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Abstract

One of the most important design factors in open-pit mining is determination of the optimal pit. Pits may be redesigned many times during the life of a mine in response to changes in design parameters as more information is obtained and to changes in the values of technical and economic parameters. Over the past 35 years the determination of optimum open-pits has been one of the most active areas of operational research in the mining industry and many algorithms have been published. The most common optimizing criterion in these algorithms is maximization of the overall profit within the designed pit limits subject to mining (access) constraints.

Almost all algorithms use a block model of the orebody, i.e. a three-dimensional array of identically sized blocks that covers the entire orebody and sufficient surrounding waste to allow access to the deepest ore blocks. Of these, the Lerchs-Grossmann algorithm, based on graph theory, is the only method that is guaranteed always to yield the true optimum pit. However, the original algorithm assumes fixed slope angles that are governed by the block dimensions. None of the subsequent attempts to incorporate variable slope angles provides an adequate solution in cases where there are variable slopes controlled by complex structures and geology.

A general method of incorporating variable slope angles in the Lerchs-Grossman algorithm is presented. It is assumed that the orebody and the surrounding waste are divided into regions or domain sectors within which the rock characteristics are the same and that each region is specified by four principal slope angles—north, south, east and west face slope angles. Slope angles can vary throughout the deposit to follow the rock characteristics and are independent of the block dimensions.

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Lerchs–Grossmann algorithm with variable slope angles

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References