Integrated Stochastic Underground Mine Planning with Long-Term Stockpiling: Method and Impacts of Using High-Order Sequential Simulations

The integrated optimization of stope design and underground mine production scheduling is an approach that has been shown to effectively leverage the synergies among these two underground mine planning components to generate truly optimal stope layouts and extraction sequences. The existing stochastic integrated methods, however, do not include several elements of a mining complex, such as stockpiles, due to the computational complexity and non-linearity that they might add to the optimization of the long-term mine plan. Additionally, sequential simulation methods that rely on two-point statistics and Gaussian distribution assumptions are commonly used to generate the input realizations of the mineral deposit. These methods, however, are not able to properly characterize complex spatial geometries or the high-grade connectivity of non-Gaussian and non-linear natural phenomena. The present work proposes an extension of previous developments on the integrated stope design and underground mine scheduling optimization through an expanded stochastic integer programming formulation that incorporates long-term stockpiling decisions. An application of the proposed method at an operating underground copper mine compares the cases in which the geological simulated orebody models are based on high-order and Gaussian sequential simulation methods. The extraction sequence and related final stope design are shown to be physically different. It is seen that the optimization process takes advantage of the better representation of high-grade connectivity when high-order sequential simulations are used, by targeting the areas with grades that follow the mill's blending requirements and by making less use of the stockpiles. Overall, a 4% higher copper metal production and a resultant 6% higher net present value are observed when high-order sequential simulations are used.