Three-dimensional upper-bound analysis of rock slopes subjected to seepage forces based on Hoek-Brown failure criterion

Abstract

Three-dimensional upper-bound analysis of rock slopes subjected to seepage flows is a classical problem in geotechnical engineering. However, it is difficult to obtain a rigorous upper-bound solution of the safety factor of slopes when seepage flows are involved. In order to address this problem, the three-dimensional (3D) hydraulic head distributions inside a slope under steady state hydraulic conditions are solved numerically. The obtained numerical hydraulic head distributions are further employed to compute the seepage forces applying to the 3D discretized rotational failure mechanism to assess the stability of a rock slope. The Hoek-Brown yield criterion is employed to characterize the failure of rock masses. The generalized tangential technique is employed to formulate the problem as a classical optimization problem. The particle swarm optimization algorithm combined with the Nelder-Mead simplex algorithm is used to search for the best solutions of slope safety factor. The proposed approach is validated by comparing with 2D plane strain analysis results in the literature. Parametric analysis shows that the safety factor increases as mi or GSI increases, but decreases with the increase of the slope angle β and B/H. It is also found that the 3D influence is significant for B/H smaller than 10, beyond which it becomes negligible. The computational results in the form of design tables are presented for practical use in rock engineering.