Noriega, R, Pourrahimian, Y & Victor, WL 2018, 'Optimisation of the undercut level elevation in block caving mines using a mathematical programming framework', in Y Potvin & J Jakubec (eds), Caving 2018: Proceedings of the Fourth International Symposium on Block and Sublevel Caving
, Australian Centre for Geomechanics, Perth, pp. 363-372, https://doi.org/10.36487/ACG_rep/1815_25_Noriega
The selection of an elevation for the placement of the undercut level is a decisive initial step in the planning and design of block caving mines. It is key for the success of a caving project to define the undercut elevation that will most likely yield the highest possible net present value (NPV) of the operation, considering the discounting periods from both the vertical draw rate extraction of the ore and the horizontal mining direction advancement.
This paper outlines a mathematical programming framework to determine the best undercut elevation by formulating a simplified linear integer programming (IP) model that captures the discounting of the profits from the vertical draw rate extraction and the horizontal advance direction that can be applied at the early stages of a caving project. The IP model comprises a simplified block caving scheduling algorithm that considers ‘mining units’ (MU), which are groupings of blocks within each column based on the minimum draw rate condition and the undercut elevation considered. The formulation considers the following constraints: mining capacity, minimum and maximum draw rate, vertical precedence within columns and a horizontal precedence based on a concave mining advancement front. The model is set on an iterative loop over the different possible levels.
The model is tested on a case study, where it provides a tool to evaluate the potential mineable reserves, define the optimal undercut elevation, and a starting schedule for future detailed engineering design.
Keywords: block caving, undercut elevation, optimisation, integer programming
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