Rock slope stability analysis based on a single statistically representative orientation for each joint set can lead to erroneous conclusions regarding the stability of a slope. The fact that joint orientations are random variables must be considered in slope reliability analysis consisting of probabilistic kinetic and kinematic analysis. This paper presents a numerical procedure to establish the probability of kinematic instability of a 2-joint rock wedge. The method is a first step in a slope reliability analysis and, can be used, by itself, for preliminary slope geometry optimization.
Stability analyses for rock slopes based on limit equilibrium approaches usually employ a two stage procedure. In the first stage one identifies bodies that can potentially move--the so called kinematic analysis. In the second stage one assesses the stability (or instability) of those bodies by examining force equilibrium--the so called kinetic analysis. In rock slopes the potential failure bodies are usually (but not necessarily) bounded by discontinuities i.e. joints, foliation surfaces, bedding planes or faults. The movement of the failure body may occur in any several modes: translational sliding, rotational sliding, toppling, falling or a combination of modes. If a limit equilibrium approach for stability is used, the kinematic analysis must be performed for each of the failure bodies and failure modes. This paper treats the kinematic analysis for a wedge bounded by two surfaces (Figure 1) within the slope and two free surfaces defining the slope, i.e., the classic 2-plane rock wedge is considered. However, the concept and approach discussed here can be applied to any of the other failure bodies. The two surfaces of the wedge within the slope consist--as indicated above--of discontinuities.* The usual procedure is either to use specific discontinuities or to determine statistically representative discontinuities to define the wedge.