Seismic and static 3D stability of two-stage rock slope based on Hoek-Brown failure criterion

Two-stage slope is beneficial to improve slope stability in comparison with single-stage slope. Based on nonlinear Hoek-Brown criterion, a three-dimensional failure mechanism is employed to estimate the stability of two-stage rock slope, with the effect of seismic inertia force being taken into account. A generalized tangential technique is used to formulate the stability factor problem as a classical optimization problem corresponding to the dissipated energy. The upper-bound solutions are obtained by minimizing the objective function with respect to the location of sliding body center and the location of tangency point. The seismic inertia force is considered and incorporated into the objective function. In comparison with previously published solutions using the linear Mohr-Coulomb criterion, the validity of the present solutions is shown. The analytical expressions for two-stage slope are derived to estimate the seismic stability of slopes. Numerical results for different types of rocks are presented for practical use in engineering, and the effects of different parameters on slope stability are discussed.