Computational tools for the analysis of circular failure of rock slopes

Abstract

Abstract Among other types of failure in slopes created by excavation or filling, circular (also referred to as rotational) type of failure plays an important role in the design and stability analysis of high rock slopes, such as those encountered in deep open pit mines. When a rock slope of significant height involves predominantly one type of jointed rock mass, the scale of the problem is frequently such that the rock mass (intact rock and rock discontinuities) can be regarded as a homogeneous isotropic material. In such case, if the rock slope is unstable and collapse occurs, circular (or rotational) failure as in failed slopes in soils is also observed for the rock slope. One main goal in practical design of deep open pit mines is to determine safe inclination angles for the pit faces to be excavated to avoid failure. Computational tools for quick assessment of the stability conditions, in particular determination of factor of safety and location of the critical circular failure surface, are useful during the preliminary stages of open pit design. Among others, such tools allow the engineer to gain insight in the role that the different variables controlling the problem have in defining the stability conditions for the rock slope. This paper provides first an overview of typical numerical techniques used to assess the stability of high rock slopes. For the case of slopes in rock masses that are assumed to obey the Mohr-Coulomb or the Hoek-Brown failure criteria, the paper discusses how application of transformation rules leads the criteria to be re-casted in dimensionless form, so when these are applied to the solution of slope problems, the results (factor of safety and coordinates that define the location of the critical circular failure surface) can be summarized in dimensionless compact forms. The paper presents then computational tools in the form of dimensionless charts and computer spreadsheets for stability analysis. These are developed from numerical limit equilibrium models that use the mentioned transformation rules. Among others, the computational tools allow the concept of mechanical similarity of rock slopes to be naturally introduced. Finally, the paper presents various rock slope examples that illustrate the use of the computational tools. In these examples, results from limit equilibrium models are also compared with results obtained with full numerical analysis, in particular with finite difference models implementing the shear strength reduction technique.