A formulation for optimum risk in open-pit mining

The selection of open-pit slope angles involves high-value decisions with small changes in slope angle, often representing significant changes in net present value. The existing methods used to define design acceptance criteria have evolved from factor of safety to probability of failure (P[F]) to risk consequence to risk frontiers, which represents current state of the art. Current design acceptance measures are based on references to published tables representing the experience and judgement of their authors, who did not specify the purpose of the measures contained therein. As the purpose of the published design acceptance criteria is not specified (i.e., definite stability, marginal stability, optimization, etc.), such tables cannot be used to achieve optimum slope angles that maximize profitability. This paper develops a design acceptance criterion that maximizes profitability by defining a formulation for optimum risk that balances expected risk and reward. The model developed is titled the Mining Risk Model (MRM), and is applied to open-pit slope angle selection through an equation for optimum probability of downside (P[D]O) that balances the upside or opportunity, the P[F], and the downside impact. This formulation for optimum risk is unique, as many authors have presented objective functions for their risk models that can be optimized, but none of the sources reviewed contained a formulation for optimum risk. The MRM is sufficiently flexible to allow the design performance measure that drives P[F], and hence P[D]O, to be selected based on the intended goal. Furthermore, the essential information that must be known to quantify optimum risk is defined. This allows users to determine what information to collect for optimum risk decisions. A further benefit of the MRM is that slope angle decisions and pit shells can be ranked to select the best option, and a threshold is provided that separates acceptable from unacceptable decisions. Finally, the workflow and information required to determine optimum risk are presented.