The stability of slopes is a major concern in the field of geotechnical engineering. Two-dimensional (2D) limit equilibrium methods are usually implemented in this field due to their simplicity. However, these methods ignore the features of the third dimension of slopes. Although three-dimensional (3D) methods tried to remove the previous limitation, most of them assumed the direction of sliding, simplified or ignored the intercolumn forces, and avoided to search for location and shape of three-dimensional critical slip surface. This study was performed to overcome the mentioned limitations. In the present study, a new slope stability method was established based on the force and moment equilibrium in two vertical directions that was able to find the unique direction of sliding. Moreover, a modified Particle Swarm Optimization was developed by replacing the worst particle of each swarm with the previous global best particle and using a dynamic inertia weight to determine the 3D critical slip surface. Then, a computer program was established to model 3D slopes and perform the required calculations. Several benchmark problems were re-analyzed to verify the results of the study and good agreements were achieved with the results of previous studies when different failure mechanisms as ellipsoid, cylindrical, and composite slip surfaces were successfully applied in the analysis. The results indicated that the 3D factor of safety of a slope is always greater than its corresponding 2D factor. Moreover, the end effect in 3D analysis was found to be more significance in the problems with lower ratio of length to the width of the sliding mass. It was also found that the presence of water and weak layer enlarged this effect. Through the verification study, it was observed that different sliding directions produce different factors of safety, while the lowest value of factor of safety and 3D critical slip surface is only reachable through the real direction of sliding. Finally, case studies of actual stability problems were analyzed to find their critical slip surfaces. Achieving the minimum factor of safety of 0.977 for the critical slip surface of a failed slope demonstrated the validity of performance of presented computer code. Based on the obtained results, this study successfully overcame the mentioned limitations of the previous methods. The results of this study provided a better understanding of the actual failure mechanism and helped to enhance the safety and reduced the economic and health costs due to slope failure by a more detailed analysis than before.
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