The Estimation of Post-Peak Rock Mass Properties:

Numerical Back Analysis Calibrated using

In Situ Instrumentation Data

Jason J. Crowder, Ph.D., and William F. Bawden, Ph.D., P.Eng. Lassonde Institute, Department of Civil Engineering, University of Toronto

February 2006

The Estimation of Post-Peak Rock Mass Properties:

Numerical Back Analysis Calibrated using

In Situ Instrumentation Data

Jason J. Crowder, Ph.D., and William F. Bawden, Ph.D., P.Eng. Lassonde Institute, Department of Civil Engineering, University of Toronto

February 2006

Executive Summary A significant component of underground mining costs stems from ground support in the form of rock bolts, mesh and screen, cable bolts, and shotcrete. Should any of this support approach or reach failure (stripped or broken cable bolts, severe bagging of screen, large numbers of broken rock bolts, etc.) then the support needs to be rehabilitated. This rehabilitation is often much more expensive than the initial support installation, due not just to the cost of the support, but to loss of access, down-time of that area of the mine, potential for injuries, and possible lost mining revenues. Many mines use instrumentation in critical infrastructure, such as haulage drifts, crusher stations, intersections, etc., to monitor the displacement of the backs and/or walls, support loads, etc. Data is generally collected by hand from time-to-time and entered into a database, but is analysed only if there is a problem (i.e. reactive engineering). Most mines today also utilize numerical modeling. These models, normally linear-elastic, are often not up to date and modeling is often done only in reaction to a problem.

In certain cases modeling of the underground mining environment requires software packages that employ non-linear constitutive models (i.e. models that allow for failure to occur). Linear elastic models unrealistically allow for stresses to build up far beyond those at failure and hence do not redistribute stresses away from failed zones. The challenge with non-linear models is that they require the input of generally unknown post-peak material properties and behaviour. Models must also be three-dimensional in order to capture the full state of mining-induced stress conditions due to the complex mine geometry.

Research at the University of Toronto has developed a technique to link between the three-dimensional linear-elastic mining-induced stress problem and two-dimensional non-linear modelling that accounts for the three-dimensional stresses from mine-wide models and allows for failure to occur. This new modeling technique has been used to explore the rock mass post-peak properties through back analyses at a case study mine. The rock mass ‘post-peak’ parameters have been calibrated in a back analysis fashion using SMART cable bolt data of displacements in mining haulage drives. The key result from back analyses demonstrates that for two areas of the case study mine (separated by almost 500 m in depth, but found in the same rock unit) the post-peak Generalized Hoek-Brown value of mr must be reduced significantly to simulate displacements observed in instrumentation data.

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Failure patterns predicted by the models using the calibrated parameters have also been verified using the spatial distribution of observed microseismic events over the same time spans.

High-quality instrumentation data is the key to post-peak rock mass parameter calibration. The procedures outlined in the paper highlight the need for a new hybrid numerical modelling package that can use the influence of three-dimensional mining-induced stresses to predict displacements in, and potential failure of, rock masses surrounding mining infrastructure in order to radically alter strategic and tactical mine design.

With high quality estimates of field-scale rock mass post-peak characteristics and stress-strain behaviour, improved confidence in explicit forward modelling of ground support can be gained. This will ultimately aid in the design and optimization of rock mass support and minimize rehabilitation, hence significantly reducing mining costs. Reliable determination of ‘post-peak’ rock mass properties, using techniques described in this paper, will improve reliability in underground mine design, as well as increase safety for mining personnel. Having high quality and reliable instrumentation that is routinely monitored and analysed is critical to being able to perform the work described here. Research is currently heading toward real-time wireless monitoring of instruments which can then also be fed into models in real-time.

NOTE that this article has been adapted from two papers:

Crowder, J.J., Coulson, A.L., and Bawden, W.F. 2006. The Field-Scale Rock Mechanics Laboratory: Estimation of

Post-Peak Parameters and Behaviour of Fractured Rock Masses. In Proceedings of the 41st U.S.

Symposium on Rock Mechanics (USRMS), Golden, CO, (CD-ROM) Paper Number 06-0926 (to appear).

Crowder, J.J., Bawden, W.F., and Coulson, A.L. 2006. Innovative use of SMART Cable Bolt Data through

Numerical Back Analysis for Interpretation of Post Failure Rock Mass Properties. CIM Bulletin (submitted

for review).

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Introduction

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

Most ground support elements are installed as dowels – un-tensioned tendons (e.g. passive cables, rebar, etc.). The issue here is that support is only provided when sufficient dilation or movement of the rock mass has occurred to generate resisting tensile forces in the support element. Significant stress-driven movement only occurs in a rock mass after the peak strength of the rock has been exceeded and it is well into a state of yield or failure. In other words, based on experience, stress-driven ground movements are not sufficient to load the support to any significant amount prior to yield of the rock mass. In DeGraaf et al. (1999), instrumentation data indicated that displacements seen in instrumented cable bolts were not significant up to model-predicted failure, and hence the cables never took any measurable load to that point. In other cases, support has been loaded to failure as shown by broken cables. In such cases, in the author’s experience, numerical models always indicate that elastic stresses in these regions significantly exceeded the peak values allowed by the constitutive model that was applied.

In order to improve underground mining infrastructure support behaviour and reduce costs associated with over-design and rehabilitation due to under-design, there needs to be better modelling capability of support behaviour prior to design and installation. Hence the need exists to model the rock mass behaviour well past the point of failure, into the post-peak regime – not just the typical elastic stress modelling that often occurs in mining today (Crowder and Bawden 2004). Most importantly, models need to be able to calculate displacements that occur due to failure, with a high degree of confidence (something generally not possible today), as displacement up to the point of failure is almost negligible. To accomplish better modelling, improved instrumentation data is required for calibration of rock mass properties, particularly post-failure or post-peak parameters. In order to accomplish this, field case studies having adequate numbers of high-quality instruments and frequency of readings are required.

This paper examines the current state of modelling and instrumentation in mining. An assessment of some typical problems with how instrumentation is monitored and used, as well as how good data can be quite valuable is shown. An overview of typical mine modelling procedures will be given, followed by a look at what types of models are required, and what input is necessary, for predictive forward modelling. A case study then demonstrates, through a back analysis, how high-quality instrumentation and monitoring can help with the estimation of the post-peak (post-failure) rock mass parameters required for a comprehensive analysis.

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The Rock Mechanics Problem

Rock mechanics is now a mature field of study, many aspects of which are well understood. To this end, the modelling capability for mining applications is also quite mature and sophisticated. In fact, the complexity and capability of models often significantly exceeds our ability to generate reliable rock mass parameters, particularly in the post peak regime (after failure). That is, once a rock mass has reached failure, it can still maintain some post-peak or residual strength. If rock mass parameters for post-failure conditions were well developed for given types of rock and stress conditions, then explicit forward modelling of rock mass support could be performed.

The ability to accurately predict the post-peak parameters of in situ rock masses is very much a black-box art at this point. Engineers often rely on the suggestions of colleagues and rules of thumb. There has been considerable debate as to how to alter the post-peak parameters of rock masses, as was discussed amongst several industry leaders and disseminated by Crowder and Bawden (2004). In that paper, the Generalized Hoek Brown failure criterion (GHB) (Hoek et al. 2002) was exclusively discussed as it is currently the most often used criteria for underground rock mechanics studies. The consensus was that the Geological Strength Index (GSI) (Hoek et al. 1995) and the Disturbance factor (D) (Hoek et al. 2002) are index parameters that are used to determine reasonable estimates of the peak strength parameters and should not enter into the determination of post-peak strength. Similarly, the unconfined compressive strength of intact rock samples, UCS or σci, and Hoek-Brown parameter mi are both properties of intact specimens determined from laboratory testing and hence should not be altered for determination of post-peak rock mass parameters. Thus, the consensus was that to effectively model the behaviour of a rock mass, any numerical model should have the option to enter peak and post-peak (elastic and plastic) values for mb, s, and a.

Although a consensus was reached, there still was considerable debate amongst these industry leaders, inferring that much research remains to be completed toward the reliable estimation of post-peak rock mass parameters. One methodology to look at this problem is discussed later in this paper.

Present State of Modelling and Instrumentation in Mining

Most mines today utilize numerical modeling as part of their strategic and/or tactical mine design efforts. These models, normally linear elastic, are often not up to date and modeling is often done only in reaction to a problem. There are some instances in which non-linear models are used, but the input parameters for the post-peak characteristics of these rock masses are generally guessed at, or some rule of thumb is followed. The most common form of analysis is to examine the results of stresses calculated by the models. If the model is elastic, then the model may calculate stresses that are much higher than a rock mass can sustain, as determined by the chosen failure criterion. The strength factor, the ratio of the maximum stress allowed by the failure criterion to the current state of stress (e.g. a strength factor less than one can be interpreted as ‘failed’), is the only result that is examined. The region of strength factor that shows ‘failure’ – often referred to as the yield zone (Figure 1) – may be used as a basis for how deep rock mass support should extend and how much reinforcement to add. However, this yield zone is not necessarily the best representation of where failure of the rock mass occurs. Using a non-linear model with perfectly-plastic post-peak parameters, the extent of the failure

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zone may be quite similar to what is predicted by the yield zone from elastic models. However under strongly strain softening conditions, non-linear models can exhibit different shapes and extents of failure zones than those from elastic models. Furthermore, displacements from elastic models are not considered valid and are hence generally not used.

However, accurate estimates of displacements are exactly what is required for support design. Mining openings are often designed to be only as large as necessary to accommodate equipment and services, since any larger openings cost more and are more difficult to support. Excessive deformations can destroy support that is costly to rehabilitate, can cause falls of ground resulting in delays or injuries, and ultimately may impact equipment access.

Predicted Yield Zone

Figure 1. Predicted ‘yield zone’ (shown in orange) from a linear-elastic Examine3D model. The yield zone is predicted (in this case) where the strength factor is less than 1.2. That is, the stresses in this zone are predicted by the model to be higher than the rock mass can support.

Most mines use instrumentation in critical infrastructure, such as haulage drifts, crusher stations, intersections, etc., to monitor the displacement of the backs and/or walls, support loads, etc. These instruments, however, are often installed long after the initial access excavation has been created – and often just before the mining front progresses through a particular area. The trouble with this approach is that the total accumulation of displacements, and hence damage, cannot be known to any degree of certainty. As well, data from the instruments are generally collected by hand, from time-to-time and entered into a database. The frequency of readings depends on whether or not a problem has been spotted, by how much time the engineer has to collect data, or by whether the mining front is approaching. The best way to collect data however is on a regular schedule, whether or not movement

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is anticipated. The other problem with instrumentation data today is that it is analysed only if there is a problem (i.e. reactive engineering). In summary, if instrumentation is to be used to aid in the design process at a mine for prediction purposes, high-quality and consistent data are required.

Basic Modelling Approach

Research at the University of Toronto has looked into the problem of what post-peak rock mass parameters should be used to reasonably represent the rock mass. This was accomplished using quality instrumentation data from one case study mine, in a back analysis mode using numerical modelling. The details of the methodology and the verification can be found in Crowder and Bawden (2005).

In order to accomplish the goals of this research it was decided that the best approach would be to use software that was readily available to the public, and software that was already familiar to the general mining and engineering fields. This meant, however, that there was no single program that could accomplish the required modelling (with reasonable computational speed), as a three-dimensional program that incorporates support elements (that were necessary for this case study) and allows for rock mass failure did not exist. Although existing three-dimensional finite element codes can handle mine-wide models, none that were familiar to the authors incorporate the required bulged cable bolt models. Even if these codes had the required bolt models, with the fineness of mesh required, such codes would have prohibitive computational run times. For these reasons, Examine3D and Phase2 were chosen for a hybrid approach.

Phase2 is a two-dimensional finite element code. It includes the required bulged cable bolt model (Moosavi et al. 2002) and does allow for the input of post-peak rock mass parameters, as well as failure of the rock mass. To overcome the two-dimensional limitation of Phase2, the ‘far-field’ (and assumedly) elastic mine-induced stresses were calculated by Examine3D, for a given stage, and were then imported as tractions onto a two dimensional slice of the model in Phase2. A typical example of a mine-wide Examine3D model is shown in Figure 2(a), while a close up of an area of analysis, as well as the mining drifts and analysis points are shown in Figure 2(b). Figure 3 demonstrates the results of Examine3D models on the left (for one given plane), and the corresponding applied stresses (as tractions) to Phase2 models on the right. Note how the three-dimensional stresses and two-dimensional tractions change in each time-step from the top to the bottom of the figure. The following paragraphs will explain the overall methodology.

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(a) (b)

Figure 2. (a) Mine-wide three-dimensional model in Examine3D. Each stope is coloured according to its mined year. (b) Three-dimensional view in Examine3D of a mine model showing the location of analysis points (spheres) where stresses are calculated for export to Phase2.

The first step in this modelling procedure is to find an instrument in an area of interest at the mine that has excellent data over a range of time and mining steps. Choose time steps throughout the instrument’s data (time steps should show appreciable displacements) that will be used as the time steps in the modelling. Create three-dimensional numerical models in Examine3D corresponding to those time steps. Take a geometry slice through the entire model through the location of the instrument. Import the geometry into Phase2 and setup the model with all excavations, boundary conditions, rock mass parameters, etc., except for field stresses (which should all be set to zero).

The model should be set up, using a material boundary to enclose a rectangular area around the chosen mining drifts and passing through the selected instrument(s), as a block of rock with no external or gravity forces. One corner of the model should be pinned, with one vertical boundary fixed in the x-direction and the bottom boundary fixed in the y-direction. The top boundary and the other vertical boundary should be free. These two boundaries are where the stresses will be applied. There should be several stages to the model, first to allow the model to come to equilibrium at the initial stresses, and then one stage for each time-step as required. Determine exactly where stresses should be calculated (by Examine3D) for input into the Phase2 model (along the two free boundaries, also called the fictitious material boundary). Stress calculation points, where tractions will be applied in Phase2, should be about 2 m apart. Details are shown in Figure 4.

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(a) (b)

Figure 3. (a) Examine3D results showing the effects of mining stopes creating three-dimensional mine-induced stresses on one chosen plane of interest (showing σxx only). (b) Corresponding boundary stresses (tractions) applied to the Phase2 model in the vicinity of the mining drifts. Also note the fineness of the finite-element mesh.

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Material boundary fixed in y-dir.

Fixed external boundary

Material boundary fixed in x-dir.

Nodes are not fixed, but have tractions (stresses) applied

Bulged cable bolts, rockbolts, and shotcrete around drift openings

Material boundary fixed in y-dir.

Fixed external boundary

Material boundary fixed in x-dir.

Nodes are not fixed, but have tractions (stresses) applied

Bulged cable bolts, rockbolts, and shotcrete around drift openings

Figure 4. Typical setup of Phase2 model showing the boundary conditions, the application of tractions representing the state of three-dimensional mine-induced stresses as calculated by Examine3D, and rock mass support of the mining drifts.

Return to Examine3D, and set up field points in each of the models so that when computed, the results will show the full stress tensor at points that correspond to the fictitious material boundary in the two dimensional model. Apply the computed stresses to the appropriate stages in the Phase2 model, either (very tediously) by hand, or by creating a program that automates that process.

Run the Phase2 model with the post-peak parameters of the rock mass set to perfectly plastic (post-peak parameters equal to the peak parameters). Check the calculated displacements in the model against those shown by the instrument in the field. If the calculated values are not deemed reasonable, then return to the Phase2 model and alter (reduce) the post-peak parameters, run the model and compare again. Repeat as necessary, likely through a parametric analysis, until reasonably comparative displacements are calculated by the Phase2 model.

Three-dimensional mining-induced elastic stresses have been obtained at the case study mine for incremental mining steps over several years using the elastic boundary element numerical analysis program Examine3D. Since this type of model can only represent one time step, several models were created to represent relevant time steps in the mine’s history, corresponding to certain times where the instrument data indicated change. For each mining step (i.e. for each Examine3D model), the stress state over a two-dimensional slice through the three-dimensional model at the location of the instrument was exported into the two-dimensional finite element analysis program, Phase2. This program allows for the rock mass to fail (i.e. it is non-linear) when stresses exceed the chosen failure criterion. Also unlike Examine3D, it allows for the explicit integration of rock mass support (such as cable bolts, rock bolts and shotcrete) directly in the model.

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After the model was created, the peak rock mass parameters were defined using the Generalized Hoek Brown (GHB) failure criterion, and the post-peak rock mass parameters were adjusted through a parametric back analysis until displacements above the back closely approximated those observed in the field from the instrumentation. Refer to Crowder and Bawden (2004) for a discussion of the importance of post-peak parameters and some guidelines on related rules of thumb.

Case Study

The case study involves The Williams Mine, which is located near Marathon in the Hemlo region of northern Ontario (Figure 5). The ore body dips to the north at about 70 degrees and ranges in thickness from 3 to 50 m over the full strike length of the ore body (~1.5 km). The majority of infrastructure development occurs in the footwall, which is for the most part composed of quartz-eye muscovite schist (Bawden et al. 2000). More details of the ore extraction methods, of drift support, and other information about the mine can be found in Crowder and Bawden (2005), and Bawden and Lausch (2000).

Williams Mine

Toronto

Ontario

Sault Ste. Marie

Thunder Bay

Figure 5. Location map of the Williams Mine in Northern Ontario.

The Williams Mine primarily uses two types of instrumentation to monitor vertical movement in the backs of mining drifts. The SMART (Stretch Measurement for Assessment of Reinforcement Tension) cable bolts are instrumented to accurately assess the deformations that occur in the cable support elements (Bawden and Lausch 2000). The MPBX (Multi-Point Borehole Extensometer) is a flexible borehole extensometer that passively measures the deformation of the rock mass itself. That is, it provides no reinforcement in contrast to the SMART cable bolt. Both instruments are manufactured by Mine Design Technologies Inc., Kingston, Ontario.

The instrumentation database for the Williams Mine, at the time of this study, had just over 200 SMART cable bolts and MPBXs combined. The case study described in this paper, however, only deals with two specific areas of the mine in which about 95 instruments are located. Although there are seemingly plenty of instruments that could be used in the back analysis, only about 10 were really usable. A few of the instruments were installed in areas well away from the stopes and hence show little movement. Other instruments were installed after a majority of the mining in the area was already

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completed. Many of the instruments were installed at different times throughout the study period (1999 – 2003), and hence a complete record through time at a given location did not exist. As well, other instruments exceeded the displacement capacity (of the instruments) and replacement instruments were installed after a time gap. One of the biggest problems with the instruments was an inadequate frequency of readings (for the purposes of this type of analysis). This is because all of the instruments are read by hand whenever mining personnel have the time to get to the instruments. Hence large gaps sometimes occur in the data, as shown in Figure 6. An example of one of the most reasonable, continuous data sets from an instrument at Williams Mine is shown in Figure 7. All of these instrumentation problems cite the need for real time acquisition of data from instrumentation. As well, instruments should be installed early on in the mining process – not just when the mining front passes a given area – so that a continuous, reliable set of data exist for monitoring and analysis. An example of a continuously monitored instrument that captures exactly when displacements occur in reaction to mining in the vicinity of the instrument is shown in Figure 8.

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Figure 6. Example of instrumentation data with a large gap in-between readings.

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Figure 7. An example of good quality instrumentation data from Williams Mine.

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Figure 8. Example of excellent quality instrumentation data. Notice the response of the instrument to the arrows which indicate timing corresponding to proximate blasting.

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Case Study Analysis

This section details the results of the back analysis procedure in two separate locations at the Williams Mine. The first location (Area 1) is a large shrinking pillar of high-grade ore located in the upper east corner of the mine (Cells 1 and 2) at a depth ranging from about 400 to 600 m and is about 200 m in strike length. Mining has occurred above, below, to the west and to the east of this area. The specific study area within this zone occurs on two levels, at about 550 m depth. The other area of interest (Area 2) occurs in what is known as the Sill Pillar (in Cell 5), which is about 80 m in height and was created as the mine originally extracted ore from two main blocks above and below this region. This pillar is located at an average depth of about 950 m. A long section of the mine showing the general locations of analysis are is given in Figure 9. All of the instruments in the study are located in the main haulage drifts that parallel the ore in the footwall rock unit. This unit is thought to be fairly consistent over the depth of the mine, except in the upper west regions of the mine – far from these study areas.

Area 2

Area 1

Area 2Area 2

Area 1Area 1

Figure 9. Long-section of the Williams Mine showing the cell arrangement and the two areas of analysis described in this paper.

In the late 1990’s mining started in the sill pillar (Area 2) and there began to be indications of mining stress induced problems such as back failures and rock bursts (Bawden and Lausch 2000, Bawden et al. 2000). Because the consequences of failure in mining infrastructure are large, the drifts were heavily supported with a combination of primary support (rock bolts, resin rebar, mesh, and/or shotcrete) and deep secondary support in the form of twin-strand cable bolts (two cable bolts in one bore hole). In 1999, the first instrumentation was installed in the sill pillar. The instrumentation of

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interest to this study are the SMART cable bolts that were installed vertically in the drifts at the cross-cut intersections to the stopes, both in Areas 1 and 2.

The haulage drifts at Williams mine are generally excavated to about a 5 m x 5 m square cross-section. Primary support in the drifts consists of resin rebar at 1.1 x 1.1 m spacing, along with 6-gauge welded wire mesh that is covered by a 7.5 cm layer of shotcrete that extends from floor to floor. Deep secondary support is provided in the back by twin-strand, modified Garford bulb cable bolts (Moosavi et al. 2002), which are installed at a spacing of about 1.5 m in-plane and 2.0 m out-of-plane.

In Phase2, the resin rebar has been installed using the fully bonded bolt model. The bolt diameter is 19 mm, the bolt modulus is 200000 MPa, with a peak capacity of 120 kN and no residual capacity. The Garford bulb cable bolts were installed using the Queen’s University plain strand cable model with 6 bulbs added at equal spacing. The twin strand cable bolts were hence represented by the following properties: a bore hole diameter of 63.5 mm, cable diameter of 21.55 mm, cable modulus of 206000 MPa, a peak capacity of 470 kN and a water:cement ratio of 0.35. The shotcrete and mesh layer is modeled in Phase2 as a single liner with the following composite properties: thickness of 75 mm; Young’s Modulus of 30000 MPa; Poisson Ratio of 0.2; a peak and residual compressive strength of 35 and 5 MPa, respectively; and a tensile peak and residual strength of 5 and 0 MPa, respectively.

At Williams Mine, the majority of the development drifts are in the footwall rock. For the purpose of this study, the rock mass properties that will be used in Phase2 and Examine3D will hence be based on this rock unit. In 1990, Kazakidis (1990) completed a rock mass classification study at the adjoining Golden Giant mine, which can be considered representative of the rock mass at the Williams Mine. Kazakidis followed the rock mass classification systems of Q (Barton et al. 1974) and RMR (Bieniawski 1976), and found that the value of Q for the footwall varied from about 5 to 9.5. These values translate to a GSI of approximately 58 to 64, averaging 60. These values correspond well to field observations at Williams Mine (W. Bawden, Pers. Comm. 2005). Kazakidis (1990) also surveyed all laboratory tests relating to the two mines and determined that the average unconfined compressive strength was about 175 MPa.

To define the rock mass properties in the model, Phase2 requires the UCS, dilation parameter, and the Hoek-Brown mb and s (peak and residual). The average value of the GSI = 60 was used to calculate the peak rock mass values of mb and s, as well as the Young’s Modulus, all according to the relationships detailed in Hoek et al. (2002). To calculate mb, an estimate of mi is required. Hoek et al. (1995) provides an estimate of mi = 10 for similar rock. A parametric analysis, carried out by Crowder and Bawden (2005), confirmed that using these average values for the rock mass was a reasonable approach. Using these values, and using the appropriate GHB equations, the rock mass peak input parameters to Phase2 are: Young’s Modulus = 17800 MPa, mb = 2.397, s = 0.0117, and a = 0.503. The GHB parameters mb, s, and a, are all unitless.

Since the estimated peak rock mass parameters were well established for this rock by previous studies, the task then became to iterate in a back analysis to determine what appropriate post-peak parameters were necessary for the model to closely simulate the displacements observed in the field from the instrumentation. The parameters to vary in the post-peak are the ‘residual’ values of mb and s, which are denoted by Phase2 as mr and sr, respectively. The dilation parameter must also be varied.

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In the first case study area, near the Cell 1 and 2 boundary in Area 1, three different instruments were examined using the back analysis procedure. A parametric study was used to independently adjust each of the three post-peak parameters from the peak value to a value approaching zero that still allowed for the model to compute – i.e. not to the point of numerical instability. That is, the residual GHB mb parameter was varied as 0 < mr < mb, or 0 < mr < 2.397; the GHB parameter sr was varied as 0 < sr < s, or 0 < sr < 0.0117; and dilation was varied as 0 < dil < mb, or 0 < dil < 2.397.

A series of time steps were chosen such that nearby mining had caused significant mine-induced stress redistribution and hence progressive failure and displacement within the rock mass. The observations from the instrument at this location are shown at the chosen time steps, as a plot of vertical displacement of the back with distance into the back (i.e. above the drift) (Figure 10). Each line represents a different time step.

Results showed that in order to most closely simulate the observed displacements the value of mb was reduced to a post-peak mr = 0.24, or 10% of the original value. The value of s was not reduced, such that a post-peak sr = s = 0.0117. The dilation parameter was set to 0. When these parameters were applied, the resulting calculated displacements are shown for the same time steps as was used for the instrument. The modelling results overlaid on the instrument data are shown in Figure 11. It must be noted that any displacements that occurred in the model prior to the step corresponding to the installation of the instrument have been zeroed out using the relative staging function in Phase2. Hence the modelling results shown in Figure 11 can be directly compared to the instrument data for the same time intervals.

9735 #5 - MPBX Instrumentation DataRock Mass Vertical Displacement, Relative to Toe

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E = 17800 GPa; ν = 0.25

Figure 10. Instrumentation data (MPBX) from Area 1 that is used for calibration in the back analysis procedure.

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9735 #5 - Run 12b2 - mr = 0.10mb, s dil = 0

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Figure 11. Results of the back analysis performed in Area 1 (at the same location as the instrument) overlaid on top of the instrumentation data. This is considered a reasonable fit.

For the second location (Area 2 - the sill pillar), a back analysis was performed in a similar fashion to the results presented previously. Again, the post-peak parameters that best simulated the observed field displacements were mr = 0.24, or 10% of the original value, and the value of s was reduced to a post-peak sr = 0.0059, or about 50% of the initial peak value. The dilation parameter was set to 0.8, or about one-third of the value of mb (Crowder and Bawden 2004). The modelling results overlaid on the instrument data are shown in Figure 12. The general results from the two regions of the mine are summarized in Table 1.

Figure 12. Results of back analysis in Area 2 compared with observations from an instrument at the same location.

9390L #26 - Run 12f: mr = 0.10mb, sr = s, dil = 1.2Rock Mass Vertical Displacement, Relative to Toe 1999-12

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SMART 2002-03

SMART 2002-09

INITIAL ROCK MASS PEAK PARAMETERSσci = 175 MPa; GSI = 60; mi = 10; mb = 2.397; s = 0.0117; a = 0.503

E = 17800 GPa; ν = 0.25

2001-08

2001-12

2002-05

2002-08

MPBX 2001-08

MPBX 2001-12

MPBX 2002-05

MPBX 2002-08

INITIAL ROCK MASS PEAK PARAMETERSσci = 175 MPa; GSI = 60; mi = 10; mb = 2.397; s = 0.0117; a = 0.503

E = 17800 GPa; ν = 0.25

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Table 1. Summary of the general back analysis results from the two regions showing the range of post-peak parameters that best simulated the displacements observed in 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 ⅓ mb < dil < ½ mb

For the parametric study, the effect of changing just one of the parameters at a time was examined. Changing the parameter, mr, seemed to have the most significant effect of increasing the depth of failure. As mr decreases, the magnitude of displacement at a given depth increases. Changing the parameter sr did not seem to significantly affect the depth of failure. In general, as sr decreases, the magnitude of displacement increases very slightly. The effect of changing the dilation ‘parameter’ had only a minor effect on depth of failure. As the dilation increases, generally the magnitude of displacement increases.

The key result of this study is that both areas of the mine require the GHB post-peak value of mr to be reduced significantly from the peak value. This suggests that after failure, the rock can only sustain a small fraction of it’s elastic shear strength. The difference in values of sr is not considered of great importance, as this value does not have a large impact on the failure criterion (especially at higher levels of confinement), does not affect the depth of failure, but does (only slightly) increase the magnitude of displacement in the models. Given the small impact of sr on the displacements and failure envelope, the range of post-peak parameters is quite tight considering that, although both areas of analysis are in the same footwall rock formation, there are some variations in this unit over the 500m (vertical) that separate the areas (Figure 9).

Using the values that best simulated the displacements observed by the instruments (0.10 mb and sr = s), the amount of failure around the drifts is shown in Figure 13. The pattern of the anticipated failed elements is driven by the geometry of mined-out stopes in the sill pillar. On-going research at the University of Toronto is investigating the nature of seismic events at the Williams Mine, with specific interest also in Area 2. The pattern, or spatial distribution, of seismicity in this area, as demonstrated in Figure 14, is strikingly similar to the anticipated distribution of failed elements shown in Figure 13. This observation serves as another form of verification of the chosen peak and post-peak rock mass parameters in the back analysis procedures described in this paper.

This back-analysis modelling procedure, using Phase2, and analysis using MS Excel, can also produce some other interesting results. For example, once confidence has been gained with the peak and post-peak rock mass parameters, the changing stresses and displacements at a given location above the mining drift can be tracked throughout each stage. Plotting these two sets of data together, as demonstrated in Figure 15, can create synthetic stress-displacement curves through the complete stress-strain history. The effect of different post-peak parameters will obviously affect these curves significantly. At the same time, the changing stress states at given points in the rock mass can be used to track the stress history (stress path), as shown in Figure 16. Hence, the power and knowledge gained by understanding the best estimated post-peak rock mass parameters is quite important.

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Figure 13. Results of analysis in Phase2 showing the maximum principle stress (σ1) contours as well as failed elements in Area 2. Notice the pattern of failure that is outlined.

Figure 14. Seismic events recorded at the same location as the previously described numerical back analysis in Area 2. Note that the pattern of seismic events trends much like the failed elements predicted by Phase2 (Figure 13).

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Run 12b - mr = 0.10mb, dil = 0sr = s,Behaviour At Different Positions into the Back

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0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020

Displacement (m)

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or P

rinci

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ss (M

Pa)

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INITIAL ROCK MASS PEAK PARAMETERSσci = 175 MPa

GSI = 60mi = 10

mb = 2.397s = 0.0117a = 0.503

E = 17800 GPaν = 0.25

Distance into the Back (m)

Figure 15. Results from Phase2 demonstrating the ability to track the stress-strain of the rock mass at different locations. Note that this particular example shows the behaviour from the same numerical run as shown in Figure 11.

9390L #26 - "7th" - Run 12f: mr = 0.10mb, sr = s, dil = 1.2 Stress Paths of the Rock Mass at Different Depths

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0 10 20 30 40 50 6

Minor Principle Stress (MPa)

Maj

or P

rinci

ple

Stre

ss (M

Pa)

0

0

0.5

1

2

4

GHB Peak Strength

POST PEAK

INITIAL ROCK MASS PEAK PARAMETERS

σci = 175 MPa, GSI = 60, mi = 10mb = 2.397, s = 0.0117, a = 0.503

E = 17800 GPa, ν = 0.25

Distance into the Back (m)

Figure 16. Results from Phase2 demonstrating the ability to track the stress path of the rock mass at different locations. Note that this particular example shows the behaviour of the rock mass with the post-peak value of mr set to 10% of the peak mb.

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Discussion

The results shown in the previous section indicate that the potential exists for numerical modelling to actually predict displacements, and hence support loads, seen in the field. However, at this point, an analysis must be completed at each given mine, as the results shown in this paper are very specific to the rock mass at the Williams Mine. In fact, the post-peak parameters determined in this study may not be the ultimate best estimate for the post-peak parameters for this rock mass. However, these values provide very reasonable results given the inherent uncertainty of the input parameters and with the use of a continuum model for a discontinuous rock mass. Most importantly, these results demonstrate that the numerical modelling and back analysis processes have been shown to be effective.

The procedures that were used in this study are quite labour intensive and took several months to complete. With that said, if numerical tools could be developed to automate or improve the usability of this process, the modelling would not be a huge undertaking. As the models currently exist, they are easy to use and do an excellent job for purposes for which they were designed, but each one on it’s own cannot handle the complex problems addressed in this paper. New tools need to be developed to handle all the issues in one numerical package. Such a program should integrate rock mass support whenever possible using the most appropriate support constitutive models (e.g. Moosavi et al. 2002 for cable bolts). The ideal numerical modelling tool would be some sort of hybrid using the ability of three-dimensional elastic models to generate mine-wide models and associated elastic mine-induced stresses, combined with the ability of non-linear models to use post-peak parameters and generate failure while including explicit models of rock mass support.

It is necessary at this point to mention that the approach taken by the authors was in fact to illustrate the point of the power of numerical tools combined with excellent quality instrumentation data. There exists other brands of numerical tools that solve parts of the problems in much the same manner as the Rocscience tools. Three-dimensional finite element, finite difference and distinct element packages that can run mine-wide models and incorporate rock mass support exist. However, for a number of reasons these programs were not used. Because of the scale of the mine wide model required to obtain appropriate global mine induced stress change combined with the accuracy and detail required for the back analysis, computation times would be excessive. Additionally, the only numerical model that incorporates the correct bulb cable constitutive behaviour [one of the key instruments used] is Phase2. It is the author’s opinion that a hybrid approach is better suited to this type of problem.

However, even if this numerical modelling tool existed, proper instrumentation, recording and input of the field data must be done. Instrumentation data needs to be available in near real-time, entered automatically into databases and transferred to numerical models. The ideal system would constantly record data so that no sudden changes were missed. This would require automated remote data collection that is promptly conveyed to computers on surface. Mining operations do not have sufficient personnel to provide instrument reading of the quality required for the proposed analysis.

If such a numerical package existed and if instrumentation data were routinely updated and recorded, the goal of using such a tool would be predictive forward modelling of ground support. That is, once the model was calibrated using a procedure similar to that described in this paper (albeit with superior numerical tools) and the rock mass parameters up to failure and in the post-peak were deemed

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sufficiently reliable, forward modelling could be used to predict the behaviour of the rock mass and ground support prior to mining in a given area. This opens up a significant potential for cost savings for mine operators. Forward modelling can lead to better support design. Different types of support can be tested in models at almost no cost. Different timing of support installation, depth of support, etc., could be studied to minimize cost, while also minimizing the potential for support rehabilitation. Forward modelling of the type discussed would be expected to lead to improved overall mine design. For example, different sequencing strategies could be tested. The impact of mining strategies resulting in pillars can be investigated and hopefully the foresight provided by such a model can minimize the chance that ore will be sterilized due to unexpected failure.

Conclusions

All of the goals that were discussed in the previous section are currently technically feasible. However the combined use of tools that are currently available to mining professionals to achieve these goals are far too labour and/or computationally intensive. Should appropriate numerical tools be developed, calibrated forward modelling of the mining process can lead to improved intelligent mine design. While more engineering time would have to be spent in monitoring and mine design, if the amount of rehabilitation of mine development could be reduced, then overall mining costs could be greatly diminished, and the return on investment would be substantial.

With these proposed new tools and upgraded monitoring systems, real time mine modelling could be performed – whether in-house or via contract. The advent of wireless instruments and real-time to surface monitoring, combined with internet technology, could mean that the mine instrumentation and modelling for all mines of a given company, could be performed at a central site or by third party. Microseismic monitoring provides an additional mine wide monitoring system to assist in validation of the location of failure predicted by the numerical models.

The key to post-peak rock mass parameter calibration is to ensure high quality instrumentation data. The frequency of readings, as already discussed, is of prime importance. What is also imperative is to install instrumentation as soon as the mining drifts are excavated. The models discussed in this paper only showed displacements relative to when the instruments were actually installed. The modelling results also showed, in some cases, large amounts of displacement prior to installation of the instruments. Perhaps the routine installation of wireless instrumentation should be part of the mine development process.

To summarize, the procedures outlined in this paper highlight the need for a new hybrid numerical modelling package that can use the influence of three-dimensional mining-induced stresses to predict displacements in, and potential failure of, rock masses surrounding mining infrastructure to radically alter strategic and tactical mine design. The early installation of high quality, real-time automated instrumentation is required for forward modelling of the mining process. A critical problem is that there exists only a small market to drive this innovation. An industry-wide strategy would be required to fund such an ambitious project.

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Acknowledgements The research program described in this paper, which occurred at the University of Toronto, was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC), and the W.M. Keck Foundation in support of the Digital Mine Project. Sincere gratitude is extended to Williams Operating Corporation for permission to use and publish data for this research. The authors also express acknowledgement to A. Coulson of University of Toronto for his work on the seismicity at Williams, in building Autocad models, and his input toward the paper. Acknowledgements also are given to J.H. Curran of the Lassonde Institute, to the staff of Rocscience Inc., to our colleagues at the University of Toronto, and to P. Lausch and J. Tod of Mine Design Technologies Inc.

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