Probabilistic Stope Stability Analysis Based on the Modified Stability Graph

The Stability Graph method is widely used to assess the stability of a stope. However, its traditional deterministic application overlooks the variability of the underlying rock mass parameters. By defining distribution functions for the rock mass parameters and running a Monte Carlo analysis on these inputs, the inherent rock mass variability is reflected in the outcome in the form of a distribution of the modified stability number N'. This paper presents guidelines on defining the input distribution functions, and particularly on elaborating the correlation between these distributions. Finally, methods are presented to interpret the obtained modified stability number distribution. The first method introduces a risk tolerance factor allowing to completely determine a stable stope. The second method identifies the drivers for instability, which could be used as variables for subsequent stope optimization. 1. STABILITY GRAPH METHOD The sizing of open stopes for underground mines is of particular importance during the mine design. Several tools are available to support the engineers throughout the process. One of the most widely used methodology in Canada is the empirical Stability Graph Method, initially developed by Mathews et al. (1981). This method was modified by Potvin (1988) to better account for the specificities of Canadian hard rock mines. 1.1. Modified Stability Graph Method The Stability Graph Method involves the calculation of two parameters: the modified stability number N′ and the hydraulic radius HR. The modified stability number is defined as follows: (equation) where Q′ is the Q-system rock mass quality as defined by Barton (1974) with the stress reduction and water factors set to 1.0, and A, B and C the rock stress, joint orientation adjustment and surface orientation factors, respectively. The modified Q′ value is defined by the following equation: (equation) with RQD the rock quality designation index, Jn the joint set number, Jr the joint roughness number and Ja the joint alteration number (Barton, 1974). The three parameters A, B and C are evaluated graphically as shown in figures 1, 2 and 3, respectively.