Celebratio Mathematica — Rubinstein

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M. Brazil, P. A. Grossman, D. H. Lee, J. H. Rubinstein, D. A. Thomas, and N. C. Wormald: “Decline design in underground mines using constrained path optimisation,” Mining Tech. 117 : 2 (2008), pp. 93–99. article

This paper focuses on the problem of optimising the design of an underground mine decline, so as to minimise the costs associated with infrastructure development and haulage over the lifetime of the mine. A key design consideration is that the decline must be navigable by trucks and mining equipment, hence must satisfy both gradient and turning circle constraints. The decline is modelled as a mathematical network that captures the operational constraints and costs of a real mine, and is optimised using geometric techniques for constrained path optimisation. A deep understanding of the geometric properties of gradient and turning circle constrained paths has led to a very efficient procedure for designing optimal declines. This procedure has been automated in a new version of a software tool, decline optimisation tool. A case study is described indicating the substantial improvements of the new version of the decline optimisation tool over the earlier one.

Peter Alexander Grossman	Related
Nicholas Charles Wormald	Related
David H. Lee	Related
Marcus Brazil	Related
Doreen A. Thomas	Related

M. Brazil, P. A. Grossman, D. A. Thomas, J. H. Rubinstein, D. Lee, and N. C. Wormald: “Constrained path optimisation for underground mine layout,” pp. 856–861 in Proceedings of the World Congress on Engineering 2007 (Imperial College, London, 2–4 July 2007), vol. II. Edited by S. I. Ao, L. Gelman, D. Hukins, A. Hunter, and A. M. Korsunsky. Lecture Notes in Engineering and Computer Science 2166. Newswood Limited (Hong Kong), 2008. incollection

The major infrastructure component required to develop an underground mine is a decline, which is a system of tunnels used for access and haulage. In this paper we study the problem of designing a decline of minimum cost where cost is a combination of development and haulage costs over the life of the mine. A key design consideration is that the decline must be navigable to trucks and mining equipment, hence must satisfy a gradient and turning circle constraint. The decline is modelled as a mathematical network that captures the operational constraints and costs of a real mine, and is optimised using geometric techniques for constrained path optimisation. This procedure to find the optimal decline has been automated in a new version of a software tool, Decline Optimisation Tool, DOT\( ^{\textrm{TM}} \). A case study is described comparing this version with the earlier one.

Len Gelman	Related
Peter Alexander Grossman	Related
David Hukins	Related
Andrew Hunter	Related
S. I. Ao	Related
A. M. Korsunsky	Related
David H. Lee	Related
Nicholas Charles Wormald	Related
Marcus Brazil	Related
Doreen A. Thomas	Related