Evaluation and Selection of Recoverable Reserves in a Sublevel Stoping Mine

RASPA, G., RINALDI, M. and MASSACCI, P. Evaluation and selection of recoverable reserves in a sublevel stoping mine. APCOM 87. Proceedings of the Twentieth International Symposium on the Application of Computers and Mathematics in the Mineral Industries. Volume 3: Geostatistics. J ohannes burg, SAIMM, 1987.

pp. 199 - 206.

Evaluation and Selection of Recoverable Reserves in a Sublevel Stoping Mine

O. RASPA, M. RINALDI and P. MASSACCI

Department ICMMPM, University of Rome 'La Sapienza', Rome, Italy

The paper describes a computer procedure for evaluating and selecting recoverable reserves in a mine worked by sublevel stoping. The boundaries of the volume to be mined are optimally defined by means of the 3-dimensional Lerchs-Grossmann algorithm, separately applied to both sides of the panels. The procedure, which has been developed for Masua Mine (Sardinia), also provides for smoothing the optimized boundaries, positioning the drilling drifts, interactive design of drilling fans and calculation of tonnage and grade of each volley. These tonnages and grades form the input of another pro-

cedure evolved for production planning.

Introduction In the case of an exploration where free selection of the mining unit is possible (open pit), the problem of evaluating recoverable reserves is resolved directly by means of nonlinear geostatistics. When, instead, selection of mining units is subject to geometrical constraints (as in underground mines), there is no direct means of calculation: here the quantity and quality of the recoverable reserves depend on the mining method adopted. The main factors that generally influence recovery are size of the mining or selection unit, the precision with which these units are estimated, the geometric constraints having a bearing on selection, ore left in slabs and pillars, dilution, etc. In this case, too, geostatistics provide basic support in the form of conditional simulation of the orebody. With such an orebody model it is theoretically possible during the feasibility study to superimpose any kind of mining method desired and to calculate the overall tonnages and grades that can be recovered.

Some work has been done in this regard in recent years. 1

-2 In addition to making a small contribution to

one aspect of this problem under particular conditions, the aim of this paper is also to sustain interest in this important problem which still calls for a considerable amount of research work to clarify various aspects.

The problem The problem of evaluating and selecting recoverable reserves generally arises both when studying the feasibility of mining an orebody and during the actual operational stage. However, the problem is not exactly the same where open pit and underground mining operations are concerned. In the former case recoverable reserves are evaluated

by the estimation of the distribution within a panel of the frequencies of grades of small blocks representing the mining units. Disjunctive kriging, indicator co-kriging, multigaussian kriging and other techniques are normally used for estimating. The final pit is established on the basis of the results of the estimate, a parametric selection being made based on the geometric constraints. When extraction actually gets under way the mining unit is selected on the basis of the grades estimated by ordinary kriging which utilizes blasthole data.

In the case of underground mining, even if mineralization is more concentrated and orebody volumes are smaller and better defined than in the case of the open pit, it is not possible at the feasibility stage of the project to define exactly the boundaries of the volumes to be broken. Extremely detailed sampling, not normally available at the feasibility study stage, would be needed to achieve such a goal. Yet at this stage, when a decision has to be taken as to whether or not to work the orebody, an estimate must be made of recoverable grades and tonnages in order to carry out the economic analysis. Other things being equal, these grades and tonnages depend on the mining method chosen.

When the grade is highly variable in the orebody, recoveries normally decrease on passing from a selective method of mining (such as cut-and-fill, for instance) to a non-selective method (such as sublevel stoping). For the same tonnage, grades are lower, while for the same grades tonnages decrease.

However, a procedure can be envisaged for use in the design stage to calculate the reserves recoverable from an underground mine. Such a procedure will involve the

EVALUATION AND SELECTION OF RECOVERABLE RESERVES 199

following three steps:

(a) subdivision of orebody into small blocks (amounting to a few hundred cubic metres), having the same size of those that will be estimated, using detailed sampling, during the actual mining stage;

(b) conditional simulation of the grades of the blocks, performed by geostatistical techniques;

(c) application of the orebody model to possible alternative mining methods using the computer either automatically or interactively, in order to evaluate tonnage and grade of the ore recovered.

The grade simulation model does not coincide locally with the actual situation, of course, but it faithfully reproduces the variability of grades in the orebody, which is the main factor affecting recovery. Since the quantity of recoverable reserves is an overall figure, it can certainly be argued that the results. provided by the simulation model are not too different from those that can be achieved on the actual ore body.

U sing this procedure a comparison can be made of the results obtained by means of alternative mining methods, thus permitting selection of the most cost-effective.

The volume to be broken locally during the actual mining operation is defined as more detailed sampling data become available prior to the actual advance. In this case the selection, which must take account of the geometric constraints, is performed on the estimated blocks, and the algorithms used are the same as those utilized to calculate recoverable reserves on the simulated orebody.

A methodology for selecting reserves in the case of sub level stoping is described below, followed by a concrete example of an application to establish the boundaries of the volumes to be broken during actual mining operations.

Selection of reserves for sublevel stoping Whether use is made of the set of simulated blocks for evaluating recoverable reserves or of the set of estimated blocks for establishing volumes to be broken, the problem of selection in underground mining consists in identifying the subset of blocks that maximizes a given benefit function and in taking into account the geometric constraints imposed by the particular mining method. Reserves must be parametered. This is done by considering the cut-off grade as the selection parameter, i.e. the minimum grade a block must have to be considered for mining. Blocks with average grade lower than the cutoff grade are left in place.

In underground mining it is necessary to use the cutoff grade as a selection parameter when the orebody does not have naturally defined limits, i. e. when it is not in the form of strata, thin veins, etc., but where the grades are distributed in an irregular manner and gradually tail out into barren ground. Selection is performed on the basis of the average grade of the blocks. When sub level stoping is the mining method adopted, as in the present case, all the broken ore is sent to the mill.

In this case, let G be the union of N blocks Bj of average grade gj, belonging to an orebody or to a part

200

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thereof (G = U BJ Having fixed a cut-off grade gc' i=!

whatever evaluation criterion is adopted, optimal selection is given by the set of blocks SkEG which ensures that L.; (gj - gJ = max.

JES,

The set of blocks Sk must be such that the geometric constraints of the sub level stoping are respected. If there are no constraints (free selection) the set Sk consists of the union of blocks Bj which ensures that gj ~ gc' It is unusual for the union of blocks selected without any geometric constraints to provide a volume that can be mined by sub level stoping. For the volume to be minable in this manner it must be connected together and its form must be such as to guarantee the stability of the stope created by the mining operation. There is also the fact that such variations as occur in the form of the surface defining the volume must be as smooth as possible so that the fans of blasthole drilled from the drifts cover the entire volume. Moreover, the form of the volume must be such as to avoid the need to open up new raises or crosscuts during the stoping operation, since this would lower productivity which, on the contrary, must be as high as possible, this being the main feature of the method.

The need to respect these constraints means that a given number of blocks whose average grade is less than the cut-off will be included in the broken material, while a number of blocks whose average grade is higher than the cut-off will be left in place. As already indicated, optimal selection is that which maximizes [gj - gJ and provides a volume of acceptable shape.

When mining is done in large panels bounded by a bottom and a top slab, as in the case studied, and the orebody is very thick, the problem of selection comes down to optimum definition of the boundaries of the volume to be broken in relation to the two sides. The problem can be tackled by utilizing one of the algorithms adopted normally for optimizing definition of the final pit.

In the procedure described the algorithm is applied to select the barren blocks to be left in place instead of selecting those to be broken. Figure 1 illustrates the significance of this concept. As the number of blocks to be dealt with is not generally high (the number concerned being that into which an underground mining panel can be subdivided), the 3-dimensional Lerchs-Grossmann optimization algorithm is certainly the most suitable, providing the mathematical optimum.3 'The mass' corresponding to block i will be - (gj - gJ and the optimization procedure, applied separately to the two sides, will select the barren block to be left in place. For these blocks the sum L.;(gc - g) will be the maximum, while for the remaining blocks the sum L.;(gj - gJ will be maximum. When applying the procedure to the first side, in order to ensure that the barren blocks on the opposite side do not affect the solution, it is convenient as a preliminary step to cancel from the data file all those blocks where gj - gc < 0 and where for all the blocks of the cone defined by each of them there is the condition: gj - gc < 0 (j E cone defined by i).

GEOSTATISTICS: CASE STUDIES

(a)

(b)

WJ\STE

(c)

FIGURE 1. Optimal establishment of sub level stoping boundaries. (a) cross-section of a panel with defined left and right boundaries, (b) and (c) left and right boundary definition using final pit optimization algorithm to select barren blocks.

An actual case: Masua Mine (Sardinia) Masua Mine works a massive Pb-Zn sulphide orebody in Cambrian carbonate rocks. The orebody has a N-S strike and dips to the east at about 70° . It is around 50 m thick and measures about 250 m in the vertical direction and some 200 m along the strike. The grade is high in the central part, but values tail out more or less uniformly to virtually nil towards the outer walls. The mine has' been exploited since 1978, and the panels measure almost 80 m x 100 m, being bounded at the top and bottom by slabs of ore 20 m thick.

Detailed sampling is performed before the individual panels are mined. Sampling is done by a fan of coreborings made from a heading on the hangingwall following the strike of the orebody (see Figure 2). The shapes of the volumes to be broken are established on the basis of the detailed sampling results which are also used to decide on the location ofthe drilling drifts, as well as for calculating the tonnage and grade of ore broken by each volley. The computer procedure developed for this purpose consists of a set of independent programs, some automatic, others interactive, running in succession. The

Lev. 80

Lev.60

Lev. 40

Lev. 20

FIGURE 2. Layout of detailed sampling for selection unit estimation.

input data are the grades and coordinates of the samples. The procedure involves the following steps:

estimation of grade of blocks and selective mining units, into which the panel has been subdivided; optimal selection of blocks in relation to a fixed cutoff grade and which respects the geometric mining constraints; three-dimensional smoothing of boundaries of selected blocks; positioning of drilling drifts; design of drilling fan patterns; calculation of tonnage and grade of oie broken per volley.

The results of the last step form the input for another procedure, the output of which is a production plan that ensures as regular as possible a feed to the mill.

Estimate of grade of block The input data for the program for this step are the grades and spatial locations of the samples, the dimensions of the blocks to be estimated, their topological matrix and the variogram parameters. The program makes the estimate by ordinary kriging of the grade of each of the blocks, calculating the relative variance of the estimate. In the case studied the blocks chosen for the estimate are parallelepipeds the edges of which run parallel to the NS (y axis), vertical (z axis) and E-W (x axis) direction. The dimensions of the blocks in these directions are respectively 10 m (which is the spacing of two consecutive exploratory sampling fans), 20 m (which is the height of a sub level) and 5 m.

Optimal selection of blocks The input of the selection program is the set of estimated blocks and the cut-off grade at which selection is made. The program first makes a free selection, calculating for the whole panel and for every cross-section the tonnages


and grades corresponding to the blocks selected. Subsequently the program makes the selection considering the cut-off grade, utilizing the Lerchs-Grossmann threedimensional algorithm. Selection is made first on one side, then on the other.

The geometric constraint is implemented by imposing the condition that for a block to be left in place it is necessary also to leave in place the blocks belonging to the cone defined by it. Having made the selection, the program calculates the average grade and tonnage of both the blocks selected and those blocks belonging to every cross-section. By means of a display program it is possible to view the results of the selection section by section. An example of the output of the display program is given in Figures 3 and 4, which refer to an E-W cross-section located at y= 35 m and to a cross-section at y= 15 m respectively.

For reasons of confidentiality grade figures have been altered by a multiplicative factor.

Figure 3 illustrates the results of free selection and of constrained selection applying a cut-off grade of 1,5070 Pb + Zn, while Figure 4 gives the results of selection obtained by applying a cut-off grade of 2,5% Pb + Zn.

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FIGURE 3. Free and constrained selections with cut-off grade of 1,50/0 Pb + Zn.

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FI GU RE 5. TQnnage versus average grade curve with free and constrained selections, with Pb + Zn cut-off grades of 1,5% and 2,5%.


The overall results of the selection on the whole panel are given in Figure 5; this indicates the average gradetonnage curve with free selection (curve joining symbols 0), as well as the two average grades and tonnage of blocks selected with cut-off grades of 1,5 % (symbol.6.) and 2,5 % (symbol x), taking into account the geometric mining constraints.

Block selection without constraints has been incorporated in the program solely to permit comparison with selection-considering constraints.

As is evident for a range of average grades around 5070, on passing from free selection to constrained selection there is a decrease in the average grade of the selected ore of about 0,3 %, for the same tonnage. This result confirms quite clearly that more selective mining, an operation which is costlier than that now adopted, would not be justified for this orebody.

It is readily apparent from the foregoing that use of an orebody simulation model to compare recoveries by alternative mining methods enables the most appropriate decision to be taken in the feasibility study stage.

Smoothing the boundaries The volume selected takes account of the geometric constraints, and ~lthough it has quite a regular shape as a whole it is nevertheless always a volume discretized in large blocks. It thus has boundaries which cannot be respected by the mining blasting. A program has therefore been developed that can smooth the surface of the body to be mined and make it more uniform. Smoothing is done in two phases. In the first boundaries are smoothed on every vertical cross-section (the number of such sections is the same as the number of blocks along the length of the body) passing through the centreline of the blocks; the boundary is discretized along the z direction by points according to a step value (P ASZ) supplied by the user.

Horizontal cross-section smoothing is dealt with in the second phase. The number of the horizontal cross-sections is the same as the number of the vertical discretization points; for every section the boundaries of the two sides are interpolated. The interpolated boundary is then aiscretized along the y direction according to a step value (P ASy) supplied by the user. In the actual case the discretization step selected was 2,5 m in both the vertical and y directions. Taken as a whole, therefore, each of the two surfaces defining the body is described by a number of points N = LIP ASY * HIP ASZ where Land H are the length and height of the panel, respectively. For each section - horizontal and vertical - the boundaries obtained by joining the calculated points are shown on the video screen by means of a display program.

Figure 6 illustrates the boundaries of a section before smoothing and the smoothed boundaries of the four corresponding sections (one every 2,5 m). The coordinates of the 2*H/PASZ points of each of the LlPASY vertical sections are stored on a random access file. Using the file as input, a subsequent program calculates the coordinates of the points that discretize the boundaries of the section for each desired value of y. The calculation is made by linear interpolation.

The program displays the boundaries obtained by join-

ing the calculated points.

Positioning the drilling drifts On the basis of the graphic output reproducing the smoothed boundaries on the horizontal section of each sublevel, the mining engineer decides the location of the mining drifts. An interactive program then enables the geometry of the drifts as defined here to be stored on disc. The program permits display of the position of the drifts as the data are gradually inputted. Each drift is numbered. The display program mentioned in the preceding point, which provides horizontal and vertical sections of the boundaries of the volume to be broken, also indicates the position of the .drifts. Figure 7 gives an example of horizontal and vertical section output. As an alternative to the manual method of positioning the drifts a program is being developed which establishes their position automatically.

Interactive design of blasthole fan At this step in the procedure the boundaries of the qrebody to be broken and the position of the drifts are stored in the computer and vertical sections can be produced at any value of y. Computer-aided design of the drilling fan can hence save considerable time. Another important benefit of the computer-aided design is the possibility of calculating the tonnage and grade of the volleys of each sublevel, since the geometry depends on that of the fans. The design of the fans is performed using an interactive program. The three following constraints are considered for the design of each fan:

the angle with the horizontal of the two end holes must not be less than a fixed minimum angle amin;

the distance between the extremities of two consecutive holes must not exceed a fixed maximum distance dmax;

the holes must radiate from a centre positioned on the axis of the drift and at a fixed height h above the floor, corresponding to the height of the drilling machine.

To simplify programming it has also been established that in two consecutive fans the first holes of the second one terminate on the last hole of the first. The volume blocked out by the end holes of two successive sub levels and by the boundaries of the orebody forms the volley with reference to the lower sub level. The program starts by displaying the vertical section at the desired value of y. The design begins from the highest sublevel and moves gradually down to the lowest. For a given sublevel the design commences from either side of the end drifts and proceeds sequentially towards the other. The possibility of modifying the design renders the procedure flexible, since:

the last fan designed can be cancelled and redesigned; all the fans of the sublevel under examination can be cancelled and redesigned; all the fans designed can be cancelled and a fresh start made.

For the fan of each section the program supplies a printout indicating the angle and the length of every hole and


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the total length of holes. For each section the program also provides a printout which indicates volley-by-volley the total length of blastholes, the tonnage of ore that will be broken, the tonnage per metre of hole and the average grade of the ore.

An example of the output of the fan design program is given in Figure 8. The sections refer to two selections made for cut-off grades of 1,5 and2,5OJo Pb + Zn. Tables 1 and 2 provide an example of the descriptive printout for Fan 16 of Section 1. The tonnage and grade of each volley are calculated by discretizing the volume, as shown in Figure 9.

The results for tonnage and grade of each volley -reported as illustrated in Figure 10 - form the input of a planning procedure whose output is the best breaking sequence for ensuring the most uniform mill feed over the short and medium term.

References 1. DERAISME, J., DE FOUQUET, Ch. andFRAISSE,

H. Geostatistical orebody model for computer optimization of profits from different underground mining

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FIGURE 9. Discretization of ore-blasting volume.

methods. 18th International Symposium, APCOM 84, London. pp. 583 - 590.

2. DOWD, P.A. and SCOTT, I.R. Application of geostatistics to mine planning in a complex silver-leadzinc orebody. 18th International Symposium, APCOM 84, London. pp. 253 - 264.

3. LERCHS, H. and GROSSMANN, I.F. Optimum design of open pit mines. C.I.M. Bulletin, vol. 58, no. 633, Jan. 1965. pp. 47 - 54.

EV ALUA nON AND SELECTION OF RECOVERABLE RESERVES 205

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TABLE 1. Geometry of fan holes.

Section no. 1 (Y = 5,0 m) Hole (no.) Angle (0) Length (m)

01 140 12,13 02 129 12,26 03 119 13,79 04 109 15,86 05 100 15,24 06 91 20,31 07 84 23,19 08 77 22,78 09 71 17,90 10 63 14,05 11 54 11,05 12 40 9,82

206

TABLE 2. Characteristics of the volleys.

Section no. 1 (Y=5,Om)

Ore blasting 60-80 Level Total hole length (m) 269,85 Tonnage broken (t) 3219,53 Tons/metre of hole (t/m) : 11,93 A verage grade (070) 2,53

Ore blasting 40-60 Level Total hole length (m) 424,15 Tonnage broken (t) 4946.10 Tons/metre of hole (t/m) : 11,66 A verage grade (070 ) 2,28

Ore blasting 20-40 Level Total hole length (m) 526,72 Tonnage broken (t) 5839,84 Tons/metre of hole (t/m) : 11,09 Average grade (070) 2,27

Ore blasting 0-20 Level Total hole length (m) 504,54 Tonnage broken (t) 6316,31 Tons/metre of hole (t/m) : 12,51 A verage grade (070 ) 2,16


Evaluation and Selection of Recoverable Reserves in a Sublevel Stoping Mine

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