## 2 Analysis of Water Accumulation in Rutted Roads
### Method for Calculating Adhesion Coefficient of Accumulated Water Pavement  
On the basis of tire-road contact characteristics and _water skiing_ analysis, the influencing factors of the road surface adhesion coefficient are analyzed. It was found that the depth of pavement structure, tire tread depth, driving speed, and water film thickness all have a certain effect on the adhesion coefficient of a rainy day waterlogged pavement, and the focus of this paper is to evaluate the driving safety of rainy day pavement, on the one hand, to provide drivers with rainy day safety speed warning, and on the other hand, to provide support for the decision-making of pavement maintenance. Therefore, this paper selects two indicators of driving speed and water film thickness to estimate and analyze the adhesion coefficient of pavement.  
The water film thickness and driving speed are taken into account, and an adhesion coefficient prediction model is established through finite element analysis. In the simulation, we select the 'C-class' two-car as a simulation model with a weight of 1270 kg, which is more suitable for China's common small car technical rutting driving safety analysis, in order to match the road surface input to the model of the road surface adhesion coefficient calculations; a width of 225 mm for a 225/60 R18 tire type is chosen. The driving trajectory of the simulated vehicle is set to be along the center line of the lane.  
According to the calculated water film thickness, the road adhesion coefficient at different vehicle speeds can be calculated. After calculating the adhesion coefficient of the road surface water film thickness (_h_) and vehicle driving speed (_v_), the adhesion coefficient model is obtained as shown in Equation (13) through regression analysis.  
\[\mu^{\prime}=1.0213-0.0053v-0.0158h \tag{13}\]  
where \(\mu^{\prime}\)--road surface adhesion coefficient under some skiing conditions; _v_--vehicle driving speed (km/h); _h_--water film thickness (mm).  
The study further analyzed the variation in roadway attachment coefficients at different vehicle speeds and water film thicknesses as shown in Figure 6; each section unit represents the change in ponding form and adhesion coefficient in the cell. The rainfall intensity of 25 mm/h was used to calculate the real-time water film thickness at different roadway locations, and the empirical regression formula was used to calculate the attachment coefficients at different vehicle speeds. The results show that the adhesion coefficient decreases as the water film thickness increases, and the adhesion coefficient in the rutted waterlogged area is significantly lower than that in the non-rutted area, showing obvious spatial differences. The effect of vehicle speed on the adhesion coefficient was relatively small. The study calculates the coefficient of adhesion by means of rainfall intensity, the water film thickness prediction model, and empirical regression formula, and proposes a method that can be used to evaluate the adhesion performance of roadways under different rainfall conditions and driving speeds, which can provide a reference for the safe of roadways.