Risk analysis of optimal stope design : incorporating grade uncertainty

Recognising, quantifying and managing risk when planning a mine operation canninfluence a project's feasibility and economic outcome. A key source directlynaffecting the design and scheduling of a deposit is the geological risk, specifically thenore reserve. With the growing acceptance of conditional simulation in the miningnindustry, the uncertainty in the grade of a deposit can be quantified through its abilitynto measure spatial variability of a given element(s). By applying a mine design and/ornscheduling procedure to equally probable orebody representations, the resulting risknof various project indicators can be quantified and assessed. Furthermore, this riskncan be used in the generation of risk based designs. As a result, the ability to managenrisk can lead to better designs and/or schedules providing a more stable and attractivenfinancial prediction of a given operation. Over the past decade the focus of thisnresearch has been in open pit operations, this thesis successfully applies thesenconcepts developed for surface mining in an underground situation and manages thenrisk in the generation of risk based designs.n The increasing use of conditional simulation in more complex ore deposits hasnrevealed the inherent limitations of computational speed and efficiency. In addition toncombating this problem, the application of more recent software developmentnconcepts will result in programs which are more readably adaptable to extendibilitynand reuse of code. In this thesis the advantages gained by implementing object-orientednconcepts are realised in the development and implementation of a newnsequential Gaussian simulation program based on the object-oriented paradigm. Thenanalysis and design of various hierarchies is detailed illustrating the reuse of code andnease of extendibility.n The concepts developed for assessing geological risk in open pit mine design arenapplied to a section of Kidd Creek Mine, Ontario, Canada. Firstly, copper assaysntaken from a series of drillholes in Kidd Creek's Mine No 3 are declustered and usednas conditioning data in the generation of an ore reserve estimate using ordinary blocknkriging. Secondly, the new object-oriented SGS program is used to conditionallynsimulate copper grades allowing the grade uncertainty to be quantified. Thirdly, antraditional stope outline based on the smooth estimate is developed using the 'floatingnstope'. The effects of grade uncertainty on the base case stope outline are revealed bynrunning the outline through each simulated orebody and analysing the risk profiles ofnvarious project parameters including ore and waste tonnes, quantity of metal, copperngrade and economic potential. With the production of risk profiles, a distribution ofnpotential outcomes is revealed and compared to the single estimate produced by thentraditional approach, highlighting both the downside risk and upside potential of thenbase case design. In quantifying the uncertainty of waste tonnes, a potential toninclude up to 35 percent waste is recognised within the traditional stope outline. Thenbehaviour of the resulting risk profiles of the copper grade and ore tonnes is importantnin the copper recovery at the mill. A basic economic evaluation of the stope outlinenproves the single base case estimate could be misleading as there is potential to earnnapproximately 58 percent more and a risk of making 50 percent less than expected. With the quantification of geological risk realised, the integration of this risk tongenerate risk based designs is implemented with a linear programming formulationnusing probabilities and expected block grades. The probabilistic mathematicalnformulation optimises the location, size and number of slopes and recovery pillarsnthrough constraints which limit the minimum and maximum size while considering anminimum acceptable level of risk. This probabilistic approach allows a number ofndesigns to be generated by varying the minimum acceptable level of risk indicated bynan average probability of stopes being above a given grade cutoff. Five designs basednon a minimum level of acceptability of 40, 60, 80, 90 and 100 percent are developednusing a cutoff of 2.5 percent copper. Risk profiles for each design are produced for allnproject parameters by running each design through all simulated orebodies. It isnshown that increasing the acceptable level of risk generally increases the averagengrade of the designs and decreases the risk profile of contained waste, ore andneconomic potential as the designs with a minimum level of acceptability of 40 and 60npercent continually produce wider risk profiles for all parameters. The financialnburden of mining the contained waste in these two designs is quantified, as there is anpotential to lose money if they are mined. Although the risk profile of the design withn100 percent average probability of selected rings being above 2.5 percent copper isnsmaller than that of the design with 90 percent average probability of rings beingnabove 2.5 percent copper, there is more upside economic potential experienced by thendesign with 90 percent average probability of rings being above 2.5 percent copper.n The work in this thesis shows the importance conditional simulation plays in thenability to quantify grade risk in an underground stope design. Using a probabilisticnmathematical formulation has allowed risk to be considered when locating an optimalnsloping layout, hence moving a step forward in the ability to manage grade risk in thenunderground design process. The use of probabilities provides a means of producingnmultiple designs which incorporate varying degrees of risk management however, thenfinal selection of a design which best suits the operation is still required. Anformulation which integrates the grade risk stochastically to produce a single designnwhich minimises downside and maximises upside would effectively alleviate thisnproblem. The mathematical formulation could be further expanded to incorporatenmore stoping information leading to the optimisation of a combined design andnscheduling problem. The integration of other sources of risk including morencomprehensive geological risk and financial risk, specifically the commodity price,nwould provide a more robust formulation for solving complex underground designnand scheduling problems.n

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