Limit equilibrium analysis on the stability of rock wedges with linear and nonlinear strength criteria

The stability of a wedge is an important research topic for rock slopes. A rock wedge is formed by two sets of intersecting discontinuous structural surfaces distributed in a rock mass and cutting the rock slope. Hence, its stability is related to the occurrence of structural surfaces. To evaluate the stability of rock wedges, the limit equilibrium (LE) methods, which do not fully consider the shear forces on the slip surface of both sides of the rock wedge, are usually adopted. As a result, the calculated rock wedge factor of safety (FOS) may be overestimated. Here, a spatial model of a rock wedge is established from the occurrence parameters of the structural planes and slope surfaces. Moreover, reasonable assumptions of internal forces on both sides of a micro-unit body are adopted with the micro-unit body in the rock wedge as the analysis object. Subsequently, the analytical formulas for the normal and shear forces of the rock wedge with full consideration of the shear forces on the slip surface of both sides are derived by applying mechanical equilibrium conditions. Furthermore, the solution of the normal stress on the slip surface of a rock wedge under the assumption of a linear distribution is given. Afterwards, the formulas for calculating the FOS of a rock wedge under the linear Mohr-Coulomb strength criterion and nonlinear generalised Hoek-Brown strength criterion are derived. By comparing and analysing some rock slope examples, the feasibility of the proposed method is verified, and it is shown that the conventional LE methods overestimate the stability of rock wedges. In addition, stability charts of rock wedges are proposed to illustrate the influence trend of dips and dip directions of discontinuous structural planes on the rock wedge FOS when the structural planes have certain discreteness and distribution ranges.