Incorporation of non-associative flow rules into rock slope stability analysis

Abstract

The circular shear failure mechanism in rock slopes occurs in large-scale, heavily jointed or weak rock masses. Most rock slope stability analysis problems do not consider the effect of flow rules, i.e., the dilatancy angle. The failure criteria commonly applied are the linear Mohr-Coulomb or the non-linear Hoek and Brown. In general, all slope stability methods originate from the assumption of the associative flow rule, calculating equivalent values of the cohesive strength and friction angle. In this study, the non-linear Hoek and Brown failure criteria are applied in the parametric form, which permits the incorporation both the associative and non-associative flow rules. A theoretical approach of the limit equilibrium method is performed for circular slip surfaces under the assumption that there are only self-weight forces acting on the failure mass of the slope, taking the critical plane failure mode as the foundation. Both the analysis and results are performed in dimensionless form. The study emphasizes the importance of the value of dilatancy angle and “non-conservative” character of the hypothesis of the associative flow law, i.e., the overestimation of the value of the factor of safety. Specific examples are analysed and compared to the finite difference method and a real case is presented.