Since the stability of slopes in infrastructures such as road and railroad embankments, excavations, and, in general, earthwork is important, analyzing the stability of these slopes has been one of the main focuses of geotechnical engineers. Although analyzing both reinforced and unreinforced slopes is needed, reinforced slopes require special attention as the reinforcement elements significantly affect the calculations. Hence, the current study’s aim is to find out the differences between obtained safety factors using the Limit Equilibrium Method (LEM) and Shear Strength Reduction Method (SSRM). For this purpose, first, the origin differences in terms of Safety Factor (SF) are theoretically determined according to basic formulas for the aforementioned techniques. Then, to verify the formula, several numerical modelings are carried out using in situ measured geotechnical data to better understand the differences in terms of safety factors. The results indicate that for the reinforced slope with an SF value of higher than 1, the SSRM provides a higher SF in comparison with the other techniques, and the origin of this difference is the definitions of the SF in the different methods.

Despite the significant contribution of sleepers to the lateral resistance of ballasted tracks, limited research has focused on improving the shape of sleepers in this aspect. This study aims to evaluate proposed sleeper shapes based on the B70 form, utilizing a linear optimization algorithm. First, a DEM model was verified for this purpose using the outcomes of the experiments. Then, using this model, the effect of the weight of the B70 sleeper was carried out on lateral resistance. Next, suggested shapes contacted with ballast materials were applied to lateral force while maintaining the mechanical ballast’s properties until a displacement of 3.5 mm was achieved. The current study’s results showed that the rate of lateral resistance increasing becomes lower for weights higher than 400 kg. Additionally, it was demonstrated that the sleeper’s weight will not always increase lateral resistance. The findings also indicated that although some proposal shapes had higher lateral resistance in comparison to other forms, these designs are not practical from an economic standpoint. Furthermore, despite the lower weight of some other suggested shapes in comparison with B70, the lateral resistances are 31.2% greater. As a result, it is possible to recommend employing a proposed sleeper rather than a B70 sleeper.