A novel upper bound limit method for rock slope stability analysis is developed in this paper. Block element method (BEM) is employed to discrete the area concerned and to construct a kinematically admissible velocity field. A nonlinear programming model for the upper bound limit of safety factor of rock slopes is formulated, in which the velocity field satisfies the constrain conditions including the Mohr-Coulomb yield criterion on the slide surface, the associated flow rule, boundary conditions, as well as the virtual work of the block system. The model is solved by the complex shape method. A wedge-block in a rock slope is studied, which verified the efficiency of the method. In the end, the application to the intake slope of Xiaowan Project shows the practicability of the method to the slope.


Rigid limit equilibrium method (RLEM) and finite element method (FEM) are widely used in slope stability analysis. The former has merits of long time experience, efficiency for computation and clear theorem. But the method bases on some suppositions, which means that RLEM is an approximate method. Moreover the stress field and displacement field of sliding slope can not be obtained. Finite element method is one of the most powerful numerical methods for stress-strain analysis. While, difficulties of FEM are that the constitutive relation of medium is hard to determine and the preprocess for the rock mass containing various discontinuities is complicated.

In most cases, for slope engineering, more attention is focused on the stability margin than on the process of failure of slopes. Based on the plastic limit theorem, limit analysis approaches the accurate solution in two directions of the upper bound and the lower bound, which provides a rigorous method for stability analysis of slopes(Chen, 1975; Donald, 1997; Chen, 1999; Wang, 2001; Wang, 2001; Chen, 2001; Chen, 2001).

By combining FEM and mathematical programming method, fruitful studies on the stability problems of slopes have been achieved(Sloan, 1988; Sloan, 1989; Sloan, 1995; Lyamin, 2002; Kim, 1999). The basic idea is to discrete the computational area by finite elements, and then to construct the programming model for rigorous upper or lower solutions of problems, in which the unknown variables are satisfied for the yield criterion, plastic flow rule, boundary conditions and virtual work principle.

In this paper, the block element method (BEM) and the upper bound theorem are used to stability analysis of rock slopes. The block element is employed to discrete the jointed rock mass of slopes, and the mathematic programming model is formulated on the basis of the upper bound theorem. In BEM, block elements are treated as rigid and the centroid velocities of which are considered as the unknown variables. In order to make the velocity field on the discontinuities admissible, the unknown variables should meet the yield criterion, plastic flow rule, virtual work principle and boundary conditions. Which formulates the constrain conditions of the model for the upper bound solution of safety factor. The complex shape is adopted to solve the programming model.

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