Planning, Designing and Optimising Production Using Geostatistical Simulation (Reprinted for...

8/12/2019 Planning, Designing and Optimising Production Using Geostatistical Simulation (Reprinted for Spectrum Series)

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Planning, Designing and Optimising Production Using

Geostatistical Simulation

P A Dowd1 and P C Dare-Bryan2

ABSTRACT

The full potential of geostatistical simulation as a tool for planning,designing and optimising production is only realised when it is integratedwithin the entire design and production cycle. In the planning and designstages this involves the simulation of components of the production cyclethat depend on (simulated) grades and geology. In the production stage itinvolves integration with the mining method and the type and use ofequipment.

This paper explores the general concepts of integrated geostatisticalsimulation and illustrates them with particular reference to blast design,equipment selection and the associated quantification of ore loss, oredilution and the ability to select ore on various scales. The criticalcomponent of most metalliferous open pit mining operations is oreselection, ie the minimisation of ore loss and ore dilution duringextraction. In general, extraction comprises drilling, blasting and loading,all of which are planned and designed on the basis of uncertain models ofgeology and grade.

The application describes the integration of geostatistically simulatedgrade, geological and geomechanical models with blast modelling toprovide a link between the estimatedin situcharacteristics of the orebodyand the locations of the same (displaced) characteristics following theblast. This approach provides a means of evaluating different types ofselection and thereby enables planners to optimise the selection processin terms of blast design, type and size of loading equipment,maximisation of ore recovery and minimisation of ore loss and dilution.This conversion of the in situ/block model resource to a realisticallyrecoverable reserve may, in many instances, be the most significantsource of uncertainty in reserve estimation.

SIMULATION

Geostatistical simulation is rarely an exercise in its own right andis usually undertaken to provide a model for further studies. Inthe simplest applications the purpose may be to estimate orereserves; or to assess the uncertainty associated with mineplanning based on specified drilling densities; or to assess theeffect on recoverability of various sizes of selective mining units.In more complex applications a simulated orebody model may beused to assess the effects of sequences of downstream activities.All of these applications, in one way or another, are assessinguncertainty and its operational consequence risk.

An effective evaluation of risk must include adequatequantifications of all sources of uncertainty. Too often in theseapplications the quantification of uncertainty is limited to in situgrade and geological variables, with little attention to the

uncertainties that arise from the technical processes that areapplied to extract ore from the in situ material. The usualassessment of recoverable reserves, for example, is limited to asimple volumetric exercise in which ore recovery is assessed as afunction of applying a range of selection volumes to a simulatedorebody. This simplistic approach ignores the practicalities of theactual mining, selection and loading processes blast design,behaviour and performance; equipment type, size and operation;ore displacement during blasting and loading; and ability toidentify ore zones within a blast muck pile. In many applications,

the uncertainties introduced by these technical processes are atleast as significant as those that derive from the in situ spatialcharacteristics of grades and geology.

In mining applications, the full effectiveness of geostatisticalsimulation can only be realised by integrating it with adequateand realistic simulations of the technical processes. The authorsdemonstrate this argument with an application to selection andrecovery of ore in open pit mining. The in situ simulation ofgeology and grades can be achieved by any of the standardalgorithms. Ore, however, is not selected and recovered from thisin situmass, but from the broken and displaced components ofthe mass that results from the blasting process. The integration ofthe simulation of blasting, selecting and loading with thesimulation of in situ grade, geology and geomechanical

characteristics provides a realistic means of evaluating selectionand recoverability, as well as an effective basis for mine planningand equipment selection.

THE METHOD

The method comprises:

generation of anin situmodel of the orebody comprising thegrade, geology, geomechanical properties and grade controlvariables within sufficiently small volumes determined bythe smallest selectable volume within a blast muck pile;

definition of a blast volume comprising a large number of thein situmodel volumes, and subjecting it to a blast simulator,which effectively moves each of the component model

volumes to its final resting place in the blast muck pile; and application of selective loading processes to the simulated

muck pile to determine the degree of selectivity that can beachieved by various sizes of loader and types of loading andto quantify ore dilution and ore loss.

The in situ model, representing perfect knowledge at allrelevant scales, is obtained by geostatistical simulation. Anin situmodel that represents the reality of knowing only the dataand information that are available from specific grade controldrilling and sampling grids can be obtained by sampling thegeostatistically simulated model on a specified grid. Thevolumes comprising the in situ model are then populated byestimates based only on the data corresponding to the specifiedgrade control drilling and sampling grids. Different drilling and

sampling grids can be used to generate different models, eachreflecting the levels of data and information available. Selectivitycan then be assessed as a function of the drilling and samplinggrids as well as the size and type of loader. Performance isassessed against the ideal selectivity that can be achieved on theperfect knowledge model, comprising the simulated values ofeach component volume. Applying costs, prices and financialcriteria enables an optimal selection of the grade control drillinggrid, size of loader, type of loading and even blast design.

Blast simulation

A discrete block modelling approach was used in the workreported here. The discrete block model is based on theSCRAMBLE code (Sophisticated CRA Model of Blasting with

Explosives) developed by CRA (now Rio Tinto PLC) AdvancedTechnical Development from the ICI SABREX code (Scientific

Orebody Modelling and Strategic Mine Planning Spectrum Series Volume 14 1

1. FAusIMM(CP), Executive Dean, Faculty of Engineering, Computerand Mathematical Sciences, University of Adelaide, Adelaide SA5005, Australia. Email: [email protected]

2. Orica Australia Pty Ltd, 1 Nicholson Street, Melbourne Vic 3000,Australia.


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Approach to Blasting Rock with Explosives) (Harries and Hengst,1977; Jorgenson and Chung, 1987; Kirby, Harries and Tidman,1987; Chung and Tidman, 1988; Mohanty, Tidman and Jorgenson,1988). The code has been revised to include, inter alia, afragmentation model based on the Bond Work Index. Details ofthe basis of the blast simulation are given in Appendix A.

A standard regular block model is input to the blast simulator,which then moves each block to its final position within the

muck pile. Although the block effectively remains intact in themuck pile, it is assigned an estimated degree of fragmentation.Movement and final position are determined from models of thebehaviour of explosive gases, energy release, heave mechanics,fragmentation, throw and velocity of movement as functions of,inter alia, bench height, burden, hole spacing, hole diameter,rock density and rock fracture density.

This approach becomes more realistic as the block size becomessmaller and approaches the average size of particles in the muckpile. In principle, the block size can be made as small as desiredbut in practice the size is limited by computing constraints.

Simulating the loading process

The Floating Stope Optimiser (FSO) routine in the Datamine

mine planning software was used to simulate an optimisedselective loading process on the muck pile block modelgenerated from a blast design. The FSO procedure is similar tothe floating cone method of open pit optimisation and providesa flexible means of locating optimal envelopes of block modelgrades (Randall and Wheeler, 1998a, 1998b).

To apply the FSO to a selective mining operation, the envelopesize is defined as the selective mining unit for the excavation ofthe muck pile. The subcell size, which defines the grid spacing atwhich the envelope is successively positioned throughout theblock model, is determined by the minimum digging width of theexcavator used.

As an excavator works through a muck pile the broken rockcontinually recovers the natural angle of repose. Thus, to recover a

pocket of ore near the bottom of a muck pile a cone of material,projected up from the ore pocket, must be removed with it. Toincorporate this in the selection process a slope of 45 is applied tothe four vertical sides of the cube envelope from its base in the XYplane, generating the envelope shape shown in Figure 1.

The output from the FSO flags all blocks as ore or waste.These are then processed to generate total tonnes mined, tonnesexcavated as ore and waste, head grade of ore and tonnes ofmetal in ore. Multiple runs are taken for each muck pile over arange of cut-off grades to find the optimum.

Optimisation procedure

A blast design is applied to the complete geostatisticallysimulated blast volume (the reality) and to the estimated blockmodels for the blast design. Once the block models have beenheaved to generate the corresponding muck piles, the muck pileblock models, with associated block grade values, are enteredinto the FSO to evaluate the ore/waste excavation boundaries togive the optimum head grade based on a selected cut-off gradeand selective mining unit size. The region of the bench that is tobe excavated as ore is evaluated on the basis of the total tonnes ofmetal/mineral within that region minus the portion ofmetal/mineral expected to be lost in the processing operation.

The 80 per cent passing size of the resulting muck pile(cf Appendix A) is then used to adjust the standard cost per tonnevalues for the downstream processes of loading, hauling andprimary crushing. The total mining cost for the bench comprises

the drilling and blasting costs derived from the blast design, therevised loading and hauling costs and the mining services costs,all as a cost per tonne blasted (cf Appendix B). The totalprocessing cost comprises the adjusted primary crushing costsand the remaining processing operations costs, which areexpressed as a cost per tonne processed.

The value of the bench is thus the value of the concentrateoutput from the processing plant less the mining and processingcosts.

CASE STUDY

The case study is based on the Minas de Rio Tinto SAL (MRT)open pit copper mine at Rio Tinto, southern Spain, which istypical of a low-grade operation in the later stages of its life. The

application described here is to the low-grade Cerro Coloradomineralisation. Ore/waste delineation for selective mining isparticularly difficult because the head grades are near theeconomic cut-off grade and there are no clear geological controlson the mineralisation.

2 Spectrum Series Volume 14 Orebody Modelling and Strategic Mine Planning

P A DOWD and P C DARE-BRYAN

FIG 1 - Envelope shape for Floating Stope Optimiser.


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The mining operation has been temporarily closed pending anincrease in the copper price. During operation the mine producedconcentrate with an average grade of 24 per cent copper.

Geological setting

The Rio Tinto deposit lies in the eastern Iberian Pyrite Belt.Submarine volcanic activity created an anticline structure, theedges of which formed pyroclastic rocks, where the massive

sulfide mineralisations are located. The volcanic mass is buriedunder carboniferous slates, but subsequent folding has exposedthe volcanic sequence locally in the eastern half of the anticlineto form the Cerro Colorado deposit (Pryor, Rhoden and Villalon,1972).

The Cerro Colorado mineralisation is a stockwork of sulfideaccumulations, fed by several near-vertical brecciated feederpipes. The predominant sulfides are pyrite and chalcopyrite, withgalena, sphalerite, tetrahedrite, arsenopyrite and cassiteritepresent in much smaller quantities.

Mining method

The operation at MRT used traditional drilling and blasting on10 m and 12 m benches that were drilled with two Buycrus Eyre

45R rigs and one 60R rig drilling 250 mm holes to a depth of11.2 m or 13.7 m depending on the bench height. A square blastpattern was employed with burden and spacing dimensionsranging from 5.5 m 6.5 m to 6.6 m 8.0 m. The holes werecharged with heavy ANFO because of water problems in thelower benches. P&H 2100 BL electric face shovels andCaterpillar 994 wheel loaders were used for loading andCaterpillar 789 dump trucks used for hauling. Two blasts, B4053and B4056, were selected for this study.

Generating block models

Experimental semi-variograms were calculated from theblasthole data using a conical search. As no significantdirectional anisotropies were detected within the two blastvolumes, all directional semi-variograms for each blast werecombined into a single omni-directional semi-variogram formodelling purposes. For both blast volumes a two-structure,spherical semi-variogram model was fitted to the experimentalsemi-variograms as shown in Figure 2.

Sequential Gaussian simulation (Journel and Alabert, 1989,1990), with the blasthole grades as conditioning data, was usedto generate a realisation of each entire bench on a block grid of0.5 m 0.5 m 0.5 m, the grid determined on the basis of blastand selection criteria. The histograms of simulated values andconditioning data are shown in Figures 3a and 3b; corresponding

statistics are given in Table 1. There were no significantdifferences between the input variogram models shown inFigure 2 and those fitted to the simulation outputs for the twoblasts.

The simulations for both benches used ordinary kriging and anoctant search strategy with an isotropic search radius of 60 m. Aminimum of two and a maximum of ten conditioning values(original data plus previously simulated values) were specified

for each octant with a minimum of three informed octants. Themaximum proportion of previously simulated values in each setof conditioning values was set to 70 per cent and the coordinatesof the original data were retained, ie data was not assigned tosimulation grid nodes. Linear extrapolation was used in the upperand lower tails for back transformation of the Gaussian simulatedvalues.

The simulation provides a realisation of the grade distributionthroughout the bench on the scale required for the blastsimulation. For each specified blast design, new sample holedata is taken from the simulation block model of the bench. Thissample data is then used to generate ordinary kriging estimatesof the block grades to produce an estimated block grade model ofthe bench. The semi-variogram used for kriging is the modelfitted to the experimental semi-variogram of the sample data

taken from the simulation block model.

Blast modelling parameters

The simulated heaving action and muck pile generation wereadapted to replicate the muck piles generated by the actual blasts,based on the data available for throw and the overall shape of themuck pile profile.

The blast pattern specifications for the two blasts used in thisstudy are shown in Table 2 and the geomechanical data used issummarised in Table 3. The modelling was calibrated against theoriginal blast designs for B4053 and B4056 using the input datain Tables 2 and 3 and the muck pile profiles from field data.


PLANNING, DESIGNING AND OPTIMISING PRODUCTION USING GEOSTATISTICAL SIMULATION

C0 = 0.015

C1 = 0.042 a1 = 9m

C2 = 0.022 a2 = 51m

(h) (h)

C0 = 0.027

C1 = 0.073 a1 = 16m

C2 = 0.020 a2 = 45m

10-2

10-2

FIG 2 - Experimental semi-variograms and two-structure spherical models for B4053 (left) and B4065 blasthole data.

Blast B4053 Blast B4056

Conditioningdata

Simulatedvalues

Conditioningdata

Simulatedvalues

Mean 0.403% 0.401% 0.494% 0.489%

Variance 0.075%2 0.072%2 0.113%2 0.105%2

No of values 1440 288 000 1200 240 000

TABLE 1Statistics of conditioning data and simulated values.


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Selection of ore/waste boundaries in muck piles

For the excavators used at MRT, with a bucket size of 13 m 3, anFSO envelope of 8 m 8 m 8 m was selected with a subcellsize of 2.7 m. More selective loading was also assessed using a6 m 6 m 6 m envelope.

Costs of the blasting and selection processes

For a given blast design it is relatively straightforward tocalculate the costs associated with drilling and blasting, bysumming the constituent costs. However, the composition of themuck pile produced by the blast directly affects the downstreamprocesses of loading, hauling and primary crushing, and theoverall cost evaluation of a blast must include the costs of theseprocesses. It is not possible to quantify directly the effect ofdifferent quality blasts on the downstream processes, and the bestcommon variable for comparisons is the degree of fragmentationachieved by the blast. It is generally recognised that the costs ofthe downstream processes, including operation and maintenance,

decrease as fragmentation improves (MacKenzie, 1966).A common practice is to use a functional relationship,formulated through in-pit operational assessment, to adjust thecost per unit weight worked as a function of the degree offragmentation. A summary of the cost functions and theirderivation is given in Appendix B.

Optimisation procedure

The flow diagram in Figure 4 shows the procedure applied toeach bench. The chosen blast design is applied to the standardgeostatistical simulation and estimated block models for thatblast design.

Once the block models are heaved to generate thecorresponding muck piles, the muck pile block models, withtheir associated block grade values, are entered into Datamine.Within Datamine, the FSO is applied to the block models to



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Grade (%)

Frequency

(%)

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Grade (%)

Fr

equency

(%)

FIG 3a - Histograms of blasthole grades for blast B4053; data (left) and simulated values (right).

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Grade (%)

Frequency

(%)

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Grade (%)

Frequency

(%)

FIG 3b - Histograms of blasthole grades for blast B4056; data (left) and simulated values (right).

Youngs modulus 750 kbars

Poissons ratio 0.25

Uniaxial compressive strength 1.2 kbars

Rock density 2.75 g.cm-3

TABLE 3Geomechanical data used in case study.

Burden 6.5 m Main explosive charge 540 kgANFO

Spacing 8.0 m Initiation sequence S1

Bench height 12 m Inter-hole delay 50 ms

Vertical blasthole length 13.7 m Inter-row delay 100 ms

Hole diameter 250 mm

TABLE 2Blast pattern specifications used in case study.


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evaluate the ore/waste excavation boundaries to give theoptimum head grade based on a selected cut-off grade andselective mining unit. The region of the bench that is to beexcavated as ore is evaluated on the basis of the total tonnes ofcopper within that region, minus the portion of copper expectedto be lost during processing.

The flow chart in Figure 4 is an example of what might betermed a transfer function that transforms the idealised/insitu/simulated, and/or estimated, block grades into realisticallyrecoverable grades and tonnages. These transfer functions are notgenerally linear and in most cases their effects cannot beapproximated by simple dilution factors.

Ore reserve statements, or resource statements expressed interms of production units, that are derived by selecting blocks

directly from in situ/block models ignore some of the mostsignificant sources of uncertainty. There may be other highlynon-linear transfer functions (eg some types of mineralprocessing operations) that have significant effects onrecoverability, but generally the extraction and loading processesare the most significant.

Results

By way of example, Figure 5 shows colour-coded simulatedgrades of sections of the 0.5 m 0.5 m 0.5 m blocks thatcomprise bench B4056 and Figure 6(a) shows the muck pilegenerated by applying the blast modelling process to this bench.

Figure 6(b) shows the muck pile that results from applying theblast modelling to the same bench but with the component blockgrades kriged from the simulated grades on the 6.5 m 8 mdrilling grid. The smoothing effect of kriging is clearly evident

when comparing Figure 6(a) and 6(b). Figure 6(a) represents themuck pile given complete information, whereas Figure 6(b) isthe interpretation of the composition of the muck pile on thebasis of the data. Selection is planned and implemented on thebasis of Figure 6(b) but the volume selected will have the gradeand tonnage of the equivalent volume in Figure 6(a).

Figure 7 shows the corresponding muck piles generated fromsimulated and estimated block grade models for B4053.Figures 6 and 7 clearly show the significantly different spatialdistribution of grades in the two muck piles with consequentimplications for selection.

By way of example, when selection is applied via the FSO tothe two muck piles shown in Figure 7, the volumes selected arethose shown in Figures 8 and 9.

For each bench there are nine block models: the simulatedblock grades, taken as reality, and eight models of estimatedblock grades kriged from simulated values on various drillinggrids, together with variations in other blast design parameters assummarised in Table 4.

The grades of the blocks that comprise the two benches aresimilar in terms of histograms (cf Figure 3) but they differsignificantly in their spatial distributions within the respectivebenches. It is the latter that has the major effect on the spatialdistribution of the grades in the muck pile and consequently onthe ability to load selectively.

Bench B4053 is subeconomic for some blast designs but muststill be blasted to allow continuing mine development. Havingblasted this bench, any losses are minimised by processing theore in the muck pile. Bench B4056 is economic for all blastdesigns and is mined and processed in the normal manner.



SIMULATION

BLOCK MODEL

BLAST DESIGN

ESTIMATION

BLOCK MODEL

SCRAMBLE -

HEAVE MODELLING

DATAMINE

FLOATING STOPE

OPTIMISER

CU IN BENCH

TONNES BLASTED

TONNES EXCAVATED AS ORE

AMOUNT CU IN ORE

MINIMUM MINING

UNIT (MMU)

BOND INDEX

FRAGMENTATION

80% PASSING

DRILLING AND

BLASTING COSTS

LOADING AND

HAULING COSTS

PRIMARY

CRUSHING COSTS

MINING COSTS

PROCESSING COSTS

VA LUE OF BENCH

LOSSES IN PROCESSING

VALUE OF CU

CONCENTRATE

FIG 4 - Flowchart for optimisation procedure.


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FIG 5 - Representations of the simulated in situbench grades for B4056 showing colour-coded grade ranges on horizontal planes (top) and

cross-sectional planes (bottom). Horizontal planes are top and bottom of 12 m bench and 6 m mid-plane. Vertical planes are extremities

(0 m and 80 m) and intermediate planes at 26 m intervals.


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FIG 6 - B4056: Muck piles generated by blast design number one (a) from simulated bench grades (top) and

(b) from kriged bench grades (bottom).


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The financial performances of each blast design against thereality of the simulated block model are summarised inFigure 10 for B4053 and in Figure 11 for B4056. These figuresshow the ideal or maximum bench values corresponding to thesimulated block grades, together with the actual bench valuesachieved by selecting from the muck piles generated from theestimated block grades for the various blast designs.

Figures 12 and 13 show the tonnages of copper within the oreselected from the muck pile generated from the simulated blockgrades, together with the actual tonnages recovered from themuck piles generated from the estimated block grades for thevarious blast designs.



FIG 7 - B4053: Muck piles generated by blast design number one

(a) from simulated bench grades (top) and (b) from kriged bench

grades (bottom).

FIG 8 - Muck piles for B4053. (Top) Muck pile generated from

simulated block grades (reality). (Bottom) Muck pile generated

from estimated block grades using blast design one. The darker

shade indicates exposed selected ore and the lighter shade is

non-selected broken rock.

FIG 9 - Volumes of ore selected from muck pile for blast design 1,

generated from simulated block grades (top) and from estimated

block grades (bottom).

Blastdesign

Designchanges

Burden(m)

Spacing(m)

Powderfactor

(kg.tonne-1)

Holediameter

(m)

1 Control 6.5 8 0.31 0.25

2 Changinghole

diameter

6 7.5 0.31 0.23

3 7 9 0.31 0.27

4 8 9.5 0.31 0.30

5 Increasingpowderfactor

6 7.5 0.37 0.25

6 5.5 7 0.43 0.25

7 Decreasingpowderfactor

7.5 9 0.25 0.25

8 8.5 10.5 0.19 0.25

TABLE 4Blast designs used in study for estimated block grades.


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-80000

-70000

-60000

-50000

-40000

-30000

-20000

-10000

0

10000

20000

1 2 3 4 5 6 7 8 1a

Control c han ging h ole diam increasing PF d ecreasing PF sma ller

FSO

envelopeblast design

Bench

Value($)

Simulated Estimated

FIG 10 - B4053 optimised bench values for blast designs.

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

1 2 3 4 5 6 7 8 1a

Control changing hole diam increasing PF decreasing PF smaller

FSO

envelopeblast design

Valueofbench

($)

Simulated Estimated

FIG 11 - B4056 optimised bench values for blast designs.

100

140

180

220

260

300

340

380

1 2 3 4 5 6 7 8 1a

Control changi ng hole diam i ncreasing PF decreasi ng PF smal ler

FSO

envelopeBlast Design

Copper(to

nnes)

Copper actually recovered Simulated copper in ore

FIG 12 - B4053: simulated (actual) copper in ore selected from muck pile and amounts recovered on the basis of estimations from

various blast designs.


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Numbers on the horizontal axes of Figures 10-13 denote theblast designs given in Table 1. Blast 1a (smaller FSO envelope) isa smaller selection envelope applied to blast one, in which theenvelope corresponds to smaller-scale selection (6 m 6 m 6 m) using a wheel loader.

Note that in some cases, more copper is recovered from themuck pile generated from the estimated block grades than fromthe muck pile generated from the simulated block grades(eg blast designs seven and eight in Figure 12). This is, however,at the expense of diluting the ore with additional waste, whichreduces profit (eg as indicated by the bench values for blastsseven and eight in Figure 10).

The differences between ideal selection and selection based onestimated block grades are more significant for B4053 becausethe economic grades are more widely dispersed through thebench and the muck piles than they are for B4056. Thedifferences are large and critical for B4053, as planning on thebasis of the estimated block grades leads, more often than not, tofinancial loss.

The real effects on the operation can be quantified bycomparing the expected performance against the actualperformance. Figures 14 and 15 show, for each blast design and

for selection based on the estimated block grade models, thedifference between the estimated copper content and the actualcopper content of the selected ore regions, together with thedifference between the estimated and actual financial values ofthe selected ore regions. It is these differences between plannedand actual performances that have the greatest impact on theviability of the operation.

The results summarised in Figures 14 and 15 are functions ofthe complex relationships among block grade values, heavemechanics of the blasting process, the spatial distribution of oreand waste blocks in the muck pile and the method of selectingfrom the muck pile. The absolute values of the bars shown inFigures 14 and 15 are the deviations from planned outcomes andare measures of the ability to plan the operation to acceptablelevels of accuracy and of the consequences of not being able to

do so. The larger differences for B4056 (Figure 15) are afunction of the more distinct ore/waste boundaries in theresulting muck pile, which in turn provide a greater propensityfor ore loss and ore dilution with small changes in the selectionvolumes. By contrast, the greater dispersion of the orethroughout the muck pile generated from B4053 offers less scopefor selectivity and less adverse consequences arising fromchanges in the selection volumes.



200

220

240

260

280

300

320

340

360

1 2 3 4 5 6 7 8 1a

C on tro l c han gi ng h ol e di am i nc re as in g PF d ec re asi ng PF s mal le r

FSO


Coppe

r(tonnes)

Copper actually recovered Simulated copper in ore

FIG 13 - B4056: simulated (actual) copper in ore selected from muck pile and amounts recovered on the basis of estimations from

various blast designs.

-20

-15

-10

-5

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 1a


FSO


Copper(tonne

s)

-22000

-17000

-12000

-7000

-2000

3000

8000

13000

18000

23000

28000

33000

Value($)

expected recovered copper less amount recoveredexpected bench value less real value

FIG 14 - Differences between planned and actual performance for B4053.


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SUMMARY AND CONCLUSIONSThis study demonstrates the potential of geostatistical simulationin the optimisation of blasting and loading in selective miningprocesses. In particular, it provides a means of quantifying theeffects of grade distribution smoothing on blast design and theselection of ore regions within the resulting muck pile. It alsoprovides a means of assessing the financial consequences of oreloss and dilution arising from planning and implementingspecific blasting and loading practices on the basis of variousdrilling grids.

Although a very specific blast modelling process has beenused in this study, it could readily be replaced by any other typeof modelling, either to provide a more realistic simulation ofheave mechanics and fragmentation or to simulate other types of

blasting and selection. Similarly, other types of geostatisticalsimulation could be used and multiple variables, includingqualitative geological variables, could be simulated andincorporated into the selection procedure, for example byselecting gold-bearing ore on the basis of observable quartz veinsand fracture networks in the muck pile (Dowd, 1995). Themethods and approach used in this study do not limit thegenerality and practical potential of the application.

A real-time, virtual reality version of the approach describedhere could also be used to guide loader operators in makingoptimal selections from muck piles. Real-time applicationswould require very rapid capture of accurate survey andlocational data, which could readily be provided by GPS.

More generally, the application described here demonstrates

that the full effectiveness of geostatistical simulation can only berealised in mining applications by integrating it with adequatesimulations of the technical processes that turn the simulatedin situcharacteristics into mined products. This is an importantissue in determining and reporting reserves.

REFERENCES

Chung, S H and Tidman, J P, 1988. Effective modelling for cast blasting,in Proceedings International Symposium for Mine Planning andEquipment Selection(ed: R K Singhal) pp 357-360 (A A Balkema:Rotterdam).

Dowd, P A, 1995. Bjrkdal gold mining project, northern Sweden,TransInst Min Metall, Section A, Mining Technology, 104:A149-A163.

Harries, G and Hengst, B, 1977. Use of a computer to describe blasting,in Proceedings 15th APCOM Symposium, pp 317-324 (The

Australasian Institute of Mining and Metallurgy: Melbourne).

Hustrulid, W, 1999. Blasting Principles for Open Pit Mining,Vol 1,General Design Concepts (A A Balkema: Rotterdam).

Jorgenson, G K and Chung, S H, 1987. Blast simulation surface andunderground with the SABREX model,CIM Bulletin, 80:37-41.

Journel, A G and Alabert, F, 1989. Non-gaussian data expansion in theearth sciences,Terra Nova, 1:123-134.

Journel, A G and Alabert, F, 1990. New method for reservoir mapping,Journal of Petroleum Technology,42(2):212-218.

Kirby, I J, Harries, G and Tidman, J P, 1987. ICIs computer blastingmodel SABREX the basic principles and capabilities, inProceedings 13th Conference on Explosives and Blasting Technique,(ed: R D Boddorff), pp 184-198 (Society of Explosives Engineers).

Leiper, G A and Plessis, M P, 1987. Describing explosives in blastingmodels, in Proceedings Second International Symposium on RockFragmentation by Blasting, (eds: W L Fourney and R D Dick) pp462-474 (Society for Experimental Mathematics).

MacKenzie, A S, 1966. Cost of explosives do you evaluate it properly?,Mining Congress Journal, pp 32-41.

Mohanty, B, Tidman, J P and Jorgenson, G K, 1988. Advanced computersimulations the key to effective blast designs in open pit andunderground mines, in Computer Applications in the MineralIndustry (eds: K Fytas, J L Collins and R K Singhal) pp 41-48,Rotterdam.

Nielsen, K, 1983. Optimisation of open pit bench blasting, inProceedingsFirst International Symposium on Rock Fragmentation by Blasting,Vol 2, pp 653-664 (Society for Experimental Mechanics).

Pryor, R N, Rhoden, H N and Villalon, M, 1972. Sampling of CerroColorado, Rio Tinto, Spain, Trans Inst Min Metall, Section A,Mining Technology, 81:A143-159.

Randall, M and Wheeler, A, 1998a. Balancing the books, MiningMagazine, pp 337-342.

Randall, M and Wheeler, A, 1998b. Where did it go? Mining Magazine,

pp 245-249.Van Zeggeren, F and Chung, S H, 1975. A model for the prediction of

fragmentation, patterns and costs in rock blasting, in Proceedings15th Symposium on Rock Mechanics (ed: E R Hoskins) pp 557-569(The American Society of Civil Engineers: Reston).

APPENDIX A: BLAST MODELLING

The adapted version of the SCRAMBLE/SABREX blastmodelling code used in this study is an energy-based approachcomprising two separate models: heave mechanics andfragmentation. The heave mechanics are based on the energyreleased from the adiabatic expansion of the explosive gasesfollowing detonation. Fragmentation is based on the powderfactor (ratio of charge weight in kilograms to mass in tonnes ofrock broken by the charge) converted to an energy equivalent viathe Bond Index.



-20

-15

-10

-5

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 1a


FSO


Copper

(tonnes)

-22000

-17000

-12000

-7000

-2000

3000

8000

13000

18000

23000

28000

33000

Valu

e($)

expected recovered copper less amount recoveredexpected bench value less real value

FIG 15 - Differences between planned and actual performance for B4056.


12/16

The velocity of detonation for each blasthole is taken asinfinite and the wall is allowed to expand until it reaches a stateof equilibrium determined by the isotropic expansion characteristicsof the quasi-static gas pressure and the elastic resistance of the rock.The expanded blasthole sets up hoop stresses in the surroundingrock, creating a system of radial cracks that, because of tensilefailure, spread away from the hole. The radial fractures, togetherwith any pre-existing geological discontinuities, define the damage

created in the rock mass by the blast.The gaseous detonation products flow into the fractured rock

mass at the local speed of sound until the gas vents through a freeface; at this stage a rarefaction wave travels back toward eachblasthole decompressing the cracks. As the rarefaction wavetravels through the rock, the pressurised crack system imparts animpulse, which heaves the broken rock mass out from the bench.

In generating the muck pile, empirical routines are used tolimit the angle of repose whilst producing a smooth surface andadding swell factors.

Equation of state for explosive gases

The equation of state for the gaseous products of detonation is:

p E

= ++

)

( )

(

1

100 1 2

3

(A1)

where:

p is the gas pressure in kbars

is the gas density in g.cm-3

E is the available energy in J.g-1

and are dimensionless constants

The available energyEis the work done by the explosive gasesin expanding adiabatically from the density to ambientconditions, and is obtained from:

1n 1nE

Eo

o o o

=

+

++

+

( ) ( ) ( )2 254

5

4

1

8

1 2

o( )1 2+

(A2)

where:

o is the initial gas density after detonation (equal to theexplosive density)

Eo is the initial available energy

The values for Eo, and can be obtained from an ideal ornon-ideal detonation model. An ideal detonation model isadequate for the large diameter holes used in this study; moreaccurate data could be obtained from non-ideal models such asCpeX (Leiper and Plessis, 1987).

Equation (A1) reduces to the ideal gas law for small gasdensities and, together with Equation (A2), allows availableenergy and pressure to be generated as a function of their densityduring the expansion process.

Heave mechanics

All regions within the gas envelope have a common gas densityand pressure. The leading edge of the envelope is regarded as thegas front, which is assumed to move at the local speed of sound(m.s-1) given by:

c p

=

1000001

2

(A3)

where is the adiabatic exponent for the gases at pressurep (kbar) and the density(g.cm-3),is given by:

= + +

+

+

+

1 1

1 2

3

1

3( )(A4)

and is derived from the equation of state given in Equation (A1).

To calculate the necessary density and pressure of the gaswithin the envelope the volume of rock within the envelope isassumed to be in a state of hydrostatic compression at pressurep.The resultant reduction in the volume of rock is given by:

V Vp

G+ (A5)

where:

V is the initial volume (m3)

G is the bulk modulus

V is the volume increase in the envelope contributing to thereduction in gas density and pressure.

Another small increase in volume is associated with the gaspressure compressing the rock below and behind the blasthole.

As the gas expands with the moving gas front, the local speedof sound in Equation (A3) falls and a time-stepping loop is usedto track the expansion of the gas. The time steps used are definedby:

t b b

c=

+(A6)

where:

b+ b is the equilibrium blasthole radius

Equation (A6) shows that, although the time steps can vary, the

corresponding spatial steps are constant and equal to theequilibrium borehole radius.

The time-stepping procedure is:

1. calculate the initial local speed of sound from Equations(A3) and (A4) prior to the expansion of gas into the rockmass;

2. calculate the appropriate time step from Equation (A6) andgenerate the appropriate gas front profile;

3. calculate the increase in volume from Equation (A5) andthen calculate the new gas pressure and density usingEquations (A1) and (A2);

4. recalculate the local speed of sound using Equations (A3)and (A4); and

5. repeat the steps while keeping track of the total elapsedtime.

Venting of the explosive gas begins when the gas front meets afree face. At that time the gas fronts retrace their original pathsand, during this period of contraction, the gas density, pressureand speed of sound are assumed to be constant within the volumeof the gas envelope. The respective constant values are those thatwere calculated at the time of venting, while the pressure beyondthe gas fronts is assumed to be insignificant.

At the time of venting, the rock mass is assumed free to move,reacting to a momentum impulse that is imparted on the rockmass. The calculated impulse is based on the assumption that therock mass does not start to move until the gas fronts havecontracted. The total impulse imparted on the rock mass

(kg.ms-1

) is given by:




13/16


14/16


15/16

where:

Ccr is the adjusted crushing cost ($.tonne-1)

is a constant

Costs unaffected by blasting practices

Costs incurred in producing a saleable product that are notaffected by blasting practices include mining services and theentire mineral processing operation downstream of the primarycrushing. These values, also expressed as $/tonne, are assumed toremain constant.




16/16


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