Evolution of Limiting Slope Face in Rock Mass Using the Stress Characteristics Method

Abstract

The limiting stability of finite rock slopes is assessed in this paper by implementing the stress characteristics method (SCM) alongside the generalized Hoek‒Brown (GHB) yield criterion. By employing the SCM, a set of differential equations governing the equilibrium stress field is derived and later combined with the rock mass failure envelope characterized by the GHB criterion. Subsequently, the limiting slope face (LSF) with a global factor of safety (FS) as unity is obtained to preserve the state of plastic equilibrium. The current approach overcomes the necessity of a preconceived slip surface in the analysis. The resulting curvilinear LSFs exhibit more excellent compatibility with the shape of the naturally occurring slope profiles. The LSFs evolved from this investigation are generally found to be steeper than the traditionally encountered planar slopes without negotiating the mechanical stability. Numerical validation of the current approach using the finite-element limit analysis (FELA) is also established to authenticate the reliability of the present outcomes. The current results are suitably compared with the solutions available in the literature. Design charts are provided in the form of curvilinear slope faces for the ease of practicing rock engineers. Finally, the proposed LSF-based stability concept is applied to two selected case studies reported in the literature. Using the nonlinear generalized Hoek‒Brown strength criterion, this study directly determines the rock slope profile required to maintain limiting stability (factor of safety = 1.0). The profile thus derived is referred to as the LSF. The LSF serves as the basis for two potential field applications: designing the optimal rock slope profile and conducting routine stability checks on existing rock slopes. Taking the derived curvilinear LSF as a reference, optimal linear, bilinear, or multilinear/stepped slopes can be designed with a sufficient safety margin. Additionally, the LSF operates as an interface between the zone of stability and instability. Therefore, a simple profile-matching scheme between any existing rock slope and the corresponding LSF can provide the safety status of that existing slope. Therefore, the present design charts containing LSFs contribute to a readymade solution for a rapid and reliable rock slope stability assessment.