A Reliability Analysis of the Dilution Graph Method for Open Stope Design: A Case Study

ABSTRACT The equivalent linear overbreak slough (ELOS) graph is a commonly used empirical design method for open stope design. Nevertheless, this method can lead to poor design performance when the geotechnical domain data lacks confidence. This is due to the inherent variability of the design input parameters, which should be considered for more reliable stope design. Hence, in this study, the First-Order Reliability Method (FORM) is used to determine the reliability index and the probability of unplanned dilution level associated with the design for each geotechnical domain. The Maleyevsky mine, located in northeast of Kazakhstan, is used as a case study. The parameters used for the analyses are the Modified Stability Number (N’), Hydraulic Radius (HR), and the actual dilution. The results indicated that the reliability indices and the probability of unplanned dilution occurrence vary between 0.1-4.63; and 0.0001% − 46.02%, respectively, depending on the rock domains. The results were in agreement with the field observations. It is concluded that the reliability-based design method could serve as a tool in the design of the open stope in connection with minimizing unplanned dilution. INTRODUCTION Open stope mining is characterized by large extraction rates and often with unsupported walls, which make it susceptible to unplanned dilution. Unplanned dilution is the mixture of ore with the waste material (hosting rocks, low grade mineralization, etc.) sloughed from the stope walls outside the planned excavation boundaries. This obviously leads to poor profitability of the mining operations. Serious profitability issues due to unplanned dilution have been reported (Clark and Pakalnis, 1997; Stewart et al., 2007) by many mines. Therefore, developing design tools that facilitate the reduction of unplanned dilution, is essential for the mining industry. Several approaches to design open stopes are currently in use, for example: numerical modelling (Henning and Mitri, 2007; Sainsbury et al., 2015; Vallejos and Díaz, 2020), analytical methods (Diederichs and Kaiser, 1999), back analysis of in situ measurements of stope overbreak (Cepuritis et al., 2010), empirical dilution graphs (Potvin, 1988; Clark, 1998; Mawdesley et al., 2001), and artificial intelligence based-design (Korigov et al., 2022). Among these methods, the empirical dilution (ELOS) graph is used in practice due to its simplicity and flexibility (Clark, 1998; Capes, 2009).