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Quantifying the cost of dilution in underground mines R.C. Pakalnis, R. Poulin and J. Hadjigeorgiou Abstract -Appro.rimately 51 % of all o1.p production irr Cunadian undergl-ound metul mines is derived dir-ec,tlyfi-om open-stope operations. Thismethod I-equiresthut lus,qe e.rcu13utionsremain nprn ur~rilthe ore i~extra(.ted with a mininnlm ac~ceprahlelevel of dilution. A survey of 14ndet.ground mines was in 1988 r.~pnr.redrhur a major- factor it1 their- c.1o~111.e uncot~trolledclilution.It hus h e m reported thut 40% ofopenstope operutions M ~ E I X Jexperienc.in,q dilrttiorz in r.rc.cj.ss of' 20%. This level ofdilution has signific.ant inlldic~~tions on the economic, \,iahility of'u project, espec~iully~,herlone cotlsidcJr-sthut u rate ( f r e t u r n on a po.siti~~c~ pr.c?j~c,tis generally between 10% utld 20%. This paper r.eporr.s otl the ~ ~ a r i o u s definitions od'dil~ition,on the nzerhods cdsropc tlesign rhat are 111-esently~csc~cl btith the ohjec,tit'e of t-cduc,irrgdilution u t ~ don a rr~c.entlyu~~ailahle sur-vey rethniyur rhat c~nuh1e.rdilrrtior~to he quanrifi~d. Introduction The importance of dilution to the economics of a mining operation is well recognized and is retlected by the fact that dilution records are kept by most operations (Mining Source Book, 1995).Asnoted by Tintor (1 988),excessivedilution is reported as a major factor in the closure of niany Canadian underground mines. Ore losses and dilution occur during all stages of mining. and, while several models can investigate the influcnce of dilution, it is the quantification of dilution that poses the greatest challenge. Furthermore, it is now recognized that what is considered an acceptable level of dilution is a function of the ore grade, the grade of thc dilution material, costs and metal prices. Consequently, the degree of acceptable dilution differs from site to site. Elbrond (1994) proposed a conceptual diagram in which the presence of ore losses and dilution during successive phases of niining are traced. Although this is ii simplified approach. it still serves to recognize the complexity of the problem. beginning with the need to define precisely the matcrial quantity and quality throughout all stages of the mining process. This includes delineating the deposit, defining the cutoff grade, selecting the optimum mining method/ R.C. Pakalnis and R. Poulin are professors with the Department of Mining and Minerals Processing Engineering, the University of British Columbia, Vancouver, Canada. J. Hadjigeorgiou is a professor with the Department of Mining and Metallurgy, Laval University, Quebec City, Canada. SME Preprint 95-260, SME Annual Meeting, March 6-9, 1995, Denver, CO. Manuscript Feb., 1995. Discussion of this peer-reviewed and approved paper is invited and must be submitted, in duplicate, prior to March 31, 1996. 1136 DECEMBER 1995

planlproduction parameters and selecting the method of processing the ore. This paper addresses the problems associated with developing and calibrating dilution models and the associated econoniic impacts of these problems. It further attempts to relate mine-design practice with predicted and recorded dilution. Dilution model Ore is generally defined through a geological model that synthesizes the known characteristics of the deposit. To nieasure dilution, one must assume that the ore is delineated in quantity and quality and that the rock volume can effectively be measured with a degree of confidence. While this model will never coincide completely with the actual deposit (Elbrond, 1994), it can be refined as information concerning the deposit accumulates. There is an even greater uncertainty concerning the grade of the waste material (i.e., material below the cutoff grade). Understandably, limited efforts are devoted to the evaluation of the grade of the waste. However. dilution is more often inferred than physically measured. Because the exact grade of all of the components of the wastelore mix is not well known, the dilution estiniate can carry a sizable error. In measuring the volume of wall slough (external dilution), the difference between the design tonnage and the tonnage actually achieved is a better measure of mining success, even if it does not resolve all of the problems. Because the metal content of the external dilution is not well known, uncertainty remains in terms of cost. This external dilution is a source of cost as it is mucked. transported. crushed, ground, processed and stored as tailings. Because it is subgrade material, it is not a source of revenue sufficient to cover all costs encountered. The rock, if void of economic value, as is generally the case with vein mining, will further exacerbate the situation. This would be a direct cost attributed to dilution. Lane (1988) showed that mining operations have l~miting factors, e.g., mining capacity and milling capacity, that influence the overall economics. These are instrumental in defining optimum operating practices. Mining of waste material through dilution results in an opportunity cost, where capacity is lost because of the displacement of ore by waste within the overall mine/rnill circuit. This displacement results in acost, expressed by the cash tlow, being distributed over a longer time period. resulting in an overall decrease in the net present value. The size of the cost is directly dependent upon the discount rate used; the higher the rate, the higher the cost of postponing the cash intlow. The examplc MINING ENGINEERING

Table 1 - Definition of dilution* (Pakalnis, 1986) Eq. (1): Dilution = (Tons waste mined)/(Tons ore mined) Eq. (2): Dilution = (Tons waste mined)/(Tons ore mined + tons waste mined) Dilution = (Undiluted in-situ grade as derived from drill holes)/(Sample assay grade at drawpoint) Eq. (4): Dilution = (Undiluted in-situ grade reserves)/(Mill head grades obtained from same tonnage)

I

WASTEIORE, WASTU(0RE + WASTE)

z

250%

Eq. (3):

Eq. (5):

Dilution = (Tonnage mucked - tonnage blasted)/ (Tonnage blasted)

Eq. (6): Dilution = Difference between backfill tonnage actually placed and theoretically required to fill void Eq. (7): Dilution = Dilution visually observed and assessed

1 I

0.5

DILUTION =

2

2.5

TONNES

WASTC

TONNCS ORE

1

given by Bawden et a]. (1989) shows a mine, operating at a constant capacity, that produces the same amount of metal but with an increasing life as dilution increases. Dilution in that example has zero grade and extra mining and milling costs associated with mining of the dilution are lumped with the opportunity cost. Another scenario would see cutoff grade increase in reaction to dilution to maintain mill-head feed grade. The quantity of total metal produced would be reduced, and the opportunity cost would then apply to the unmined portion of the deposit.

Defining dilution A dilution value is routinely recorded by most mine operators (Mining Source Book, 1995). However, it is not always determined in an identical fashion. While it is accepted that the resulting dilution is influenced by the mine design, there exists several methods of defining and recording dilution. Table 1 summarizes the definitions that are now used to calculate dilution. These definitions (Eqs. ( I ) through (9))were derived from a survey of 22 mine operators throughout Canada (Pakalnis, 1986).The term "waste" in Table 1 and Fig. 1 refers to the external dilution, or unplanned dilution, that is mined, whereas the term "ore" refers to that which is expected to be mined, i.e., drilled and blasted. A review of Canadian miningpractice (Scobleet al., 1994) has shown that the two most widely used definitions are Eq. (1 ) and Eq (2) in Table 1. Figure 1 shows the sensitivity of the above two definitions to the amount of wall slough, calculated as afunction of the ore width. An ore body whose width is "n" meters (from footwall to hanging wall) and has "n" meters of slough (i.e, the depth of slough is equal to the width of the ore body) would result in adilution of 100% according to Eq (I ) and 50% according to Eq. (2). In fact, the maximum dilution that one can realize by Eq. (2) is loo%, because it is insensitive to wall slough. The relative difference is less at lower dilution. It is for this reason that Eq. (1) was selected and recommended as a standard measure of dilution.

Mine design Modem mine design employs analytical, numerical and empirical methods. In a comprehensive survey of ground control practices in Ontario mines (Barclay and Kat, 1989). MINING ENGINEERING

1.5

Fig. 1 (a) - Dilution vs. depth of slough.

Eq. (9): Dilution = (Tons drawn from stopes)/(Calculated reserve tonnage) over the last ten years * Dilution is generally expressed as a percentage.

1

DEPTH OF SLOUGH (TlMES ORE WIDTH F M I TO HNV)

Eq. (8): Dilution = ("xuamount of meters of footwall slough + "y"amount of hanging wall slough)/(ore width)

1

0

/

ORE/RFSERVFS PUNNED DRILLED AND B U S I E D

WASTE/ NOT PLANNE NOT ORILL.ED/B

BLOCK O r ORE

WIDTH OF ORE HANGING WALL(H/W)

Fig. 1 (b) - Schematic definition of dilution.

it was shown that empirical methods are the most popular design tools. Empirical tools are based on local experience or on some geomechanical-based classification system. Such systems should promote economical, yet safe, designs and must correctly be calibrated against case studies that are representative of their future applications. The level of dilution budgeted for a particular method of extraction is critical to the overall economics of a project, considering that dilution values of between 10% and 30% are generally employed and that the rate of return for project economics are between 10% and 20%. Thevalues for dilution that are employed are largely based upon the type of method, stope width and/or experience of the person conducting the feasibility study (O'Hara, 1980). Methods have been available that relate the critical factors of stope design to the estimated dilution. These methods are largely based on relating the critical parameters to the observed stope behavior. Nonentry mining methods, such as open stoping, are gaining increased prominence in Canadian mines. Acceptable dilution is highly dependent upon grade. A higher-grade stope can still be economical. However, a lower-grade stope with the same dilution will no longer be feasible. Nonentry methods of mining can accept a certain degree of wall slough without endangering mine personnel. Of the empirical methods of open-stope design, the following two have received increased prominence in the last 15 years: the "dilution approach" and the "modified stability graph" method. While both methods rely heavily on a rock mass classification, they differ in that the stability graph relies on data collected from several mine operations, and the DECEMBER 1995

1137

M O D I F I E D STABILII'Y GRAPE1

DILUTION APPROACH DESIGN EQUATIONS

ISOlATED STOPES(61 OBS)

ECHELON STOPES(44 OBS)

RIB STOPES(Z8 OBS)

OIL.(%) - Slope 01lulion(%1,le. 10%. DIL(%) - I 0 R M R - CSlR flock Mass RalinalX1, te. 60%. R M R - 60

DATABASE

.

Slope Oilu~an - 10% 6% hydraulic Radius = 1 lrn 3m S I O ~Width = 15m 2 8m S l o p RMR = 56% 20% ER 180m~irn1h 9om' m Excaval,oo Rate 2700m',A:n Soan(Sl,che lsnglh) 3 i m * He,gnl - 68m 1 2Or.l Stone Depln - J608rr 1 4dm Delo* Slope I n ~ l ~ l a l i a=n 68' 9'

-

5

10

1:>

-

20

-

Jo#m#np Psrrliel 10 Hangng w * , hang l g Wall n Relaxallon

HYDRAULIC RADIUS ( m ) Fig. 2 - Modified stability graph (after Potv~n,1988).

-

-

Fig. 3(a) - Dilution-approach design equations (after Pakalnis, 1993).

ISOLATED STOPEf61 obsl STOPE C A T E G O R Y - P L A N

la,

5

10

15

HYDRAULIC RADIUS(m)

Fig. 3(b)- Dilution-approach design chart for isolated-stope configuration dilution approach relies upon information collected initially from one operation.

Stability graph method This is an empirical method for open-stope design proposed by Mathews et al. (1981). I t was only after Potvin (1988) modified the method, based on more field data. that the method was widely accepted in the industry. In its present form, the stability graph (Fig. 2) links a stability number (N') to the hydraulic radius (HR) of the studied stope surface. The stability number is calculated according to the following equation

N'=QxAxBxC where

1130

DECEMBER

1995

N' = stability number, Q = modified tunneling-quality index (NGI) w ~ t ha stress reduction factor ret to one (after Barton, 1974). A = stress factor. B = joint-orientation factor, and C = gravity factor The hydraulic radius (HR) equals the surface areadivided by the perimeter. The method has been the subject of recent work by Nickson ( 1 992) and Hadjigeorgiou and Leclair ( 1994). During the last three years. an extensive data-collection field program was undertaken. In the updated stability graph geomechanical database. there are now 228 documented case studies of unsupported open stopes and 163 stopes where cable bolts were installed. The updated database has permitted a qualitative and quantitative reevaluation of the stability MINING ENGINEERING

MODlFlFD STABILITY GRAPH

Underbreak (unrecoveredore)

Overbreak (dilution)

16 15 14 13 12 11 10 9 8 7 6

Read Contour',

161514131211109 8 7 6

5

4

3 2

1

@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ J

-

Blast Holes Layout -- - -

--

--- -

Fig. 5 - Vertical section of open stope at Louvicourt mine showing planned and actual stope profile - laser survey.

-

10

0

15

HYDRAULIC RADIUS

20

25

(m)

Fig. 4 - Recorded dilution at Ruttan plotted on modified stability graph.

graph guidelines. While the design guidelines have been refined, the method is considered a valid design tool. The stability graph method, however, is subjective (i.e., "stable" vs. "cave" conditions), and, despite the use of quantifiable values, the precise degree of inherent conservatism is not known. Furthermore, the method reflects "current" and "past"practice, which may have been influenced by factors such as legislation, local practices and particular geological peculiarities and, therefore, does not necessarily constitute an optimum-design methodology. Research is being conducted by the authors in quantifying the observed stability in terms of dilution values, as assessed by survey methods and discussed subsequently.

Dilution approach The dilution approach for estimating open-stope dimensions was aculmination of a five-yearjoint effort between the Ruttan mine of the Hudson Bay Mining & Smelting Inc., CANMET and the Department of Mines of Manitoba (Pakalnis, 1993). The overall objective of the project was to develop ground stability guidelines for the mining of large stopes. The parameters most critical to the open-stope design were established after an extensive statistical and observational approach showed that, for a particular stope, the resultant dilution was largely a function of the following: the rock-mass rating of the hanging wall (Bieniawski, 1976), the hydraulic radius of the hanging wall, the rate that the hanging wall is exposed, and the stope configuration (isolated, rib or echelon). Figure 3(a) shows the derived relationships that were subsequently modified into design charts. An example of the "isolated-stope" configuration is shown in Fig. 3(b). The design chart shows the resultant dilution employing an exposure rate equal to zero, as defined in Fig. 3(a). The "isolatedMINING ENGINEERING

stope" design chart is based upon 6 1 observations of dilution, as estimated visually and by assay. Figure 4 shows the original "isolated-stope" database superimposed upon the "stability graph" method. It is interesting to note that the "stable zone" on Fig. 2 is generally associated with dilution values ranging from 0% to 5%, whereas the "caved zone" has values in excess of 15%. This, however, is largely based upon observational, assay and muck tonnage and not on a surveyed volume, as will be discussed subsequently.

Cavity monitoring Until recently, one of the major problems was quantifying open-stope dilution. The use of laser survey systems has provided a considerable tool in determining undergroundexcavation volumes in a precise and efficient manner (Miller et al., 1992). The instrument generally employs a lasersurvey range finder integrated within a motorized scanning head. The range finder can be suspended in a stope or inserted down a borehole as small as 200 mm (7.8 in.). Through calibrated rotation of the laser range finder, a three-dimensional stope outline can be generated and, subsequently, a volume can be determined. This technology is becoming more routinely employed throughout Canadian mining operations. Germain et al. (1995) reported on such a cavity monitoring system in operation at the Louvicourt mine, Quebec, Canada. In that system, a laser survey is conducted after excavating each stope. In a typical section, it is possible to compare planned stope contours to the actual profile after blasting. This enables the operator to estimate the amount of underbreak and overbreak (Fig. 5). Pakalnis et al. (1995) reported on the use of a laser survey at the Detour Lake mine, where it was necessary to develop design guidelines for sublevel retreat mining. This particular case study was of interest in that the mine was operating narrow open stopes with average widths approaching 5 m (16 ft.). As shown in Fig. 6, dilution is particularly critical for narrow stopes; the narrower the stope, the higher the dilution for the same amount of wall slough. The open stope at Detour Lake is generally steeply dipping (70") with a strike length in excess of 300 m (985 ft.) and a vertical height of I00 m (328 ft.). Widths range between 3 m (9.8 ft.) to over 10 m (33 ft.). The mining method used is sublevel retreat with the goldbearing ore comprised of competent mafic and weaker talcschist material. The study was conducted over a two-year period. The main objective was the development of a mining method that incorporated maximum stope dimensions with DECEMBER 1995 1139

r-1

I

Dilution I

Induced & Inherent

I 7 ----]I -

1

Geolog~cStructure

Tme

+

Overhangs

lncreaslng Hydraulic Radlus

-

Stress

Blast Darnageloverbreak

1

Slope Geometry

t

idqlegr dip, r h I

Drill Deviation

Human Error lor lling ruweylng etc i

Fig. 7 - Sources of dilution at Detour Lake mine (Pakalnis, et al., 1995).

Fig. 6 - Dilution as a function of stope width

BLAST HOLES SURVEY CON7

$g

EL. 5 6 7 5 . h

undernut

UNDERCl

UNDERCUT J.

r

: .

.

':

,:::

Scale

)

,\

EL.,5C25.0m

no

VERTICAL SECTION Fig. 8 - Stope-laser survey showing dilution due to undercutting of the hanging wall. Dilution recorded as tons per meter of stope length.

minimal dilution. The major sources of dilution were as shown in Fig. 7. A major contributor to dilution was the degree of undercut that resulted when developing the individual sublevels for purposes of mining, as shown in Fig. 8. In all instances, the undercut had failed along an existing parallel structure. This would result in dilution levels in excess of 5%, solely due to the existence of the undercuts. In addition, irregularities (doglegs) in the stope geometry resulted in wall slough, as shown in Fig 9. The above analysis is only made possible by using the cavity monitoring system. The laser system was also employed to verify the "dilution approach" (Fig. 3), which was found to closely approximate the measured motion to within 5% of actual. The above enables one to quantify the effects of increased stope dimensions on dilution and determine the associated benefits that may arise through increased support and lower development 1140 DECEMBER 1995

--

DRAWPOINTS PLUGGED DUE TO FALL OF

GROUNO

SCALE

Fig. 9 - Adverse geometry resulting in wall slough.

requirements (i.e., slots for blasting). Once the mine operator quantifies the level of resulting dilution, it is possible to introduce the necessary modifications to the mine plan, such as stope dimensions, sequencing, ground support, rate of mining and other parameters that are at his control.

Conclusions While dilution is a major concern in underground mines, it has been difficult to quantify. Consequently, attempts to assign a cost value have been severely hindered. This paper discusses empirical techniques that have been applied to mine design with the aim of controlling the amount of dilution. The validity of these methods improves when field data are further calibrated. In this respect, rock-mass classifiMINING ENGINEERING

cation and laser cavity monitoringsystems are valuable aids. A reliable methodology to quantify ore dilution enables the operator to perform a costbenefit assessment of implementing alternative designs. The alternate design may incorporate the modification of span, support, mine sequence, rate of extraction, geometry, etc., to arrive at a calculated overall economic value for a project.

+

Acknowledgments The authors would like to thank the operations that participated in this study and, in particular, would like to thank the Detour Lake mine of Placer Dome Canada Ltd., CANMETDepartment of Natural Resources, Canada, and the National Science and EngineeringCouncil of Canada. Particular thanks i s extended to Dr. S. Vongpaisal of CANMET.

References Barclay. R , and Kat, M.. 1989, "The state of ground control in Ontario mlnes." Ontario Ministry of Labour, Minlng, Health and Safety Report. Sept.. 79 pp. Barton. N., Llen. R.. and Lunde, J.. 1974, "Engineer~ngclassification of rock massesforthe design of tunnel support,'' Rock Mechanics. May, pp. 189-236. Bawden. J.W., Nantel. J , and Spron, D., 1989. "Practical rock engineering in the opt~m~zalion of stope dimenslons. applicat~onand cost effectiveness," CIM Bulletin, Vol. 82, No. 926, pp 63-71 Bieniawskl, Z.T., 1976. "Rock mass classifications in rock engineering." Proceed~ngsofthe Syrnpos~urnon Exploration for Rock Engmeering. A.A Balkema. Johannesburg. South

MINING ENGINEERING

Atrlca, pp. 97-106. Elbrond. J., 1994, "Economic effects of ore losses and rock dilution." CIMBulletin, Vol. 87, NO. 978. pp 131-134. Germain P.. Hadjigeorgiou J., and Leuard J.F.. 1995, "Rock mass characterization studies a1 Louvicourt mine." ISRM Congress, Tokyo. Japan. Hadjigeorgiou. J., and Leclair, 1994. Stability Method, Internal Reports. University of Laval. Lane. K.F.. 1988, The Econom~cDefinition of Ore, Mlnlng Journal Books Ltd.. London, England. 149 pp. Mathews, K.E., e l al.. 1981, "Prediction of stable excavation spans for mining at depths below 1000 meters in hard rock," Canada, CANMET-Department of Energy, Mines and Resources. DSS Serial No. OSQ80-00081, DSS File No. 17SQ.23440-0-9020.

Miller. F.. Potvin, Y., and Jacob, D ,1992, "Laser measurement of open stope d~lution."CIM Bulletin. Vol 85. July-August, pp. 96-102. Mining Source Book, 1995. Southam Publications Inc Nickson, S.. 1992. Cable Support Guidelines for Underground Hard Rock Mine Operations." M.S. thesis. University of British Columbia, pp. 223. O'Hara, T.A., 1980, "Quick guide to the evaluation of orebodies," CIM Bulletin, pp. 87-99. Pakalnis. R.. and Vongpaisal. S.. 1993, "Mlne design an empirical approach.'' Innovatfve Mine Deslgn for the 21sr Century, Bawden and Archlbald, eds., Balkema, Rotterdam, Netherlands. pp. 455 - 467. Pakalnis. R., Dunne, K., and Cook. K.. 1995, "Design guidelinesfor sub-level retreat mining method," Canada Centre for Mineral and Energy Technology, Energy. Mines, and Resources. Canada. DSS File No. 15 SQ.23440-2-9142. Pakalnis, R.. 1986, Empirical Stope Design at Runan M~ne,Ph.D. thesls. University of British Columbia, 276 pp. Potvin. Y., 1988, Emplrlcal Open Stope Design in Canada." Ph D thesis, Univers~tyof British Columbia. Scoble M.J., and Moss. A., 1994, "Dilution underground bulk mining: implications for production management, mineral resource evaluation 11. methods and case histories," Geological Soc~etySpecial Publication No 79, pp. 95-108. Tintor. N.. 1988, "Why some mines fail to work." The Northern Miner Journal, October

DECEMBER 1995 1141