Posted by : Jounaldo Safputra Wednesday, October 19, 2011

Approximately 5 1% of all ore production by underground metal mines in Canada is derived directly from open stoping operations. This method requires that large excavations remain open until the ore is extracted under a minimal acceptable dilution. A survey of underground mines in 1988 reported that a major factor for mine closures has been due to uncontrolled dilution. It has been reported that 40% of open slope operations were experiencing dilution in excess of 20%. This value has large implications on economic viability of a project considering a rate of return on a positive project is generally between 10% to 20%. This paper reports on the various existing interpretations on the definition of dilution, the methods of slope design presently used with the objective of reducing dilution and finally on a recent survey technique that has become available that enables dilution to be quantified. The observations in this paper are based on work conducted at the University of British Columbia and CANNET over the past ten (10) years and on present studies in the qantification of empirical design techniques. 

The importance of dilution in the economics of a mining operation is well recognized and is reflected in the fact that dilution records are kept by most operations, mining Sourcebook (1995). As noted by Tintor (1988), excessive dilution is a major factor of reported mine closures for Canadian underground mines.
Ore losses and dilution are present at all stages of mining and while several models can investigate the influence of dilution it is its quantification that poses the most serious challenge. Furthermore it is now recognized that what is considered acceptable dilution is a function of ore grade, grade of dilution material costs and that of metal prices. Consequently the degree of acceptable dilution differ from site to site.
Elbrond (1994) has proposed a conceptual diagram in which the presence of ore losses and dilution during successive phases of mining is traced. Although this is a simplified approach it still serves to recognize the complexity of the problem, beginning with the need to define precisely the material quantity and quality throughout all stages of the mining process. This includes delineating the deposit, defining the cutoff grade, selecting the optimum mining method/plan/production parameters and the subsequent processing of the ore. This paper addresses the problems associated with developing and calibrating dilution models, and the associated economic impact. 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 for the deposit. In order to measure dilution, one must assume that the ore is delineated in quantity and quality, and 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 a information concerns the deposit accumulates.
There is an even greater uncertainty concerning the grade of the waste material (below cutoff). Understandably, limited efforts are devoted to the evaluation of the grade of the waste. However, dilution is more than often inferred than physically measured. Because the exact grade of all the components of the waste/ore mix are not well known, the dilution estimate can carry a sizeable error.
Measuring the volume of wall slough (external dilution), the difference between design tonnage and actual achieved, is a better measure of mining success even if it does not resolve all the problems. Uncertainty remains in terms of cost since the metal content of the external dilution is not well known. This external dilution is a source of cost as it is mucked, transported, crushed, ground, processed and stored as tailings. Since it is sub-grade material it is not a source of revenue sufficient to cover all costs encountered. The rock if void of economic value as is the case generally with vein mining will further exacerbate the situation. This would be a direct cost attributed t
Lane (1988) shows that mining operations have limiting factors that influence the overall economics, two of them being mining capacity and milling capacity. 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/mill circuit. This displacement results in a cost expressed by the cash flow 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 inflow. The example given by Bawden et al. (1989) shows a mine operating at 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 the mining of the dilution are lumped with the opportunity cost. Another scenario would see cutoff grade increase in reaction to dilution to maintain millhead feed grade. Quantity o 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 determined in an identical fashion. While it is accepted that the resulting dilutions influenced by the mine design on the surrounding rock mass, in fact there exists several methods of defining and recording dilution. Table 1 summarizes the definitions in use as derived from a survey of twenty-two (22) mine operators throughout Canada (Pakalnis, 1986). The term "waste" in Table I and Figure 1 refers to the external dilution or unplanned dilution that is mined whereas the "ore" refers to that which is expected to be mined ie. drilled and blasted. 

Table 1. Definition of Dilutions (Pakalnis, 1986)

EQ 1 Dilution =(Tonnes waste mined)/(Tonnes ore mined)
EQ 2 Dilution =(Tonnes waste mined)/(Tonnes ore mined + Tonnes waste mined)
EQ 3 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 for same tonnage)
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
EQ 8 Dilution =("x" amount of metres of footwall slough + "y" amount of hanging wall slough)/(ore width)
EQ 9 Dilution =(Tonnes drawn from stopes )/(Calculated reserve tonnage) over last ten years 

(Dilution is generally expressed as a percent) 
A review of Canadian mining practice (Scoble et al. 1994) has shown that the two most widely used definitions are EQ I and EQ 2 in Table 1. Figure I shows the sensitivity of the above two definitions to the amount of wall slough as calculated as being a function of the ore width. An orebody whose width is "n" meters from footwall to hanging wall and has "n" meters of slough (depth of slough equal to orebody width) would result in a dilution of 100% employing EQ I and 50% by EQ 2. In fact the maximum dilution that one can realize by EQ 2 is 100% since it e to wall slough. The relative difference is less at lower dilutions. It is for this reason that E I has been 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), 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 systerm. Such systems should promote economical yet safe designs and must correctly be calibrated against case studies that are representative of the future applications.
The level of dilution budgeted for a particular method of extraction is critical to the over economics of a project considering values between 10-30% dilution are employed generally and rate of return for project economics between 10-20%. The values for dilution 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 which relate the factors critical towards stope design to the estimated dilution. These are largely based upon relating critic parameters to observed stope behaviour.
Non-entry 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 be economical however, a lower grade stope with the same dilution will no longer be feasible. Non-entry method of mining such as open stoping can accept a certain degree of wall slough without endangering mine personnel.
Of the empirical methods of open stope design, 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 whereas the DilutionApproach relies upon information collected from one operation.

Stability Graph Method
This is an empirical method for open slope design proposed by Mathews et al. (1981). It was only after Potvin (1988) modified the method based on more field data that the method was wide accepted in the industry. In its present form the Stability Graph links a stability number, N, to the hydraulic radius of the studied stope surface, Figure 2.
N= Q x A x B x C
N = Stability Number
Q = Modified Tunneling Quality Index (NGI) with stress reduction factor set to one after Barton, 1974)
A =Stress Factor
B = Joint Orientation Factor
C = Gravity Factor
HR = Hydraulic Radius = Surface Area/Perimeter
The method has been the subject of recent work by Nickson (1992) 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 currently 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 re-evaluation of the stability graph guidelines. While the design guidelines have been refined the method is considers a valid design tool
The Stability Graph method however is subjective (ie. "stable" versus "cave" conditions) and despite the use of quantifiable values the precise degree of inherent conservatism is not know. Furthermore the method reflects "current and past practice", which may have been influenced b local practices, particular geological peculiarities and 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 subsequent.

Dilution Approach
The Dilution Approach for estimating open stope dimensions was a culmination of a five (5) years joint effort between the Ruttan Mine of Hudson Bay Mining & Smelting Inc., CANNET 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 slopes. The parameters most critical to design were established after an extensive statistical and observational approach showed that for particular stope that the resultant dilution was largely a function of:
  • the rock mass rating of the hanging wall (Bieniaws4 1976)
  • the hydraulic radius of the hanging wall
  • the rate that the hanging wall is exposed
  • the stope configuration (isolated, rib or echelon)
Figure 3 shows the derived relationships which were subsequently modified into design charts example of which is shown in Figure 4 for the "isolated stope". The design chart shows the resultant dilution employing an exposure rate equal to zero as defined in Figure 3. The "isolated stope" design chart is based upon sixty-one (6 1) observations of dilution as estimated visually and by assay.
Figure 5 shows the original "isolated" stope database superimposed upon the "Stability Graph" method. It is interesting to note that the "Stable Zone" on Figure 2 is generally associated dilution values ranging from 0-5% whereas the "Caved Zone" has values in excess of 15%. This, however, is largely based upon observational assay and muck tonnage and not a surveyed volume as will be discussed subsequently.  

Cavity Monitoring
Until recently one of the major problems was quantifying open stope dilution. Use of laser survey systems have provided a considerable tool in determining underground excavation volumes in a precise and efficient manner, Miller et al. (1992). The instrument generally employs a laser survey (rangefinder) integrated within a motorized scanning head. The rangefinder can be suspended in a stope or inserted down a borehole as small as 20cm. Through calibrated rotation of the laser rangefinder a three dimensional stope outline can be generated and subsequently a volume determined. In a typical section it is possible to compare planned stope contours to the actual after blasting. This enables the operator to estimate the amount of underbreak and overbreak.
Pakalnis et al. (1995) reports on the use of a laser survey at the Detour Lake Mine where it was necessary to develop design guidelines for sub-level retreat mining. This particular case study was of interest in that the mine was operating narrow open stopes with widths approaching 5m on average. Dilution is particularly critical for narrow stopes as shown in Figure 6 whereby 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') having a strike length in excess of 300m and a vertical height of 100m with widths ranging between 3m to over 10m. The mining method is sublevel retreat with the gold bearing ore comprised of competent mafics and weaker talc schist material. The study was over a two-year period with the main objective of developing a mining method that incorporates maximum stope dimensions with minimal dilution being incurred. The major sources of dilution were as shown in Figure7. A major contributor to dilution was the degree of undercut that resulted when developing the individual sub-levels for purposes of mining as shown in Figure 8. In all instances the undercut had failed along existing parallel structure. This would result in dilution levels in excess of 5% solely due to the existence of the undercuts. In addition, irregularities (dogleg) in the stope geometry resulted in wall slough as shown in Figure 9.

The above analysis is only made possible by the use of the cavity monitoring system. The laser system was also employed to verify the "Dilution Approach", Figure 3, which was found to close approximate the measured dilution to within 5% of actual. The above has enabled one to quantify the effects of increased stope dimensions on dilution and the associated benefits that may arise through increased support and the lower development requirements (ie. slots for blasting).
Once the mine operator quantifies the level of resulting dilution it is possible to introduce the necessary modifications to the n2ine plan such as stope dimensions, sequencing, ground support, rate of minimize and other parameters that are at his control. 

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 aiming to control the amount of dilution. The validity of these methods improves when field data are further calibrated. In this respect rock mass classification and laser cavity monitoring systems are valuable aids.
A reliable methodology to quantify ore dilution enables the operator to perform a cost/benefit assessment of implementing alternative designs. The alternate design may incorporate modifying span, support, mine sequence, rate of extraction, geometry among other options in order to arrive at a calculated overall economic value for a project.

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JO (Jounaldo Safputra),
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Have studied in ES No. 21 OKU, JHS No. 9 OKU, SHS No. 1 OKU, and Mining Engineering Dept University of Sriwijaya Palembang South Sumatera.

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