Massmin 2004 121

1. INTRODUCTION

Conventional mine planning encompasses all or part ofthe development of a mine, including feasibility, profitability,detail development, scheduling of extraction sequences,operation of equipment and transportation. Mine plannersusually estimate the different parameters used for theplanning process from standard procedures available in theengineering field such as cost information databases fromsimilar operations, experience and engineering judgement.This standard approach is usually based on the ‘state of theart’ associated with a given mining method.

Nevertheless, these procedures, databases andexperience are usually incomplete or have a large degree ofuncertainty related to the nature of basic estimations onsuch as the heterogeneity of the rock mass, geologicalenvironment and etc.

These uncertainties are present in every stage of the mineplanning and design process and include: • Definition of the geological model.• Ore resource or mineral inventory estimation.• Rock mechanics behaviour of a design.• Metallurgical performance.• Operational performance.• Cost and economic estimations.• Local political conditions and regulations.• Market product price forecasting.• Environmental issues.

From the above abbreviated list, it is readily apparent thatmining, and especially block caving, is inherently risky.

Traditionally, the decision making process under uncertaintyhas been managed using standard risk and sensitivity analysesfor the cash flows of projects. However, sensitivity analysesalone are not sufficient, and to be rigorous it is necessary tocheck and adjust major assumptions used to define a projectsuch as the final exploitation limits and cut-off grade applied toore, and further re-evaluate cash flows.

The risk is greater with block caving as opposed toconventional mining because the response time required foradjustments of cut-off grades and mine costs, even if theseare possible, is large.

This paper proposes a method for managing uncertaintyduring the block cave mine planning process under a multi-

metal scenario, including identification and quantification ofassociated risks at an early stage of the planning process.

2. RISK RELATED TO COSTS, GRADES AND METAL PRICES

The mining business is intrinsically more risky than mostother common business areas. Figure 1 shows a scheme ofuncertainties for open pit planning associated with the stageof the development of the pit (Blackwell,1993), and thisfigure defines the uncertain information and conditions thatapply to mining generally.

Figure 1: Uncertainty of Factors in Mine Planning versus PitDevelopment (Blackwell, 1993)

Traditionally mine planners have been managinguncertainty in the planning and design process by usingiterative estimations and sensitivity analyses of projectcash flows. This process demands substantial andintensive use of resources to identify the most importantparameters influencing the results of mine planning anddesign.

Santiago Chile, 22-25 August 2004

AbstractThe common practice in mine planning, irrespective of mining method, is to make decisions based on deterministicfuture metal prices. Later, during the economic evaluation of the project, stochastic tools are employed to identify andquantify risk factors such as metal prices when mine design and planning has already been completed. Given thecapital-intensive nature and long preproduction periods of mining projects, especially in block caving, incorrect priceassumptions present a significant source of uncertainty to project feasibility. This proposal outlines the introduction of astochastic simulation method in the primary phase of mine planning, assigning metal prices based on probabilisticdistributions. Utilizing this method combined with standard procedures for defining mining areas in block caving permitscharacterizing and prioritizing ore reserves based on price uncertainty, giving an additional decision tool to mineplanners.

Block caving planning under metal price uncertainty

Sergio Fuentes S., Mining Civil Engineer, Universidad de Chile, M.Sc. (Eng), Queen’s University, 2003, Director, Metálica Consultores S.A., Chile

122 Massmin 2004

Currently, many tools are available to produce data,conduct sensitivity analyses, and produce ‘final numbers’from a base scenario. These tools include geostatisticalapproaches for ore grade estimations, probabilistic risk andsensitivity analyses for cash flows, and economic indexes.

In most cases, operating and capital costs and similartechnical variables are defined within reasonable limits withlimited impact on project economics. This is in contrast tothe risk associated with external variables such as metalprices and market forecasts that have much greater impact.

Although several tools are being used in the miningindustry for risk management, low metal price trends ofimportant commodities, along with the lack of availability ofhigh grade deposits, are pressing the mining industry toproduce, and improve on, more reliable designs andproduction schedules. This is especially true in low grade(marginal) and impurity rich (penalty producing) ore bodieswhere profit margins are small, if they exist at all.

3. RISK AND UNCERTAINTY

Decision theory literature indicates two distinct types ofuncertainty (Rose, 1976): • Risk is a concept used to characterize situations where

past data can be useful in predicting an occurrence in thefuture such as the probability of a road accident or thetossing of a coin.

• Uncertainty is a concept referring to situations wherethere is no suitably supported past data or experience.

Metal prices fall more reasonably under the ‘uncertaintyconcept’ as it is not known when the metal price will returnto some past value.

The main questions here are, firstly how could wecharacterize this uncertainty factor, and secondly, how couldwe manage this characterization in block caving mineplanning procedures.

4. METAL PRICES UNCERTAINTY

Metal price uncertainty and its impact have been underdiscussion for many years. The effects on mine planning arecritical, hence the continuing recurrence in mining industrypublications. Metal prices are critical inputs in defining oreand waste, and the foundations of the mining business,including ‘ore reserves’, are defined based on commodity(metal) prices.

In 1903, Williams (in Rickard et al, 1907, page 1) wrote "Ithas been estimated that 95 per cent of the commercial andindustrial enterprises which are started every year ultimatelyprove unprofitable. Such business failures are primarily dueto incorrect estimation of the trade conditions which obtainin every field of commercial operation". This quotationshows that this problem has been of concern for at least acentury.

During the 1930’s, other authors affirmed that forecastingmetal prices is perhaps the most doubtful and speculative ofany of the elements in mineral valuation. At that time someof the important elements affecting price forecasts wereidentified, including relative rate of growth of supply anddemand, competition, substitution of commodities,technology trends, and international market conditionsbeing the most relevant.

More recently, organizations, such as the Chamber ofMines of South Africa have stated (Storrad, 1981); "…theuncertainties associated with risk factors such as sellingprices can not be defined in a completely objective way.Human judgement unavoidably plays the major part inassessing these uncertainties, and the quality of the finalanswer obtained therefore depends critically on the qualityof the judgement involved at this stage".

The future is never certain and so metal price forecastscannot be expected to be accurate. Indeed, it thereforefollows that any economic evaluation will never be exact.

5. STOCHASTIC SIMULATION

"The fundamental rationale for using simulation in anydiscipline (whether or not this is economics or operationsresearch) is man’s unceasing quest for knowledge about thefuture. This search for knowledge and the desire to predictthe future are as old as the history of mankind." (Naylor,Balintfy, Burdick & Chu, 1968).

Although simulation has been applied to some extremelydiverse forms of model building, ranging from Renaissancepainting and sculpture to the spacing and computing ofneurological processes, it has come to mean somethingquite specific.

Modern use of the word traces its origin to the late 1940’swith the work of Neumann and Ulman (Naylor, Balintfy,Burdick & Chu, 1968). They used an original mathematicaltechnique termed "Monte Carlo Analysis" to solve certainnuclear-shielding problems (Monte Carlo simulation wasnamed after Monte Carlo, Monaco, where the primaryattractions are casinos and games of chance).

At the beginning the term "Monte Carlo" applied only tothe use of stochastic simulation methods for solving strictlydeterministic problems. Later it was generalized andbecame "a popularized synonym for ‘simulation ofstochastic processes’ " (Naylor, Balintfy, Burdick & Chu,1968).

Generally speaking Monte Carlo simulation is a form ofsimulation where randomly generated values for uncertainvariables are used over and over again to simulate a model(Goldman, 2000).

Stochastic or Monte Carlo simulations are based on thegeneration of pseudo random numbers (usually between 0and 1), which are introduced into the cumulative probabilityfunctions for predefined variables. As a result of thisprobabilistic definition of values, the model is fed a newstate permitting the updating of the internal databasedescribing the model.

Consequently, this procedure is repeated 100 to 1000times or more, each time prompting a random choice of oneor more values for variables. A counter controls thesimulation, and the counter is increased until a predefinedcondition or imposed constraint is met, as Figure 2 shows ina very simplistic scheme.

Figure 2: Stochastic Simulations, Simplistic and SchematicRepresentation

Santiago Chile, 22-25 August 2004

Massmin 2004 123

The number of times the simulation must be carried outdepends on the confidence limits required for the final result.

6. GENERAL PROPOSAL FOR MINE PLANNING & METAL PRICE UNCERTAINTY

Figure 3 shows the traditional procedure used to evaluatemetal price uncertainty in a project. In this example a MonteCarlo Simulation (MCS) of the cash flow varying under arandom evaluation of a metal price distribution is used forthe entire life of the project.

Figure 3: Traditional Mine Planning and Decision Process

During this standard deterministic mine planning process,no probabilities of outcomes are specified, so the decisionmaker (mine planner) must rely on personal judgement andintuition to put the sensitivities of the variables intoperspective, and to assess what might happen with manyinter-related sources of price uncertainty, especially in thecase of a multiple metals ore body.

In this paper it is proposed to introduce probability metalprice distributions for the different valuable metals present inthe ore body in the primary economic evaluation of theresource.

By providing a measure of this uncertainty will allow themine planner to make decisions during the many stages ofthe planning process. As this measure represents thecertainty generated from metal price variability, the authorwill name it the ‘Price Certainty Parameter’ (PCP), which willprovide a value for the probability that any block has achance to participate in a profitable design, i.e. beconsidered for mining in the planning process, even thoughit may not be ore.

This Price Certainty Parameter (PCP) will not reflect theexact final economic value of the mine plan and design,because detailed estimation is carried out downstream ofthis process. Even if the reserves are well scheduled, thefinal certainty of the project should be less than the averageof the PCP when the discount rate and dilution are takeninto account.

Using a simple open pit ‘moving cone’ example, it ispossible to deduce that the PCP is the probability of aresource block being considered inside a profitable design.That does not mean the block is profitable by itself, but, byleading to ore, it might increase the value of the design as awhole. Cleary we could observe this concept if we analysea block of waste located above a high grade ore block in anopen pit planning process as shown in Figure 4.

Figure 4: Simple Open Pit Cross Section, Defining PriceCertainty Parameter (PCP)

Assuming a metal price probability distribution wasprovided for the economic model, and each block wasevaluated independently N times (with N large), then 100%of the time block W1 will be waste, but will always beincluded in the design because it leads to the mining of thehighly profitable block O9.

The Price Certainty Parameter for this waste block is100%, and the block has a 100% economic certainty ofbeing included in the design envelope for any given metalprice and should be mined.

On the other hand, if the peripheral block O6 wereincluded only 50 % of the time in a series of open pitoptimizations, then its PCP value is 50%.

Figure 5 below shows a flow sheet diagram describing theproposed assignment and management of a stochasticcertainty index to each ‘block of resources’ in the blockmodel as a result of a mine planning evaluation.

Figure 5: Proposed Mine Planning Flow Sheet

Santiago Chile, 22-25 August 2004

124 Massmin 2004

The Price Certainty Parameter of a ‘resource block’could be defined as "The probability of that resourceblock being included in a specific design, taking intoaccount metal price probability distributions". Thisprobability could be estimated as a result of severalrandom metal price evaluations of the mining limits for agiven mining plan or method.

For block caving the PCP parameter can be estimatedby evaluating each column of ore using randomlyobtained metal prices for each block in the columnseveral times. In the case of an open pit thoseparameters could be obtained by carrying out severaloptimization evaluations (e.g. Lerchs-Grossmann (1965)or moving cone, Lizotte(1988)), where the PCP for eachblock is re-calculated several times.

Using this characterization of "Certainty" as associatedwith metal prices, it is possible to generate alternativedesigns, envelopes and sequences, and make decisions byreferencing PCP values as a numerical parameter. Thisparameter quantifies, in some way, the economic advantageof mining a defined volume of material (ore or waste)considered in the design before any economical evaluationis carried out.

This characterization, with a numerical qualification ofresources in the entire block model, will help support themaking of decisions during the mine planning process.

The assumptions used to assign a certainty ‘index’ (PCP)to each block in the block model are:

• Unknown Metal Price in the FutureThe first assumption is that the market price of any given

metal in the future is unknown; intuitions, opinions, short-term trends, etc. all produce a rough expected value range.

• Metal Prices as Probability DistributionsIt is assumed that we can represent each metal price

with a probability distribution describing possible futureprice behaviour. There are so many factors affectingmetal price behaviour that it is impossible todemonstrate that metal prices are deterministicvariables. It is also impossible to demonstrate that metalprices are truly random variables taking values inaccordance with a probability distribution.

The author considers the characterization of the uncertainbehaviour of metal prices as a random variable, and this isfar more reasonable than the assumption of a deterministicmodel. The same assumption is made by all risk analysissoftware packages.

There is a direct relation between the profitability of acolumn and PCP because a high PCP value is anindication of the profitability of the column for a widerange of metal prices as used in the metal pricesimulation.

7. MANAGING PRICE CERTAINTY PARAMETER IN BLOCK CAVING

Specifically in block caving, using the "Price CertaintyParameter" it is possible to characterize each column in theentire area, representing the probability of each columnbeing included in a mine design for a given metal pricesdistributions.

Additionally, as a result of the several evaluations for thecolumns, an expected economic value is available for eachcolumn and should to be used, together with PCP values, tomake a single informed decision in the mine planningprocess without waiting for several economic evaluations tobe completed.

A footprint representation for PCP values associated toeach column can be observed graphically in Figure 6.

Figure 6: PCP Footprint Output for a Block Cave ColumnValuation

The ore reserves included as part as mineable envelopcan be characterized using standard tonnage-"certainty"curves, as is shown in Figure 7.

This "tonnage - certainty" distribution (orcertainty/tonnage curve, comparable to a grade/tonnagecurve) can be obtained and should provide a good generalnumerical measure of the risk in any particular design. Thisdistribution can give a global indicator of the resourcesalready considered in the mining envelope, including allnon-profitable columns added to the design due tooperational or geotechnical reasons.

Figure 7: Tonnage – Certainty Curves

This information provides the planning engineer someconfirmation that the operational mine envelope developedis adequately mining with the available resource.

For the definition of an operational area to mine, eachproject board should select the minimum "cut off certainty",taking into account PCP distribution resulting from the areaunder analysis, "risk guidelines" for the project, etc.

Santiago Chile, 22-25 August 2004

Massmin 2004 125

At this stage, some of the most important definitions inblock cave planning are achieved, only using mine planningoutputs

Once mineable envelope and final column heights to beexploited are defined, the mining sequence definition ismade. Again, this situation could be solved using PCPvalues as a good guideline for profitability of the oreresources.

Scheduling columns that show highest PCP values at thebeginning of the mining sequence will imply highest profitresulting in the initial production periods of the project.

8. CASE STUDY

A case study was developed using information fromCodelco-Chile, El Salvador Mine. The A- Norte Sector, locatedin the Northern part of the main ore body as shows Figure 8,was evaluated using the standard process (fixed metal prices)and also using this proposed and complementary methodology(stochastic metal price distributions).

Figure 8: General Plan View of El Salvador Mine

This marginal area was studied using five deterministiccopper prices (75, 80, 85, 90 and 95¢US$/lb), keepingconstant Mo, Ag and Au prices.

The stochastic scenario considered trapezoidalprobabilistic price distributions for Cu, Mo, Ag and Au. Thespecific distributions are shown in Figure 9.

This probabilistic distribution is usually used when thebehaviour of the variable is unknown, maximum andminimum values are defined, clearly highlighting best andworst commodity price scenarios. As well, a range withequal probability (uniform) in between indicates the mostprobable expectation, guess or feeling, etc., about the futuretrend of mean prices.

In consequence, this probabilistic approach for our lack ofknowledge appears as a reasonable representation of thisignorance and actual metal price forecasting.

If we consider that this sector will not be in productionbefore 2010, then the question is what metal price must beused for ore reserve definition. Generally speaking, to makethe decision, we can use several metal price valuations, aneconomical envelope using our best "engineeringjudgement".

Standard methodology used in block caving planning,permitted to obtain outputs associated with metalproduction, ore production rate and copper ore gradeprofiles as shown in Figure 10 to Figure 12.

Figure 10: Fine Copper Production

Figure 11: Mine Production Rate

Santiago Chile, 22-25 August 2004

Figure 9: Trapezoidal Distributions Used

126 Massmin 2004

Figure 12: Mine Production Rate

The main differences can be observed in 95 centsscenario with longer exploitable reserves due to the graterarea to mine. Indeed, this scenario has approximately threemore times of ore reserves compared with the 90 cents orstochastic scenario.

If we develop a standard economic evaluation, meansdeterministic metal prices for each of them, we obtainoutputs such are shown in Figure 13.

Figure 13: Deterministic NPV Evaluation

Same cash flows were evaluating using MCS, obtainingan expected NPV for several discount rates for eachscenario, as is shown in Figure 14.

Figure 14: Expected NPV Values using MCS

Using the certainty characterization made in theStochastic Scenario, it is possible to observe a directrelation between the mean PCP value of each scenario andNPV variability by metal prices and discount rate.

Figure 15: NPV Variability & Certainty by Scenario andDiscount Rate

9. CONCLUSIONS

The introduction and estimation of a certainty parameterduring the primary definition of the (ore) block model in theblock cave planning process, based on metal priceprobabilistic distributions and Monte Carlo simulationtechniques, shows that:• There is a direct relationship between values of the price

certainty parameter (PCP) and the profitability of a givenresource block.

• Independent of the cut-off certainty value used by themine planner, it is possible to obtain in one step acomplete picture of the economic potential of the

Santiago Chile, 22-25 August 2004

Massmin 2004 127

resources under analysis, and consequently an advancedmeasure of the economic risk associated with any givendesign.

• This proposed procedure provides mine planners with asafe and profitable exploitation envelope and miningsequence far more quickly than the standard(deterministic plus sensitivity) methodology.

• The estimation of the certainty value for each resourceblock permits the concept of risk management to beapplied during the entire block caving planning process,obtaining quantifiable support for many decisions insteadof using "engineering judgement". Further, theidentification of material in the (say) 40-50% and 50-60%certainty range by location and volume would provide anequivalent sensitivity analysis to several deterministicscenarios.

• In a similar manner to the development of the metal pricecertainty concept, it would be advantageous to introducethe same concepts to other uncertain variables such asmineral inventory estimates (grades) and geotechnicalparameters to provide a more complete characterizationof the certainty of any given resource block.

The methodology developed can still be improved upon,especially the fixed ‘metal price probability distribution’which will continue to be a subject for discussion.

The basic objective of providing block caving planners withan additional tool for making decisions prior to reaching thestage of the final cash flow evaluation has been met. Withoutthis tool, and without substantial investment of time and humanresources, a single mine plan could lead to the rejection of thedecision to start a mine, or the starting of a mine with noprospects of making a return on capital employed.

REFERENCES

• Blackwell, G. H., (1993). Computerized Mine Planning forMedium-Size Open-Pits, Trans. Instn. Min. Metall. (Sect.A: Min, Industry), 102, May- August 1993, A83 – A88.

• Fuentes, S., (2003). Planning Block Caving Operationswith Metal Price Uncertainty, M Sc Thesis, Queen’sUniversity, Kingston, Canada.

• Goldman, L., (2000). Risk Analysis and Monte CarloSimulation, Decisioneering Inc.,h t t p : / / w w w. d e c i s i o n e e r i n g . c o m / m o n t e - c a r l o -simulation.html.

• Lane, K.F., (1991). The Economic Definition of Ore,Mining Journal Books Ltd., London, England, ISBN 0900117 45 1, pp 6 – 33

• Leith, C.K., (1938). Mineral Valuation of the Future, TheMaple Press Co., New York.

• Lerchs, H. and I. Grossmann, (1965), Optimum Design ofOpen-pit Mines, Transactions, CIM, Vol LXVIII, pp. 17-24

• Lizotte, Y., (1988). The Economics of Computerized OpenPit Design, International Journal of Surface Mining, A.A.Balkema, Rotterdam, Netherlands,Vol 2, 59-78.

• Metálica S.A., (2001). Ingeniería Básica A-Norte ElSalvador, Internal Report.

• Metálica S.A., (1998). Manual de uso Módulo dePlanificación Block Caving, MineSight, Internal Report.

• Naylor, T., J. Balintfy, D. Burdick and K. Chu, (1968).Computer Simulation Techniques, John Wiley & Sons,U.S.A., pp 1 – 22; 68-71.

• Rickard, T.A. and H.C. Hoover, (1907). The Economics ofMining, Ingalls, Gilman & Others (eds.), 2nd Edition, NewYork, Hill Publishing Co, pp 1.

• Rose, L.M., (1976). Engineering Investment Decisions,Planning under Uncertainty, Elsevier Scientific PublishingCo., Amsterdam, The Netherlands, ISBN-0 444 41522 X,pp 42 – 136.

• Storrad, C.D. (1981). South African Mine Valuation,Chamber of Mines of South Africa, Johannesburg, ISBN 0620 02155 1, pp 448 – 456.

Santiago Chile, 22-25 August 2004