Rock Wedge Stability Analysis Using Plastic Limit Analysis Method

The failure of the rock slope containing a tetrahedral wedge is a common geological disaster in rock slope engineering. The rigid body limit equilibrium method has been widely used to analyze wedge stability. However, equilibrium equations are not completely satisfied in. this method because of unreasonable assumptions, which may result in false results. This paper presents plastic limit analysis method for rock wedge stability analysis without making extra assumptions based on the lower and upper bound limit theorem. In lower bound analysis, the statically admissible stress fields are constructed by using Mohr-Coulomb yield conditions, and the lower bound nonlinear programming models are established to calculate strength safety coefficient of wedge slopes. And in upper bound analysis, the kinematically admissible velocity fields are obtained by employing association flow rule and deformation compatibility conditions, the upper bound nonlinear programming models are established to calculate strength safety coefficient. Then, the optimization strategies of nonlinear mathematical programming problem are provided. The stabilities of two wedge slopes are analyzed by the presented methods. The comparisons among the analytical results of conventional method are carried out, and the validity of the methods is indicated.