Limit Equilibrium Analysis Incorporating the Generalized Hoek–Brown Criterion

Abstract

Both the limit analysis and the limit equilibrium approach require the formulation of a failure criterion in terms of components of stress vector acting on a potential failure plane. For applications in Rock Mechanics, the generalized Hoek–Brown (GHB) criterion is commonly used, for which no analytical form of the Mohr failure envelope is, in general, available. In this work, a new approximation of the Mohr envelope for the GHB criterion is developed, which is valid in a broad range of GSI (i.e. Geological Strength Index) values. The approach is based on the orthogonal projection of a function for best-fitting the quadratic or cubic polynomials to the Balmer’s equations that define the relationship between the normal stress acting on the failure plane and the minor principal stress. The methodology is illustrated by a limit equilibrium analysis, which involves assessment of the safety factor of a rock slope that has a vertical tension crack embedded in the upper horizontal surface. The analysis employs an approximate Mohr envelope based on the cubic polynomial fitting as the failure condition along the rupture surface. The results indicate that the safety factor for stability of the slope is very sensitive to the geometry of the crack (i.e. its location and depth) as well as the selection of the value of GSI.