**TRANSACTION PAPERS**

**A comparison of limit equilibrium and numerical modelling approaches to risk analysis for open pit mining**

**H.T. Chiwaye; T.R. Stacey**

School of Mining Engineering, University of the Witwatersrand, Johannesburg, South Africa

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**SYNOPSIS**

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 done 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 20 000, in order to produce statistically valid results of the POF. Such an approach is clearly not practical when using numerical modelling programs due to the high computational effort required. This paper explores the impact of using numerical modelling instead of the traditional LE techniques in evaluating the probability of slope failure. The difference in the overall assessed risk, in terms of economic impact, for the mining operation is then evaluated. With numerical models, approximate methods are used in the calculation of the probability of failure instead of full Monte Carlo simulations. This paper will use a method called the response surface methodology (RSM) for estimating the POF from numerical analyses. Simple slope models were used to verify the accuracy of the RSM method by comparing the results with those obtained from full Monte Carlo simulations. It is shown that there is good agreement between the POF values computed using full Monte Carlo simulation and those obtained using the RSM method. Finally, the use of numerical modelling in the assessment of risk is shown to bring a significant difference in the result compared with that from LE methods. One of the reasons for the difference is that LE models tend to underestimate the failure volumes and hence the consequences of slope failure.

**Keywords:** Risk, probability of failure, limit equilibrium, numerical modelling, Monte Carlo simulation, response surface methodology

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