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GEOLOGICAL RESERVES - CUT-OFF GRADES

K F LANE

This is a philosophical paper. Itdiscusses some of the concepts underlying theestimati on of geol ogi cal reserves and thedetermination of cut-off grades. It exploreshow they i nterrel ate and how they mergeeventually with mine design and miningreserves. The main intent is clarification,particularly in certain areas wheremisconceptions are common.

WHAT IS A GEOLOGICAL RESERVE?

It is usually defined as an estimate of themineralisation in the ground without referenceto any mining restraints. The objective of sucha reserve is to gi ve a quanti tati ve descri pti onof the grade distributions of the minerals,:,ithin ~ deposit based only upon sampl ing1nformat10n.

9f course, tb~ purpose of an explorationsampl1ng programme 1S usually the identificationand delineation of a deposit ai a potentialtarget for mining. However, it is important tohave methods for describing the mineralisationwhi ch are independent of mi ni ng consi derati ons.One reas~n for this is that, in the earlystages, llttle attention may have been paid tothe feasibility of mining; another is that it

i~ often valuable to have figures which are notb1assed by the premature imposition of miningparameters.

The quantities quoted for a geologicalr~serve are always tonnages and grades (orf1gures.related to tonnages and grades) in gradecategor1es. There may be several minerals orseveral kinds of mineralisation; there may beseve~al. zones;. ~ut the crucial summarystat1st1cs descn ptlVe of a mining target aresize and quality - tonnage and grade.

WHAT IS A CUT-OFF GRADE?

In common us~ge, cut-off grade is anexpression which 1S used with insufficientdiscrimination in several contexts. Here, as inthe book "The Economic Definition of Ore" itwill be taken as the term used in an operati~nal

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mining context to define ore as distinct fromwaste. Material with a grade in excess of thecut-off grade is mined and treated as ore;material below cut-off grade is left or dumpedas waste.

HOW DO CUT-OFF GRADES RELATE TO GEOLOGICALRESERVES?

The answer is that there is no directrelationship at all. One is an operationalparameter which is relevant only to an operatingmine, and the other is a set of statisticsdescribing grade variations within a deposit forwhich even a preliminary proposal to mine mightnot exist.

Nonethel ess the expressi on 'cut-off grade'is sometimes applied to geological reservefigures. Tables are compiled quoting tonnagesat different 'cut-off grades'. These tablesactually gi ve the cumul ati ve tonnages abovecertai n grade 1evel s. The expressi on 'cut-offgrade I can be gi ven a perfectly good meani ng inthis context but it is inconsistent with itsmeaning in an operational mining context.

Of course, popular usage can ascribedifferent meanings to the same expression indifferent contexts, but the practice can bemisleading. In this case it is more than justmisleading; it is the cause of a number ofserious misconceptions.

1. The fact that certain grade levels arequoted as cut-off grades in geologicalreserve tabul ati ons is often construed asimplying that they constitute consideredvalues for' an operational cut-off grade.This is not necessarily the case at all.The subj ect may well not have been gi veneven passing consideration.The grade level s for describing gradedistributions should be chosen withreference to the range and pattern of gradevariations in the deposit. Their purposeis to reveal the detail of the gradedistribution because this is likely to bean important factor influencing theeconomics and the choice of mining methodand mine design.

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!t is true that the grade distribution may,1n the event, affect the choice of cut-offgrade. For exampl e, a natural gradeboundary is an obvi ous candi date forconsideration as an operational cut-offgrade because of the convenience ofimplementation. However, there are manyother factors which are also important.Despite the observations of the precedingparagraphs, it was the practice some timeago to. try to choose grade categoryboundar1es which were coincident with1i kely operati ona1 cut-off grades. Themotive was primarily to save work. Thecampi 1ati on of grade tonnage di stri buti ons

fo~ massive deposits was a huge undertakingWh1 ch coul d be simpl ifi ed if only a fewgrade categori es were i dentifi ed and thei rboundaries were taken at possibleoperational cut-off grade values.Nowadays, with computer systems for reserveestimati on, the work content is far 1essimportant than the qua1ity of theanalysis. In these circumstances, it is a

~rave .mi s~ake to prej udi ce any subsequent1nvest1gat1ons of the economic and miningfactors determining cut-off grades by1imi ti ng the range of grade tonnage datathat is available.

There is the obvi ous temptati on to assumethat if a mine were to be established andif it were to operate at one of the quotedcut-off grade levels then the correspondingtonnages and grades woul d be estimates ofwhat might be achieved. This assumption isfalse for four main reasons.

Geometry. It does not follow that thetonnage quoted as exceeding a gi ven gradelevel will necessarily be encompassed~ithin any feasible mine envelope. Even if1t were to be, all of it might still not berecoverable because of practical miningconsiderations such as access or roofsupport.Economics. The fact that material is abovethe operational cut-off grade does notnecessarily mean that it will be or shouldbe cl assi fi ed as ore. The cut-off gradecri~e~ion only applies at the point ofdec1s1on. In other words the material mustbe accessed and ready for mi ni ng. Whethercreating the access, by, for example, stopedevelopment underground or another' pushback in the pit, is justified is a capitalinvestment decision which depends upon thequantity and average grade of the materialexposed. It must be above the cut-offgrade, of course, to qua 1i fy as ore butthis condition alone is not sufficient:

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This point is a frequent source ofmisunderstanding. Even when thesignificance of the cut-off grade solely asthe final criterion for determining ore

~rom developed sources is accepted, there1S often still a persisting belief thatthere must be another cut-off grade whi chwill determine whether material as yetundeveloped shoul d be considered as ore.This is unfortunately not the case. Thereis no similar simple criterion. Minedesign in the sense of determining theultimate limits of mine development isactually a quite intricate economicexercise. Often it involves investmentevaluation techniques when the developmentexpenditure has to be incurred well ina?v~nce of mining the ore. Ultimate pitllm1ts are an example; stripping may haveto be undertaken long before the orebeneath can be mined.Selectivity. The grade tonnagedistributions have to be based upon someassumed discrete unit size of material.The grade measurements are associated withthese units and, statistically, the wholedeposit is regarded as aggregated of them.In geostatistical jargon the unit is calledthe support. Some assumpti on aboutsupport, either implicit or explicit,underlies every mineral distribution.The support underlying geological reservesvari es according to the methods used forestimating the grade tonnage distributionsand it. is often implicit. The supportunderlY1ng any grade tonnage distributionwhich is used for estimating the tonnagesand average grades at different operationalcut-off grades should be of minimum miningunit size. This is the smallest size onwhich grade control is likely to beeffectively practiced and is a measure ofthe sel ecti vity of the mi ni ng method.Where the two supports differ, as isgenerally the case, the geological gradetonnage di stri buti ons must be modifi edbefore any valid conclusions about theeffects of cut-off grades can be reached.Control. In practice, grade control has tobe exerci sed through a sampl i ng programmewhi ch wi 11 introduce a further source ofvariability. The imposition of a cut-offgrade will be subject to somemisclassification, ore as waste and viceversa, because of the inaccuracies of thegrade estimation method. This is anothercause of deviation from the geologicalgrade tonnage distribution.

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This effect, sometimes called theinformation effect, is often referred to asdilution although the concept of dilutioni ncl udes a component resulti ng from afail ure to achi eve the assumed degree ofselectivity as well as a component frommisclassification. Also inaccurate gradecontrol causes some misclassification ofore as waste which is hardly dilution.

WHAT IS A MINING RESERVE?

There appears to be 1ess of a consensusabout the definition of a mining reserve than ageological reserve. If it is taken as being aset of estimates of the tonnages and grades thatmight be achievable in practice, then the grade1imi ts in the di stri buti ons can be referred tounambiguously as 'cut-off grades'. The tonnagesand grades above each 1imi tare genui neestimates of the consequences of worki ng to acut-off grade set at that limit.

RECOMMENDATIONS

In the interests of greater clarity thefollowing suggestions are offered.

1. The term 'cut-off grade' should not beapplied to geological reserve gradedistributions. An alternative term couldbe invented but one is not reallynecessary. It is perfectly possible torefer to a deposit as conta i ni ng anestimated tonnage above a certain gradewithout employing the prefi x 'cut-off'. Inother contexts it is never used. Forexampl e, it woul d be strange to say, "thereare only 10% of geologists above a cut-offIQ of 140" rather than "only 10% ofgeologists have IQs above 140".

2. The support underlying a geological reserveesti mate shoul d al ways be quoted, or somestandard support shoul d be agreed. Thereis a strong case for the latter in order toavoid the chore of having to quote a figurewhich means little to anyone who is not anexpert in the field.

3. A mining reserve should, as its nameimplies, be a set of estimates of thetonnages and grades that mi ght be achi evedin practice. This means that the tonnagegrade distributions should be based uponvalid estimates of the effects of operatingat different cut-off grades. With thisdefinition a mining reserve can be seen asthe outcome of imposing a mining method, amine design and a mine plan on a geologicalreserve.

The si gni fi cance of these poi nts goes farbeyond semantics. A mineral deposit is oftenregarded as a resource. To regard it in thisway, though, can be misleading. It is notusually some clearly defined entity awaitingexploitation. Rather, it is a concentration ofmineralisation that might provide an opportunityfor an economi c investment. Whether it does ornot depends not only upon the deposit itself butalso upon the way it is developed and mined.

Fundamental to the formulation of astrategy for mining is an understanding of thepattern of grade variations. These determinewhere to mine, how to mine and what to treat asore. It is important in the search for anoptimum strategy, or even a feasible one, thatno options are closed off prematurely.

It is for this reason that the preservationof the status of a geological reserve asindependent of mi ni ng cons i derati ons isessential. It is a description of the targetdeposit which remains unbiassed by anyprel iminary concl usions about mining method ormine design.

It should be possible to test severalmining methods against the geological reservedata and to derive mining reserves for a rangeof mine desi gns and pl ans. Cut-off gradepolicies and plant capacities can then be chosento yield optimum economic returns.

This process frequently involves thegenerati on of i ntermedi ate reserves. Theseshoul d be recognised as such. For exampl e, ifin the early stages a block model isconstructed, this may immediately impose impliedvalues for mining parameters such as benchhei ght and sel ecti vity. Hence a reserve basedupon the model is no longer strictly ageological reserve: it already incorporatesassumptions about the method of mining and sizeof equipment. Then the same model may form thebasis of a mining reserve after the impositionof pit profiles. This again is not strictlyaccording to definition because no allowance forgrade control inaccuracies has been made.

Such intermediate reserves serve animportant purpose but they shoul d not obscurethe underlying concepts of a geological reservewhi ch descri bes the deposit, and a mini ngreserve which gives valid estimates of theeffects of operational cut-off grades.

REFERENCESHancock, M C, Gooday, P E, and Breech, G E, 1987.

Ore reserve systems pri nci pl es andpracti ce, in Resources and ReservesSymposium pp 137-147. (AustralaslanInstltute of Mining and Metallurgy, SydneyBranch)

King, H F, McMahon, D Wand Bujtor, G J, 1982.A guide to the understanding of ore reserveestimation, Supplement to Proc Australas.Inst. Min. Metall., No.281:p.21.

Lane, k F, 1988. The Economic Definition of Ore.(Mining Journal Books:London).

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