Explicit limit equilibrium solution for slope stability

Abstract

Conventional methods of slices used for slope stability analysis satisfying all equilibrium conditions involves generally solving two highly non-linear equations with respect to two unknowns, i.e. the factor of safety and the associated scaling parameter. To solve these two equations, complicated numerical iterations are required with non-convergence occasionally occuring. This paper presents an alternative procedure to derive the three equilibrium equations (horizontal and vertical forces equations and moment equation) based on an assumption regarding the normal stress distribution along the slip surface. Combination of these equations results in a single cubic equation in terms of the factor of safety, which is explicitly solved. Theoretical testing demonstrates that the proposed method yields a factor of safety in reasonable agreement with a closed-form solution based on the theory of plasticity. Example studies show that the difference in values of factor of safety between the proposed method, the Spencer method and the Morgenstern-Price method is within 5%. Application of the proposed method to practical slope engineering problems is rather straightforward, but its solution is of the same precision as those given by the conventional rigorous methods of slices since it is still within the rigorous context. Copyright © 2002 John Wiley and Sons, Ltd.