M. Brazil, D. Lee, J. H. Rubinstein, D. A. Thomas, J. F. Weng, and N. C. Wormald :
“A network model to optimise cost in underground mine design Trans. S. Afr. Inst. Electr. Eng.
93 : 2
(2002 ),
pp. 97–103 .
article
Abstract
People
BibTeX
This paper examines the problem of designing an underground mine so as to optimise the development and haulage costs. It focusses particularly on the costs associated with the ramps and shafts which provide passage to and from the ore zones. This mine optimisation problem is modelled as a weighted network. The controls (variables for the optimisation process) and operational constraints are described. A main constraint in mining networks is that all ramps have gradients no more than a given maximum value \( m \) . In this paper we describe the mine design problem as an optimisation problem, and prove that under reasonable conditions the cost function of an underground mining network with maximum gradient constraint \( m \) is convex. The convexity of the objective function ensures the existence of minimum cost mining networks, and theoretically any descent algorithms for finding minimal points can be applied to the design of minimum cost mining networks.
@article {key86311505,
AUTHOR = {Brazil, M. and Lee, D. and Rubinstein,
J. H. and Thomas, D. A. and Weng, J.
F. and Wormald, N. C.},
TITLE = {A network model to optimise cost in
underground mine design},
JOURNAL = {Trans. S. Afr. Inst. Electr. Eng.},
FJOURNAL = {The Transactions of the South African
Institute of Electrical Engineers},
VOLUME = {93},
NUMBER = {2},
YEAR = {2002},
PAGES = {97--103},
URL = {http://cat.inist.fr/?aModele=afficheN&cpsidt;=13957402},
ISSN = {0038-2221},
}
M. Brazil, D. Lee, M. Van Leuven, J. H. Rubinstein, D. A. Thomas, and N. C. Wormald :
“Optimising declines in underground mines Mining Tech.
112 : 3
(2003 ),
pp. 164–170 .
article
Abstract
People
BibTeX
This paper describes a method for optimising the layout of a decline in an underground mine. It models a decline as a mathematical network connecting the access points at each level of the proposed mine to the surface portal. A feasible decline is one satisfying all operational constraints such as gradient and turning radius requirements. The task is to find the decline that minimises a given cost objective. Typically, the cost objective will be some combination of development and operational costs representing a project cost or a life-of-mine cost. The procedure to find the optimal decline has been automated and the paper describes the current capability of Decline Optimisation Tool (DOT) software. A case study on the optimisation of a decline to service the Jandam gold mine in the Pajingo field of Newmont Australia Limited demonstrates the practical application of the technique.
@article {key26756511,
AUTHOR = {Brazil, M. and Lee, D. and Van Leuven,
M. and Rubinstein, J. H. and Thomas,
D. A. and Wormald, N. C.},
TITLE = {Optimising declines in underground mines},
JOURNAL = {Mining Tech.},
FJOURNAL = {Mining Technology},
VOLUME = {112},
NUMBER = {3},
YEAR = {2003},
PAGES = {164--170},
DOI = {10.1179/037178403225003546},
ISSN = {1474-9009},
}
M. Brazil, D. A. Thomas, J. F. Weng, J. H. Rubinstein, and D. H. Lee :
“Cost optimisation for underground mining networks Optim. Eng.
6 : 2
(2005 ),
pp. 241–256 .
MR
2136609 Zbl
1093.90067 article
Abstract
People
BibTeX
In this paper we consider the problem of optimising the construction and haulage costs of underground mining networks. We focus on a model of underground mine networks consisting of ramps in which each ramp has a bounded maximum gradient. The cost depends on the lengths of the ramps, the tonnages hauled through them and their gradients. We model such an underground mine network as an edge-weighted network and show that the problem of optimising the cost of the network can be described as an unconstrained non-linear optimisation problem. We show that, under a mild condition which is satisfied in practice, the cost function is convex. Finally we briefly discuss how the model can be generalised to those underground mine networks that are composed not only of ramps but also vertical shafts, and show that the total cost in the generalised model is still convex under the same condition. The convexity of the cost function ensures that any local minimum is a global minimum for the given network topology, and theoretically any descent algorithms for finding local minima can be applied to the design of minimum cost mining networks.
@article {key2136609m,
AUTHOR = {Brazil, Marcus and Thomas, Doreen A.
and Weng, Jia F. and Rubinstein, J.
Hyam and Lee, David H.},
TITLE = {Cost optimisation for underground mining
networks},
JOURNAL = {Optim. Eng.},
FJOURNAL = {Optimization and Engineering},
VOLUME = {6},
NUMBER = {2},
YEAR = {2005},
PAGES = {241--256},
DOI = {10.1007/s11081-005-6797-x},
NOTE = {MR:2136609. Zbl:1093.90067.},
ISSN = {1389-4420},
}
M. Brazil, D. Lee, J. H. Rubinstein, D. A. Thomas, J. F. Weng, and N. C. Wormald :
“Optimisation in the design of underground mine access 121–124
in
Orebody modelling and strategic mine planning: Uncertainty and risk management models .
Edited by R. Dimitrakopoulos .
Spectrum Series 14 .
Australasian Institute of Mining and Metallurgy (Melbourne ),
2005 .
incollection
Abstract
People
BibTeX
Efficient methods to model and optimise the design of open cut mines have been known for many years. The design of the infrastructure of underground mines has a similar potential for optimisation and strategic planning.
Our group has developed two pieces of software to tackle this problem–UNO (underground network optimiser) and DOT (decline optimisation tool) over the last 5 years. The idea is to connect up a system of declines, ramps, drives and possibly shafts, to minimize capital development and haulage costs over the lifetime of a mine. Constraints which can be handled by the software include: gradient bounds (typically \( 1:7 \) ), turning circle restrictions for navigability, and obstacle avoidance. The latter constraint keeps development at stand off distances from ore bodies and ensures that it avoids regions which involve high cost, such as faults, voids and other geological features.
The software is not limited to only interconnecting fixed points. It has the useful feature that a group of points can be specified such that the development is required to connect to one member of the group. So for example, if an existing ventilation rise must be accessed at some level, then a group of points along the rise can be selected. Similarly this gives the opportunity to use variable length crosscuts from a decline to an ore body. The latter gives important flexibility and can significantly reduce the development and haulage cost of a design.
Finally the goals for the next phase of development of this project will be discussed, including speeding up the algorithms and allowing for heterogeneous materials, such as aquifers and faults, as additional costs rather than obstacles.
@incollection {key49128372,
AUTHOR = {Brazil, M. and Lee, D. and Rubinstein,
J. H. and Thomas, D. A. and Weng, J.
F. and Wormald, N. C.},
TITLE = {Optimisation in the design of underground
mine access},
BOOKTITLE = {Orebody modelling and strategic mine
planning: {U}ncertainty and risk management
models},
EDITOR = {Dimitrakopoulos, Roussos},
SERIES = {Spectrum Series},
NUMBER = {14},
PUBLISHER = {Australasian Institute of Mining and
Metallurgy},
ADDRESS = {Melbourne},
YEAR = {2005},
PAGES = {121--124},
URL = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.134.6454},
ISBN = {9781920806422},
}
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
Abstract
People
BibTeX
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.
@article {key84900638,
AUTHOR = {Brazil, M. and Grossman, P. A. and Lee,
D. H. and Rubinstein, J. H. and Thomas,
D. A. and Wormald, N. C.},
TITLE = {Decline design in underground mines
using constrained path optimisation},
JOURNAL = {Mining Tech.},
FJOURNAL = {Mining Technology},
VOLUME = {117},
NUMBER = {2},
YEAR = {2008},
PAGES = {93--99},
DOI = {10.1179/174328608X362668},
ISSN = {1474-9009},
}
M. Brazil, P. A. Grossman, D. A. Thomas, J. H. Rubinstein, D. Lee, and N. C. Wormald :
“Constrained path optimisation for underground mine layout 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
Abstract
People
BibTeX
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.
@incollection {key16036470,
AUTHOR = {Brazil, M. and Grossman, P. A. and Thomas,
D. A. and Rubinstein, J. H. and Lee,
D. and Wormald, N. C.},
TITLE = {Constrained path optimisation for underground
mine layout},
BOOKTITLE = {Proceedings of the {W}orld {C}ongress
on {E}ngineering 2007},
EDITOR = {Ao, S. I. and Gelman, Len and Hukins,
David and Hunter, Andrew and Korsunsky,
A. M.},
VOLUME = {II},
SERIES = {Lecture Notes in Engineering and Computer
Science},
NUMBER = {2166},
PUBLISHER = {Newswood Limited},
ADDRESS = {Hong Kong},
YEAR = {2008},
PAGES = {856--861},
URL = {http://www.iaeng.org/publication/WCE2007/WCE2007_pp856-861.pdf},
NOTE = {(Imperial College, London, 2--4 July
2007).},
ISSN = {2078-0958},
ISBN = {9789889867126},
}
