A comparison of the limit equilibrium and numerical modelling approaches to risk analysis for open pit mine slopes

Abstract

Risk analysis is an important step in the design of rock slopes in open pit mining. Risk is defined as the product of the probability of slope failure and the consequences of the failure, and is generally evaluated in terms of safety and economic risk. Most of the risk analysis carried out at present is based on the use of Limit equilibrium (LE) techniques in evaluating the probability of failure (POF) of the slopes. The approach typically makes use of full Monte Carlo simulations of the Limit Equilibrium models, with all uncertain variables randomly varied. The number of required simulations is generally over a thousand, at times as high as 20000, in order to produce statistically valid results of the POF. Such an approach is clearly not amenable to the use of numerical modelling programs due to the high computational effort required, hence the major use of LE methods. This project explores the impact of using numerical modelling (with the program PHASE 2) instead of the traditional LE techniques (using the program SLIDE) in evaluating the probability of slope failure. The difference in the overall assessed risk, in terms of economic impact, for the mining operation was then evaluated. Instead of full Monte Carlo simulations within the numerical analysis stability model, an alternative method called the Response Surface Methodology was used for the probabilistic analysis. The use of numerical modelling in the assessment of risk results in a significant difference in the assessed risk. LE models tend to be conservative in terms of stability and POF results. However, they give lower estimates of failure volumes than the numerical models. As a result, the assessed risk from LE models can be lower or higher than that from numerical analyses. A case study of an open pit mine was used to validate these findings. The effect of using 2D plane strain models instead of 3D analysis was also investigated. Numerical models built with FLAC were compared with FLAC3D models. Circular and elliptical pits were considered, with varying radii of curvature. The results showed that for circular pits 2D assumptions are adequate if the radius of curvature is sufficiently large or, for an elliptical pit, if the distance from the small radius ends is sufficiently large. In situations other than these the 2D models give conservative estimates of stability and probability of failure. A detailed comparison of failure volumes was difficult due to the fact that the 2D models do not give the out of plane extent of the failure. However, using simplistic assumptions, the overall assessed risk from FLAC and FLAC3D is shown to be different.