecting lateral deviation, while rainfall intensity and travel speed have dynamic effects. Higher speeds and deeper rutting imbalances can seriously affect driving safety, so careful road maintenance and adaptive driving strategies are needed on waterlogged roads.