Ore Dilution Sources in Underground Mines - Interpretationand Evalution MethodsS Planeta1 and J Szymanski2

ABSTRACTIn the first part of this paper, the principal sources of dilution duringunderground evaluation and mining are discu sed, then definitions of oredilution currently in use are analysed. These definitions vary dependingon the authors. Ten different analytical expressions of dilution percentagecurrently exist. It is demonstrated, with the help of a numerical examplefor a given mining condition, that dilution percentage results varyconsiderably and that they depend on the definition used. This situationmakes it difficult to compare different results regarding the dilutionproblem, often because some of the terms used are contradictory. A newore dilution evaluation methodology is proposed, replacing the tendifferent analytical expressions by only two: the planned dilution factorrelated to the stoping selectivity, done at the mine planning level, and theadditional dilution factor related to the efficiency of the dilution controlmeasures during stoping operations. The conclusion shows that the use ofthis methodology would be a definitive asset in planning, in stopingoperations follow-up, and in future costs comparison studies betweenmining operations.

INTRODUCTIONUnderground mining of a deposit is inevitably associated to oredilution. Dilution is generally understood to be waste rock or lowgrade ore (lower than the cut-off grade) added to the mined ore,hence having a final run-of-the-mine tonnage greater thanplanned with lower grade and ore values. Ore dilution is animportant economic and environmental component, but it is oftenneglected by mine operators. It can be planned, intentional or not,but it can also be unplanned, unforeseen and detrimental becauseof its high volume of waste rock. An analysis carried out inseveral underground mines in Canada (Knoll, 1989) brought outthat additional dilution, over-estimated grade, poorly estimatedreserves and inadequately conceived mining methods were themain factors in mine closings or their financial difficulties. Evenif the general definition of dilution is understandable, the term'dilution' is a 'glory hole' for a number of mine operators, whoinclude in it miscalculations in grade estimation, mining reservestonnages, and mining operations. Furthermore, the term 'dilution'is defined in technical litterature in many different ways, if at all.Because of the use of contradictory terms, this situation bringsdifficulties when the time comes to compare different studies onvarious mines, analysed by different authors.

The main objective of this paper is to analyse the differentdefinitions of the term 'dilution' currently in use, and to develop atrue dilution estimation methodology that is easy to use indifferent mining conditions and that integrates all the knowndefinitions. Such a methodology is all the more crucial since thedilution problem is considered to be more and more importantregarding its excessive costs and its negative impact on theenvironment.

I. Departement de mines et metallurgie, Universite Laval,Quebec (Que), Canada G IK 7P4.

2. University of Alberta, Edmonton (Alberta), Canada.

DILUTION SOURCESDuring the evaluation and the mining of a deposit, there areusually two main sources of dilution: Planned dilution (Figure I); and Additional dilution (Figure 2).

The sum of these two dilution sources constitutes the finaldilution that is found in the run-of-the-mine.

WotIdng _ too 1oIgo:

--- Tho -*lng"_ lenwlnly""" to :

111....._-

OponIng .......... bJ .... -""""

S PLANETA and J SZYMANSKI

Planned dilutionThe geometry of an orebody fequires that, during the planning ofthe stope, some waste rock be included, especially when theworking thickness of the stope exceeds the thickness of theorebody (Figure I), primarily when we encounter lode-golddeposits in quartz veins (mines: Joe Mann, Dome, Silidor, etc)that have a general thickness of 3 cm to 50 cm (mines: Forest Hillor Joe Mann, for example). This waste rock mixing with the oreconstitutes ore dilution, which can be planned, and is inherent tothe stoping method.

Additional dilutionDuring the mining of an orebody, there is, on top of the planneddilution, additional dilution (Figure 2) from stoping, ore andbackfill handling operations (technical aspect of the dilution) andfrom wall caving (geotechnical aspect of the dilution).

ORE DILUTION DEFINITIONSCURRENTLY IN USE

Geologlc.1 rrv..CTgl

Mining rerv

Tonnag

Grad

FIG 3 - Main parameters caracteristic of mining the ore.

Run-oj-mine ore (Tt)The tonnage generally sent to the mill. It is the sum of the miningreserves and the additional waste.

Parameters and terminologyThe main parameters caracteristic of mining the ore are illustratedin Figure 3 and are defined within the context of this paper asfollows.

Tt=Tm + Wa

Inserting equation I in equation 3 we have:

Tt=Tg + Wp + Wa=Tg + Wt

(3)

(3a)Geological reserves (Tg)The tonnage of ore contained within the natural geological limitsor drawn to a specified cut-off grade.

Table I summarises the principal components of dilution andTable 2 shows the main relations between diluted and non-dilutedore.

TABLE 1Principal components ofwaste diluting the ore.Planned waste (Wp)

The waste rock and/or rock with a lower mineralisation contentthan the cut-off grade, expressed in tonnes, within the plannedstope limits, which are a function of the stoping methodconsidered. It is estimated at the stope planning stage and isbased on the geological reserves (Tg).

ParameterTonna e

PlannedW

Waste dilutin the oreAdditional Total

Wa W,=W+Wa

TABLE 2Main relations between diluted and non-diluted ore.

Mining reserves (Tm)The ore tonnage within the planned stope limits, which are afunction of the stoping miming method considered. Miningreserves include geological reserves and a certain plannedamount of waste rock (Wp). They are estimated at the stopeplanning level.

Grade tpw taw _~...!:p:..-x_t!:.:pw~+,.,......~..:.a_X....:ta:.;;,wtrw= W

t

Tm=Tg+Wp (I) OreDiluted

_Tgxtg+Wpxtpw Tmxtm+Waxtawtm - It = -.::.:_::.:....,,~:.-.-=-Tm Tt

Additional waste (Wa)The waste rock and/or rock with a lower mineralisation contentthan the cut-off grade, expressed in tonnes, coming from beyondplanned stope limits. It is unforeseen, undesirable and detrimentalto the operation of the mine and can only be roughly estimated atthe stope planning stage. It is based on the mining reserves (Tm).

Total waste (Wt)

Tonnage

Grade

Geologicalreserves

Tg

tg

Miningreserves

Tm=Tg+Wp

Run-oC-mineore

T,=Tm+Wa=Tg+Wp+Wa=T +W,

The waste rock and/or rock with a lower mineralisation contentthan the cut-off grade, expressed in tonnes. It is the sum ofplanned and additional waste and is based on the geologicalreserves (Tg).

Wt=Wp+Wa

In this paper, the term waste rock refers to the barren rockand/or the rock which includes mineralisation below theoperating cut-off grade.

(2)

Definitions of ore dilutionThere are several definitions of dilution currently in use and theirinterpretation varies depending on the author. Generally, the term'dilution' can either be expressed in tonnage or in percentage. Inthe technical literature, the term 'dilution', is often defined aspercentage of dilution which is based either on the tonnage or onthe grade. Figure 4 shows a classification of the three differentdefinitions of the percentage of dilution, and the reader will findtheir analytical expressions in Table 3.

88 Kalgoorlie, 13 - 14 November 1995 Underground Operators' Conference

ORE DILUTION SOURCES IN UNDERGROUND MINES

TABLE 3Analytical expressions of the three different definitions ofpercentage ofdilution.

Defini Percental!e of dilution (%)tion Additional

Planned Alternative Alternative Finalnumber 1 number 2

No I W w. w. W,PD, =.!..!..P.. x 100 ADll =-x 100 AD'2=-x 100 FD, =-x 100Tg Tm Tg Tg

No 2 W W" W,Pfh=.!..!..P.. x 100 A~=-xIOO Ffh=-x 100Tg Tt Tt

No3Pf>} = Ig - Im X 100 Af>} = Im - It x 100 Ff>} = Is - I, x 100

Ig Im Ig

tg =10.0 gl Au : ore grade

Tg 8,100 tonne.: orelonnage

limit.True .to

2. DIutJon ~ x 100

_no'

t . Dluted on. f'lOftoCItwttd ........

FIG 4 - Classification of the three different definitions ofpercentage of dilution.

FIG 5 - SlOpe schematic (numerical example).

Some authors (Almgren, 1981; Quesnel and Ley, 1991;Pakalnis, Miller and Madill, 1985; Ashcroft, 1991; Elbrond andDemers, 1990) use definition number I.

Others (White, 1984; Mathews, 1990) use definition number 2and some others (Gunzert, 1983; Badwen, Nantel and Sprott,1989; David and Toh, 1989; Ingler, 1975) use definition numberfine dilution. Furthermore, definition number I could beinterpreted in two different ways (Table 3) by some companiesand autors.

Analysis of the applications of the three differentdefinitions of 'dilution' currently in use.

Why are different definitions of dilution used inthe mining industry?

The choice to use one of the definitions given in Table 3 tocalculate the percentage of dilution is based on the miningconditions. Indeed, in most cases, one must work with theavailable data. But it is very important to lay emphasis on themethod used to calculate the percentage of dilution, since there isa lot of variation in the results. A simple numerical examplewillillustratethis situation.

TABLE 4Calculation parameters.

Tonnaj1;e (tonnes) Grade (I!1t Au)Geolol!:ical reserves T. - 8100 T. = 10.0Planned waste Wn-8100 lnw = 2.0Mininl!: reserves Tm - 16200 tm = 6.0Additional waste Wa- 3925 law = 1.0Run-of-mine ore T,=20 125 tt = 5.0248

The percentages of dilution calculated with the three differentdefinitions (Table 3) are given in Table 5.

This numerical example clearly demonstrates the wide varietyin the obtained results (Table 5), which depend on the definitionused. The two alternatives in definition number 1 affecting theadditional dilution calculation are due to the fact that someauthors base their calculations on mining reserves (alternativenumber I) and some others on geological reserves (alternativenumber 2).

Numerical exampleA gold deposit illustrated in Figure 5 has the following geologicalreserves.

The planned working thickness is 2.0 m when considering longhole sublevel stoping. The planned was te grade is tpw = 2.0 gftAu. The run-of-mine ore, after blasting and caving of the walls is20 125 tonnes of diluted ore. The additional waste grade wasesti~ated a~ taw = 1.0 gft Au. We suppose (fo! sake of clarity) aspecIfic weIght for waste and ore of 2.7 t/m' The calculationparameters used in this example are summarised in Table 4.

TABLESPercentages ofdilution calculated with the three different

definitions (numerical example).Definition Percentaj1;e of dilution (%)

Planned Additional FinalNol PD,-IOO.OO AD,! -24.23 AD 12 -48.46 FDl= 148.46No2 PD2 - 50.00 AD2 - 19.51 FD2= 59.76No3 PD3 -40.00 AD3 - 16.25 FD3 =49.75

Underground Operators' Conference Kalgoor1ie, 13 - 14 November 1995 89

S PLANETA and J SZYMANSKJ

Fields ofapplication of the three different definitionsDefinition number 1: This definition is generally used inevaluating the percentage of dilution at the stope design stagewhere the planned waste tonnage (Wp) is easy to evaluate fromthe geometric parameters of the orebody and of the stope(thickness of ore versus the working thickness). On the other hand,this definition is far from being practical in evaluating the additionalpercentage of dilution; it is generally difficult to estimate theadditional waste tonnage (Wa) included in the run-of-mine ore.Moreover the additional percentage of dilution can be calculatedbased on mining reserves (alternative number 1) or based ongeological reserves (alternative number 2). Considering that theadditional dilution is caused by the waste rock coming from beyondplanned stope limits, dilution should only be estimated, in ouropinion, based on the mining reserves (alternative number I).

Definition number 2: This definition indicates the percentage ofwaste included in the diluted ore. The percentage of dilution can becalculated from this definition, based either on tonnage or on grade.For example, we can write the following equations for additionaldilution:

The 3925 tonnes of additional waste at 1.0 gjt Au, added to the16 200 tonnes of mining reserves at 6.0 gjt Au produce apercentage of dilution of : 24.23 per cent (definition number I, alternative number I) 48,46 per cent (definition number I, alternative number 2) 19.51 per cent (definition number 2) 16.25 per cent (definition number 3)

It is very difficult to compare numbers when it comes todilution because of the shear number of interpretations that exist.Some publications (Mining Sourcebook - 1994, for example) donot even state what definition they are using in the percentage ofdilution calculations: definition number I, number 2, or maybenumber 3? The table titled 'Underground mining methods'(Mining Sourcebook - 1994, pp 19-22) gives a comparison ofthe percentage of dilution in several Canadian mines, but does notexplain how the calculations were done. It is very difficult todepict then what exactly the numbers representing: a planneddilution percentage, additional, or final? Let's take a value ofpercentage of dilution (Mining Sourcebook - 1994, pp 19-21). A20 per cent dilution at the Chimo mine (Cambior), Kierens mine(Aur) or Joe Mann mine (Meston), for example, could result in: 0.2 tonne of waste per tonne of non-diluted ore (definition

number I), 0.25 tonne of waste per tonne of non-diluted ore (definition

number 2), a reduction of 20 per cent in the diluted ore grade over the

non-diluted ore grade(definition number 3).Dealing with ore dilution without a common methodology

presents a lot of difficulties when one tries to compare miningconditions and case studies. This is mainly due to the existingcontradictions in terms. Furthermore, for a given scenario, theinterpretation of results may differ. Therefore, it seems relevant todevelop a methodology to evaluate the dilution, that would beapplied by all contributors both at the mining and at the researchlevel. Such a methodology is all the more needed since thisproblem is considered to be more and more important,considering the excessive costs of dilution and its negative impacton the environment. Moreover, several mining companies(Sauriol, 1991; Ashcroft, 1991; Miller, Potvin and Jacob, 1991;Planeta, 1993; Saperstein, 1993) do their best in reducing oredilution and, in general, most of the mining operators agree thatthe key to increased competivenes and even survival of severalunderground mines will mostly depend on increased stopingselectivity and on a reduction in ore dilution.

PROPOSED METHODOLOGY FOR THECALCULATION OF DILUTION

(5)

(6)

(7)

(8)

(11)

(10)

(12)

(13)

(tonnes)

(tonnes)

In transforming equation 4 we obtain:

After introducing the last equation in equation 5 we obtain:

Grouping the elements, we obtain:

w. - 7' tm - Ita- l,Xtm - taw

Tt X tl = Tm X tm+Wax taw

Wa (tm- taw) = TI (tm- tt)

Tm=Tt - Wa

Tt X tt = (TI - Wa) X tm+ Wax taw

W. =20125 6.0-5.0248 =3925a X 6.0- 1.0

This way of calculating the percentage of dilution proves to bevery interesting for a possible reconciliation in the appraisal ofore reserves and it gives an estimation of the amount of wastepassing through the mill.

Definition number 3: Once the ore is diluted, the run-of-mineore that enters the mill is characterised by a grade lower than thatof the mining reserves. The dilution, calculated according to thisdefinition, enables us to find the percentage of drop in gradebetween the diluted ore and the non-diluted ore. Consequently,the relation between the diluted and non-diluted grades on onehand and the additional percentage of dilution on the other hand,for example, would be:

where:RV: Reduction in the Value of treated ore ($);PM: Price of Metal;MRF: Metal Recuperation Factor.

And finally we obtain the additional percentage of dilution:Wa tm - t,ADJ.=-x loo=--x lOO (9)T, tm - taw

This last equation is very useful in calculating the amount ofwaste contained in the run-of-mine ore sent to the mill. We obtainthe following from equation 9:

Parameters Tt and tt can be measured at the mill feed, andparameters tm and taw are evaluated by the geologists in thecalculations of the mining reserves. When introducing the datafrom the numerical example, we can find the amount of waste:

AD3t, = tm x (I - 100)

This way of calculating the percentage of dilution allows anestimation of the reduction in the grade of the treated ore from themining reserves grade:

Methodology for the calculation of dilutionDilution was defined in the introduction as being an addition ofwaste to the mined ore. Dilution is thus the action of increasingthe mined tonnage and reducing its grade. Figure 6 shows thegeneral process of dilution and gives a definition of a 'dilutionfactor' .(4)Tt=Tm+Wa

90 Kalgoorlie, 13 - 14 November 1995 Underground Operators' Conference

ORE DILUTION SOURCES IN UNDERGROUND MINES

FIG 6 - Process of dilution; definition of a dilution factor.

PDF Pl-.cl DlIulIon FK1Or,ADF -A_ DlIulIon flor;FDFF ..... DI__

FIG 7 - Ore dilution process at a mining site; definitions ofdilution factors.

(I6a)

(16)

(I Sa)

(15)

Tt=TgxFDF

and the total waste tonnage

W1=Tg{FDF-I)

T1=TmxADF

and the additional waste tonnage

Wa=Tm(ADF-I)

International competition, lower metal prices and high labourcosts forced several mining companies into employing highoutput (bulk) stoping methods. However, the success of thesemethods are not always assured because of the additional oredilution (often higher than the planned dilution. It is obvious thatthe key to increased competivenes and even to the survival ofseveral underground mines depends, in the most part, on anincrease in stoping method selectivity and on a reduction ofoperating costs pertaining to the dilution of ore.

This is why several large mining companies (Noranda, INCO,etc) and numerous authors are striving to adopt the differentsolutions involving a reduction in dilution. However, as studiesmade by mining companies have shown, and as indicated intechnical literature, several definitions of dilution are currentlyused.

This situation makes any comparative study on the impact ofdilution in separate mining conditions very difficult.

The methodology presented in this paper enables thereplacement of the ten different definitions of dilution currently in

Quantitative relations between dilution factors and thepercentages of dilutionIn our opinion, using only three factors (pDF, ADF and FOF)instead of the ten analytical equations of the percentage ofdilution makes any analysis of dilution easier. However, to give achoice of definitions to the user, depending on the availablemining condition parameters, this methodology presents theanalytical relations between proposed dilution factors and thepercentages of dilution currently in use (Table 7). Therefore, aresult obtained by which ever way of calculation in use canalways be expressed as one of the three dilution factors, namelyPDF, ADF or FOF.

Taking the values obtained in numerical example number 1(Table 5) and placing them in the equations of Table 7, we realisethat, no matter which definition of the percentage of dilution isused, the dilution factors always give the same values (Table 8)for a given source of dilution.

CONCLUSIONS

3. The last factor, called the Final Dilution Factor (FOF), is theproduct of the two previous factors (pDF x ADF).If it is known, we can calculate, based on the geologicalreserves (Tg) : run-of-mine ore tonnage

2. The Additional Dilution Factor (ADF) is very important atthe dilution impact evaluation level during the stoping,allowing us to evaluate the ratio between the run-of-mineore and the mining reserves (TIffm) and thus theefficiency of control measures on the dilution inherent tothe stoping method.

If this factor is known, we can calculate, based on themining reserves (Tm) : run-of-mine ore tonnage

(l4a)

(14)

~._ ..

...........

...~-

---r---{:]!~~~::} - - -~r I II II I

III5:

I ~I

~==:;f=~~~~:r--, ~:l I:IIIIIII

'-_.-l_--;:::~~~:r -,- --,

Tm=Tgx PDF planned waste tonnage

Wp=Tg(PDF-I)

TABLE 6Ore dilution factors.

In fact, each different numng condition can be evaluatedsimply by the following factors:I. The Planned Dilution Factor (pDF), useful at the mine

planning stage (stope design), allows us to consider theratio of mining reserves over geological reserves (Tnlfg),and thus the stoping method selectivity.

If this factor is known, we can calculate, based on thegeological reserves (Tg) mining reserve tonnage

This dilution factor is defined as a ratio of the diluted oretonnage over the non-diluted ore tonnage.

Therefore each dilution source on a mining site shall bedefined with its own dilution factor (Figure 7).

Table 6 presents these three dilution factors.

Dilution Factor (OF)Planned Additional Final

PDF MininR reserves ADF Run-of-mineore FDF Run--if-mineoreGeological reserves Mining reserves GeologiCLl1 reserves

PDF= Tm ADF=.!i FDF= Tt =PDFxADFT, Tm T,

Underground Operators' Conference Kalgoorlie, 13 - 14 November 1995 91

S PLANETA and J SZYMANSKI

TABLE 7Relations between dilution factors and percentages ofdilution.

Number I

Number 2

Number 3

DefinitionPlanned

PDF=_I-1_ PI>z

100

Dilution factorAdditional

ADlADF= I +100

ADF=_I-1- AI>z

100

AD:!--xtm

ADF= I __1007="__+ AD3

tm(l -1"00) - taw

Final

FDF== PDFx ADF

TABLE 8Relations between the dilution factors and the percentages ofdilution (values from numerical example).

Number I

Number 2

Number 3

DefmitionPlanned

PDF= I + 100=2100

PDF=_I_=21-1Q.

100

~xlOPDF=I+ 100 2

IO(l-..iQ..)-2100

Dilution factorAdditional

ADF~ I + 24.23 = I 2423100 .

ADF I 1.24231- 19.51

100

16.25 x6ADF= I + 100 1.2423

6(1 _ 16.25) _ I100

Final

FDF== 2 x 1.2423 = 2.4846

Methodology PDF=2 ADF= 1.2423

use, by only two dilution factors, each giving a precise value fora given dilution source: Planned Dilution Factor (PDF), estimated at the mine

planning stage (stope design). It allows the evaluation of theratio between the mining reserves and the geological reserves,and thus the stoping method selectivity.

Additional Dilution Factor (ADF>, very important duringthe operation of the stope (dilution control), allows theevaluation of the ratio between the run-of-the-mine and themining reserves, and thus the control measures efficiency onthe dilution inherent to the stoping method.

Such a methodology should be all the more useful since thedilution problem is considered to be more and more importantdue to its excessive costs and its negative impact on theenvironment. The possible use of this methodology wouldfacilitate a classification of the different mining conditions and ofthe stoping methods used, regarding the stoping methodselectivity and the efficiency of the dilution control mesures.

REFERENCESAlmgren, G, 1981. Rock mechanics and the economics of cut-and-fill

mining, in Application of Rock Mechanics to Cut-and-FiII Mining(Eds: 0 Stephansson and M J Jones) pp 28-34 (Institution of Miningand Metallurgy: London).

Asheroft, J W, 1991. Dilution a total quality improvement opportunity, inProceedings 93rd Annual General Meeting of ClM, Vancouver,28 April 28 - 2 May, pp 47.

Badwen, J W, Nantel, J and Sprot!, D, 1984. Practical rock engineering inthe optimization of stope dimensions - application and costeffectiveness, ClM Bulletin, June:63-64.

David, M and Toht, E, 1984. Grade control problems dilution andgeostatistics : choosing the required quality and number of samplesfor grade control, ClM Bulletin, November:53-58.

Gunzert, G, 1983. Erzverdiinnung - Nutzen oder Ubel? E17J1U!tall36(1):14-22.

Ingler, D, 1975. Rock dilution in underground stopes, World Mining,28(9):54-55.

Mathews, K E, 1990. Planning to reduce dilution. Points to the future.(unpublished) pp 1-6.

Mining Sourcebook, 1994. (Southam Mining Group).PakaInis, R, Miller, H D S and MadiIl, T, 1985. Development of a

geo-numerical model as an aid in stope design, in Proceedings 26thUS Symposium on Rock Mechanics, Rapid City, June, pp 1173-1180.

Planeta, S, 1993. Aspect geotechnique de la dilution du minerai dans lesmines metaIIiferes souterraines au Canada, in 4" ColloqueFranco-Polonais Geotechnique et environnement (Edite par J PPiguet et F Homand) Nancy, France, 16-17 novembre, pp 3-11.

Quesnel, W J F, Ley and G M M, 1991. The development of mine designguidelines for dilution control, Bousquet Division no I Shaft LacMinerals Ud, in Proceedings 93rd Annual General Meeting of ClM,Vancouver, 28 April - 2 May.

White, L, 1984. Boliden Cut-and-fill: not just a means of mining weakground, E & M J, I85(August):30-36.

92 Kalgoorlie, 13 - 14 November 1995 Underground Operators' Conference

Management and Human Resources

0102030405060708091011121314151617181920212223242526272829303132333435363738394041424344454647484950