A rigorous method for three-dimensional asymmetrical slope stability analysis

Most slope failures exhibit remarkable asymmetrical variation in the transverse direction. A rigorous method satisfying all six equilibrium conditions is proposed for evaluating three-dimensional (3-D) asymmetrical slope stability. As there is no need to predefine a symmetrical plane in this analysis, the method is applicable to slopes with complex geometries, geologies, and loading conditions. The proposed method can not only calculate the factor of safety, but also predict the direction of sliding of the potential failure mass. Global equilibrium equations are formulated in light of the safety factor, sliding direction, and an assumed distribution of normal stress on the slip surface. The Newton method is then used to solve these equations, which has been proven to enjoy both a large range of convergence and a fast convergence rate. Thereafter, physical admissibility conditions of the solutions, and the effects of the size of discretized columns on solution accuracy, are discussed in the present 3-D analysis. The method is validated by using five typical examples documented in the literature. The failure of the Kettleman, California, waste landfill slope is also re-evaluated using the proposed method. The calculated stability and direction of sliding match field observations.