Ultimate load of nonhomogeneous slopes determined by using the method of characteristics

Abstract

Most prior studies on nonhomogeneous slopes have focused on the spatial variation of the cohesion, while the influence of a variable friction angle on slope stability is difficult to investigate. This study adopts the method of characteristics to generate a statically admissible failure mechanism in order to address the ultimate load of nonhomogeneous slopes. Three types of boundary value problems are used to generate discretized grid points in the plastic zone in order to build a stress field. Hence, it is easy to account for variations in the shear strength in a slip line field, especially for variations in the friction angle. Considering the edge distance of a surcharge loading, face and toe failure mechanisms are proposed to determine the influence of the variable shear strength. The proposed approach is compared with the upper bound method and numerical simulations. The good agreement shows that the novel approach is reliable and effective. Then, the ultimate load of nonhomogeneous slopes is calculated considering that the cohesion and friction angle vary linearly with depth. Moreover, the ultimate load obtained by the proposed method can be regarded as a lower bound solution, which supplements the limit analysis of nonhomogeneous slopes.