Seismic displacement along a log-spiral failure surface with crack using rock Hoek-Brown failure criterion

Earthquakes can trigger slope instability, especially in the case of slopes with cracks. The most commonly used method for analyzing seismic slope stability is the pseudo-static analysis technique. However, information about slope displacements is difficult to obtain. The purpose of this paper is to present a model for calculating the seismic displacements of rock slopes with cracks using the upper bound limit analysis and the rigid block displacement technique. The Hoek-Brown (H-B) failure criterion is employed in this model, and actual horizontal and vertical earthquake ground motion records are utilized. The equivalent Mohr-Coulomb (M-C) parameters including friction angle and cohesive strength are determined by fitting an average linear relationship to the curve of relationship between major and minor principle stresses for H-B failure criterion. A comparison of the seismic displacements obtained by using the equivalent M-C parameters and the H-B failure criterion is performed. The difference of the seismic displacements obtained by using the two methods is significantly larger than the difference of factor of safety for rock slopes with cracks under seismic action. The results indicate that the equivalent M-C parameters method may cause an overestimation of the stability of a slope. To understand the influence of rock strength parameters and crack depth, a detailed parametric study is carried out. These parameters can significantly influence seismic displacement, especially for large crack depths. For the numerical example considered in this study, the ratio of crack depth to slope height varied from 0 to 0.2, and the increase in seismic displacement can exceed 23%.