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Paper 7 Rock Engineering

INTRODUCTION

A significant component of underground miningcosts stems from ground support in the form of rockbolts, mesh and screen, cable bolts, and shotcrete.Should any of this support approach or reach failure(stripped or broken cable bolts, severe bagging ofscreen, large numbers of broken rock bolts, etc.), thesupport needs to be rehabilitated. This rehabilitationis often much more expensive than the initial supportinstallation, due not just to the cost of the support,but to loss of access, down-time of that area of themine, potential for injuries, the slow nature of thework, and possible lost mining revenues. The ques-tion then becomes: can support design be madesmarter? That is, can the initial design of mining sup-port be done to a level such that the right type andlength of support is installed the first time around,hence greatly reducing overall direct mining costs.

Most ground support elements are installed asdowels – un-tensioned tendons (e.g. passive cables,rebar, etc.). The issue here is that support is only pro-vided when sufficient dilation or movement of therock mass has occurred to generate resisting tensileforces in the support element. Significant stress-driven movement only occurs in a rock mass after the

Innovative use of SMART cable bolt data throughnumerical back analysis for interpretation of postfailure rock mass propertiesJ.J. Crowder, W.F. Bawden, A.L. Coulson, Lassonde Institute, University of Toronto, Toronto, Ontario

ABSTRACT Ground support is a significant component of underground mining costs. The rehabilita-tion of failed support, however, is often much more expensive than the initial installation. Thispaper investigates whether the right type and length of support can be designed correctly the firsttime, through forward modelling of the support and the mining process. Back analyses demonstratehow high-quality instrumentation and monitoring can help with the estimation of the post-peak(post-failure) rock mass parameters required for a comprehensive analysis. A hybrid modellingapproach combines a three-dimensional mine-wide boundary element model with a non-linearfinite element model to allow for the failure process in the rock mass. The back analyses demon-strate that, for the case study site, the post-peak Generalized Hoek-Brown value of mr must bereduced significantly in order to properly simulate displacements observed in instrumentation data.High-quality instrumentation data is the key to post-peak rock mass parameter calibration. The pro-cedures outlined in the paper highlight the need for a new hybrid numerical modelling package thatcan use the influence of three-dimensional mining-induced stresses to predict displacements in, andpotential failure of, rock masses surrounding mining infrastructure in order to radically alter strate-gic and tactical mine design.

KEYWORDS Post-peak rock mass parameters, Back analysis, Predictive modelling, Instrumentation data,SMART cable bolts, Mine-induced stresses, mine-wide modelling

peak strength of the rock has been exceeded and it iswell into a state of yield or failure. In other words,based on experience, stress-driven ground move-ments are not sufficient to load the support to anysignificant amount prior to yield of the rock mass. InDeGraaf, Hyett, Lausch, Bawden, and Yao (1999),instrumentation data indicated that displacementsseen in instrumented cable bolts were not significantup to model-predicted failure and, hence, the cablesnever took any measurable load to that point. Inother cases, support has been loaded to failure, asshown by broken cables. In such cases, in the authors’experience, numerical models always indicate thatelastic stresses in these regions significantly exceededthe peak values allowed by the constitutive modelthat was applied.

In order to improve underground mining supportbehaviour and reduce costs associated with over-design and rehabilitation due to under-design, thereneeds to be better modelling capability of supportbehaviour prior to design and installation. Hence, theneed exists to model the rock mass behaviour wellpast the point of failure, into the post-peak regime,not just the typical elastic stress modelling that oftenoccurs in mining today (Crowder and Bawden, 2004).Most importantly, models need to be able to calculate

displacements that occur due to failure with a highdegree of confidence (something generally not possi-ble today), as displacement up to the point of failureis almost negligible. To accomplish better modelling,improved instrumentation data is required for calibra-tion of rock mass properties, particularly post-failureor post-peak parameters. In order to accomplish this,field case studies having adequate numbers of high-quality instruments and frequency of readings arerequired.

This paper examines the current state of model-ling and instrumentation in mining. An assessment ofsome typical problems with how instrumentation ismonitored and used, as well as how good data can bequite valuable, are shown. An overview of typicalmine modelling procedures will be given, followed bya look at what types of models are required and whatinput is necessary for predictive forward modelling. Acase study then demonstrates, through back analysis,how high-quality instrumentation and monitoring canhelp with the estimation of the post-peak (post-fail-ure) rock mass parameters required for a comprehen-sive analysis.

THE ROCK MECHANICS PROBLEM

Rock mechanics is now a reasonably mature fieldof study, many aspects of which are well understood.To this end, the modelling capability for mining appli-cations is also quite mature and sophisticated. In fact,the complexity and capability of models often signifi-cantly exceeds the ability of mining, rock mechanics,or geotechnical engineers to generate reliable rockmass parameters, particularly in the post peak regime(after failure). That is, once a rock mass has reachedfailure, it can still maintain some post peak or residualstrength. If rock mass parameters for post-failure con-ditions were well developed for given types of rockand stress conditions, then explicit forward modellingof rock mass support could be performed.

The ability to accurately predict the post-peakparameters of in situ rock masses is very much an artat this time. Engineers often rely on the suggestionsof colleagues and empirical rules of thumb. There hasbeen considerable debate as to how to alter the post-peak parameters of rock masses, as was discussedamong several industry leaders and disseminated byCrowder and Bawden (2004). In that paper, the Gen-eralized Hoek Brown failure criterion (GHB; Hoek,Carranza-Torres, and Corkum, 2002) was exclusivelydiscussed as it is currently the most often used crite-rion for underground rock mechanics studies. Theconsensus was that the Geological Strength Index(GSI; Hoek, Kaiser, and Bawden, 1995) and the Dis-turbance factor (D; Hoek et al., 2002) are indexparameters that are used to determine reasonableestimates of the peak strength parameters andshould not enter into the determination of post-peakstrength. Similarly, the unconfined compressivestrength of intact rock samples, UCS or σci, and Hoek-Brown parameter mi are both properties of intactspecimens determined from laboratory testing and,

hence, should not be altered for determination ofpost-peak rock mass parameters. Thus, the consensuswas that to effectively model the behaviour of a rockmass, any numerical model should have the option toenter peak and post-peak (elastic and plastic) valuesfor mb, s, and a.

Although a consensus was reached, there stillwas considerable debate among these industry lead-ers, inferring that much research remains to be com-pleted toward the reliable estimation of post-peakrock mass parameters. One methodology that can beutilized to look at this problem is discussed later inthis paper.

PRESENT STATE OF MODELLING ANDINSTRUMENTATION IN MINING

Most mines today utilize numerical modelling aspart of their strategic and/or tactical mine designefforts. These models, normally linear elastic, areoften not up to date and modelling is often done onlyin reaction to a problem. There are some instances inwhich non-linear models are used, but the inputparameters for the post-peak characteristics of theserock masses are generally guessed at, or some rule ofthumb is followed. The most common form of analy-sis is to examine the results of stresses calculated bythe models. If the model is elastic, then the modelmay calculate stresses that are much higher than arock mass can sustain, as determined by the chosenfailure criterion. The strength factor, the ratio of themaximum stress allowed by the failure criterion to thecurrent state of stress (eg. a strength factor less thanone can be interpreted as ‘failed’), is one of the keyresults examined. The region of strength factor thatshows ‘failure’—often referred to as the yield zone—may be used as a basis for how deep rock mass sup-port should extend and, to a lesser degree, how muchreinforcement to add. However, this yield zone is notnecessarily the best representation of where failure ofthe rock mass occurs. Using a non-linear model withperfectly-plastic post-peak parameters, the extent ofthe failure zone may be quite similar to what is pre-dicted by the yield zone from elastic models. How-ever, under strongly strain softening conditions,non-linear models can exhibit different shapes andextents of failure zones than those from elastic mod-els (Crowder, Coulson, and Bawden, 2006). Further-more, displacements from elastic models are notconsidered valid and are hence generally not used.

However, accurate estimates of displacementsare exactly what is required for support design. Min-ing openings are often designed to be only as large asnecessary for equipment and services because anylarger openings cost more and are more difficult tosupport. Excessive deformations can destroy supportthat is costly to rehabilitate, may cause falls of groundresulting in delays or injuries, and ultimately mayimpact equipment access.

Most mines use instrumentation in critical infra-structure, such as haulage drifts, crusher stations, inter-sections, etc., to monitor the displacement of the backs

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and/or walls, support loads, etc. These instruments,however, are often installed long after the initial accessexcavation has been created—and often just soonbefore the mining front progresses through a particulararea. The trouble with this approach is that the totalaccumulation of displacements and hence damage can-not be known to any degree of certainty. As well, datafrom the instruments are generally collected by hand,from time-to-time and entered into a database. The fre-quency of readings depends on whether or not a prob-lem has been spotted, by how much time the engineeror technician has to collect data or by whether the min-ing front is approaching. The best way to collect data,however, is on a regular schedule, whether or notmovement is anticipated. The other problem withinstrumentation data today is that it is analysed only ifthere is a problem (ie. reactive engineering). In sum-mary, if instrumentation is to be used to aid in thedesign process at a mine for prediction purposes, high-quality and consistent data are required.

DERIVING PARAMETERS FOR MODELLING FROMINSTRUMENTATION

Research at the University of Toronto has lookedinto the problem of what post-peak rock massparameters should be used to reasonably representthe rock mass. This was accomplished using qualityinstrumentation data from one case study mine, in aback analysis mode using numerical modelling. Thedetails of the methodology and the verification canbe found in Crowder and Bawden (2005). A shortsummary of the method follows.

Three-dimensional mine-wide elastic stresseshave been obtained at the case study mine for incre-mental mining steps over several years using theelastic boundary element numerical analysis pro-gram Examine3D. Because this type of model canonly represent one time step, several models werecreated to represent relevant time steps in the mine’shistory, corresponding to certain times where theinstruments were recording data. For each miningstep (i.e. each Examine3D model), the stress stateover a two-dimensional slice through the three-dimensional model at the location of an appropriateinstrument was exported into the two-dimensionalfinite element analysis program, Phase2. This pro-gram allows for the rock mass to fail (i.e. it is non-linear) when stresses exceed the chosen failurecriterion. Also, unlike Examine3D, it allows for theintegration of rock mass support (such as cablebolts, rock bolts and shotcrete) explicitly in themodel. After the model was created, the peak rockmass parameters were defined using the General-ized Hoek Brown (GHB) failure criterion, and thepost-peak rock mass parameters were adjusted,through a parametric back analysis, until displace-ments above the back closely approximated thoseobserved from the field instrumentation. Refer toCrowder and Bawden (2004) for a discussion of theimportance of post-peak parameters and someguidelines on related rules of thumb.

The case study involves the Williams Mine, whichis located near Marathon in the Hemlo region ofnorthern Ontario (Fig. 1). The orebody dips to thenorth at about 70 degrees and ranges in thicknessfrom 3 to 50 m over the full strike length of the ore-body (~1.5 km). The majority of infrastructure devel-opment occurs in the footwall, which is for the mostpart composed of quartz-eye muscovite schist (Baw-den, Dennison, and Lausch, 2000). More details ofthe ore extraction methods, of drift support, andother information about the mine can be found inCrowder and Bawden (2005) and LeBlanc and Mur-doch (2000).

The Williams Mine primarily uses two types ofinstrumentation to monitor vertical movement in thebacks of mining drifts. The Stretch Measurement forAssessment of Reinforcement Tension (SMART) cablebolts are instrumented to accurately assess the defor-mations that occur in the cable support elements(Bawden et al., 2000). The Multi-Point BoreholeExtensometer (MPBX) is a flexible borehole exten-someter that passively measures the deformation ofthe rock mass itself. That is, it provides no reinforce-ment in contrast to the SMART cable bolt. Bothinstruments are manufactured by Mine Design Tech-nologies Inc. in Kingston, Ontario.

The instrumentation database for the WilliamsMine, at the time of this study, had just over 200SMART cable bolts and MPBXs combined. The casestudy described in this paper, however, only dealswith two specific areas of the mine in which a total ofabout 95 instruments are located. Although there areseemingly plenty of instruments that could be used inthe back analysis, only about 10 were really usable. Afew of the instruments were installed in areas wellaway from the stopes and hence show little move-ment. Other instruments were installed after a major-ity of the mining in the area was already completed.Many of the instruments were installed at differenttimes throughout the study period (1999–2003) and,hence, a complete record over time at a given loca-

Rock Engineering

Fig. 1. Location map of the Williams Mine in northern Ontario.

tion did not exist. As well, other instrumentsexceeded the displacement capacity (of the instru-ments) and replacement instruments were installedafter a time gap. One of thebiggest problems with the instru-mentation was an inadequate fre-quency of readings (for thepurposes of this type of analysis).This is because all of the instru-ments are read by hand whenevermining personnel have the time.Hence, large gaps occur in thedata, as shown in Figure 2. Anexample of one of the most rea-sonable, continuous data setsfrom an instrument at theWilliams Mine is shown in Figure3. All of these instrumentationproblems cite the need for real-time acquisition of data frominstrumentation. As well, instru-ments should be installed early onin the mining process, not justwhen the mining front passes agiven area, so that a continuous,reliable set of data exist for moni-toring and analysis. An example of

a continuously monitored instrument that capturesexactly when displacements occur in reaction to min-ing in the vicinity of the instrument is shown in Fig-ure 4.

CASE STUDY ANALYSIS

This section details the results of the back analy-sis procedure in two separate locations at theWilliams Mine. The first location is a large shrinkingpillar of high-grade ore located in the upper east cor-ner of the mine (Cells 1 and 2) at a depth rangingfrom about 400 to 600 m and is about 200 m in strikelength. Mining has occurred above, below, to thewest, and to the east of this area. The specific studyarea within this zone occurs on two levels, at about550 m depth. The other area of interest occurs inwhat is known as the Sill Pillar (in Cell 5), which isabout 80 m in height and was created as the mineoriginally extracted ore from two main blocks aboveand below this region. This pillar is located at an aver-

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Fig. 2. Example of instrumentation data with large gaps in betweenreadings.

Fig. 3. An example of good quality instrumentation data from Williamsmine.

Fig. 4. Example of excellent quality instrumentation data. Notice theresponse of the instrument to the arrows which indicate timingcorresponding to proximate blasting.

Fig. 5. Long-section of the Williams mine showing the cell arrangement and the two areas of analysisdescribed in this paper.

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age depth of about 950 m. A long section of themine showing the general locations of analysis isshown in Figure 5. All of the instruments in the studyare located in the main haulage drifts that parallel theore in the footwall rock unit. This unit is thought tobe fairly consistent over the depth of the mine, exceptin the upper west regions of the mine, far from thesestudy areas.

The determination of GHB parameters of thefootwall rock mass at the Williams Mine has beenwell researched and discussed (Kazakidis, 1990;Crowder and Bawden, 2005) and need not berepeated here. The rock properties used are: uncon-fined compressive strength (UCS or σci) = 175 MPa;Poisson’s Ratio = 0.25; Geological Strength Index(GSI) = 60; and mi (GHB material constant for intactrock) = 10. Using these values, and using the appro-priate GHB equations, the rock mass peak inputparameters to Phase2 are: Young’s Modulus = 17800MPa; mb = 2.397; s = 0.0117; and a = 0.503. TheGHB parameters mb, s, and a are all unitless.

Because the estimated peak rock mass parame-ters were well established for this rock by previousstudies, the task then became to iterate in a backanalysis fashion to determine what appropriate post-peak parameters were necessary for the model toclosely simulate the displacements observed in thefield from the instrumentation. The parameters tovary in the post-peak are the (so-called) ‘residual’ val-ues of mb and s, which are denoted by Phase2 as mrand sr, respectively. The dilation parameter must alsobe varied.

In the first case study area, Cells 1 and 2, threedifferent instruments were examined using the backanalysis procedure. A parametric study was used toindependently adjust each of the three post-peakparameters from the peak value to a value approach-ing zero that still allowed for the model to compute,i.e. not to the point of numerical instability. A seriesof time steps were chosen such that nearby mininghad caused significant mine-induced stress redistribu-tion and, hence, progressive failure and displacementwithin the rock mass. The observations from theinstrument at this location are shown at the chosentime steps, as a plot of vertical displacement of theback with distance into the back, ie. above the drift(Fig. 6). Each line represents a different time step.

In order to most closely simulate the observeddisplacements, the value of mb was reduced to apost-peak mr = 0.24, or 10% of the original value.The value of s was reduced to a post-peak sr = 0.002,or about 20% of the initial peak value. The dilationparameter was set to 0.4, or about one-sixth of thevalue of mb (Crowder and Bawden, 2004). Whenthese parameters were applied, the resulting calcu-lated displacements are shown for the same timesteps as was used for the instrument. The modellingresults overlaid on the instrument data are shown inFigure 7. It must be noted that any displacements thatoccurred in the model prior to the step correspondingto the installation of the instrument have been zeroedout (Crowder et al., 2006). Hence, the modelling

results shown in Figure 7 can be directly compared tothe instrument data for the same time intervals.

For the second location, the Cell 5 sill pillar, aback analysis was performed in a similar fashion tothe results presented previously. Again, the post-peakparameters that best simulated the observed field dis-placements were mr = 0.24, or 10% of the originalvalue, and the value of s was reduced to a post-peaksr = 0.0059, or about 50% of the initial peak value.The modelling results overlaid on the instrument dataare shown in Figure 8. The dilation parameter was setto 0.8, or about one-third of the value of mb. The

Rock Engineering

Fig. 6. Instrumentation data (MPBX) from Area 1 that is used for calibration in the back analysisprocedure.

Fig. 8. Results of back analysis in Area 2 compared with observations from an instrument at the samelocation.

Fig. 7. Results of the back analysis performed in Area 1 (at the same location as the instrument) overlaidon top of the instrumentation data. This is considered a reasonable fit.

results from the two regions of the mine are summa-rized in Table 1.

The key result is that both areas of the minerequire the GHB post-peak value of mr to be reducedsignificantly from the peak value. This suggests thatafter failure, the rock can only sustain a small fractionof its original shear strength. The difference in valuesof sr is not considered of great importance, as smallchanges in sr do not affect the depth of failure, butincrease (only slightly) the magnitude of displacementin the models (Crowder et al., 2006). Similarly, thedilation parameter does not greatly affect the depthof failure, but does influence the curvature of the dis-placement versus depth plots. The greatest influenceon the displacements is controlled by mr. The influ-ence of slight variations in post-peak parameters canbe best explained by examining Figure 9. This figureshows the GHB strength envelopes in σ1-σ3 stressspace. The peak curve applies to both areas of analy-sis in the mine. The variation of post-peak parametersthat seemed to best fit the field data are shown as theband of strength envelopes well below the peakcurve. This range is quite tight considering that,although both areas of analysis are in the same foot-wall rock formation, there are some variations in thisunit over the 500 m (vertical) that separate the areas(Fig. 5).

DISCUSSION

The results shown in the previous section indicatethat the potential exists for numerical modelling topredict actual displacements and hence supportloads, observed in the field with reasonable confi-dence. However, at this point, an analysis must becompleted for each mine, as the results shown in thispaper are very specific to the rock mass at theWilliams Mine. In fact, the post-peak parametersdetermined in this study may not be the ultimate bestestimate for the post-peak parameters for this rockmass. However, these values provide very reasonableresults, given the inherent uncertainty in many of theinput parameters and the use of a continuum modelfor a discontinuous rock mass. Most importantly,these results demonstrate that the numerical model-ling and back analysis processes have been shown tobe effective.

The procedures that were used in the process ofthis study are quite labour intensive and took severalmonths to complete. With that said, if numericaltools could be developed to automate or improve theusability of this process, the modelling would not bea huge undertaking. As the models currently exist,they are easy to use and do an excellent job for the

purposes for which they were designed, but each oneon its own cannot handle the complex problemsaddressed in this paper. New tools need to be devel-oped to handle all the issues in one numerical pack-age. Such a program should integrate rock masssupport using the correct support constitutive models(Moosavi, Bawden, and Hyett, 2002). In the authors’opinion, the ideal numerical modelling tool would bea hybrid using the ability of three-dimensional elasticmodels to generate mine-wide elastic mine-inducedstresses, combined with the ability of non-linear (eg.finite element, finite difference, distinct element, etc.)models to use post-peak parameters to model failureand deformation while including explicit models ofrock mass support.

It is necessary at this point to mention that theapproach taken by the authors was in fact to illustratethe point of the power of numerical tools combinedwith excellent quality instrumentation data. Thereexist other brands of numerical tools that solve partsof the problems in much the same manner as theRocscience tools. Three-dimensional finite element,finite difference, and distinct element packages thatcan run mine-wide models and incorporate rock masssupport exist. For a number of reasons, these pro-grams were not used. Because of the scale of themine-wide model required to obtain appropriatemine induced global stress change, combined withthe accuracy and detail required for the back analysis,the computation time would not be feasible. Addi-tionally, the only numerical model that incorporatesthe bulb cable constitutive behaviour (one of the keyinstruments used in this study) is Phase2. The authors’believe that a hybrid approach is better suited to thistype of problem.

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Table 1. Summary of the general back analysis results from the two regions showingthe range of post-peak parameters that best simulated the displacements observedin the field

mb mr s sr Dilation

Area 1 2.397 0 < mr < 0.10mb 0.0117 0.10s < sr < s 0 < dil < 1/6 mb

Area 2 2.397 0.10 mb 0.0117 0.50s < sr < s σ mb < dil < σ mb

Fig. 9. Generalized Hoek-Brown peak strength envelope and a tight bandrepresenting the post-peak strength envelopes that produced the best backanalysis results in Areas 1 and 2.

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However, even if the ideal numerical modellingtool existed, proper instrumentation, recording, andinput of the field data needs to be done. Instrumen-tation data needs to be available in near real-time,entered automatically into databases, and transferredto numerical models. The ideal system would con-stantly record data so that no sudden changes in dis-placements were missed. This would requireautomated remote data collection that is promptlyconveyed to computers on surface. Mining opera-tions do not have sufficient personnel to providemanual reading of instruments of the quality requiredfor the proposed analysis.

If such a numerical package existed and if instru-mentation data were routinely updated and recorded,the goal of using such a tool would be predictive for-ward modelling of ground support. That is, once themodel was calibrated using a procedure similar tothat described in this paper (albeit with more directlyrelevant numerical tools) and the rock mass parame-ters up to failure and in the post-peak were deemedsufficiently reliable, forward modelling could be usedto predict the behaviour of the rock mass and groundsupport prior to mining in a given area. This opens upa huge potential for cost savings for mine operations.Forward modelling can lead to better support design.Different types of support can be tried out in modelsat almost zero cost. Different timing of support instal-lation, depth of support, etc. could be studied to min-imize support cost, while minimizing the potential forsupport rehabilitation. Forward modelling of the typediscussed would be expected to lead to improvedoverall mine design. For example, different sequenc-ing strategies could be tested. The impact of miningstrategies that result in unwanted pillars can be inves-tigated and hopefully the foresight provided by sucha model can minimize the chance that ore will be ster-ilized due to unexpected ground failure.

CONCLUSIONS

All of the goals that were discussed in the previ-ous section are currently technically feasible. How-ever, the combined use of tools that are currentlyavailable to mining professionals to achieve thesegoals are far too labour and/or computationallyintense. Additionally, these techniques today require avery high level of technical expertise. Should appro-priate numerical tools be developed, calibrated for-ward modelling of the mining process can lead toimproved intelligent mine design. While more engi-neering time would have to be spent on monitoringand mine design, if the amount of rehabilitation ofmining drifts could be reduced, then overall miningcosts could be greatly diminished and the return oninvestment would be substantial.

With these proposed new tools and upgradedmonitoring systems, real-time mine modelling couldbe performed, whether in-house or via contracts. Theadvent of wireless instruments and real-time to-sur-face monitoring, combined with internet technology,could mean that the mine instrumentation and mod-

elling for all mines for a given company could be per-formed at a central site or by a third party. Microseis-mic monitoring provides an additional mine-widemonitoring system to assist in validation of the loca-tion of failure predicted by the numerical models.

The key to post-peak rock mass parameter cali-bration is to ensure high-quality instrumentationdata. The frequency of readings, as already discussed,is of prime importance. It would also be imperative toinstall instrumentation as soon as the mining driftsare excavated. The models discussed in this paperonly showed displacements relative to when theinstruments were actually installed. The modellingresults also showed, in some cases, large amounts ofdisplacement prior to installation of the instruments.Perhaps the routine installation of wireless instrumen-tation should be part of the mine developmentprocess.

To summarize, the procedures outlined in thispaper highlight the need for a new hybrid numericalmodelling package that can use the influence ofthree-dimensional mining-induced stresses to predictdisplacements in, and potential failure of, rock massessurrounding mining infrastructure in order to radicallyalter strategic and tactical mine design. The earlyinstallation of high-quality, real-time automatedinstrumentation is required for forward modelling ofthe mining process. A critical problem is that thereexists only a small market to drive this innovation. Anindustry-wide strategy would be required to fundsuch an ambitious project.

ACKNOWLEDGMENTS

The research program described in this paper,which occurred at the University of Toronto, wasfunded by the Natural Sciences and EngineeringResearch Council of Canada (NSERC) and the W.M.Keck Foundation in support of the Digital Mine Pro-ject. Sincere gratitude is extended to Williams Oper-ating Corporation for permission to use and publishdata for this research. The authors also expressacknowledgement to A. Coulson of the University ofToronto for his work in building the Autocad modelsand his input toward the paper. Acknowledgementsalso are given to J.H. Curran of the Lassonde Institute,to the staff of Rocscience Inc., to our colleagues atthe University of Toronto, and to P. Lausch and J. Todof Mine Design Technologies Inc.

Paper reviewed and approved for publication by theRock Engineering Society of CIM.

Jason Crowder graduated from Queen’s University with aB.A.Sc. in geological engineering and a PhD from the University ofToronto in mining/civil engineering. After his PhD, he was a post-doctoral researcher at the Lassonde Institute, University ofToronto. He has worked for BGC Engineering (Vancouver), GolderAssociates Ltd. (Mississauga), and is currently a geotechnicalengineer with Terraprobe Ltd. (Brampton).

William F. Bawden graduated with a B.A.Sc. in geologicalengineering from Queen’s University in 1970, an M.Sc. from theUniversity of Illinois at Urbana in 1972, and a PhD in rockmechanics in geotechnical (civil) engineering from the University

Rock Engineering

of Toronto in 1980. Following a period as head of mininggeomechanics at the Noranda Technology Center, he returned toacademia. He is presently a professor and the director of theLassonde Mineral Engineering Program at the University ofToronto.

Adam L. Coulson graduated in 1990 from the Camborne Schoolof Mines, England, with a B.Eng. (honours) degree in mining

engineering and later received a M.Sc.Eng. from the miningengineering department, Queen’s University at Kingston. He hasworked as a consultant for the Engineering Seismology Group(ESG) Canada Inc. and as a rock mechanics engineer andresearcher with Noranda Inc. Mr. Coulson is currently pursuing hisPhD with the Lassonde Institute, in the Department of CivilEngineering at the University of Toronto, and acts as anindependent consultant to the mining industry.

8 Copyright © 2007. All rights reserved. ISSN 1718-4169 CIM Bulletin n Vol. 100, N° 1100

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