## 5 Conclusions  
Based on the rut detection and the three-dimensional shape of the rut, this paper conducts road surface water shape recognition and driving safety impact analysis, establishes a water-filled rut driving safety simulation model, and then evaluates the water rut driving safety. The main research conclusions are as follows:  
1. We realized the distribution calculation of the water film thickness of the whole road area of the rutted road section. According to the characteristics of pavement runoff and the three-dimensional shape of ruts, a calculation method for the water catchment process of rutted pavement based on grid division is proposed, and the pavement is divided into rutted pavement and non-rutted pavement. According to the three-dimensional shape and distribution characteristics of rutting water, the water film thickness of the rutting water pavement is calculated. The water film thickness of the non-rutting water pavement is calculated, and the gridded water film thickness of the whole lane road surface under the influence of rutting is obtained.
2. The length of the dangerous braking zone and the side deflection time are proposed as the driving safety evaluation indexes of water-filled ruts. The three-dimensional morphological indicators of ruts, such as rut length, width, depth, and depth difference between left and right ruts, were selected together with rainfall intensity and driving speed to establish a combination of control variable simulation conditions. According to the correlation analysis of influencing factors, the results show that the rut length, rut depth, rainfall intensity, and driving speed are strongly correlated with the braking distance, and the rut width, left and right rut depths, rainfall intensity, and driving speed are strongly correlated with the side deflection distance.
3. The effects of rut length, rut depth, rainfall intensity, and driving speed on the braking distance are analyzed, and a safety evaluation model for driving in water-filled ruts is established. The influence of rut width, left and right rut depth difference, rainfall intensity, and driving speed on the side deflection distance is analyzed, and a vehicle lateral safety evaluation model for water-filled ruts is established.
4. On this basis of the establishment of a waterlogged rut driving brake safety evaluation model and waterlogged rut driving side deviation safety evaluation model, the actual waterlogged rut in different sections of the road is calculated, as is the critical safe speed under different rainfall intensities, and the real-time early warning of water-logged rut driving safety is realized. In the future, the results of the study can be used in intelligent driving systems to optimize driving strategies in rainy days, providing automatic deceleration warnings in rutted areas of pavement that are experiencing ponding.  
Conceptualization, Y.L. and J.Y.; methodology, Y.L.; investigation, J.Y.; writing--original draft preparation, Y.L.; writing--review and editing, Y.L. and J.Y.; funding acquisition, J.Y. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the Fundamental Research Funds for the Central Universities, CHD, China, under Grant 300102214504, and the Natural Science Foundation of Shaanxi Province, China, under Grant 2022J0-547, and 2024 JC-YBQN-0429.  
Not applicable.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.