Three-dimensional method for slope stability with the curvilinear route of the main sliding

The route of the main sliding is considered to be a linear line in the existing three-dimensional limit equilibrium methods for slope stability analysis. However, there is a curvilinear route for the main sliding caused by the translational movement and the rotation of the sliding body in slope failures. In this study, a three-dimensional limit equilibrium method was proposed for slope stability with the curvilinear route of the main sliding. The basic physical quantities for slope stability analysis in the orthogonal curvilinear coordinate system were obtained by the mapping between the orthogonal curvilinear coordinate system and the Cartesian coordinate system. The four equilibrium equations (a force equilibrium equation and three moment equilibrium equations) were established by the equilibrium conditions of the entire sliding body. The three-dimensional factor of safety for the slope with the curvilinear route of the main sliding was deduced by an analytical or a numerical method. Some examples proved that the present method can calculate the factor of safety and evaluate the stability of the slope. The results of examples showed that the factor of safety of the curvilinear route was significantly smaller than that of the linear route. The three-dimensional limit equilibrium method for slope stability analysis was further developed in this study, which provided a theoretical basis for the scientific and reasonable evaluation of slope stability.