Road embankments may fail without warning, with devastating results. Thus, it is essential to understand the slope stability mechanism of road embankments under traffic load and optimize mathematical models of slope stability to enhance the computation of safety factors and the position and shape of the slip surface. This study's main aim is to examine the effect of soil nailing on the applicability of optimized mathematical models of the slope stability of road embankments under traffic load. Mathematical analysis was conducted using SLOPE/W software, which is based on the theories and principles of the limit equilibrium method (LEM) and enhances its results using an optimization function. The effect of Soil nailing on the applicability of optimized mathematical models of the slope stability was studied in terms of inclination, spacing, and length of the case study slope, located at Salmona village in Akhmim city, Sohag governorate for the head regulator of Nag Hamady canal. The results indicate that the optimized LEM enhanced the value of the safety coefficient in all cases considered by this study, and also modeled the slip surface's shape and position more realistically. Additionally, when the length of the soil nails and number of rows increased, the factor of safety (FOS) also increased: the proper inclination of the soil nails determined in this study was 10° to 20°.
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