As a type of horizontal curve, the reverse horizontal curves (RHCs) are one of the most critical types of road locations where many accidents occur due to slippage resulting from the centrifugal force of the vehicles. These crashes can increase dramatically if the RHC is combined with a longitudinal slope (downgrade or upgrade). In this study, by using the vehicle dynamic modeling (VDM) method, the lateral acceleration of vehicles (including E-Class Sedan, E-Class SUV, and Truck) passing through the RHC combined with three scenarios of downgrades, upgrades, and no slope was evaluated. Finally, in order to present the final model, the RHC lateral acceleration model was presented based on the effective parameters, including different design velocities ( V ), the direct distance between two horizontal curves (D), and different longitudinal slopes ( G ) by the multiple regression model method. The results of the VDM modeling showed that the slide potential of Sedans, SUVs, and Trucks when crossing the RHC combined with the downgrade was more significant than the upgrade and the no-slope paths. On the other hand, the modeling results showed that the proposed models for Sedans and SUVs with a very high level of importance (R2 = 0.920 and R2 = 0.967) could be used to assess the safety of vehicles crossing the RHC. According to the mentioned models, increasing the speed ( V ) and reducing the direct distance (D) in both models reduced the lateral acceleration (increased safety) of both Sedans and SUVs.

Reverse Horizontal Curves (RHCs) are among the most accident-prone road points, with many annual fatalities and injuries. These fatalities can increase dramatically if the RHCs and longitudinal slopes are combined. The importance of increasing the safety of RHCs, especially in mountainous routes, is doubled due to the possibility of combining RHCs with vertical extensions or combining them with so-called steep slopes. This study used vehicle dynamic modeling to evaluate the lateral friction of various vehicles. Including the E-Class Sedan, E-Class SUV, Truck, and Bus, moving on RHCs combined with a longitudinal slope (downgrade, upgrade, and direct distance). Then, the RHC lateral friction model was presented using the multiple regression model based on the effective parameters, including design speeds, direct distance, and different longitudinal slopes. The results showed that speed, longitudinal slope, and vehicle type had the most impact, and direct distance had the most negligible impact in friction coefficient models. Based on the modeling results, the higher the design’s speed and the shorter the direct distance, the lower the lateral friction coefficient for the Sedan and SUV. Hence, the safety of the vehicles is greater. For trucks, reduced speed, increased direct distance, and reduced slope led to increased safety. In the results, the most critical state was the lateral friction coefficient at a speed of 80 km/h and a direct distance of 116 m for the SUV.