iii On a personal note, I would like to thank my valued friend Suzanne for her support and motivation.

Transcription

1 Shear-slip induced seismic activity in underground mines: a case study in Western Australia A THESIS BY: MARC REIMNITZ THIS THESIS IS PRESENTED FOR THE DEGREE OF MASTER OF ENGINEERING SCIENCE OF THE UNIVERSITY OF WESTERN AUSTRALIA SCHOOL OF CIVIL AND RESOURCE ENGINEERING AUSTRALIAN CENTRE FOR GEOMECHANICS PERTH, WESTERN AUSTRALIA OCTOBER 2004

2 i ABSTRACT Mining induced seismic activity and rockbursting are critical concerns for many underground operations. Seismic activity may arise from the crushing of highly stressed volumes of rock around mine openings or from shear motion on planes of weakness. Shear-slip on major planes of weakness such as faults, shear zones and weak contacts has long been recognized as a dominant mode of failure in underground mines. In certain circumstances, it can generate large seismic events and induce substantial damage to mine openings. The Big Bell Gold mine began experiencing major seismic activity and resultant damage in Several seismic events were recorded around the second graphitic shear between April 2000 and February It is likely that the seismic activity occurred as a result of the low strength of the shear structure combined with the high level of mining induced stresses. The stability of the second graphitic shear was examined in order to gain a better understanding of the causes and mechanisms of the seismic activity recorded in the vicinity of the shear structure as mining advanced. The data were derived from the observation of the structure exposures, numerical modelling and seismic monitoring. The numerical modelling predictions and the interpreted seismic monitoring data were subsequently compared in order to identify potential relationships between the two. This thesis proposes the Incremental Work Density (IWD) as a measure to evaluate the relative likelihood of shear-slip induced seismic activity upon major planes of weakness. IWD is readily evaluated using numerical modelling and is calculated as the product of the average driving shear stress and change in inelastic shear deformation during a given mining increment or step. IWD is expected to correlate with shear-slip induced seismic activity in both space and time. In this thesis, IWD was applied to the case study of the second graphitic shear at the Big Bell mine. Exposures of the second graphitic shear yielded information about the physical characteristics of the structure and location within the mine. Numerical modelling was used to examine the influence of mining induced stresses on the overall behaviour of the shear structure. A multi-step model of the mine was created using the three-

3 ii dimensional boundary element code of Map3D. The shear structure was physically incorporated into the model in order to simulate inelastic shear deformation. An elastoplastic Mohr-Coulomb material model was used to describe the structure behaviour. The structure plane was divided into several elements in order to allow for the comparison of the numerical modelling predictions and the interpreted seismic data. Stress components, deformation components and IWD values were calculated for each element of the shear structure and each mining step. The seismic activity recorded in the vicinity of the second graphitic shear was back analysed. The seismic data were also gridded and smoothed. Gridding and smoothing of individual seismic moment and seismic energy values resulted in the definition of indicators of seismic activity for each element and mining step. The numerical model predicted inelastic shear deformation upon the second graphitic shear as mining advanced. The distribution of modelled IWD suggested that shear deformation was most likely seismic upon a zone below the stopes and most likely aseismic upon the upper zone of the shear structure. The distribution of seismic activity recorded in the vicinity of the shear structure verified the above predictions. The seismic events predominantly clustered upon the zone below the stopes. The results indicated that the seismic activity recorded in the vicinity of the second graphitic shear was most likely related to both the change in inelastic shear deformation and the level of driving shear stress during mechanical shearing. Time distribution of the seismic events also indicated that shear deformation and accompanying seismic activity were strongly influenced by mining and were time-dependant. Seismic activity in the vicinity of the second graphitic shear occurred as a result of the overall inelastic shear deformation of the shear structure under mining induced stresses. A satisfactory relationship was found between the spatial distribution of modelled IWD upon the shear structure and the spatial distribution of interpreted seismic activity (measured as either smoothed seismic moment or smoothed seismic energy). Seismic activity predominantly clustered around a zone of higher IWD upon the second graphitic shear as mining advanced. However, no significant statistical relationship was found between the modelled IWD and the interpreted seismic activity. The lack of statistical relationship between the modelled and seismic data may be attributed to several factors including the limitations of the techniques employed (e.g. Map3D modelling, seismic monitoring) and the complexity of the process involved.

4 iii ACKNOWLEDGEMENTS This research was part of the Mine Seismicity and Rockburst Risk Management project, which was funded by the Western Australian mining industry and the Minerals & Energy Research Institute of Western Australia (MERIWA). I would like to thank my supervisor Professor Yves Potvin, for giving me the opportunity to undertake this research and his indispensable assistance and guidance throughout this project. I extend special thanks to Marty Hudyma, John Albrecht, Michelle Owen and the Australian Centre for Geomechanics staff for their valuable support and help. Thanks also go to John Hadjigeogiou for his encouragement and advice. On a personal note, I would like to thank my valued friend Suzanne for her support and motivation.

5 iv TABLE OF CONTENTS Abstract...i Acknowledgements...iii Table of Contents...iv List of Figures...vi List of Tables...viii 1. Introduction Background Problem statement Research objectives Thesis structure Deviation Literature review Introduction Shear strength of planes of weakness Elasto-plastic Mohr-Coulomb model Asperity and barrier models Shear instability model Loading system stiffness versus source stiffness Shear instability mechanical model Seismic monitoring Description of a seismic event Source location Source parameters Source mechanism Description of seismic activity Seismicity parameters Energy-moment relation Frequency-magnitude distribution Clustering of seismic activity Numerical modelling Numerical modelling methods Numerical modelling program selected - Map3D Modelling shear-slip seismicity using Excess Shear Stress Modelling shear-slip mechanisms using Map3D Previous studies on shear-slip induced seismic activity Summary Incremental Work Density Introduction Description of Incremental Work Density Numerical modelling of Incremental Work Density Conclusion Big Bell Gold mine...46

6 5. Exposures of the second graphitic shear Introduction Characteristics of the second graphitic shear Model of the second graphitic shear Summary Numerical modelling Introduction Description of the Map3D model Map3D results Numerical modelling limitations and uncertainties Summary Seismic monitoring Introduction Selected seismic events Gridding and smoothing of the selected seismic data Seismic monitoring limitations and uncertainties Summary Comparison of the modelled and seismic data Introduction Spatial distribution of the modelled and seismic data State of Incremental Work Density versus interpreted seismic activity Statistical relationship between the modelled and seismic data Summary Conclusions and recommendations...98 References Appendix A Appendix B Appendix C v

7 vi LIST OF FIGURES Figure 1.1. Conditions for unstable motion (a) and quasi-stable motion (b) on a plane of weakness...4 Figure 2.1. Influence of scale on the three components of the shear strength of a rough joint (Bandis et al 1981)...11 Figure 2.2. Elasto-plastic Mohr-Coulomb model...13 Figure 2.3. Asperity model (Aki 1984)...15 Figure 2.4. Barrier model (Aki 1984)...16 Figure 2.5. Shear instability model...17 Figure 2.6. Shear instability mechanical model...18 Figure 2.7. Stress drop...19 Figure 2.8. Conditions for stable (a) and unstable (b and c) slip...20 Figure 2.9. Ground velocity waveform and corresponding far-field S-wave displacement amplitude spectrum (McGarr 1984)...23 Figure P-wave first motion distribution generated by a shear-slip event...28 Figure Six models for mine seismicity in Canada (Hasegawa et al 1989)...28 Figure Four models of radiation patterns (Hasegawa et al 1989)...29 Figure Energy-moment relation...31 Figure Frequency-magnitude distribution...32 Figure Conceptual stress and strength conditions along a plane (Ryder 1988)...36 Figure Loading System Response (Wiles 2002b)...38 Figure 3.1. Concept of Incremental Work Density...44 Figure 4.1. Local geology of the Big Bell deposit (Barrett and Palyer 2002)...47 Figure 4.2. Simplified model of the Big Bell mining geometry...48 Figure 5.1. Variability of the structure thickness...52 Figure 5.2. View looking east (a) and view looking north (b) showing the modelled plane and exposure locations...54 Figure 6.1. Isometric view of the Big Bell Map3D model...57 Figure 6.2. View looking west (a) and view looking north (b) showing the physical dimensions of the Map3D model...58 Figure 6.3. Mining sequence used in Map3D...59 Figure 6.4. Principal stress magnitudes...60 Figure 6.5. Principal stress orientations...61 Figure 6.6. Displacement discontinuity boundary elements along the modelled shear structure...65 Figure 6.7. Views looking west showing the distribution of change in inelastic shear deformation upon the second graphitic shear after mining step 2 (a), mining step 3 (b) and mining step 4 (c). The values are cumulative from mining step Figure 6.8. View looking east showing the distribution of normal stress upon the second graphitic shear as at mining step Figure 6.9. View looking east showing the distribution of shear stress upon the second graphitic shear as at mining step Figure Views looking west showing the distribution of IWD upon the second graphitic shear after mining step 2 (a), mining step 3 (b) and mining step 4 (c). The values are cumulative from mining step Figure 7.1. Seismic events recorded within 30 metres on each side of the second graphitic shear (585 Level)...73 Figure 7.2. Number of seismic events recorded around the second graphitic shear as a function of distance...74

8 Figure 7.3. Source location error distribution of the selected seismic events...76 Figure 7.4. View looking west showing the distribution of seismic events around the second graphitic shear after mining step 2 (a), mining step 3 (b) and mining step 4 (c). The seismic data are cumulative from mining step Figure 7.5. Frequency-moment magnitude distribution of the selected seismic events.78 Figure 7.6. Energy-moment relation of the selected seismic events...79 Figure 7.7. S- to P-wave energy ratio distribution of the selected seismic events...80 Figure 7.8. Time distribution of the selected seismic events...82 Figure 7.9. Gridding of selected seismic data...83 Figure Smoothing of gridded data...84 Figure Views looking west showing the distribution of smoothed seismic moment values upon the second graphitic shear after mining step 2 (a), mining step 3 (b) and mining step 4 (c). The values are cumulative from mining step Figure Views looking west showing the distribution of smoothed seismic energy values upon the second graphitic shear after mining step 2 (a), mining step 3 (b) and mining step 4 (c). The values are cumulative from mining step Figure 8.1. Spatial distribution of smoothed seismic moment versus spatial distribution of modelled IWD upon the second graphitic shear. Values are cumulative as at mining step 2 (a), mining step 3 (b) and mining step 4 (c) Figure 8.2. Spatial distribution of smoothed seismic energy versus spatial distribution of modelled IWD upon the second graphitic shear. Values are cumulative as at mining step 2 (a), mining step 3 (b) and mining step 4 (c) Figure 8.3. State of IWD versus smoothed seismic moment for all the yielding elements upon the second graphitic shear. Values are cumulative as at mining step Figure 8.4. State of IWD versus smoothed seismic energy for all the yielding elements upon the second graphitic shear. Values are cumulative as at mining step Figure 8.5. Log of smoothed seismic moment versus IWD for all the seismically active elements upon the second graphitic shear. Values are cumulative as at mining step Figure 8.6. Log of smoothed seismic energy versus IWD for all the seismically active elements upon the second graphitic shear. Values are cumulative as at mining step Figure C.1. Distribution of shear stress upon the second graphitic shear as at mining step 4 for DOC = Figure C.2. Distribution of shear stress upon the second graphitic shear as at mining step 4 for DOC = Figure C.3. Distribution of shear stress upon the second graphitic shear as at mining step 4 for DOC = vii

9 viii LIST OF TABLES Table 4.1. Mean intact rock properties at Big Bell (Turner and Player 2000)...49 Table 4.2. Stress measurements at Big Bell (Barrett and Player 2002)...49 Table 4.3. Rockburst history at Big Bell (Barrett and Player 2002)...50 Table 5.1. Exposure data used to model the structure geometry...53 Table 5.2. Position and orientation of the modelled structure and corresponding rootmean-square value...55 Table 6.1. Pre-mining stress state used in Map3D...61 Table 6.2. Elastic rockmass properties used in Map3D...62 Table 6.3. Structure properties used in Map3D...63 Table 6.4. Control parameters used in Map3D...64

10 1 1. INTRODUCTION Mining induced seismic activity and rockbursting are critical concerns for many underground mining operations. In addition to the unstable crushing of rock volumes around mine openings (e.g. pillars, abutments), seismic activity may also arise from unstable sliding on distinct planes of weakness (e.g. faults). Physical inspection and measurement of rockmass deformation allow for the direct investigation of the problem but are limited to available exposures. In a more general manner, numerical modelling offers the possibility to simulate the rockmass response to mining and seismic monitoring offers the ability to measure the seismic response of the rockmass to mining. Both numerical modelling and seismic monitoring can be used to enhance our understanding of the causes and mechanisms of rockmass deformation. This thesis presents a case study in which the response to mining of a mine-wide and seismically active geological discontinuity is examined. Field observations, numerical modelling and seismic monitoring formed the basis of this study Background Mining induced seismicity has been and is still a significant cause of fatalities and damage in underground mines around the world. As active mining extends toward greater depths and promotes higher extraction ratios, seismicity induced by mining activities has also increased significantly. Mining induced seismicity generally takes place where large volumes of rock are excavated to create underground openings. During excavation, the removed rock no longer supports the stress produced by overlying rock and tectonic movement, and the stress is redistributed around the opening of the excavation. This redistribution may cause areas of highly concentrated stress that may cause the rockmass to fail in a violent and sudden manner. Mendecki et al (1999) define a seismic event as a sudden inelastic deformation within a given volume of rock that radiates detectable seismic waves. If such a rockmass failure causes significant damage to an opening, it is classified as a rockburst.

11 2 Rockburst source and damage mechanisms Seismic events are created by unstable deformation processes that release a pulse of seismic energy. The source mechanism of a seismic event describes the mode of failure at the source of the event. Source mechanisms of seismic events can be divided into two broad categories: volumetric and shear related events. Volumetric events are generally associated with the unstable crushing of highly stressed volumes of rock around mine openings while shear events are generally associated with unstable motion on planes of weakness. Ryder (1988) describes in some detail the characteristics of these two modes of failure. Both types of source mechanisms can induce serious damage to mine workings. There is no simple correlation between the event mechanism and the severity of the damage. Physical damage to the mine infrastructure is a function of the seismic source characteristics (e.g. ground motion properties, radiation pattern), the distance between the source and the mine openings, and the ability of the openings to resist damage. Based on the Canadian rockbursting experience, damage mechanisms include rock bulking due to fracturing, rock ejection due to seismic energy transfer and rock fall due to seismic shaking (CAMIRO 1997). The reduction of rockburst hazards should be based on a sound understanding of the source and damage mechanisms leading to rockbursting. Shear-slip instability Spatial distribution of seismic events, radiation patterns generated by seismic events and field observation of rockmass deformation confirm that motion on major planes of weakness such as faults, bedding planes, shear zones and weak contacts, is a dominant mode of failure in underground mines. Motion along pre-existing geological structures is a very efficient way to displace large volumes of rock. It can generate large seismic events and induce substantial damage to mine openings. Damaging events associated with unstable shear motion on planes of weakness are usually referred to as fault-slip or shear-slip bursts. Shear-slip bursts have been experienced in several mining districts around the world. This is particularly true for the South African mining industry where several cases of shear related seismic events have been reported over the years.

12 3 All the major seismic events (above magnitude 4.1) are closely associated with faults. (Van Der Heever 1982) A high proportion of damaging rockbursts are thought to be underlain by seismic events that represent shear or rupture along planes of weakness (faults, joints, dyke contacts). (Ryder 1988) Slipping on existing faults and the sudden creation of a shear rupture are the two modes of violent unstable failure that are the source of the larger seismic events which, under certain circumstances, are the immediate cause of major rockbursts. (Ortlepp 2001) Shear-slip bursts have also been reported in North America. The Sudbury mining district (Morisson 1989) and the Coeur d Alene mining district (Morisson 1989, Jenkins et al 1990, Williams et al 1992) have been particularly affected. In Western Australia, the Mount Charlotte mine has experienced large seismic events induced by shear motion on faults over the years. A seismic event of magnitude 3.0 on the Richter scale that was associated with widespread shear displacement on a fault has been documented by Lee et al (1990). In the standard model of shear-slip instability, it is assumed that sliding begins on a plane of weakness when the forces imposed are sufficient to overcome the shear resistance mobilized along the plane. Once sliding initiates, the shear resistance decreases. This strength degradation process may result in a dynamic instability depending on the stiffness of the loading system. Figure 1.1 illustrates the idealized stress-displacement curve of a plane of weakness during shear deformation. Seismic energy is radiated whenever a stress drop is accompanied by an unstable deformation process. This phenomenon can occur at various stages during the overall deformation process: pre-peak, near peak and postpeak. Unstable deformation processes and the release of seismic energy depend on the stiffness of the loading system. Figure 1.1a illustrates the conditions for unstable motion on a plane of weakness. The response of the loading system is softer than the post-peak response of the plane. This results in an unstable motion. Figure 1.1b

13 4 illustrates the conditions for quasi-stable motion on a plane of weakness. Stability is achieved at various stages during the post-peak deformation process. This results in a gradual or quasi-stable motion. Quasi-stable is used to denote the presence of smallscale unstable processes during the larger scale gradual deformation. With a very stiff loading system, the deformation process would be aseismic. The amount of seismic energy released into the surrounding rockmass depends on the scale of failure, the postpeak constitutive behaviour of the plane and the loading system stiffness. A possible initiation mechanism for the release of large amounts of seismic energy is believed to be the shear rupture of strong irregularities or asperities along planes of weakness. (a) UNSTABLE MOTION S h e a r s t r e s s Plane response Loading system response Radiated seismic energy Shear displacement (b) QUASI-STABLE MOTION S h e a r s t r e s s Plane response Loading system response Radiated seismic energy Shear displacement Figure 1.1. Conditions for unstable motion (a) and quasi-stable motion (b) on a plane of weakness

14 Problem statement The Western Australian mining industry is faced with the challenge of dealing with mines that are increasingly seismically active. Rockbursts put both mine viability and safety at risk. This risk is best controlled by implementing mine design strategies that account for, and minimize the release of seismic energy. The development of such mining strategies requires a sound understanding of the causes and mechanisms leading to rockbursting. This may be achieved with detailed interpretation of seismic monitoring data and the application of advanced numerical modelling techniques. In 1999, the Australian Centre for Geomechanics created the Mine Seismicity and Rockburst Risk Management project. The project is sponsored by the Western Australian mining industry and the Minerals & Energy Research Institute of Western Australia (MERIWA). The main goal of the project is to develop a better understanding of seismicity, rockbursts and the associated risks as it relates to underground mining conditions in Western Australia. Better understanding of the problem offers the opportunity to reduce the probability of occurrence of a large seismic event, reduce the damage that may be done, or reduce the risk of exposing the workforce and equipment to the potential hazard. This thesis forms a component of this project and deals with further understanding of shear-slip induced seismic activity in underground mines. In particular, the thesis examines the behaviour of a mine-wide graphitic shear structure at the Big Bell Gold mine in Western Australia. As this thesis focuses on the complex mechanical aspects of shear-slip induced seismic activity, the research strategy concentrates on a single high quality case history rather than the superficial analysis of a number of case studies. The Big Bell mine began experiencing major seismic activity and accompanying damage in The mine uses a sublevel caving method and deals with a high stress regime and a complex geological setting. Two mine-wide and low-strength graphitic shear structures are located in the footwall and parallel the orebody. The first shear structure is located within 15 metres of the footwall/orebody contact and intersects all crosscut drives. The second structure is located at approximately 150 metres from the footwall/orebody contact and crosses the development drives at several locations. The

15 6 level of seismic activity recorded in the vicinity of the second graphitic shear clearly indicates that the shear structure is seismically active. The behaviour of that particular structure is believed to offer a valuable opportunity to develop a better understanding of shear-slip induced seismic activity in underground mines Research objectives To gain a better understanding of the causes and mechanisms of the seismic activity recorded in the vicinity of the second graphitic shear as mining advanced. This is achieved by interpretation of field observations, numerical modelling data and seismic data. To identify potential relationships between the numerical model predictions and the seismic data. This is achieved by comparing the modelled and seismic data. This thesis introduces the Incremental Work Density (IWD) as a measure to evaluate the relative likelihood of seismic activity upon major planes of weakness. IWD can be determined from numerical modelling results and is calculated as the product of the average driving shear stress and change in inelastic shear deformation during a given mining increment or step. IWD is expected to correlate with shear-slip induced rockmass damage and accompanying seismic activity. The thesis is based on the premise that there is an observable link between mining induced stresses, permanent shear deformation upon the second graphitic shear and recorded seismic activity in the vicinity of the shear structure Thesis structure Literature review Chapter 2 reviews literature on shear-slip mechanics (e.g. shear strength of planes of weakness, asperity and barrier models, shear instability model), seismic monitoring and numerical modelling. Previous studies on shear-slip induced seismic activity have also been reviewed.

16 7 Incremental Work Density Chapter 3 introduces the concept of Incremental Work Density (IWD) and presents how the parameter can be calculated using numerical modelling. Big Bell Gold mine Chapter 4 marks the beginning of the case study and provides background information related to the Big Bell Gold mine. Exposures of the second graphitic shear Chapter 5 describes the physical characteristics of the second graphitic shear. The information was collected from underground inspection of the structure exposures. The chapter also describes the work undertaken to construct a model of the structure geometry. The information collected and work done in this chapter provided important input data for the numerical modelling and seismic analysis. Numerical modelling Numerical modelling was conducted in order to simulate the inelastic behaviour of the second graphitic shear in response to mining induced stresses. The three-dimensional boundary element code of Map3D was used. The numerical model required information on the mining and structure geometries, pre-mining stress state, mining sequence, rockmass elastic properties and structure mechanical properties. An elastoplastic Mohr-Coulomb material model was used to describe the behaviour of the shear structure. During automatic discretization, the modelled structure was divided into smaller elements. Stress and deformation components were calculated for each element and mining step. IWD upon the shear structure was subsequently calculated from the numerical modelling results. Chapter 6 presents and discusses the results. Seismic monitoring A total of 1476 seismic events were recorded in the vicinity of the second graphitic shear between April 2000 and February The seismic events were analysed and subsequently gridded and smoothed. Gridding and smoothing of individual seismic moment and seismic energy values resulted in the definition of indicators of seismic activity for each element of the shear structure and each mining step. Chapter 7 presents and discusses the results.

17 8 Comparison of the modelled and seismic data The modelled Incremental Work Density (IWD) was compared to the interpreted seismic activity (measured as either smoothed seismic moment or smoothed seismic energy) in order to identify potential relationships between the numerical modelling predictions and seismic data. Chapter 8 presents and discusses the results. Conclusions and recommendations The final chapter discusses and summarizes the findings. recommendations for further research. It also provides 1.5. Deviation One of the main aspects of the initial project was to physically monitor the distribution of shear displacement along the second graphitic shear to compare to the modelled and seismic data. Unfortunately, the proposed monitoring could not be undertaken due to technical problems encountered at the mine site. It is believed that these measurements would have given important insights into the structure behaviour.

18 9 2. LITERATURE REVIEW 2.1. Introduction Literature on seven main topics has been reviewed in this chapter. The first section examines the factors which influence the shear strength of planes of weakness. The second section describes a material model appropriate for the explicit modelling of the second graphitic shear at the Big Bell Gold mine. Section three describes the asperity and barrier models. The fourth section presents a model of shear instability. The fifth and sixth sections review literature in the area of seismic monitoring and numerical modelling respectively. Finally, previous case studies of shear-slip induced seismic activity have been examined Shear strength of planes of weakness Mechanical shearing on major planes of weakness such as faults can induce substantial seismic activity. Shear movement on a plane is initiated when the shear stress overcomes the shear resistance. In order to examine the phenomenon of shear-slip induced seismic activity, it is necessary to understand the factors that control the shear strength of planes of weakness. These questions are addressed in the following discussion. For more details, the reader should refer to available texts such as Hoek and Brown (1980), Scholz (1990), Bouchard (1991), Brady and Brown (1994) and Hoek et al (1995). The shear strength of a plane is controlled by: the magnitude of the applied normal stress, the persistence or extent of the plane, the roughness of the adjacent surfaces, the nature of the host rockmass itself, the degree of weathering or alteration, the aperture or distance separating the adjacent surfaces and the properties of the filling material. Normal stress and pore water pressure The shear strength of a plane increases with increasing normal stress. The relationship takes the following general form:

19 10 t = f (σ ) n t = shear strength σ = normal stress n When pore water pressure is present, the plane is forced apart and the normal stress is reduced. The reduced normal stress is usually called the effective normal stress. However, in underground mining, the influence of water is generally insignificant because of drainage into mine openings. Roughness and influence of scale The roughness of the adjacent surfaces may have an important influence on the shear strength of a plane. Roughness is particularly important when the plane is clean, closed and constrained. Alternatively, the influence of roughness declines with increasing aperture, filling thickness and previous displacement. Roughness can cause the shear strength to be a directional property. Sliding on asperities and shearing/crushing of asperities are generally combined in varying proportions during mechanical shearing. The shear strength of a rough and closed plane is therefore strongly influenced by the strength of those asperities. Barton and Choubey (1977) studied the behaviour of natural rock joints and proposed an empirical relationship based on three components: a residual frictional component, a geometric component and an asperity failure component. The geometric and asperity components combine together to give an effective roughness component. Based on the same relationship, Bandis et al (1981) proposed that the shear strength of rough joints decreased as the scale increased (Figure 2.1). This strength reduction was attributed to a decrease in the effective roughness component.

20 11 Shear stress Asperity failure component Geometrical component Roughness component Shear deformation Residual frictional component Total frictional resistance Figure 2.1. Influence of scale on the three components of the shear strength of a rough joint (Bandis et al 1981) Alteration The host rockmass is in its strongest state when unaltered. When weathered or altered, it becomes weaker and softer. The shear strength of a plane can be reduced drastically when the asperities are altered. The depth of penetration of alteration depends on the host rockmass type. Its permeability is particularly important. Aperture The aperture is the distance separating the adjacent surfaces of a plane. The aperture of a natural plane of weakness is likely to vary widely over the extent of the plane and can be extremely difficult to measure. The aperture has an important influence on the shear strength of a plane. A large aperture can result in shear displacement of a plane having significant roughness. Filling materials Filling materials can have an important influence on the shear strength of planes of weakness. Planes filled with relatively strong materials (e.g. calcite, quartz, pyrite) usually have higher shear strength. However, such planes may have broken up again, forming new planes. On the other hand, planes filled with soft materials (e.g. fault gauge, chlorite, clay, silt) generally have lower shear stiffness and shear strength than comparable clean and closed planes. The shear strength of such planes is influenced by the thickness of the filling material relative to the amplitude of the asperities of the adjacent surfaces. For a rough plane, the filling thickness has to be greater than the amplitude of the asperities before the shear strength is reduced to that of the filling material. For a smooth plane, a thin filling layer can result in a significant shear

21 strength reduction. Low-friction materials such as chlorite, graphite, talc and serpentine can markedly decrease friction angles especially when wet. 12 At a laboratory-scale, Ladanyi and Archambault (1977) studied the behaviour of discontinuities filled with soft and weak materials. They reached the following conclusions: For a filled discontinuity, the peak shear strength envelope is normally located between that of the filling material and that of a similar unfilled discontinuity. The stiffness and shear strength of a filled discontinuity decrease with increasing filling thickness, but always remain higher than the stiffness and shear strength of the filling material alone. The shear stress-shear displacement curve of a filled discontinuity often has two portions. The first reflects the deformability of the filling material before any rockto-rock contact. The second reflects the deformability and shear rupture of the rock in contact. The shear strength of a filled discontinuity does not always depend on the thickness of the filling material. If the contacting surfaces are flat and covered with a lowfriction material, the weakest shear surface will be located at the contact between the filling material and the rock. Swelling clay is a dangerous filling because it loses strength on swelling and can develop high swelling pressures if swelling is inhibited. Residual conditions The residual shear strength represents the minimum shear strength remaining after a considerable shear displacement. In the case of a clean, rough and closed plane, the asperities of the adjacent surfaces are destroyed during mechanical shearing and the residual plane can be considered as smooth and planar. At residual conditions, the shear strength depends only on the effective normal stress and residual friction angle. The residual friction angle is a property of the contacting surfaces. In unaltered conditions, it corresponds to the basic friction angle. The value of the basic friction angle for most smooth unaltered planes lies between 25 to 35 (Barton and Choubey 1977). The basic friction angle does not apply for weathered or filled planes. When the plane is altered or filled with a soft material, the value of the residual friction angle can decrease drastically. Figure 2.1 shows that the residual shear strength is independent of scale.

22 13 Morisson (1989) reported that large shear-slip seismic events are usually found to occur on strong planes. The loss in strength from peak to residual can potentially generate large and sudden stress drop. Lee et al (1990) studied a large fault-slip event that occurred at the Mount Charlotte mine in Western Australia. They concluded that mechanical shearing on a thin rough plane is more likely to generate more energy more suddenly than a thick planar fault or shear zone. In the same way, Ryder (1988) reported that seismically active faults are said to be in tight contact and free of gauge Elasto-plastic Mohr-Coulomb model The factors controlling the shear strength of a plane of weakness were reviewed in the previous section. When a numerical method is used to simulate the non-linear behaviour of a plane, it is necessary to use an idealized material model to describe the mechanical properties of the plane. A material model relates the deformation state to the stress state at any point along the plane. Several models exist in rock engineering and are always simple representations of real and complex problems. Figure 2.2 represents an elasto-plastic Mohr-Coulomb model. (a) τ (b) τ Inadmissible Elastic Shear deformation σ n Figure 2.2. Elasto-plastic Mohr-Coulomb model Figure 2.2a is the idealized shear stress-shear deformation curve for a given state of normal stress. Shear deformation is linearly elastic and reversible up to a limiting shear stress and then perfectly plastic. Shear stress reversal after plastic yield is accompanied

23 by permanent shear deformation. The constant relating shear stress and shear deformation in the elastic range is referred to as the shear modulus. 14 The relationship between normal stress and normal deformation is linearly elastic up to a limiting value of normal deformation. The plane separates when the normal stress is less than the tensile strength of the plane (usually zero). The constant relating normal stress and normal deformation in the elastic range is referred to as the normal modulus. The relationship between the limiting shear stress and normal stress is given by a linear Mohr-Coulomb strength criterion (Figure 2.2b). The criterion is assumed to be cohesionless and can be described by the following empirical relationship: τ = σ tanφ n τ = shear strength σ = normal stress n φ = frictionangle The shear strength is a function of two parameters: the friction angle and the normal stress. The slope of the Mohr-Coulomb relation defines the friction angle. The normal stress across the plane increases the shear strength by an amount proportional to the magnitude of the normal stress. The strength envelope divides the stress space into two separate domains. The domain below the envelope is the elastic domain within which the shear deformation is reversible. The domain above the envelope is the inadmissible domain. A stress state above the line is impossible since the shear stress would have been already dissipated in inelastic shear deformation. The elasto-plastic Mohr-Coulomb model presented here may be appropriate for smooth discontinuities such as faults at residual states of shear strength (Brady and Brown 1994). This material model was used in this study to examine the non-linear behaviour of a mine-wide and low-strength geological structure (i.e. the second graphitic shear at the Big Bell Gold mine).

24 2.4. Asperity and barrier models 15 Many investigators in earthquake and rockburst research suggest that a possible initiation mechanism for the release of considerable amounts of seismic energy is the shear rupture of large-scale irregularities along major planes of weakness. Seismologists often refer to asperities to describe such irregularities (Scholz 1990, Gibowicz and Kijko 1994). Asperities are defined as strong regions that resist slip movements and where stress builds up prior to an eventual rupture. Figure 2.3 illustrates the asperity model. Initial stress concentrations exist at the asperities that lock up the plane. After the rupture of the asperities, the stress is uniform over the plane. The breaking of asperities can be seen as a smoothing process. Before rupture After rupture Asperity (strong region of stress concentration) Figure 2.3. Asperity model (Aki 1984) Asperities are often mentioned together with barriers. In contrast to asperities, barriers are defined as strong regions that remain unbroken after a rupture. Barriers may arrest the rupture or the rupture may skip over them. Figure 2.4 illustrates the barrier model. In this model, the initial state of stress over the plane is uniform. After the rupture, stress concentrations exist at the barriers. The presence of barriers may be seen as a roughening process.

25 16 Before rupture After rupture Barrier (strong region of stress concentration) Figure 2.4. Barrier model (Aki 1984) Van Aswegen (1990), Van Aswegen and Butler (1993) and Dennison and Van Aswegen (1993) have shown that the asperity model may be applicable to fault behaviour observed in South African gold mines. From seismological observations, they noticed that large-scale asperities are characterized by either the clustering of small seismic events of relatively high apparent stress (due to stress concentration) or by seismic quiescence. On the other hand, they noticed that regions that deform under lower stress are characterized by small seismic events of relatively small apparent stress. Geometric complexities, local areas of high friction and mining induced areas of high normal stress have been mentioned by these authors as potential asperities. Urbancic et al (1992b) noticed that asperities and barriers correspond to higher values of seismic moment and static stress drop without increases in source radius Shear instability model A conceptual shear instability model is shown in Figure 2.5. The model assumes that shear-slip begins when the shear resistance is reached. Once slip initiates, the shear strength drops to a reduced level and is accompanied by an unstable shear deformation. This strength drop is also termed the shear stress drop. Both the magnitude and rate of this strength degradation process influence the potential for violent shear deformation. The amount of seismic energy radiated from the source during the dynamic process depends on the scale of failure, the loading system stiffness and the strength degradation process (i.e. source stiffness). The strength degradation may be considered in terms of a displacement-weakening process or in terms of a velocity-weakening process (Scholz 1990, Gibowicz and Kijko 1994, Brady and Brown 1994).

26 17 τ Slip initiation point Shear stress drop Source strength degradation (source stiffness) Radiated seismic energy Loading system stiffness Unstable shear deformation Shear deformation Figure 2.5. Shear instability model The shear instability model is an important concept in mine seismicity. Seismological theories and some numerical modelling techniques (e.g. Local Energy Release Density/Loading System Stiffness concept) are based on similar models Loading system stiffness versus source stiffness Cook (1965) discovered that a violent failure of rock occurs when an excess of energy becomes available during the post-failure deformation stage. The amount of excess energy available is a function of the loading system stiffness and the post-failure response of the collapsing rock itself. Stable shear motion occurs when the loading system response is stiffer than the postfailure response of the yielding plane. The strain energy stored in the loading system is consumed in the yielding process and dissipated as heat. There is no excess energy that has to be liberated as kinetic energy in the surrounding rockmass. Unstable shear motion occurs when the loading system response is softer than the postfailure response of the yielding plane. The strain energy released by the loading system

27 is greater than the energy that can be absorbed by the yielding process and the slip is sudden and violent Shear instability mechanical model The concept of shear instability can be described using the simple mechanical model shown in Figure 2.6 (Hedley 1993). A block under a constant normal stress (σ n ) rests on a flat surface. A shear stress (τ) is applied through a spring of stiffness k. The stiffness of the spring represents the stiffness of the surrounding rockmass or loading system. Movement of the block is initiated when the shear stress (τ) reaches the static shear strength (τ s ) between the block and the flat surface. Once movement is initiated, the shear strength falls and a new equilibrium is achieved when the shear stress (τ) reduces to the dynamic shear strength (τ d ). σ n τ s, τ d k Spring τ Figure 2.6. Shear instability mechanical model Figure 2.7 illustrates the shear displacement history of the block. The stress drop (τ s - τ d ) is a necessary condition for violent shear instability.

28 19 τ Static strength τ Static strength envelope Stress drop Stress drop Dynamic strength Dynamic strength envelope Shear deformation σ n Figure 2.7. Stress drop Figure 2.8a illustrates the conditions for stable slip. In this case, the high stiffness of the spring permits stable loading and displacement of the block. No excess energy is available during the post-failure deformation stage. Figure 2.8b illustrates the conditions for unstable slip. In this case, the spring is softer than the post-failure response of the block and causes unstable loading of the block. The area between the unloading curve of the spring (dashed linear curve) and the postfailure response of the block (non-linear curve) represents the excess energy that has to be liberated has kinetic energy (WK) in the surrounding rockmass. Figure 2.8c illustrates the conditions for unstable slip if the spring stiffness is reduced. In this case, both the displacement of the block and the amount of kinetic energy released are increased. By analogy, Hedley (1993) noted the importance of the loading system stiffness on both the amount of slippage and seismic energy released during a shear type event. It is important to note that this model has a single degree of freedom. In a more complicated multi-dimensional loading situation, the other components of loading must be considered. The model also assumes that the shear motion is simultaneous everywhere on the failure surface. On a major plane, the slip is more likely to progress in a non-uniform fashion.

29 20 (a) τ τ s k τ d Shear deformation (b) τ (c) τ τ s k WK τ s k WK τ d τ d Shear deformation Shear deformation Figure 2.8. Conditions for stable (a) and unstable (b and c) slip Hedley (1993) studied the influence of the loading system stiffness with respect to faultslip instability. Assuming a circular dislocation and based on the simple shear instability mechanical model, he found that the loading system stiffness is inversely proportional to the fault size subject to slip. Esterhuizen (1994) carried out two-dimensional numerical analyses in which a tabular excavation and a fault plane were simulated. He found that the loading system stiffness decreases as the fault length subject to slip increases.

30 2.6. Seismic monitoring 21 Mining activity induces elastic (i.e. reversible) and inelastic (i.e. permanent) deformation within the rockmass. The potential energy stored during elastic deformation may be released gradually or suddenly during the inelastic deformation processes. These processes are associated with fracturing and frictional sliding and radiate seismic waves. The frequency and amplitude of these seismic waves depends on the strength, state of stress, size and rate of deformation of the seismic source. Seismic monitoring is a tool used to measure the seismic response of the rockmass to mining. Seismic monitoring provides only information about the seismic component of the inelastic deformation processes i.e. the portion of the processes associated with the radiation of seismic waves and recorded by the seismic network. A seismic network consists of an array of sensors that record ground motions in real time. Sensors used are accelerometers and geophones. They are either uniaxial or triaxial. Uniaxial sensors measure ground motions along one axis while triaxial sensors measure ground motions along three orthogonal axes (full tensor). Depending on the type of sensor used, the original seismograms or waveforms provided by a seismic system are either ground acceleration records in the case of accelerometers or ground velocity records in the case of geophones. Proper processing of the recorded waveforms permits quantitative description of the seismic events and seismic activity. These seismological observations contribute to understanding the causes and mechanisms of rockmass deformation Description of a seismic event Source location The source location of a seismic event is assumed to be a single point within the seismic source that triggered the set of seismic sensors used to locate it. Seismic source location is a fundamental piece of information because all subsequent seismological processing

31 22 depends, to some degree, upon the event position and distances to the sensors. Basically the source location of a seismic event is retrieved from the P- and/or S-wave arrival times, the velocity model and the seismic station coordinates. Several source location techniques are presented and discussed by Gibowicz and Kijko (1994) Source parameters The source parameters are used to describe quantitatively each individual seismic event. The source parameters can be estimated in time and frequency domains based on signals recorded from triaxial sensors. However, the source parameters are usually estimated from the spectral parameters of the seismic records. The spectral parameters are calculated from the amplitude spectra of the recorded waveforms. The amplitude spectra are obtained from the Fourier transformation of the seismic waveforms from the time domain into the frequency domain. Gibowicz and Kijko (1994) and Mendecki (1997) describe in more details the techniques used for the determination of the source parameters. Figure 2.9 illustrates a typical ground velocity waveform for a particular seismic event and the far-field S-wave displacement amplitude spectrum computed from it. The displacement amplitude spectrum remains constant at low frequencies and becomes inversely proportional to some power of frequency at higher frequencies. The key spectral parameters are the low frequency spectral level (Ω ο ), the corner frequency (f o ) and the energy flux. The source parameters are calculated separately for the P- and S- waves on the basis of these spectral parameters.

32 23 Figure 2.9. Ground velocity waveform and corresponding far-field S-wave displacement amplitude spectrum (McGarr 1984) Seismic Moment The seismic moment is a scalar that measures the co-seismic inelastic deformation at the source assuming a double-couple shear source mechanism (Mendecki et al 1999). The seismic moment is the most reliable and useful measure of the strength of a seismic event (Gibowicz and Kijko 1994). Seismic moment can be expressed as (Aki and Richards 1980): M o = G A D M o = seismic moment G = shear mod ulus at the source A = seismic source area D = average displacement over the source area In practice, the seismic moment is usually calculated from the low frequency level of the displacement amplitude spectra of the body waves radiated from the source:

33 24 M o 4 π ρ Vc = F 3 c R Ω o M ρ = rock density V c R = distance between the source and receiver Ω F c = seismic moment = P or S wave velocity o o = low frequency spectral level = P or S wave radiation pattern coefficient The total seismic moment is then calculated as: M o M = P wave o + M 2 S wave o where M S wave o = ( M SH wave o ) 2 + ( M SV wave o ) 2 The seismic moment tensor is a more robust expression of the seismic moment. Its six independent components contain all the information about the point source mechanism. The moment tensor concept has not been used in this study. Reliable moment tensor analyses need exceptional source coverage from triaxial sensors. Radiated Seismic Energy The radiated seismic energy is the portion of the energy released or work done at the source that is radiated as seismic waves (Mendecki et al 1999). Like the seismic moment, the seismic energy is a measure of seismic event strength. The seismic energy is better related to the damage potential while the seismic moment provides a better description of the overall size of a seismic event (Boatwright and Choy 1986). In practice, the seismic energy can be estimated from the energy flux as:

34 π ρ Vc R J c 2 E = F 2 c F c E = radiated seismic energy ρ = rock density V R = distance between the source and receiver J c F F c c c = P or S wave velocity = energy flux = P or S wave average radiation pattern coefficient = P or S wave radiation pattern coefficient The total radiated seismic energy is then calculated as: E = E P wave + E S wave where E S wave = E SH wave + E SV wave The ratio of S- to P-wave energy is recognized as an important indicator of the source mechanism (Urbancic et al 1992b, Urbancic and Young 1993, Gibowicz and Kijko 1994, Cai et al 1998). Seismic events with an S- to P-wave energy ratio greater than ten are dominated by a shearing component of failure. Any enrichment of P-wave energy and/or depletion of S-wave energy indicate that additional non-shearing volumetric components have been added to the failure mechanism. Moment-Magnitude According to Hanks and Kanamori (1979) the magnitude of a seismic event can be determined from the seismic moment as follows: M 2 = logm o M = moment magnitude M o = seismic moment in Newton metres

35 26 Source Radius Estimates of the source dimensions are model dependent. In mine-induced seismicity, the source is usually modelled as a simple circular dislocation where a uniform stress release over the entire source area is assumed (Brune 1970, Madariaga 1976). The source radius of such a dislocation is inversely proportional to the corner frequency of either the P-wave or S-wave and is expressed as: r o Kc V = 2π f c o r o K V f c o = source radius c = constant that dependson the source mod el = P or S wave velocity = P or S wave corner frequency Static Stress Drop The static stress drop can be defined as the difference between the initial and final stress levels during faulting. The static stress drop is a model dependent measure of stress release. It assumes a complete stress release along the fault surface and is calculated from the seismic moment and source radius. According to Brune (1970), it can be estimated from: 7 M = 16 r o σ 3 o σ = static stress drop M r o o = = seismic moment source radius ( Brune mod el ) Apparent Stress The apparent stress is another measure of stress release. It is recognized as a model independent measure of the stress change at the seismic source (Mendecki et al 1999). The apparent stress is estimated from the radiated seismic energy and seismic moment as follows:

36 27 σ A = G E M o σ = apparent stress G = shear mod ulus at the source E = radiated seismic energy M A o = seismic moment Source mechanism The observed direction of first motions of seismic sensors provides information on the rupture mechanism at the source. The direction of the P-wave first motion can be determined at each sensor from recorded waveforms. The first motion (polarity) is either up (positive) or down (negative) depending whether the rockmass was in compressional or dilatational mode. Different types of seismic events produce different first motion distributions around the source. Stereographic projections are usually used to interpret these distributions. First motion distributions or radiation patterns generated by fault-slip and shear-slip events have a particular signature. Figure 2.10 illustrates the P-wave first motion distribution generated by a shear-slip event. As shown, the space around the source is divided into four quadrants with respect to the direction of the P-wave first motions. Two quadrants are compressional and the other two are dilatational. The two orthogonal lines separating the compressional and dilatational quadrants are the nodal planes. One of them corresponds to the rupture plane and the other is referred to as the auxiliary plane. The distinction between the rupture plane and the auxiliary plane cannot be made from first motion analysis alone. Seismological and geological observations can give additional information. Estimates of the dip, dip direction and slip direction of the rupture plane are determined from a stereographic projection. An adequate coverage of the source is essential.

37 28 Dilatation First motion down Compression First motion up Source Fault trace Sensor Compression First motion up Dilatation First motion down Figure P-wave first motion distribution generated by a shear-slip event Hasegawa et al (1989) proposed six specific models for mine seismicity in Canada. Figure 2.11 illustrates the proposed models and Figure 2.12 shows the corresponding radiation patterns for both the P-wave and the S-wave. In practice, rupture processes are complex and first motion analyses reveal more complex radiation patterns. Figure Six models for mine seismicity in Canada (Hasegawa et al 1989)

38 29 Figure Four models of radiation patterns (Hasegawa et al 1989) First motion analyses provide more information about the source mechanisms and can be used to outline seismically active geological planes (Urbancic and Young 1995, Trifu and Urbancic 1997). Solutions can coincide with known orientation of planes of weakness or can reveal the presence of previously unknown planes.

39 Description of seismic activity Seismicity parameters The seismicity parameters are used to describe quantitatively the seismic activity within a volume V over a period t. The seismicity parameters characterize the changes in the stress and strain regime within the rockmass affected by the seismic radiations. Seismic activity can be described quantitatively by at least the following four independent parameters (Mendecki 1997): Average time between seismic events Average distance between seismic events Sum of seismic moment Sum of seismic energy Several other parameters can be derived from these four basics quantities (e.g. seismic stress, seismic strain, seismic viscosity, seismic Deborah number, seismic Schmidt number). Mendecki (1997) describes and discusses these parameters. Basically, the procedure for calculating these parameters includes the selection of seismic events associated with a particular volume of rock and the gridding/smoothing of seismic energy and seismic moment values. These parameters can be applied for the characterization of fault behaviour. Simser (1997) used the seismic viscosity parameter (i.e. the rockmass resistance to the flow of co-seismic inelastic deformation) to analyse the seismic behaviour of a large normal fault in South Africa. Mercer (1999) used a smoothing procedure to compare seismic and numerical modelling data. He described the procedure as a method for eliminating some of the local variation in the seismic data and therefore facilitating the linkage with modelled data.

40 Energy-moment relation 31 The energy-moment relation describes the relationship between the log of the radiated seismic energy and the log of the seismic moment for a given population of events (Figure 2.13). Log ( seismic energy) log( E ) = c + d log( Mo ) Log (seismic moment) Figure Energy-moment relation The relation takes the form of: log( E ) = c + d log( M o ) E = estimated seismic energy M o = seismic moment c and d are parameters describing the relation In general, the parameter c increases with stress while the parameter d, known as the d- value, increases with the system stiffness (Mendecki et al 1999) Frequency-magnitude distribution The frequency-magnitude distribution describes the relative number of small and large events in a given population as a function of magnitude (Figure 2.14).

41 32 Log (cumulative frequency) log( n ) = a bm Moment magnitude Figure Frequency-magnitude distribution Introduced by Gutenberg and Richter (1954), the relation takes the following form: log n = a bm n = number of events with magnitude m m = event magnitude a and b are parameters describing the relation The parameter a is a measure of the level of seismic activity. The parameter b, known as the b-value, is the slope of the distribution in the magnitude range over which the distribution is linear. In general, the b-value is influenced by the stiffness, the level of stress, and the rockmass heterogeneity of the geomechanical system under consideration (Mendecki et al 1999). Spatially, a decrease in the b-value has been attributed to regions under higher stress (Urbancic et al 1992a), whereas temporally, decreasing b-values have been observed prior to the occurrence of impending large events (Trifu et al 1997) Clustering of seismic activity The spatial distribution of seismic activity can be used to delineate seismically active zones within the rockmass and can possibly lead to the identification of particular hazardous geological structures (Van Der Heever 1982, Joughin and Jager 1984).

42 33 Principal Component Analysis (PCA) of microseismicity can be used to outline seismically active geological structures (Urbancic et al 1993, Trifu and Urbancic 1996, 1997). PCA is a statistical technique based on the spatial distribution of seismic events. The method is used to quantify the degree of clustering and shape and orientation of seismic clusters. A cluster associated with a geological discontinuity would typically have a planar shape and orientation parallel to the structure. The method assumes that seismic events occurring close to each other in both space and time are related. PCA derived solutions have been found to correlate well with fault-plane solutions and mapped structures. The main benefit of using PCA is the rapid identification of active structures.

43 2.7. Numerical modelling 34 Computer-based numerical modelling methods are normally used for the analysis of mining induced stresses. Numerical modelling is a tool used to simulate the rockmass response to mining and contributes to understanding the causes and mechanisms of rockmass deformations. Numerical modelling can be used to provide explanations for the recorded seismic activity (Wiles 2002a) Numerical modelling methods Computational methods of stress analysis can be divided in two classes: boundary methods and domain methods. The mathematics and the detailed description of the boundary and domain methods are well documented by Brady and Brown (1994). Boundary methods Boundary methods include the direct boundary element method, the indirect boundary element method and the displacement discontinuity method. These methods require only the problem boundaries to be divided into elements. The rockmass is considered as an infinite continuum and distinct discontinuous planes can be modelled explicitly using the displacement discontinuity approach. The boundary methods are ideally suited to model complex geometry problems where the rockmass is considered as linearly elastic, homogeneous and isotropic. The simplicity of these methods is due to the small number of parameters involved in the analysis. Domain methods Domain methods include the finite element method, the finite difference method and the distinct element method. These methods require the entire problem domain to be divided into elements. In the finite element and finite difference methods, the rockmass is treated as a continuum where each element inside the domain can be described by a non-linear constitutive model. Distinct discontinuous planes can also be represented explicitly using specific joint elements. In the distinct element method, the rockmass is treated as a discontinuum where an assembly of quasi-rigid blocks interacts through deformable joints. The domain methods are well suited to model the more complex

44 overall behaviour of the rockmass but are generally limited to more simple geometry problems Numerical modelling program selected - Map3D Numerical modelling was used in this study to examine the behaviour of a mine-wide shear structure in response to mining. The following guidelines were set regarding the choice of an appropriate numerical modelling program: The program must be capable of modelling large-scale, complex, three-dimensional geometry problems. The program must be capable of incorporating multi-step mining sequence problems. The program must be capable of including the non-linear constitutive behaviour of distinct discontinuous planes. Map3D (Wiles 2002b) was selected for the purpose of this study. Map3D is a threedimensional numerical modelling program based on the boundary element method. The program uses an indirect boundary element solver. Both fictitious force and displacement discontinuity elements can be employed. In Map3D, the rockmass is considered linearly elastic, homogeneous and isotropic. The non-linear or plastic behaviour of distinct discontinuous planes can be modelled using the displacement discontinuity method. Fictitious force elements are used to specify the location of excavation boundaries and displacement discontinuity elements are used to specify the location of distinct discontinuous planes. The program is used to build models, run models and view the results. Stress, strain and displacement values can be displayed on grids or displacement discontinuity elements Modelling shear-slip seismicity using Excess Shear Stress Ryder (1988) introduced the Excess Shear Stress (ESS) concept. The ESS method is a technique used to estimate the likelihood of shear-slip related seismic activity.

45 36 Figure 2.15 summarizes the ESS concept. Shear stress and strength conditions along a plane are shown. The static strength (τ s = c + σ N tanφ s ) is represented as an irregular line to show the effects of irregularities or asperities on the plane. The dynamic strength (τ d = σ N tanφ d ) is shown as a smooth line and represents the resistance that pertains once the static strength is overcome and slip initiates. Also shown is the variation in shear stress along the plane. The shaded zone corresponds to the ESS or stress drop and is expressed as: ESS ESS = prevailing shear = τ σ tanφ n d stress prior to slip dyamic strength of plane τ = shear stress on the plane before rupture σ tanφ = dynamic friction of plane φ = dyamic friction angle of plane d n n d σ = normal stress on the plane before rupture Shear stress (MPa) Stress drop ESS Static strength Dynamic friction Shear stress prior to rupture A P Distance along fault/rupture (m) B Figure Conceptual stress and strength conditions along a plane (Ryder 1988) Ryder (1988) describes the ESS as a measure that controls the initiation, propagation, and termination of shear-slip events. According to the concept, rupture initiates at some point along the plane when the shear stress reaches the static strength or when the ESS reaches a critical value at that point. Once rupture begins, the shear stress drops to the dynamic value. It is now assumed that the dynamic strength pertains and that continuation of rupture depends on the ESS distribution. The extent of the zone of rupture is assumed to correspond approximately to the zone of positive ESS.

46 37 In this concept, it is assumed that the forces and energies needed to propagate the rupture are small compared to the other forces and energies involved. This means that, once the rupture is in motion, the halting effects of strong barriers are ignored. Another assumption is that the dilatation effects of the rupturing plane have been neglected. Finally, the dynamic effects have not been considered. This restrains the rupture to overshoot the zone of positive ESS, as it could be the case with a soft loading system. ESS analyses can easily be carried out with elastic numerical models. Beforehand, further assumptions or estimations must be made: Dynamic friction properties of planes must be determined. A working assumption of 30, until better evidence becomes available, is proposed (Ryder 1988). Applied stress on planes must be modelled with appropriate mining and plane geometries and initial stress field. The critical value of ESS or difference between the static strength and dynamic strength must be established. For unstable slip on planes of weakness, a working assumption of 5 to 10 MPa is proposed (Ryder 1988). For unstable rupture of intact rock, a working assumption of 20 MPa is proposed (Ryder 1988). As proposed by Ryder (1988), the likelihood of seismic activity can then be evaluated after the maximum ESS and extent of the positive zone of ESS. The ESS concept has been widely used in the South African mining industry to evaluate fault stability. Ryder (1988) observed that ESS analyses tend to produce conservative results. High levels of ESS do not always result in seismic activity. Webber (1990) noticed that the concept is very sensitive to the virgin stress levels and the friction properties of faults. Van Aswegen (1990) concluded that ESS analyses can predict locations of movement on faults but cannot predict whether the slip is seismic or aseismic Modelling shear-slip mechanisms using Map3D For a given seismic event, the loading system response can be determined in a numerical model by comparing the load-deformation state before the event with the load-deformation state after the event. This is done in Map3D (Wiles 2002b) by

47 38 specifying an energy test volume or surface with a special material code. This special material code is used to temporarily alter the material properties in the test surface to cause the model to deform. This approach is known in Map3D as the Local Energy Release Density (LERD)/Loading System Stiffness (LSS) technique. For example, consider a simple one-dimensional model in which a shear-slip seismic event is simulated. The load-deformation response of the loading system is illustrated in Figure Stage I corresponds to the load-deformation state before the event. At this stage, the fault is intact. Stage II corresponds to the load-deformation state after the event. At this stage, the model has flexed due to a reduction of the fault strength to its residual value. From stage I to stage II, a stress drop and a shear displacement have occurred on the fault surface. The load-deformation state at stage I is compared to the load-deformation state at stage II. Assuming that the post-peak constitutive response of the fault is brittle (i.e. the loss in strength from peak to residual occurs with no or very little shearing displacement of the fault surface), the following values can be deduced from the load-deformation response of the loading system: WK = excess energy released as seismic energy WF = energy dissipated in the frictional deformation WT = WK + WF = total energy released LSS = Loading System Stiffness Load Stage I LSS WK Stage II WF Deformation Figure Loading System Response (Wiles 2002b)

48 39 Since Map3D calculates the stresses acting on the boundary elements, the contribution from each element on the energy test surface must be considered. For a multi-dimensional loading situation, the contribution from the normal and the two shear components on each element must be considered. Then, in a general manner, the components of the energy released can be calculated as follows: 3 n 1 I II II I WK = ( tij tij )( uij uij ) i= 1 j= 1 2 WF = 3 n II II I ( t )( u u ) ij ij ij i= 1 j= 1 3 n 1 I II II I WT = WK + WF = ( tij + tij )( uij uij ) i= 1 j= 1 2 t i u i = load components = deformatio n components n = number of elements on the energy test I = stage I II = stage II surface The WK and WF components for multi-dimensional loading situations are easily calculated in this way. The calculation of the loading system stiffness is more ambiguous because the LSS value is different for each element and for each direction in the model. The technique may be used to simulate the shear rupture of a potential large-scale asperity along a major plane of weakness. Seismic source parameters (e.g. modelled seismic moment, modelled seismic energy) can then be estimated Previous studies on shear-slip induced seismic activity Dennison and Van Aswegen (1993) examined the seismic behaviour of a major fault in a South African mine. An elastic model was used to calculate the distribution of Excess

49 40 Shear Stress upon the fault and a discontinuum model was used to simulate the nonelastic behaviour of the rockmass. Seismic and numerical modelling data were subsequently compared. They concluded that shear deformation of the fault, as predicted by the distribution of Excess Shear Stress and modelled shear displacement, was aseismic in areas of low normal stress and seismic in areas of high normal stress. Simser (1997) examined the stability of a large normal fault at the President Steyn Gold mine in the Welkom Goldfields in central South Africa. Seismic monitoring and numerical modelling formed the basis of his study. An elastic model (modelling of Excess Shear Stress) and an inelastic model (explicit modelling of shear deformation) were used to predict the shear displacement of the fault under mining induced stresses. The results indicated that the shear deformation of the fault was seismic in areas of high clamping stress. By analogy, Yabe et al (2003) studied the activity of acoustic emission during stable sliding of a granite specimen with a pre-cut fault. Several acoustic emission events were found to be generated on the pre-cut fault during mechanical shearing of the sample. The composite focal mechanism solution of the acoustic emission events, as determined from a first motion analysis, was consistent with that expected for the slip on the pre-cut fault. They also suggested that the activity of acoustic emission on the pre-cut fault was directly related to the surface roughness and normal stress level Summary This chapter reviewed the factors influencing the shear strength of major planes of weakness. An elasto-plastic Mohr-Coulomb model was proposed as a material model to describe the behaviour of the second graphitic shear at the Big Bell Gold mine. Asperities and barriers were presented as strong regions of stress concentrations along planes of weakness and as potential sources of large seismic events. The standard model of shear instability was introduced. It was shown that the strength of a seismic event is related to the scale of failure, the loading system stiffness and the post-failure source stiffness.

50 41 The relevant aspects of seismic monitoring and numerical modelling were also reviewed. Seismic monitoring provides information about the seismic component of the dynamic processes within the rockmass. Numerical modelling gives an overall view of potential rockmass behaviour. Both techniques contribute to understanding the causes and mechanisms of rockmass deformation. These techniques are therefore appropriate for investigating shear-slip induced seismic activity. Previous studies clearly demonstrate that seismic deformation along planes of weakness occurs in areas of higher shear resistance. Both the frictional properties of a plane and the level of confining normal stress along the plane serve to increase the shear resistance of the plane.

51 42 3. INCREMENTAL WORK DENSITY 3.1. Introduction Mechanical shearing along major planes of weakness is associated with rockmass damage and degradation. This very complicated phenomenon can generate substantial seismic activity. In this study, rockmass damage is defined as the damage induced around the plane region during mechanical shearing and does not necessarily refer to the damage caused to underground excavations. Denison and Van Aswegen (1993) and Simser (1997) examined the seismic behaviour of major faults in South African mines. Elastic modelling was used to calculate the distribution of Excess Shear Stress and non-linear modelling was used to examine the distribution of inelastic shear deformation upon the faults. The distribution of shear displacement, as predicted by either the distribution of Excess Shear Stress or the distribution of modelled inelastic shear deformation, was subsequently compared with the observed seismic activity upon the faults. Comparison of the modelled and seismic data indicated that fault-slip induced seismic activity occurred predominantly in areas of higher confining normal stress. The work by Denison and Van Aswegen (1993) and Simser (1997) showed that the distribution of inelastic shear deformation alone is not sufficient to describe the mechanical consequence of shear movement along major planes of weakness. Shear motion may be seismic or aseismic depending on the level of confining normal stress and the frictional properties along the planes. Based on these observations, the Incremental Work Density (IWD) is proposed as a measure that can be used to evaluate the relative likelihood of seismic activity during mechanical shearing on pre-existing planes of weakness. IWD adds another dimension to predicting the shear displacement alone. IWD is a function of both the level of driving shear stress and the change in inelastic shear deformation during mechanical shearing. IWD is expected to correlate with the level of rockmass damage and seismic activity induced during inelastic shear deformation. This chapter describes IWD in more details and presents how it can be modelled using Map3D.

52 Description of Incremental Work Density Work is done and energy is transferred when a force acts through a distance. The amount of work done or energy transferred depends on the amount of force exerted and the distance over which the force is applied. The displacement must be in the same direction of the applied force. IWD is related to the work done by the loading system during mechanical shearing. IWD measures the work done per unit area during a given increment of inelastic shear deformation. IWD is calculated as the product of the average shear stress and the change in inelastic shear deformation during a given mining increment or step. The general equation takes the following form: IWD = ( average shear stress ) ( change in inelastic shear deformatio n ) IWD is directly related to the frictional properties and the magnitude of the applied normal stress along a given plane of weakness. At low confining normal stress the plane displaces under low driving shear stress while at high confining normal stress the plane displaces under high driving shear stress. The effect of increasing the confining normal stress increases the frictional resistance of the plane. The plane then requires a greater shear stress to move. When the plane does move, it has the potential to induce more damage in the surrounding rockmass. IWD is intended to simulate the general phenomenon leading to rockmass degradation during mechanical shearing and is therefore expected to correlate with induced seismic activity Numerical modelling of Incremental Work Density IWD is readily calculated using Map3D. The plane of interest must be modelled using displacement discontinuity boundary elements and allowed to undergo inelastic shear deformation as mining advances. A multi-step mining sequence is required in order to simulate the progressing mining extraction. IWD is intended for planes of weakness at residual conditions. An elasto-perfectly plastic Mohr-Coulomb material model is

53 therefore well suited to describe the plane behaviour. IWD is calculated for each boundary element of the plane. 44 The nature of the solution for a given element is illustrated in Figure 3.1. The element deforms under a variable shear stress as mining advances. IWD compares the stressdeformation state of the element before and after a given mining step. IWD is simply taken as the area below the stress-deformation curve. IWD, between two subsequent mining steps (say mining step I and mining step II), is calculated as the product of the average shear stress and the change in inelastic shear deformation as follows: IWD IWD = S S D S ( II ) ( I ) SS + S = 2 Incremental Work = shear stress component I = min ing step I II = min ing step II ( II ) S ( ( D II ) ( ) D I ) Density = inelastic shear deformation component S S Shear stress (S S ) Mining Step IWD (2) IWD (3) IWD (4) Inelastic shear deformation (D S ) Figure 3.1. Concept of Incremental Work Density

54 3.4. Conclusion 45 The concept of Incremental Work Density (IWD) was developed to examine the seismic behaviour of a mine-wide and low-strength geological structure (i.e. the second graphitic shear at the Big Bell Gold mine). The modelled IWD was subsequently compared to the interpreted seismic activity in order to identify potential relationships between the numerical modelling predictions and the seismic data. The application of IWD to the case study of the second graphitic shear at the Big Bell Gold mine is described in the subsequent chapters.

55 46 4. BIG BELL GOLD MINE The Big Bell Gold mine is located in the Murchison province of Western Australia approximately 30 km west of the township of Cue. The gold deposit was discovered in 1904 and substantial ore production started in Historical production involved both open pit and underground mining. This chapter introduces to the Big Bell mine. Background information about the geological setting, actual mine setting, rockmass properties, stress state and rockburst history is included. Geological setting The Big Bell deposit is hosted by a regional greenstone and sedimentary sequence within the Murchison mineral field of the Yilgarn block (Handley and Cary 1990). The greenstone sequence forms the west limb of a regional anticlinal structure and is strongly attenuated and locally overturned. The greenstone is enclosed on either side by granite and, in the vicinity of the mine, is 1500 metres thick (Barrett and Player 2002). The lithological contacts adjacent to the orebody generally strike at around 30 from magnetic north and dip at around 72 to the east. The orebody dip varies locally from 55 to 80. Foliation is omnipresent but variably developed throughout the deposit (Barrett 1999). The local stratigraphy consists of several rock types. The geology of the deposit is illustrated in Figure 4.1 (Barrett and Palyer 2002). The mineralisation is hosted within potassium-feldspar schist (KPSH), altered schist (ALSH) and biotite schist (BISH). The mineralised zone has been defined along strike for over 1000 metres and to a depth of 1430 metres (Turner and Player 2000). In plan view the lode system is lensoid varying from 5 to 8 metres in width at the extremities and up to 50 metres in the central area of the deposit (Turner and Player 2000). The footwall sequence consists of cordierite schist (CRSH), felsic volcanic (FLVL) and amphibolite (AMPH). The CRSH unit is 1 to 6 metres thick while the FLVL unit is 5 to 10 metres thick (Barrett 1999). The CRSH unit forms the direct footwall followed respectively by the FLVL and AMPH units. The footwall excavations are predominantly located in the AMPH unit. Two major graphitic shears are located in the footwall of the orebody. The first structure forms the boundary between the AMPH and FLVL units and is located 5 to 15 metres from the footwall/orebody contact. The second structure is hosted within the

56 47 amphibolite unit and located at approximately 150 metres from the footwall/orebody contact. The hangingwall consists of intermediate schist (INSH). Several pegmatite dykes (PEGM) are also found to intrude all rock units. Footwall Lode Hangingwall Figure 4.1. Local geology of the Big Bell deposit (Barrett and Palyer 2002) Mine setting The Big Bell Gold mine is a low grade, high tonnage operation using a longitudinal sublevel caving method. The underground infrastructure consists of a series of sublevels. Access to each sublevel is provided by a footwall decline from an adit that can be accessed via the open pit. The mining procedure follows a top-down approach. A starting slot is cut and a series of ring patterns are subsequently drilled and blasted. The broken ore is drawn off after each blast and the method relies on the hangingwall to cave as mining progresses. Production is undertaken from one or two ore drives depending on the orebody width. The method is described as a high-production and low-cost method. This study covers the time period between April 2000 and February Figure 4.2 is a simplified model of the mining geometry showing the mining sequence used in the analysis. As illustrated, mining occurred in the lower levels and southern side of the upper levels. Mining step 1 corresponds to the production period prior to the installation of the seismic system. Mining step 2 corresponds to a period of extensive mining in the lower levels. This period was followed by a production shutdown. Production resumed in the upper levels at mining step 3 and resumed in the lower levels

57 48 at mining step 4. In Figure 4.2, the arrows indicate the direction of mining within the multi-step sequence. In the lower levels, mining retreated outwards from a central slot and inwards from the extremities of the orebody. In the upper levels, mining progressed from both extremities as indicated in Figure 4.2. Upper Levels - Level Level Level Level Level Level 410 Lower Levels - Level Level Level Level Level 535 Mining Step 1 Mining Step 2 Mining Step 3 Mining Step 4 Up to Apr 2000 Apr 2000 to Dec 2000 Dec 2000 to Dec 2001 Dec 2001 to Feb 2002 Figure 4.2. Simplified model of the Big Bell mining geometry Rockmass properties The rockmass at Big Bell can be divided into two broad domains: the footwall and the ore zone (Player 2000). The footwall is foliated but more massive. The ore zone is schistose with mica well developed on foliation planes. Seven joint sets have been identified within the mine. At any location two or three joint sets plus the foliation are generally present. The joints are usually planar, rough, clean and widely spaced. All rock units have a Rock Quality Designation (RQD) between 90% and 100% (Player 2000), which is classified as excellent. The Rock Tunnelling Quality Index (Q) ranges usually from 2.1 to 15.0 within the footwall (Player 2000) and is considered to be poor

58 49 to good. The value of Q ranges from 0.4 to 12.5 within the ore zone (Player 2000) and is considered to be extremely poor to good. The mean intact rock properties of some of the major rock units are presented in Table 4.1 (Turner and Player 2000). Rock Type UCS 50 Young's Modulus Poisson's Ratio Density MPa GPa kg/m3 Amphibolite (AMPH) Altered Schist (ALSH) Biotite Schist (BISH) Cordierite Schist (CRSH) Table 4.1. Mean intact rock properties at Big Bell (Turner and Player 2000) Stress state Stress measurements were undertaken at four sites using the HI cell overcoring method. The results are presented in Table 4.2 (Barrett and Player 2002). The results indicate that the stresses are high and deviatoric. The results also indicate that, at depth, the major principal stress is oriented perpendicular to the strike of the orebody. Site Principal Stress Depth Magnitude Dip Direction Dip m MPa 1 Major (S1) Intermediate (S2) Minor (S3) Major (S1) Intermediate (S2) Minor (S3) Major (S1) Intermediate (S2) Minor (S3) Major (S1) Intermediate (S2) Minor (S3) Table 4.2. Stress measurements at Big Bell (Barrett and Player 2002) Rockburst history The Big Bell Gold mine started experiencing relatively large seismic events and accompanying damage in February 1999 (Turner and Player 2000). Table 4.3 presents the rockburst history. The table has been reproduced from Barrett and Player (2002). A total of nineteen rockbursts were reported between February 1999 and May The

59 50 majority of these rockbursts were located in the footwall drives in the northern half of the mine. The mining step sequence used in this study is also shown in Table 4.3. Seven rockbursts were recorded during mining step 1, height rockbursts were reported during mining step 2, one rockburst occurred during mining step 3 and one rockburst was recorded during mining step 4. Date of rockburst Magnitude (Australian Geological Survey Organization) Cubic meter fallen/ejected Location MStep 1 MStep 2 MStep 3 MStep 4 12 February Level 460 Ore drive 16 June Level 435 Footwall drive 7 July Level 485 Footwall drive 9 August Level 485 Footwall drive 22 August Level 460 Footwall drive 25 November Level 460 Footwall drive 25 November Level 485 Footwall drive 6 April Level 510 Footwall drive 11 April Level 485 Footwall drive 8 May Level 535 Footwall drive 23 May Level 535 Footwall drive 17 June Level 535 Footwall drive 4 July Level 510 Footwall drive 9 July Level 510 Ore drive 2 September Level 510 Ore drive 5 May Level 410 Access drive 6 February Level March Level May Level 585 Table 4.3. Rockburst history at Big Bell (Barrett and Player 2002)

60 51 5. EXPOSURES OF THE SECOND GRAPHITIC SHEAR 5.1. Introduction The second graphitic shear at the Big Bell Gold mine intersects the development drives at several locations within the mine. Underground inspection of the structure exposures provided valuable information regarding its characteristics while surveyed exposure data were used to construct a model of the structure geometry. The structure model was essential in subsequent numerical modelling and seismic analysis. Interpretation of the shear resistance of the structure from the information collected was also incorporated in the numerical modelling. This chapter describes the characteristics of the second graphitic shear and details how the structure geometry was modelled Characteristics of the second graphitic shear The second graphitic shear is a major, mine-wide, continuous structure. The structure parallels the orebody. It is located in the footwall of the orebody at approximately 150 metres from the footwall/orebody contact. The structure is hosted within the amphibolite rock unit (AMPH) and intersects the development drives at several locations. The second graphitic shear is variably developed within the mine. The thickness of the structure varies from a few millimetres (Figure 5.1a) to several centimetres (Figure 5.1b). The filling consists of sheared rock materials within a graphitic matrix. The filling material is particularly weak and the graphite can serve as a lubricant on individual slip-surfaces within the shear zone. Physical degradation of the structure exposures is observed at several locations within the mine. Given the nature of the filling material, the second graphitic shear is believed to have a very low shear resistance. Sandy and Lee (1997) stated that small perturbations by mining are likely to initiate shearing on the structure. From visual inspection, no clear

61 52 apparent movement has occurred on the structure since mining started. This may be attributed to the limited number of exposures. Morrow et al (2000) carried out sliding experiments for fault gauge minerals at a laboratory scale. A friction angle of 8 was reported for the graphite mineral. (a) (b) 40 cm Figure 5.1. Variability of the structure thickness

62 Model of the second graphitic shear The second graphitic shear was modelled as a planar feature by linear regression of surveyed exposure data. Each exposure was assumed to be a single point within the exposure area. The coordinates of each exposure are summarized in Table 5.1. The location of exposure E4 deviates from the average of the overall data set and was not used to model the structure geometry. Exposure E4 was interpreted as a local irregularity along the structure. Given the very few exposure data available, it was difficult to verify the persistence of that irregularity and it was decided to reject this exposure location. The model was then constructed by linear regression of the remaining exposure locations. The plane was modelled to fit the points as well as possible. The plane with the smallest root-mean-square value or with the smallest normal distance from all points to the plane was selected. Exposure Northing Easting Depth m m m E E E E4 (Rejected) E Table 5.1. Exposure data used to model the structure geometry Figure 5.2 shows the modelled structure (i.e. fitted plane) and the exposure locations. Table 5.2 details the position and orientation of the plane and gives the corresponding root-mean-square value. Considering the calculated root-mean-square value and extent of the structure within the exposure array, the fitted plane was assumed to be representative of the actual structure geometry. Comparison with the seismic activity recorded around the second graphitic shear confirmed the position and orientation of the modelled structure (Chapter 7).

63 54 (a) C1 C4 E1 E3 E2 E5 E4 (Rejected) C2 Second Graphitic shear C3 (b) Second Graphitic shear E1 E2 E3 E4 E5 Figure 5.2. View looking east (a) and view looking north (b) showing the modelled plane and exposure locations

64 55 Fitted Plane Corner Coordinates Corner Northing Easting Depth m m m C C C C Fitted Plane Orientation Dip Direction 88 Dip 68 Fitted Plane Root-Mean-Square Value RMS Value 2 m Table 5.2. Position and orientation of the modelled structure and corresponding rootmean-square value 5.4. Summary Exposure data of the second graphitic shear were essential for the study. Underground inspection of the exposures provided a means to describe the characteristics of the structure. Information collected clearly suggested that the second graphitic shear is potentially very weak in shear. Surveyed exposure data were used to model the geometry of the second graphitic shear. The structure was modelled as a planar feature through the surveyed exposure data. This work was used in subsequent numerical modelling and seismic analysis.

65 56 6. NUMERICAL MODELLING 6.1. Introduction It is likely that the stability of the second graphitic shear was influenced by the geometry and sequence of the stopes, the geometry and nature of the shear structure itself, the pre-mining stress state and the nature of the rockmass. Numerical modelling was undertaken in order to investigate how mining induced stresses contributed to generate seismic activity in the vicinity of the second graphitic shear. A multi-step model of the Big Bell Gold mine was created using the three-dimensional boundary element code of Map3D. The model was used in order to simulate the non-linear response of the second graphitic shear. An elasto-plastic Mohr-Coulomb material model was used to describe the behaviour of the shear structure. The model was designed to provide a high definition of the structure, which was automatically discretized into 2048 displacement discontinuity boundary elements. The stress and deformation components upon the structure were calculated for each element and mining step. The Incremental Work Density (IWD) was subsequently calculated from the numerical modelling results for each element of the structure and each mining step. This chapter presents the numerical model that was created for this study. The modelling results are then presented and discussed. Space contouring is used to display the results Description of the Map3D model The numerical model required information on the mining geometry, the geometry of the second graphitic shear, the mining sequence, the pre-mining stress state, the elastic properties of the rockmass and the mechanical properties of the shear structure. Mining and structure geometries The model geometry is illustrated in Figure 6.1. The model consists essentially of an open pit, underground stopes and the second graphitic shear. The second graphitic

66 shear was physically incorporated within the model in order to simulate its non-linear behaviour. 57 The open pit and underground stopes were constructed using Fictitious Force blocks (FF blocks) while the second graphitic shear was constructed using a single Displacement Discontinuity plane (DD plane). The model of the second graphitic shear was created from surveyed exposure data and has been described in Chapter 5. For modelling purposes, the shear structure was given a very low thickness (i.e metres) in order to prevent any elastic deformation to occur on the plane. The physical dimensions of the model are given in Figure 6.2. The local influence of the development drives was ignored because the analysis focused on modelling the mine-scale behaviour of the second graphitic shear. The influence of the localized cave zone was also ignored because of the high strike length to thickness ratio of the mining geometry. The influence of other major structures (e.g. first graphitic shear) was deemed negligible due to their significant distance from the second graphitic shear. It could be demonstrated that these influences are not significant on the modelled response of the second graphitic shear. Open pit Underground stopes Second Graphitic Shear (Modelled area = m 2 ) Figure 6.1. Isometric view of the Big Bell Map3D model

67 58 (a) Mining Blocks 536m 274m 504m (b) Mining Blocks Second Graphitic Shear 536m m Figure 6.2. View looking west (a) and view looking north (b) showing the physical dimensions of the Map3D model

68 59 Mining sequence A multi-step mining sequence was incorporated within the model. The mining steps were determined from the production-blasting database. The four mining steps used in the model are illustrated in Figure 6.3. Mining step 1 included the mining prior to the installation of the seismic system. This mining step was essentially used to initialise the model. Mining step 2 included the subsequent mining until the production shutdown. Mining occurred predominantly in the lower levels during step 2. Mining resumed in the upper levels at mining step 3 and resumed in the lower levels at mining step 4. Upper Levels Lower Levels Mining Step 1 Mining Step 2 Mining Step 3 Mining Step 4 Figure 6.3. Mining sequence used in Map3D

69 60 Pre-mining stress state The pre-mining stress state was determined from previous stress measurements. The results have been listed in Table 4.2. The first measurement was rejected because it deviated from the normal trend observed at depth. The measurements 2, 3 and 4 were relatively consistent with each other and were assumed to more accurately describe the pre-mining stress state. The principal stress magnitudes were determined from the best-fit lines illustrated in Figure 6.4. These lines were forced to intercept zero. The principal stress orientations were determined from the stereographic projection illustrated in Figure 6.5. The premining stress state used in the model is summarized in Table 6.1. Depth is negative down. Principal Stress Magnitude VS Depth Rejected Principal Stress Magnitude (MPa) S1 S2 S Depth (m) Figure 6.4. Principal stress magnitudes

70 61 S3 S1 S2 Figure 6.5. Principal stress orientations Pre-mining Stress State Principal Stress Magnitude Dip Direction Dip MPa Major (S1) x Depth Intermediate (S2) x Depth Minor (S3) x Depth Table 6.1. Pre-mining stress state used in Map3D

71 62 Rockmass properties The rockmass behaviour was modelled using a linearly elastic constitutive scheme. The general theory of linear elasticity is based on the assumption that the stress components at a point are directly proportional to the strain components at that point. The proportionality constants are the Young s modulus and the Poisson s ratio. The Young s modulus defines the gradient of the stress-strain curve while the Poisson s ratio defines the ratio of radial to axial strain. Linearly elastic materials are characterized by the absence of mechanical failure regardless of the stress applied and by the reversibility of the deformation when the stress is removed. The two elastic constants used in the model are given in Table 6.2. These elastic constants have been determined from previous laboratory measurements and are typical of the footwall amphibolite rock unit (AMPH). Elastic Rockmass Properties Young's Modulus (MPa) 67,100 Poisson's Ratio 0.28 Table 6.2. Elastic rockmass properties used in Map3D Properties of the second graphitic shear The second graphitic shear was modelled using a linearly elastic-perfectly plastic constitutive scheme. A standard Mohr-Coulomb strength criterion was used as the yield function. This material model was introduced in Chapter 2. According to this model, the structure is deemed to behave in a linearly elastic fashion up to the point where it reaches its strength and after that, the structure behaviour is deemed to be perfectly plastic. This model requires four parameters: the normal modulus, the shear modulus, the cohesion and the friction angle. The normal and shear moduli are used to describe the response of the structure in the elastic range. The cohesion and friction angle are used to define the Mohr-Coulomb linear strength envelope. The linearly elasticperfectly plastic constitutive behaviour is only a gross approximation of the actual structure behaviour.

72 63 The structure properties used in the model are given in Table 6.3. In practice, the normal and shear moduli are rather difficult to determine. However, these values were not of high importance given the very low thickness assigned to the structure plane. For modelling purposes, the normal and shear moduli were estimated from the rockmass Young s modulus and Poison s ratio as follows: E Normal mod ulus = 3 1 E Shear mod ulus = 2 1 where v = Poisson' s ratio ( 2v) ( v) E = Young' s mod ulus The residual values were set equal to the peak values in the model because the shear structure was considered to be at a residual state of shear strength. Structure Properties Normal Modulus (MPa) 50,800 Shear Modulus (MPa) 26,200 Cohesion (MPa) 0 Friction Angle ( ) 8 Table 6.3. Structure properties used in Map3D Control parameters and discretization of the model The control parameters are used to control the discretization process, the lumping processes and the accuracy of the model solution. The parameters NLD, NIT, STOL and RPAR are the basic solution parameters. During the discretization process, the model geometry is divided into boundary elements and grid planes are divided into a series of field points. The parameters DOL and DON control the FF blocks, DD planes and grid planes discretization based on their proximity to other FF blocks, DD planes and grid planes. The parameter AL is used to control the minimum boundary element length and should be set equal to twice the smallest pillar or stope width. The parameter AG is used to control the minimum grid spacing and should be set equal to the smallest dimension of interest. The parameters DOC, DOE and DOG are related to the lumping

73 processes. All the control parameters directly impact on solution accuracy, model size and run-time. 64 The control parameters that were used in this study are given in Table 6.4. The parameters NLD, NIT, STOL and RPAR were set as recommended by the Map3d manual. The parameters DOL, DON, DOC, DOE and DOG were set as recommended by the Map3D manual to expect a numerical solution with less than 5% error. AL and AG were set to 5, which was within the guidelines previously described. The parameter DOR was set to 5 as recommended by the Map3D manual. A maximum element width of 30 metres was assigned to the shear structure in order to generate a fine and uniform discretization of the plane. The structure was therefore divided into 2048 equal-area boundary elements as illustrated in Figure 6.6. The complete Map3D input file (INP) is given in Appendix A. The input file is an editable ASCII file and contains all the input data required by Map3D to perform an analysis. The file is organized into seven sections: project title, control parameters, block specification list, coordinate specification list, material properties list, grid specification list and mining step specification list. Appendix B contains the complete Map3D log file (LOG). The log file records the activity during a Map3D analysis. The accuracy of the model solution was found to be particularly affected by the parameter DOC. Appendix C illustrates the distribution of shear stress upon the second graphitic shear for different values of DOC. DOC was set to 4 in this study in order to maximize the accuracy of the model solution. Control Parameters Maximum Number of Load Steps (NLD) 10,000 Maximum Number of Iterations (NIT) 10,000 Stress Tolerance (STOL) 0.1 Relaxation Parameter (RPAR) 1.2 Element Length (AL) 5 Grid Spacing (AG) 5 Grid Discretize (DOL) 4 Element Discretize (DON) 1 Matrix Lumping (DOC) 4 Element Lumping (DOE) 8 Grid Lumping (DOG) 8 Aspect Ratio (DOR) 5 Table 6.4. Control parameters used in Map3D

74 equal-area elements Figure 6.6. Displacement discontinuity boundary elements along the modelled shear structure 6.3. Map3D results The stress and deformation components upon the second graphitic shear were calculated for each element and mining step as part of the modelling process. The Incremental Work Density (IWD) was subsequently computed from the numerical modelling results. IWD was calculated for each element of the shear structure and each mining step as the product of the average driving shear stress and the change in inelastic shear deformation. The procedure followed was described in Chapter 3. The numerical model predicted permanent or inelastic shear deformation upon the second graphitic shear as mining advanced. Figure 6.7 illustrates the distribution of change in inelastic shear deformation after mining step 2, mining step 3 and mining step 4. The values are cumulative from mining step 1. The changes in inelastic shear deformation ranged from 0 to metres. The change in inelastic shear deformation was higher upon a zone below the stopes during the overall period considered. Shear deformation occurred predominantly upon the northern half of the zone below the stopes during mining step 2. The zone extended

75 66 to the south during mining step 3 and continued to grow during mining step 4. The highest values of shear deformation were recorded upon the southern side of the zone below the stopes. The model also predicted permanent shear deformation upon the upper zone of the shear structure. However, shear deformation upon the upper zone was less significant than upon the zone below the stopes. Figures 6.8 illustrates the distribution of normal stress and Figure 6.9 illustrates the distribution of shear stress upon the second graphitic shear as at mining step 4. These figures indicate that shear deformation upon the zone below the stopes was triggered by a decrease in normal stress and an increase in shear stress. Shear deformation upon the upper zone was associated with a significant decrease in both normal and shear stresses. Mining created a stress shadow effect that reduced the stress levels upon the upper zone. Figure 6.10 illustrates the distribution of IWD upon the second graphitic shear after mining step 2, mining step 3 and mining step 4. The values are cumulative from mining step 1. The IWD values ranged from 0 to Joules per square metre. IWD was higher upon the zone below the stopes during the overall period considered. IWD was higher upon the northern half of the zone below the stopes during mining step 2. The zone extended to the south during mining step 3 and continued to grow during mining step 4. The highest values of IWD were recorded upon the central part of the zone below the stopes. The low values of IWD upon the upper zone of the second graphitic shear were attributed to the stress shadow effect created by mining. The confining normal stress was reduced by the stress shadow. Therefore, the driving shear stress needed to cause shear deformation was lower upon the upper zone. Low values of IWD were therefore predicted upon the upper zone of the shear structure. Inelastic shear deformation is expected to induce more significant rockmass damage and seismic activity upon areas of higher driving shear stress. IWD is related to both the level of driving shear stress and the change in elastic shear deformation and is therefore expected to correlate with the level of seismic activity induced during mechanical shearing. The distribution of IWD upon the second graphitic shear indicates that shear deformation was most likely seismic upon the zone below the stopes and most likely aseismic upon the upper zone of the shear structure.

76 67 (a) (b) (c) Figure 6.7. Views looking west showing the distribution of change in inelastic shear deformation upon the second graphitic shear after mining step 2 (a), mining step 3 (b) and mining step 4 (c). The values are cumulative from mining step 1.

77 68 Figure 6.8. View looking east showing the distribution of normal stress upon the second graphitic shear as at mining step 4. Figure 6.9. View looking east showing the distribution of shear stress upon the second graphitic shear as at mining step 4.

78 69 (a) (b) (c) Figure Views looking west showing the distribution of IWD upon the second graphitic shear after mining step 2 (a), mining step 3 (b) and mining step 4 (c). The values are cumulative from mining step 1.

79 6.4. Numerical modelling limitations and uncertainties 70 In this study, numerical modelling was undertaken to simulate the response of the second graphitic shear to mining activity and to investigate how mining induced stresses contributed to generate seismic activity in the vicinity of the shear structure. In order to use the techniques presented, one must have a reasonable degree of confidence in the model predictions. The applicability of numerical modelling techniques is limited by the lack of detailed knowledge of the input parameters, the approximations in the model formulation, the inherent limitations of the modelling approach and the error in the numerical solution. Due to model limitations and uncertainties, numerical modelling does not provide absolute results. Even the most complicated model cannot predict exactly the very complicated response of the rockmass to mining. However, it is commonly accepted that numerical modelling provides valuable information about the rockmass response to mining activity and remains a powerful tool well adopted at exploring the behaviour of major geological structures subject to various loading conditions Summary A multi-step Map3D model was created in order to examine the effect of mining induced stresses on the second graphitic shear. The shear structure was divided into 2048 elements. Stress components, deformation components and Incremental Work Density (IWD) were calculated for each element and mining step. Numerical modelling predicted permanent shear deformation upon the second graphitic shear as mining advanced. Higher values of change in inelastic shear deformation and IWD were recorded upon a zone below the stopes. Permanent shear deformation was also predicted upon the upper zone of the shear structure but occurred under lower normal and shear stresses due to a stress shadow effect created by mining. This stress shadow effect directly resulted in low values of IWD upon the upper zone of the shear structure. The distribution of IWD upon the second graphitic shear indicates that shear

80 deformation was most likely seismic upon the zone below the stopes and most likely aseismic upon the upper zone of the shear structure. 71

81 72 7. SEISMIC MONITORING 7.1. Introduction The Big Bell Gold mine uses an ISS seismic system to monitor the seismic activity within the mine. The system was installed in April 2000 in response to increasing seismic activity and rockburst severity at the mine. The system has been upgraded several times as mining advanced. The initial seismic sensors were located in the lower levels to provide an adequate coverage of the mining front. When mining started in the upper levels, additional sensors were installed in both the upper and lower levels. The system was comprised of 12 sensors in April 2000 when it was first installed. In February 2002, the seismic array consisted of 15 sensors. Several types of sensors have been used over the life of the system including: triaxial accelerometers, uniaxial accelerometers, triaxial geophones and uniaxial geophones. The seismic activity recorded in the vicinity of the second graphitic shear between April 2000 and February 2002 was back analysed in order to examine and characterize the seismic behaviour of the shear structure. This chapter presents and discusses the analysis Selected seismic events Figure 7.1 is a plan view of the 585 Level illustrating the spatial distribution of seismic events that were recorded on this level during the overall period considered. The first and second graphitic shears are also shown. For ease and clarity of presentation, the seismic events recorded within a distance of 30 metres on each side of the second graphitic shear are shown in red. The clustering of seismic events around the shear structure clearly indicates that the structure was seismically active during the period considered. Figure 7.2 illustrates the number of seismic events recorded around the second graphitic shear as a function of distance away from the shear structure. The density of seismic events decreases as a function of distance and reaches a plateau at a distance of 30

82 73 metres from the shear structure. This suggests that the seismic events recorded within a distance of 30 metres of the second graphitic shear were predominantly induced by the shear structure and that the seismic events recorded at a distance greater than 30 metres from the second graphitic shear were not caused by the shear structure. The seismic events recorded within a distance of 30 metres on each side of the second graphitic shear were therefore selected from the seismic database. A total of 1476 seismic events were selected from the database during the overall period considered. Plan View Level First Graphitic Shear Easting (m) DataBase GrSh2 30m 30m Second Graphitic Shear Northing (m) Figure 7.1. Seismic events recorded within 30 metres on each side of the second graphitic shear (585 Level)

83 74 Number of Events Versus Distance Number of Events Seismic events were predominantly caused by the second graphitic shear seismic events were recorded within a distance of 30 meters on each side of the second graphitic shear Seismic events were not caused by the second graphitic shear Distance (m) Figure 7.2. Number of seismic events recorded around the second graphitic shear as a function of distance Source location errors of the selected seismic events The location of a seismic event is calculated from the P- and/or S-wave arrival times, which are determined from recorded waveforms, the P- and/or S-wave velocity model and the seismic sensor coordinates. These data have associated errors that can reduce source location accuracy. Source location accuracy also depends on the number of seismic sensors used to locate the event, the distribution of sensors with respect to the position of the event, the nature and complexity of the event mechanism and the numerical method used to locate the event. Poor location accuracy can severely limit seismic data interpretation. It is recognized that seismic events recorded with an optimised array can be used to delineate areas of seismic activity within a mine and can be used to identify geological structures that are activated as a result of mining. Event location is usually sufficient to relate events to a particular structure. It is also accepted that reasonable location can be obtained for events within half an array diameter outside the array.

84 75 The Big Bell seismic system was established in 2000 to record seismic activity around active excavations. In order to keep a rigid control on the collected seismic data, the following processing guidelines were undertaken: Only signals that triggered at least five seismic sensors were manually processed. Blasts and mining noises were rejected. P- and/or S-wave arrivals times of seismic events were manually determined from recorded waveforms. Seismic events were processed using a calibrated velocity model. Albrecht (2000) determined the seismic wave velocities using signals from blasts with known locations. The average velocities for the P- and S-waves were evaluated to be approximately 6250 m/s and 3670 m/s respectively. The second graphitic shear is located at some distance from the mine workings. In this context, one must recognize that the seismic sensors are not optimally distributed around the shear structure. However, the level of clustering on each side of the shear structure clearly indicates that the structure was active during the time period considered and suggests that one must be able to accept the errors in source location calculation and use the data with a reasonable level of confidence. Figure 7.3 illustrates the source location error distribution of the selected seismic events as calculated by the ISS seismic system. The computed location errors were found to be generally small with eighty-nine per cent of the seismic events having an error of less than 6 metres.

85 76 Source Location Error Distribution of Selected Seismic Events % of the seismic events Source Location Error < 6m Number of Seismic Events % of the seismic events 6m < Source Location Error < 20m Source Location Error (m) Figure 7.3. Source location error distribution of the selected seismic events Space distribution of the selected seismic events The spatial distribution of seismic events upon the second graphitic shear as mining advanced is presented in Figure 7.4. The data were incrementally increased for each subsequent mining step to account for the past seismic activity and more recent activity around the shear structure. The mining geometry is also shown. For ease and clarity of presentation, the seismic events are divided into three intervals of moment magnitude. Figure 7.4 indicates that the seismic events predominantly clustered upon a zone below the stopes during the overall period considered. Seismic events predominantly clustered upon the northern half of the zone below the stopes during mining step 2. The seismically active zone extended to the south during mining step 3 and continued to grow during mining step 4. Seismic shear deformation, as predicted by the numerical model (i.e. modelled Incremental Work Density), was found to follow a similar pattern as mining advanced.

86 77 (a) View Looking West Depth (m) MoMag < 0 0 =< MoMag < 1 MoMag >= Northing (m) (b) View Looking West Depth (m) MoMag < 0 0 =< MoMag < 1 MoMag >= Northing (m) (c) View Looking West Depth (m) MoMag < 0 0 =< MoMag < 1 MoMag >= Northing (m) Figure 7.4. View looking west showing the distribution of seismic events around the second graphitic shear after mining step 2 (a), mining step 3 (b) and mining step 4 (c). The seismic data are cumulative from mining step 1.

87 78 Source parameters of the selected seismic events Figure 7.5 shows the frequency-moment magnitude distribution of the selected seismic events. The moment magnitudes ranged from -1.7 to 1.3. A straight line of parameter a (2.0) and parameter b (1.9) was fitted to the slope of the distribution. The distribution indicates that the sensitivity of the seismic network began to fall off at approximately moment magnitude -0.6 in the vicinity of the shear structure during the period considered. Figure 7.6 shows the energy-moment relation of the selected seismic events. The seismic moments ranged from 3.8E+06 to 1.1E+11 Newton-metres and the seismic energies ranged from 1.4E-01 to 8.5E+05 Joules. Frequency - Moment Magnitude Distribution The sensitivity of the seismic network began to fall off at moment magnitude -0.6 Number of Events Log (n) = a - b (MoMag) a = 2.0 b = Moment Magnitude Figure 7.5. Frequency-moment magnitude distribution of the selected seismic events

88 79 Seimic Energy - Seismic Moment Relation 1.00E E E+05 Seismic Energy (J) 1.00E E E E E E E E E E E E E E+12 Seismic Moment (Nm) Figure 7.6. Energy-moment relation of the selected seismic events Source mechanisms of the selected seismic events The S- to P-wave energy ratio is recognized as an important indicator of the mechanism of a seismic event. A seismic event with an S- to P-wave energy ratio greater than ten is dominated by a shearing component of failure. Any enrichment of P-wave energy and/or depletion of S-wave energy indicate that additional non-shearing volumetric components have been added to the failure mechanism. Figure 7.7 illustrates the distribution of the S- to P-wave energy ratio of the selected seismic events. The distribution indicates that 20% of the seismic events were dominated by a shearing component of failure and that the remaining population of events contained additional non-shearing volumetric components of failure. The distribution simply reflects the diversity of the seismic failure mechanisms that accompanied the overall shear movement of the second graphitic shear. Seismic failure mechanisms may have included frictional sliding, shearing and volumetric fracturing. Albrecht (2001) conducted a first motion analysis on the largest seismic events recorded in the vicinity of the second graphitic shear. The combined fault-plane solution roughly

89 80 matched the orientation of the second graphitic shear/foliation planes. His results suggest that the mechanism of the largest events was shearing or sliding and that it may have occurred on the second graphitic shear structure or foliation planes. S:P Energy ratio 100% 90% 80% 80% of the seismic events Frequency (%) 70% 60% 50% 40% S- to P-wave energy ratio < 10 20% of the seismic events S- to P-wave energy ratio > 10 30% 20% 10% 0% 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 S:P Energy ratio Figure 7.7. S- to P-wave energy ratio distribution of the selected seismic events Time distribution of the selected seismic events The cumulative number of seismic events recorded in the vicinity of the second graphitic shear during the period considered is given in Figure 7.8. The overall period is further divided into the mining steps. The geometry of the stopes for each mining step has been shown in Figure 6.3. The time of the production blasts taken in the lower and upper levels are also shown in Figure 7.8. The slope of the cumulative curve indicates the rate of occurrence of seismic events. A steeper slope corresponds to a higher rate of occurrence. Mining Step 1 (up to April 2000) Mining step 1 was the period prior to the installation of the seismic monitoring system. Obviously, no seismic events were recorded during this period.

90 81 Mining Step 2 (April 2000 to December 2000) Extensive mining occurred in the lower levels during mining step 2 (April 2000 to August 2000). A relatively high occurrence rate of seismic events accompanied this period. Mining was subsequently followed by a production shutdown (August 2000 to December 2000). When mining ceased in August 2000, the occurrence rate decreased slowly. A relatively constant occurrence rate was attained after five months of inactivity when mining resumed in the upper levels. Mining Step 3 (December 2000 to December 2001) Production resumed in the upper levels at mining step 3. The occurrence rate was relatively constant and the lowest recorded during the overall period considered. Mining Step 4 (December 2001 to February 2002) Production resumed in the lower levels at mining step 4 and was accompanied by an increase in the occurrence rate. Time distribution of the selected seismic events gave important insights into the seismic behaviour of the second graphitic shear. It was shown that the seismic activity recorded around the shear structure was strongly influenced by mining and was predominant when mining occurred in the lower levels. The decreasing rate of occurrence of seismic events during the shutdown period may indicate that the shear displacement of the shear structure in response to mining activity was time-dependant.

91 82 Cumulative Number of Events VS Time 1600 Shutdown 1400 Cumulative Number of Events Mining Step 1 Mining Step Events 4.2 Events/Day Mining Step Events 0.8 Events/Day Mining Step Events 2.4 Events/Day /01/ /05/ /08/ /11/ /02/ /06/ /09/ /12/25 Time (YYYY/MM/DD) Blasts - Upper Levels Blasts - Lower Levels Figure 7.8. Time distribution of the selected seismic events 7.3. Gridding and smoothing of the selected seismic data Gridding and smoothing were used to examine the spatial distribution of seismic activity around the second graphitic shear as mining advanced. Seismic activity upon the shear structure was interpreted from individual seismic moment and seismic energy values. The gridding and smoothing techniques are described below. Gridding Gridding was used to generate a two-dimensional ordered array of values from the three-dimensional irregularly distributed seismic data. A grid containing 2048 equalarea elements was fitted to the modelled structure. The grid provided by Map3D during the discretization process was used. The grid has been shown in Figure 6.6. The grid spacing was 17.2 metres along the strike and 20.6 metres along the dip of the plane. Each grid element was square metres. Each seismic event was assumed to be a point in space and time with a given seismic moment value and seismic energy value. The sum of seismic moments and sum of seismic energies were calculated for each element and mining step from the seismic events included within the corresponding element. Figure 7.9 illustrates the gridding technique.

92 83 Element Seismic Event Figure 7.9. Gridding of selected seismic data The gridded values were calculated for each element and mining step as follows: Mo E Gridded Gridded = = NEv i= 1 NEv i= 1 E Mo i i NEv = number of seismic events within the element Smoothing Smoothing was used to reduce the local variability of the gridded values due to the local complexities along the shear structure. Smoothing also accounted for source location accuracy and source size, which was initially ignored in the gridding process. A simple inverse distance weighting method was used. For each node and mining step, the gridded values were smoothed by averaging the weighted sum of all the nodes included within a search radius. A node was taken as the centre point of a given element. Close nodes were heavily weighted and more distant nodes were lightly weighted. In this study, the search radius was set to 30 metres. To eliminate the outliers, only smoothed values estimated from at least three seismic events were kept. Figure 7.10 illustrates the smoothing technique.

93 84 Node Search Radius (R) Weighting Distance (d i ) Figure Smoothing of gridded data The smoothed values were calculated for each node or element as follows: Mo E Smoothed Smoothed = = NNo i= 1 NNo i= 1 E Mo Gridded i NNo i= 1 Gridded i NNo i= 1 w i w i w w i i NNo = number of di wi = 1 R nodes within the search radius The gridding and smoothing techniques were used to interpret the seismic behaviour of the second graphitic shear in space and time. These techniques also provided a means to compare and identify potential relationships between the numerical modelling predictions and the seismic data (Chapter 8). The spatial distributions of smoothed seismic moment and smoothed seismic energy values upon the second graphitic shear as mining advanced are presented in Figure 7.11 and Figure 7.12 respectively. The values were incrementally increased for each

94 85 subsequent mining step to account for the past seismic activity and more recent activity around the shear structure. The distributions of smoothed seismic moment and smoothed seismic energy values were found to be very similar. This was expected since seismic moment increases with increasing seismic energy. By comparing the unprocessed seismic data (Figure 7.4) with the manipulated seismic data (Figures 7.11 and 7.12), it can be seen that the gridding and smoothing techniques have not changed the character of the original dataset. In particular, the zones of low and intense seismic activity were preserved. The interpreted seismic monitoring data indicate that seismic activity was predominant upon a zone below the stopes during the overall period considered. Seismic activity occurred predominantly upon the northern half of the zone below the stopes during mining step 2. The seismically active zone extended to the south during mining step 3 and continued to grow during mining step 4. The recorded seismic patterns were found to be very similar to the predicted modelled patterns (Chapter 6). However, the seismic patterns were more complex than the modelled patterns. The seismic patterns reflected the spatial and temporal variation in stress and displacement along the shear structure, while the numerical model only gave an overall view of the structure behaviour. The complexity of the seismic patterns may have been attributed to the presence of irregularities along the shear structure. A zone of low seismic activity has been outlined in Figure 7.11 and Figure This zone can be justified by multiple explanations. For example, the zone may indicate the presence of an asperity. The low level of seismic activity recorded within the asperity region may indicate that shear deformation was arrested in that region. However, the high level of seismic activity outside the asperity region may indicate that the surrounding part of the shear structure deformed. This may indicate that shear stress was building up within the asperity region and that an eventual violent rupture of the asperity could have occurred. This asperity would have radiated a considerable amount of seismic energy if it yielded. Another explanation for this zone of low seismic activity may be the presence of a weaker region that deformed mainly aseismically.

95 86 (a) Zone of Low Seismic Activity (b) (c) Figure Views looking west showing the distribution of smoothed seismic moment values upon the second graphitic shear after mining step 2 (a), mining step 3 (b) and mining step 4 (c). The values are cumulative from mining step 1.

96 87 (a) Zone of Low Seismic Activity (b) (c) Figure Views looking west showing the distribution of smoothed seismic energy values upon the second graphitic shear after mining step 2 (a), mining step 3 (b) and mining step 4 (c). The values are cumulative from mining step 1.

97 7.4. Seismic monitoring limitations and uncertainties 88 It is commonly accepted that seismic data provide important information about the rockmass response to mining activity. However, the applicability of seismic monitoring techniques to mining induced seismic activity involves significant inherent limitations that can reduce the usefulness of the seismic data. The applicability of seismic monitoring techniques is limited by our lack of knowledge about source rupture characteristics. The use of simplistic source models to characterize the nature and complexity of such rupture processes limits the amount of useful information that can be obtained from the recorded waveforms. The applicability of seismic monitoring techniques is also limited by the inability of the seismic system to retrieve all useful information about the rockmass behaviour within the volume of interest. There are several factors limiting the resolution or sensitivity of the seismic system. These factors include characteristics of the seismic system in terms of frequency range and amplitude range, rate at which seismic events can be recorded and processed by the seismic system, distribution of seismic sensors around or throughout the volume of interest and mine ambient noise level. In this study, individual seismic energy and seismic moment values were used to interpret the seismic activity recorded around the second graphitic shear. In order to use the approach presented, one must have a reasonable degree of confidence in the calculated source parameter estimates. Source parameter estimates are affected by several factors including the characteristics of the seismic system in terms of frequency range and amplitude range, the number of seismic sensors used for source parameter calculation, the source location accuracy, the seismic sensor coordinates, the signal-to-noise ratio, the P- and S-wave velocity model, the P- and S-wave attenuation, the P- and S-wave scattering, the rock density at the source, the window length used for source parameter calculation and the uncertainties between the processed data and the source model fit. Since many of the influencing factors are uncertain or variable, the measured source parameter estimates will also reflect that uncertainty. However, it is recognised that the variation in source parameter estimates is significantly greater than the uncertainty in the data (Mendecki et al 1999).

98 Therefore, these uncertainties should not prevent the interpretation and comparison of seismic data collected by the same seismic system. 89 If seismic monitoring techniques are to be of any use, one must accept the fundamental limitations of these techniques and accept the inherent uncertainties of the measured seismic data Summary The seismic behaviour of the second graphitic shear was examined. Back analysis of the seismic data indicated that the seismic activity occurred predominantly upon a zone below the stopes. The failure mechanism of individual seismic events included shearing and non-shearing volumetric processes. Time distribution of the seismic events showed that the shear deformation of the structure and accompanying seismic activity were strongly related to mining activity and were predominant when mining occurred in the lower levels. Time distribution also indicated that the shear deformation and accompanying seismic activity were time-dependant.

99 90 8. COMPARISON OF THE MODELLED AND SEISMIC DATA 8.1. Introduction The modelled Incremental Work Density (IWD) was defined for each element of the second graphitic shear and each mining step in Chapter 6. The interpreted seismic activity (measured as either smoothed seismic moment or smoothed seismic energy) was defined for each element of the shear structure and each mining step in Chapter 7. This chapter examines the relationship between the modelled IWD and the interpreted seismic activity Spatial distribution of the modelled and seismic data Figure 8.1 (smoothed seismic moment) and Figure 8.2 (smoothed seismic energy) illustrate the spatial distributions of interpreted seismic activity upon the second graphitic shear as mining advanced. The seismic values were incrementally increased for each subsequent mining step to account for the past seismic activity and more recent activity around the shear structure. In order to facilitate the comparison of the modelled and seismic data, the zone of IWD greater than J/m 2 is highlighted. A satisfactory relationship was found between the spatial distribution of interpreted seismic activity (measured as either smoothed seismic moment or smoothed seismic energy) and the spatial distribution of modelled IWD. The seismic events recorded in the vicinity of the second graphitic shear predominantly clustered around a zone of higher IWD upon the shear structure as mining advanced. The IWD parameter was found to be reasonably successful in delineating the seismically and non-seismically active zones upon the second graphitic shear.

100 91 (a) IWD > J/m 2 (b) IWD > J/m 2 (c) IWD > J/m 2 Figure 8.1. Spatial distribution of smoothed seismic moment versus spatial distribution of modelled IWD upon the second graphitic shear. Values are cumulative as at mining step 2 (a), mining step 3 (b) and mining step 4 (c).

101 92 (a) IWD > J/m 2 (b) IWD > J/m 2 (c) IWD > J/m 2 Figure 8.2. Spatial distribution of smoothed seismic energy versus spatial distribution of modelled IWD upon the second graphitic shear. Values are cumulative as at mining step 2 (a), mining step 3 (b) and mining step 4 (c).

102 8.3. State of Incremental Work Density versus interpreted seismic activity 93 Figures 8.3 (smoothed seismic moment) and 8.4 (smoothed seismic energy) illustrate the state of IWD for all the elements of the second graphitic shear. The values are cumulative as at mining step 4. The cumulative values were calculated at the end of each mining step but revealed similar patterns as the ones illustrated in Figures 8.3 and 8.4. Therefore, only the cumulative values as at mining step 4 are presented. Each coordinate point on the graphs corresponds to a yielding or shearing element of the second graphitic shear. The x-axis scales the change in inelastic shear deformation while the y-axis scales IWD per unit shear deformation. IWD per unit shear deformation is also equivalent to the average level of driving shear stress during mechanical shearing. For ease and clarity of presentation, the seismically active elements are divided into four smoothed seismic moment intervals in Figure 8.3 and divided into four smoothed seismic energy intervals in Figure 8.4. The curve for a constant IWD of J/m 2 is also plotted on the graphs. A high proportion of elements with high values of smoothed seismic moment and smoothed seismic energy clustered in the top right zone of each corresponding graph. The elements in that zone are characterized by higher values of IWD. It was found that 87% of the total smoothed seismic moment and 94% of the total smoothed seismic energy occurred on the elements with an IWD value higher than J/m 2. These observations further demonstrate that a satisfactory relationship exists between the distribution of interpreted seismic activity (measured as either smoothed seismic moment or smoothed seismic energy) and the distribution of modelled IWD. The results indicate that the seismic activity recorded around the shear structure was most likely related to both the change in inelastic shear deformation and the level of driving shear stress during mechanical shearing.

103 94 State of Incremental Work Density VS smoothed seismic moment (MStep 4 - MStep 1) 1.60E+07 IWD per meter Shear Deformation (J/m2-m) 1.40E E E E E E E+06 Element IWD = J/m2 3E07 Nm < Mo < 3E08 Nm 3E08 Nm < Mo < 8E08 Nm 8E08 Nm < Mo < 2E09 Nm 2E09 Nm < Mo < 3E10 Nm 0.00E E E E E E E E-02 Change in Inelastic Shear Deformation (m) Figure 8.3. State of IWD versus smoothed seismic moment for all the yielding elements upon the second graphitic shear. Values are cumulative as at mining step 4. State of Incremental Work Density VS smoothed seismic energy (MStep 4 - MStep 1) 1.60E+07 IWD per meter Shear Deformation (J/m2-m) 1.40E E E E E E E+06 Element IWD = J/m2 1E00 J < E < 4E01 J 4E01 J < E < 2E02 J 2E02 J < E < 2E03 J 2E03 J < E < 5E05 J 0.00E E E E E E E E-02 Change in inelastic Shear Deformation (m) Figure 8.4. State of IWD versus smoothed seismic energy for all the yielding elements upon the second graphitic shear. Values are cumulative as at mining step 4.

104 8.4. Statistical relationship between the modelled and seismic data 95 A statistical approach was used in order to assess the strength of the relationship between the interpreted seismic activity and the modelled IWD. Figure 8.5 (smoothed seismic moment) and Figure 8.6 (smoothed seismic energy) compare the interpreted seismic activity and the modelled IWD of all the seismically active elements upon the second graphitic shear. The values are cumulative as at mining step 4. The cumulative values were calculated at the end of each mining step but revealed similar trends as the ones illustrated in Figures 8.5 and 8.6. Therefore, only the cumulative values as at mining step 4 are presented. Each coordinate point on the graphs corresponds to a seismically active element of the shear structure. The best-fit lines, which were calculated by linear regression of the data sets, are also shown on the graphs. The strength of each regression was determined using the R Square value (i.e. the coefficient of determination). The R Square value represents the fraction of the variation about the mean that is explained by the fitted regression model. The R Square value can range between 0 and 1. A R Square value of 1 indicates that 100% of the variation from the total variation is attributed to the regression model. A R Square value of 0 indicates that 0% of the variation from the total variation is attributed to the regression model. Figure 8.5 compares the log of smoothed seismic moment and IWD for all the seismically active elements of the second graphitic shear. The measured R Square value indicates that only 29% (R Square = 0.29) of the variation in the log of smoothed seismic moment is explained by the linear regression model. Figure 8.6 compares the log of smoothed seismic energy and IWD for all the seismically active elements of the second graphitic shear. The measured R Square value indicates that only 24% (R Square = 0.24) of the variation in the log of smoothed seismic energy is explained by the linear regression model. The high variability of the interpreted seismic data around the regression models resulted in very low R Square values. Therefore, no significant statistical relationship was found between the numerical modelling predictions and the interpreted seismic data.

105 96 Log of Smoothed Seismic Moment VS Incremental Work Density (MStep4 - MStep1) 12.0 R 2 = Log10 (Smoothed Mo in Nm) IWD (J/m2) Figure 8.5. Log of smoothed seismic moment versus IWD for all the seismically active elements upon the second graphitic shear. Values are cumulative as at mining step 4. Log of Smoothed Seismic Energy VS Incremental Work Density (MStep4 - MStep1) 6.0 R 2 = Log10 (Smoothed E in J) IWD (J/m2) Figure 8.6. Log of smoothed seismic energy versus IWD for all the seismically active elements upon the second graphitic shear. Values are cumulative as at mining step 4.

106 8.5. Summary 97 The relationship between the modelled Incremental Work Density (IWD) and the interpreted seismic activity (measured as either smoothed seismic moment or smoothed seismic energy) was examined: A satisfactory relationship was found between the spatial distribution of interpreted seismic activity and the spatial distribution of modelled IWD. The IWD parameter was found to be reasonably successful in delineating the seismically and nonseismically active zones upon the second graphitic shear. The finding indicates that the seismic activity recorded around the shear structure was most likely related to both the change in inelastic shear deformation and the level of driving shear stress during mechanical shearing. However, no significant statistical relationship was found between the modelled IWD and the interpreted seismic activity. The lack of statistical relationship between the modelled and seismic data may be attributed to several factors including the limitations of the techniques employed (e.g. Map3D modelling, seismic monitoring) and the complexity of the process involved.

107 98 9. CONCLUSIONS AND RECOMMENDATIONS Numerical modelling and seismic monitoring were undertaken in order to gain a better understanding of the causes and mechanisms of the seismic activity recorded in the vicinity of the second graphitic shear and to identify potential relationships between the numerical modelling predictions and the seismic data. The thesis introduced the Incremental Work Density (IWD) as a measure to evaluate the relative likelihood of seismic activity upon major planes of weakness. The distribution of modelled IWD was expected to correlate with the distribution of interpreted seismic activity upon the second graphitic shear. Behaviour of the second graphitic shear Numerical modelling provided an overall understanding of the behaviour of the second graphitic shear. The numerical model predicted inelastic shear deformation upon the shear structure as mining advanced. Relatively high IWD values indicated that shear deformation was most likely seismic upon a zone below the stopes and relatively low IWD values indicated that shear deformation was most likely aseismic upon the upper zone of the shear structure. Within the zone below the stopes, shear deformation was triggered by a decrease in normal stress and an increase in shear stress. Within the upper zone, shear deformation was induced by a decrease in both normal and shear stresses. Mining created a stress shadow effect that considerably reduced the stress levels upon the upper zone of the shear structure. Since inelastic shear deformation occurred under lower stress levels, the modelled IWD values upon the upper zone were relatively low. Seismic monitoring verified the above predictions and provided information about individual seismic events and overall seismic activity. The seismic events recorded in the vicinity of the second graphitic shear predominantly clustered upon a zone below the stopes. The distribution of S- to P-wave seismic energy ratio indicated that shearing and non-shearing volumetric components of failure were involved during the overall shear displacement of the structure. Fracturing, crushing, shearing and sliding may have been involved in the seismic event mechanisms. Time distribution of the seismic events indicated that shear deformation and accompanying seismic activity were

108 strongly influenced by mining, were predominant when mining was undertaken in the lower levels and were time-dependant. 99 The results indicate that the primary cause of seismic activity in the vicinity of the second graphitic shear was the overall shear displacement of the shear structure under the influence of mining induced stresses. The spatial distribution of interpreted seismic activity upon the shear structure was found to be related to both the level of driving shear stress and the change in inelastic shear deformation as mining advanced. The overall shear displacement of the structure was gradual at a mine-scale and accompanied by unstable processes at a smaller scale. By analogy, the observed phenomenon was found to be very similar to the release of acoustic emissions during frictional sliding on laboratory samples (Yabe et al 2003). Normal stress versus interpreted seismic activity The confining normal stress was found to have an important influence on the seismic behaviour of the second graphitic shear. The seismic activity predominantly clustered around a zone below the stopes where the shear structure deformed under higher normal stress. The change in inelastic shear deformation combined with a higher level of normal and shear stresses caused the zone below the stopes to deform seismically. However, the upper zone of the shear structure deformed mainly aseismically during the time period considered. The stress shadow effect created by mining decreased the confining normal stress upon the upper zone. The combination of normal and shear stresses was sufficient to cause the shear structure to deform but insufficient to generate detectable seismic waves. Incremental Work Density versus interpreted seismic activity A satisfactory relationship was found between the spatial distribution of modelled Incremental Work Density (IWD) and the spatial distribution of interpreted seismic activity (measured as either smoothed seismic moment or smoothed seismic energy). The IWD parameter was found to be reasonably successful in delineating the seismically and non-seismically active zones upon the second graphitic shear. The findings indicate that the seismic activity recorded around the shear structure was most

109 likely related to both the change in inelastic shear deformation and the level of driving shear stress during mechanical shearing. 100 However, no significant statistical relationship was found between the modelled IWD and the interpreted seismic activity (measured as either smoothed seismic moment or smoothed seismic energy). Recommendations A parameter to evaluate the relative likelihood of shear-slip induced seismic activity was presented. Modelled IWD is intended to describe the seismic behaviour of major planes of weakness at residual states of shear strength. The parameter was applied to the case study of the second graphitic shear at the Big Bell Gold mine. A satisfactory relationship was revealed between the spatial distribution of modelled IWD and the spatial distribution of interpreted seismic activity upon the second graphitic shear. The results indicate that seismic activity predominantly clustered around a zone of higher IWD upon the shear structure as mining advanced. However, no significant statistical relationship was found between the numerical modelling predictions and the interpreted seismic data. The lack of statistical relationship between the modelled and seismic data may be attributed to several factors including the limitations of the techniques employed (i.e. Map3D modelling, seismic monitoring) and the complexity of the process involved. The results obtained may indicate that the technologies used in this study are not advanced enough to allow sophisticated correlation. The relationship between the Incremental Work Density (IWD) and shear-slip induced seismic activity remains to be demonstrated in other case studies. The practicality and significance of the IWD parameter need to be further demonstrated and investigated in real mining applications.

110 101 REFERENCES Aki, K. (1984) Asperities, barriers, characteristic earthquakes and strong motion prediction. Journal of Geophysical Research, 89, Aki, K. and Richards, P.G. (1980) Quantitative Seismology: Theory and Methods, W.H. Freeman, San Francisco. Albrecht, J. (2000) Big Bell Velocity Survey. Mine Seismicity and Rockburst Risk Management project, Australian Centre for Geomechanics. Albrecht, J. (2001) An Analysis of Seismicity and Rockbursting at the Big Bell Mine. Advanced Rock Mechanics Practice for Underground Mines, Australian Centre for Geomechanics. Bandis, S.C., Lumsden, A.C. and Barton, N.R. (1981) Experimental studies of scale effects on the shear behaviour of rock joints. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 18, Barrett, D. (1999) Big Bell, Underground Again and Going Deeper. Mining in High Stress and Seismically Active Conditions, Australian Centre for Geomechanics. Barrett, D. and Player, J. (2002) Big Bell, High Stress at Shallow Depth. International Seminar on Deep and High Stress Mining, Australian Centre for Geomechanics. Barton, N.R. and Choubey, V. (1977) The shear strength of rock joints in theory and practice. Rock Mechanics, 10, Boatwright, J. and Choy, G.L. (1986) Teleseismic estimates of the energy radiated by shallow earthquakes. Journal of Geophysical Research, 91, Bouchard, S. (1991) Stabilité des Ouvrages Miniers, Collège de la région de l amiante, Teknix, Éditions Odile Germain.

111 Brady, B.H.G. and Brown, E.T. (1994) Rock Mechanics for Underground Mining, Second Edition (Reprinted), Chapman & Hall, London. 102 Brune, J.N. (1970) Tectonic stress and the spectra of seismic shear waves from earthquakes. Journal of Geophysical Research, 75, (Correction, Journal of Geophysical Research, 76, 5002, 1971). Cai, M., Kaiser, P.K. and Martin, C.D. (1998) A tensile model for the interpretation of microseismic events near underground openings. Pure and Applied Geophysics Journal, 153, CAMIRO. (1997) Canadian Rockburst Research Program , CAMIRO Mining Division, Sudbury, Canada. Cook, N.G.W. (1965) A note on rockbursts considered as a problem of stability. Journal of the South African of Mining and Metallurgy, 65, Dennison, P.J.G. and Van Aswegen, G. (1993) Stress modelling and seismicity on the Tanton fault: A case study in a South African Gold Mine. Rockbursts and Seismicity in Mines 93, A.A. Balkema, Rotterdam, Esterhuizen, G.S. (1994) Preliminary study of the effects on faults properties and mining geometry on the stiffness of the loading system in fault slip seismic events as a basis for identifying situations prone to seismic activity. SIMRAC Report GAP003, Department of Mining Engineering, University of Pretoria. Gibowicz, S.J. and Kijko, A. (1994) An Introduction to Mining Seismology, Academic Press, New York. Gutenberg, B. and Richter, C.F. (1954) Seismicity of the earth and associated phenomena, Second Edition, Princeton University Press, Princeton, N.J. Handley, G.A. and Cary, R. (1990) Big Bell Gold Deposit. Geology of the Mineral Deposits of Australia and Papua New Guinea, The Australasian Institute of Mining and Metallurgy: Melbourne,

112 103 Hanks, T.C. and Kanamori, H. (1979) A moment magnitude scale. Journal of Geophysical Research, 84, Hasegawa, H.S., Wetmiller, R.J. and Gendzwill, D.J. (1989) Induced Seismicity in Mines in Canada An Overview. Pure and Applied Geophysics Journal, 129(3-4), Hedley, D.G.F. (1993) Loading Stiffness and Rockburst Potential. MRD Mining Research Directorate Canadian Rockburst Research Program (CRRP). Hoek, E. and Brown, E.T. (1980) Underground Excavations in Rock, The Institution of Mining and Metallurgy, London. Hoek, E., Kaiser, P.K. and Bawden, W.F. (1995) Support of Underground Excavations in Hard Rock, A.A. Balkema, Rotterdam. Jenkins, F.M., Williams, T.J. and Wideman, C.J. (1990) Analysis of Four Rockbursts in the Lucky Friday Mine, Mullan, Idaho, USA. International Deep Mining Conference: Technical Challenges in Deep Level Mining, South African Institute of Mining and Metallurgy, Johannesburg, South Africa, Joughin, N.C. and Jager, A.J. (1984) Fracture of rock at stope faces in South African gold mines. Rockbursts: Prediction and Control. Transactions of the Institute of Mining and Metallurgy, 93, Ladanyi, B. and Archambault, G. (1977) Shear strength and deformability of filled indented joints. Proc. Int. Symp. Geotechnics of Structurally Complex Formations, Associazione Geotechnica Italiana, 1, Lee, M.F., Beer, G. and Windsor, C.R. (1990) Interaction of stopes, stresses and geological structures at the Mount Charlotte Mine, Western Australia. Rockbursts and Seismicity in Mines, A.A. Balkema, Rotterdam,

113 Madariaga, R. (1976) Dynamics of an expanding circular fault. Bulletin of the Seismological Society of America, 66, McGarr, A. (1984) Some applications of seismic source mechanism studies to assessing underground hazard. Rockbursts and Seismicity in Mines, The South African Institute of Mining and Metallurgy, Johannesburg, Mendecki, A.J. (1997) Seismic Monitoring in Mines, Chapman & Hall, London. Mendecki, A.J., Van Aswegen, G. and Mountfort, P. (1999) A guide to routine seismic monitoring in mines. A Handbook on Rock Engineering Practice for Tabular Hard Rock Mines, SIMRAC, South Africa. Mercer, R.A. (1999) The quantitative analysis of integrated seismic and numerical modelling data at Creighton mine, Sudbury, Ontario. Ph.D. Thesis, Department of Mining Engineering, Queen s University, Kingston, Ontario, Canada. Morisson, D.M. (1989) Rockburst Research at Falconbridge s Strathcona Mine, Sudbury, Canada. Pure and Applied Geophysics Journal, 129, Morrow, C.A., Moore, D.E. and Lockner, D.A. (2000) The effect of mineral bond strength and adsorbed water on fault gouge frictional strength. Geophysical Research Letters, 27(6), Ortlepp, W.D. (2001) Thoughts on the rockburst source mechanism based on observations of the mine-induced shear rupture. Rockbursts and Seismicity in Mines RaSiM5, The South African Institute of Mining and Metallurgy, Johannesburg, Player, J. (2000) Longitudinal Sublevel Caving, Big Bell Mine. Underground Mining Methods, Engineering Fundamentals and International Case Studies, SME, Ryder, J.A. (1988) Excess shear stress in the assessment of geologically hazardous situations. Journal of the South African Institute of Mining and Metallurgy, 88(1),

114 Sandy, M.P. and Lee, M.F. (1997) Big Bell Mine: Overcoring Stress Measurement. AMC A, Australian Mining Consultants. 105 Scholz, C.H. (1990) The Mechanics of Earthquakes and Faulting, Cambridge University Press, Cambridge. Simser, B.P. (1997) Numerical modelling and seismic monitoring on a large normal fault in the Welkom goldfields, South Africa. M.Sc.Eng. Thesis, Faculty of Engineering, University of the Witwatersrand, Johannesburg, South Africa. Trifu, C.I., Shumila, V. and Urbancic, T.I. (1997) Space-time analysis of microseismicity and its potential for estimating seismic hazard in mines. Rockbursts and Seismicity in Mines, A.A. Balkema, Rotterdam, Trifu, C.I. and Urbancic, T.I. (1996) Fracture coalescence as a mechanism for earthquakes: Observations based on mining induced microseismicity. Tectonophysics, 261, Trifu, C.I. and Urbancic, T.I. (1997) Characterization of rock mass behaviour using mining induced microseismicity. CIM Bulletin, 90, Turner, M. and Player, J. (2000) Seismicity at Big Bell Mine. MassMin 2000, Brisbane, Queensland, Urbancic, T.I., Trifu, C.I., Long, J.M. and Young, R.P. (1992a) Space-time Correlations of b Values with Stress Release. Pure and Applied Geophysics Journal, 139, Urbancic, T.I., Trifu, C.I. and Young, R.P. (1993) Microseismicity derived fault-planes and their relationship to focal mechanism, stress inversion, and geologic data. Geophysical Research Letters, 20, Urbancic, T.I. and Young, R.P. (1993) Space-time variations in source parameters of mining-induced seismic events with M < 0. Bulletin of the Seismological Society of America, 83,

115 106 Urbancic, T.I. and Young, R.P. (1995) Structural characterization of highly stressed rock masses using Microseismic fault-plane solutions. Fractured and Jointed Rock Masses, A.A. Balkema, Rotterdam. Urbancic, T.I., Young, R.P., Bird, S. and Bawden, W. (1992b) Microseismic source parameters and their use in characterizing rock mass behaviour: Considerations from Strathcona Mine. CIM/AGM, Montreal, Van Aswegen, G. (1990) Fault stability in SA gold mines. Proc. Of Conf. On Mechanics of Jointed and Faulted Rock, A.A. Balkema, Rotterdam, Van Aswegen, G. and Butler, A.G. (1993) Application of quantitative seismology in South African gold mines. Rockbursts and Seismicity in Mines 93, A.A. Balkema, Rotterdam, Van Der Heever, P. (1982) The influence of geological structure on seismicity and rockbursts in the Klerksdorp Goldfield. M.Sc. Thesis, Rand Afrikaans University. Webber, S.J. (1990) Numerical modelling of a repeated fault slip. Journal of the South African Institute of Mining and Metallurgy, 90(6), Wiles, T. (2002a) Interpretation of microseismic monitoring data using numerical modelling. Australian Centre for Geomechanics Newsletter, 17, 5-7. Wiles, T. (2002b) Map3D on-line user manual, Mine Modelling Pty Ltd. Williams, T.J., Wideman, C.J. and Scott, D.F. (1992) Case History of a Slip-type Rockburst. Pure and Applied Geophysics Journal, 139(3-4), Yabe, Y., Kato, N., Yamamoto, K. and Hirasawa, T. (2003) Effect of Sliding Rate on the Activity of Acoustic Emission during Stable Sliding. Pure and Applied Geophysics Journal, 160,

116 107 APPENDIX A Map3D Input File

117 108 * * MAP3D Version 1.48 * * PROJECT TITLE - one line of data (maximum 70 characters) * 'Big Bell - GrSh2 Plastic Model 2003:05:23 ' * * CONTROL PARAMETERS - one line of data * * NLD - number of load steps (10000) * NIT - number of iterations (10000) * NPS - number of planes of symmetry (0) * RPAR - maximum relaxation parameter (1.2) * STOL - stress tolerance (0.1% of far field stress) [MPa:psi] * AG - minimum grid side length (dimension of interest) [metres:feet] * AL - minimum element side length (dimension of interest) [metres:feet] * DOL - D/L ratio for grid-element discretization (1) * DON - D/L ratio for element-element discretization (0.5) * DOC - D/L ratio for coefficient lumping (1) * DOE - D/L ratio for element-grid lumping (2) * DOG - D/L ratio for grid-element lumping (2) * DOR - maximum element aspect ratio (5) * * NLD,NIT,NPS, RPAR,STOL, AL,AG must be specified * DOL,DON,DOC,DOE,DOG,DOR are optional * * NLD NIT NPS RPAR STOL AL AG DOL DON DOC DOE DOG * * * BLOCK SPECIFICATION LIST - one line per block - end list with N=0 * * N - block identification number - also defines colour 1,6,11 etc.... blue * 2,7,12 etc.... green * 3,8,13 etc.... yellow * 4,9,14 etc.... red * 5,10,15 etc.... grey * 'BLOCK NAME' - maximum of 20 characters must appear in single quotes * I1,I2,I3,I4 - coordinate numbers of corners of plates * I1,I2,I3,I4,I5,I6,I7,I8 - coordinate numbers of corners of blocks * TYPE - block type - 1 for Fictitious Force elements - excavation surfaces * 2 for Displacement Discontinuites - fault planes * 98 for inactive blocks (excavations) * 99 for inactive planes (faults) * THICKNESS - thickness for TYPE 2 blocks [metres:feet] * WIDTH - maximum width [metres:feet] * * N, I1,I2,I3,I4 must be specified * I5,I6,I7,I8,TYPE,THICNESS,SPACING,'BLOCK NAME' are optional * * N 'BLOCK NAME' I1 I2 I3 I4 I5 I6 I7 I8 TYPE THICK WIDTH * '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 '

118 109 1 '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '1 ' '2 ' '2 ' '2 ' '2 ' '2 ' '2 ' '2 ' '2 ' '2 ' '2 ' '3 ' '3 ' '3 ' '3 ' '3 ' '3 ' '3 ' '3 ' '3 '

119 110 3 '3 ' '3 ' '3 ' '3 ' '4 ' '4 ' '4 ' '4 ' '4 ' '4 ' '4 ' 'GrSh2 ' * * COORDINATE SPECIFICATION LIST - one line per coordinate - end list with N=0 * * N X (East) Y (North) Z (Elev) [metres:feet] *

120

121

122

123 * * MATERIAL PROPERTIES LIST - 3 lines per material - end list with N=0 * * LINE 1 - STRESS STATE SPECIFICATION - 1 line per material * N S1,S2,S3 ds1,ds2,ds3 T1,P1,T3,Surf S=S+dS*(Z-Surf) * * N - material number - 1 host rock mass - 2,3... for other materials * S1,S2,S3 - far field stress values at depth Surf [MPa:psi] * ds1,ds2,ds3 - variation with depth S = S + ds.(z-surf) [MPa/metre:psi/foot] * T1 - trend of S1 from Y (north) towards X (east) [degrees] * P1 - plunge of S1 (+) positive down from horizontal plane [degrees] * T3 - trend of S3 from Y (north) towards X (east) [degrees] * Surf - elevation for S1,S2,S3 [metres:feet] * * LINE 2 - ELASTIC PROPERTY SPECIFICATION - 1 line per material * * MT=0, 0,0, 0,0, GN,GS (element type 1 or 2) * MT=1, Ep,Er, PRp,PRr, GN,GS (element type 1 or 2) * Ep,Er - Young's modulus - peak and residual values [MPa:psi] * PRp,PRr - Poisson's ratio - peak and residual values * GN,GS - viscous modulus - normal and shear components [MPa:psi] * MT=2, Bp,Br, Sp,Sr, GN,GS (element type 1 or 2) * Bp,Br - Bulk modulus - peak and residual values [MPa:psi] * Sp,Sr - Shear modulus - peak and residual values [MPa:psi] * MT=3, KNp,KNr, KSp,KSr, GN,GS (element type 2 only) * KNp,KNr - normal stiffness - peak and residual [MPa/metres:psi/feet] * KSp,KSr - shear stiffness - peak and residual [MPa/metres:psi/feet] * 'MATERIAL NAME' - maximum of 20 characters must appear in single quotes *

124 115 * LINE 3 - STRENGTH PARAMETER SPECIFICATION - 1 line per material * * MF=0 no strength parameters specified (elastic response only) * MF=1, Top,Tor,Cop,Cor,Sop,Sor,PHIp,PHIr for Mohr-Coulomb (element type 1 or 2) * To - tension cut-off - normally 0 or negative [MPa:psi] * Co - pillar strength - field scale [MPa:psi] * So - joint cohesion - only use for type 2 elements [MPa:psi] * PHI- friction angle - rock mass value [degrees] * MF=2, Top,Tor,scp,scr,mp,mr,sp,sr for Hoek-Brown (element type 1 only) * To - tension cut-off - normally 0 or negative [MPa:psi] * sc - unconfined compressive strength - lab scale [MPa:psi] * m - mi*exp[(rmr-100)/28] - Hoek-Brown parameter * s - Exp[(RMR-100)/9] - Hoek-Brown parameter * * N, S1,S2,S3 must be specified, GN,GS are optional * * N S1,S2,S3 ds1,ds2,ds3 T1,P1,T3,Surf,P,dP S=S+dS*(Z-Surf) * MT 0 1,Ep/r,PRp/r,GN,GS 2,Bp/r,Sp/r,GN,GS 3,KNp/r,KSp/r,GN,GS 'MATERIAL NAME' * MF 0 1,Top,Tor,Cop,Cor,Sop,Sor,PHIp,PHIr 2,Top,Tor,scp,scr,mp,mr,sp,sr * * Host Material E E E E E E E E E E E E E E E E E E+0 'Host Material ' E E E E E E E E E E E E E E E E E E E E E E E E E E+0 'GrSh2 ' E E E E E E E E E+0 0 * * GRID SPECIFICATION LIST - 1 line per grid - end list with N=0 * * N - grid number * 'GRID NAME' - maximum of 20 characters * I1,I2,I3,I4 - coordinate numbers of corners of grid plane * I5,I6,I7,I8,TYPE,THICK - not used * WIDTH - maximum width [metres:feet] * * N 'GRID NAME' I1 I2 I3 I4 I5 I6 I7 I8 TYPE THICK WIDTH * * * MINING STEP SPECIFICATION LIST - 1 line per block - end list with N=0 * * N - block identification number ( ) * MC - material code * MC= 0 for zero surface stresses (mined out) * MC=-M to set surface stresses of block N to stress state of material M * MC=+M to insert material number M into block number N * * N MC ME * '2000-MAR-30 6PM ' '2000-AUG-26 6PM ' '2001-DEC-20 6PM ' 0 3 0

125 116 '2002-FEB-10 6PM ' 0 4 0

126 117 APPENDIX B Map3D Log File

127 118 INFO Loading input file: F:\BB - GrSh2 Plastic.inp <<<<<<<<<<< MAP3D Version 1.48 >>>>>>>>>>> INFO: Reading job title INFO: Reading block list INFO: Reading coordinate list INFO: Reading material property list INFO: Reading grid list WARNING: No grids INFO: Reading mining steps INFO: Reading mining step 1 INFO: Reading mining steps INFO: Reading mining step 2 INFO: Reading mining steps INFO: Reading mining step 3 INFO: Reading mining steps INFO: Reading mining step 4 INFO: Reading mining steps INFO: Checking coordinates INFO: Checking for duplicate surfaces INFO: Reordering negative volumes INFO: Generating surfaces INFO: Grouping blocks INFO: File load completed WARNING: No grids INFO: Deleting common sides Deleting common surfaces complete, # surfaces is 352 INFO: Delete duplicated elements INFO: Deleting duplicates complete Number of surfaces is 352 INFO: Collapsing elements on single interfaces INFO: Collapsing elements complete Number of surfaces is 352 INFO: Testing for edge intersections INFO: Block edge intersection testing complete Number of surfaces is 378 INFO: Testing for edge intersections INFO: Block edge intersection testing complete Number of surfaces is 378 INFO: Testing for edge intersections INFO: Block edge intersection testing complete Number of surfaces is 378 INFO: Delete duplicated elements INFO: Deleting duplicates complete Number of surfaces is 342 INFO: Checking element shapes INFO: Resequencing block numbers INFO: Grouping blocks INFO: Checking for element size and shape INFO: Checking for double defined surfaces INFO: No unclosed surfaces found INFO: Checking for contacts INFO: Checking mining sequence INFO: Intersection analysis completed INFO: Lumping pass 1 INFO: Lumping pass 2 INFO: Lumping pass 3 INFO: Block discretization Block discretization complete Number of boundary elements is 4020 INFO: Grid discretization INFO: Grid sorting Grid discretization complete Number of grid points is 0 Primary swap drive is F: CGM solver will be used Accelerated solver will be used Amount of RAM requested 200 MBytes Testing calculation rate for this computer Measured calculation rate MFLOPS Testing disk read rate for this computer

128 119 INFO: asynchronous I/O was achieved Measured disk rate (DIO) MB/second Number of mining steps 4, maximum number 40 Number of block surfaces 342, maximum number Number of lump surfaces 977, maximum number Number of coordinate points 446, maximum number Number of material types 2, maximum number 100 Number of field point grids 0, maximum number 1000 Number of boundary elements 4020, maximum number Number of boundary nodes 6150, maximum number Number of field points 0, maximum number Number of seismic points 0, maximum number Estimated space required , available space MBytes Estimated analysis time hours INFO: Discretization analysis completed -rn Renumber negative volumes -cc Collinearity checking -co Collapse elements -Npc No Planarity check -cl Closure check -Nms No MSpoint calculations -Nlerd No LERD/LSS calculation -Ninit No initialize calculation -Nlc No Lumping calculations -la Lumping accuracy required -Ncreep No Creep calculations -cgm CGM solver -accel Accelerated solver -Nzsp No Zero strain placement -Nlinear No Linear elements -Nvo No Verbose output -mp Move points -ram 200 MBytes INFO: Begin BEM Analysis INFO: VirtualAlloc bytes, successful INFO: VirtualAlloc bytes, successful Primary swap drive is F: Accelerated solver will be used ( 24 MBytes) CGM solver will be used ( 24 MBytes) Amount of RAM allocated for matrix 151 MBytes INFO: Matrix assembly Matrix assembly complete mcnt= 0 Matrix size MBytes Lumping ratio R Time factor F seconds Matrix assembly hours INFO: Matrix solution INFO: Pre-conditioning matrix INFO: Building accelerator is=1 it=1 ser=-7.49e+01 fer= 0.00E+00 rms= 1.31E+01 ratio=1.000 converging is=1 it=2 ser=-5.24e+01 fer= 8.50E-07 rms= 5.77E+00 ratio=0.440 converging is=1 it=3 ser=-2.24e+01 fer= 1.36E-06 rms= 2.13E+00 ratio=0.370 converging is=1 it=4 ser=-7.31e+00 fer= 1.38E-06 rms= 1.27E+00 ratio=0.597 converging is=1 it=5 ser=-6.79e+00 fer= 1.75E-06 rms= 1.07E+00 ratio=0.838 converging is=1 it=6 ser=-6.24e+00 fer= 1.71E-06 rms= 9.57E-01 ratio=0.896 converging is=1 it=7 ser=-5.69e+00 fer= 1.61E-06 rms= 8.65E-01 ratio=0.903 converging is=1 it=8 ser=-5.22e+00 fer= 2.07E-06 rms= 7.90E-01 ratio=0.913 converging is=1 it=9 ser=-4.79e+00 fer= 2.85E-06 rms= 7.22E-01 ratio=0.915 converging is=1 it=10 ser=-4.40e+00 fer= 2.63E-06 rms= 6.62E-01 ratio=0.917 converging is=1 it=11 ser=-4.06e+00 fer= 2.99E-06 rms= 6.10E-01 ratio=0.920 converging is=1 it=12 ser=-3.75e+00 fer= 3.02E-06 rms= 5.62E-01 ratio=0.923 converging is=1 it=13 ser=-3.48e+00 fer= 2.93E-06 rms= 5.19E-01 ratio=0.923 converging is=1 it=14 ser=-3.22e+00 fer= 2.80E-06 rms= 4.80E-01 ratio=0.925 converging is=1 it=15 ser=-2.99e+00 fer= 2.78E-06 rms= 4.45E-01 ratio=0.927 converging is=1 it=16 ser=-2.78e+00 fer= 3.02E-06 rms= 4.13E-01 ratio=0.927 converging is=1 it=17 ser=-2.59e+00 fer= 3.03E-06 rms= 3.84E-01 ratio=0.929 converging is=1 it=18 ser=-2.41e+00 fer= 3.15E-06 rms= 3.57E-01 ratio=0.931 converging is=1 it=19 ser=-2.25e+00 fer= 3.64E-06 rms= 3.32E-01 ratio=0.931 converging is=1 it=20 ser=-2.10e+00 fer= 3.14E-06 rms= 3.10E-01 ratio=0.932 converging is=1 it=21 ser=-1.96e+00 fer= 3.08E-06 rms= 2.89E-01 ratio=0.933 converging

129 120 is=1 it=22 ser=-1.83e+00 fer= 3.17E-06 rms= 2.70E-01 ratio=0.933 converging is=1 it=23 ser=-1.71e+00 fer= 3.70E-06 rms= 2.52E-01 ratio=0.934 converging is=1 it=24 ser=-1.60e+00 fer= 3.17E-06 rms= 2.35E-01 ratio=0.935 converging is=1 it=25 ser=-1.49e+00 fer= 3.35E-06 rms= 2.20E-01 ratio=0.935 converging is=1 it=26 ser=-1.40e+00 fer= 3.10E-06 rms= 2.06E-01 ratio=0.935 converging is=1 it=27 ser=-1.30e+00 fer= 3.58E-06 rms= 1.92E-01 ratio=0.935 converging is=1 it=28 ser=-1.22e+00 fer= 3.25E-06 rms= 1.80E-01 ratio=0.936 converging is=1 it=29 ser=-1.14e+00 fer= 4.11E-06 rms= 1.69E-01 ratio=0.936 converging is=1 it=30 ser=-1.07e+00 fer= 4.76E-06 rms= 1.58E-01 ratio=0.936 converging is=1 it=31 ser=-1.00e+00 fer= 5.50E-06 rms= 1.48E-01 ratio=0.937 converging is=1 it=32 ser=-9.38e-01 fer= 4.85E-06 rms= 1.39E-01 ratio=0.937 converging is=1 it=33 ser=-8.79e-01 fer= 5.64E-06 rms= 1.30E-01 ratio=0.937 converging is=1 it=34 ser=-8.23e-01 fer= 5.19E-06 rms= 1.22E-01 ratio=0.937 converging is=1 it=35 ser=-7.71e-01 fer= 5.77E-06 rms= 1.14E-01 ratio=0.937 converging is=1 it=36 ser=-7.23e-01 fer= 5.12E-06 rms= 1.07E-01 ratio=0.937 converging is=1 it=37 ser=-6.78e-01 fer= 5.25E-06 rms= 1.00E-01 ratio=0.938 converging is=1 it=38 ser=-6.36e-01 fer= 5.01E-06 rms= 9.41E-02 ratio=0.938 converging is=1 it=39 ser=-5.95e-01 fer= 5.00E-06 rms= 8.82E-02 ratio=0.937 converging is=1 it=40 ser=-5.58e-01 fer= 5.24E-06 rms= 8.27E-02 ratio=0.938 converging is=1 it=41 ser=-5.24e-01 fer= 5.38E-06 rms= 7.76E-02 ratio=0.938 converging is=1 it=42 ser=-4.91e-01 fer= 5.65E-06 rms= 7.28E-02 ratio=0.938 converging is=1 it=43 ser=-4.60e-01 fer= 5.96E-06 rms= 6.83E-02 ratio=0.938 converging is=1 it=44 ser=-4.32e-01 fer= 4.96E-06 rms= 6.41E-02 ratio=0.938 converging is=1 it=45 ser=-4.05e-01 fer= 5.09E-06 rms= 6.01E-02 ratio=0.938 converging is=1 it=46 ser=-3.80e-01 fer= 5.66E-06 rms= 5.64E-02 ratio=0.939 converging is=1 it=47 ser=-3.56e-01 fer= 5.35E-06 rms= 5.30E-02 ratio=0.939 converging is=1 it=48 ser=-3.34e-01 fer= 5.22E-06 rms= 4.97E-02 ratio=0.938 converging is=1 it=49 ser=-3.13e-01 fer= 5.76E-06 rms= 4.67E-02 ratio=0.939 converging is=1 it=50 ser=-2.94e-01 fer= 5.64E-06 rms= 4.38E-02 ratio=0.939 converging is=1 it=51 ser=-2.76e-01 fer= 5.81E-06 rms= 4.11E-02 ratio=0.939 converging is=1 it=52 ser=-2.59e-01 fer= 5.60E-06 rms= 3.86E-02 ratio=0.939 converging is=1 it=53 ser=-2.43e-01 fer= 5.78E-06 rms= 3.62E-02 ratio=0.938 converging is=1 it=54 ser=-2.28e-01 fer= 5.26E-06 rms= 3.40E-02 ratio=0.939 converging is=1 it=55 ser=-2.14e-01 fer= 5.44E-06 rms= 3.19E-02 ratio=0.939 converging is=1 it=56 ser=-2.01e-01 fer= 5.43E-06 rms= 3.00E-02 ratio=0.939 converging is=1 it=57 ser=-1.88e-01 fer= 5.60E-06 rms= 2.81E-02 ratio=0.939 converging is=1 it=58 ser=-1.77e-01 fer= 5.48E-06 rms= 2.64E-02 ratio=0.939 converging is=1 it=59 ser=-1.66e-01 fer= 5.38E-06 rms= 2.48E-02 ratio=0.939 converging is=1 it=60 ser=-1.56e-01 fer= 5.68E-06 rms= 2.33E-02 ratio=0.939 converging is=1 it=61 ser=-1.46e-01 fer= 5.59E-06 rms= 2.19E-02 ratio=0.939 converging is=1 it=62 ser=-1.37e-01 fer= 5.81E-06 rms= 2.05E-02 ratio=0.939 converging is=1 it=63 ser=-1.29e-01 fer= 5.49E-06 rms= 1.93E-02 ratio=0.939 converging is=1 it=64 ser=-1.21e-01 fer= 5.72E-06 rms= 1.81E-02 ratio=0.939 converging is=1 it=65 ser=-1.13e-01 fer= 5.65E-06 rms= 1.70E-02 ratio=0.939 converging is=1 it=66 ser=-1.06e-01 fer= 5.58E-06 rms= 1.60E-02 ratio=0.939 converging is=1 it=67 ser=-9.98e-02 fer= 5.75E-06 rms= 1.50E-02 ratio=0.939 converging is=1 it=68 ser=-9.37e-02 fer= 5.26E-06 rms= 1.41E-02 ratio=0.939 converging is=2 it=1 ser=-8.79e-02 fer= 8.83E-07 rms= 1.32E-02 ratio=0.939 converging is=2 it=2 ser=-7.81e-02 fer= 1.02E-06 rms= 1.06E-02 ratio=0.806 converging Matrix convergence achieved Load step convergence achieved Total iterations 70 Time factor F seconds Matrix solution hours INFO: Matrix solution INFO: Pre-conditioning matrix INFO: Building accelerator is=1 it=1 ser=-5.33e+02 fer= 3.83E-07 rms= 2.94E+01 ratio=1.000 converging is=1 it=2 ser=-8.76e+01 fer= 8.55E-07 rms= 5.17E+00 ratio=0.176 converging is=1 it=3 ser=-1.31e+01 fer= 9.67E-07 rms= 1.20E+00 ratio=0.232 converging is=1 it=4 ser=-4.68e+00 fer= 8.23E-07 rms= 4.85E-01 ratio=0.404 converging is=1 it=5 ser=-1.68e+00 fer= 9.76E-07 rms= 2.66E-01 ratio=0.549 converging is=1 it=6 ser= 1.40E+00 fer= 1.04E-06 rms= 2.09E-01 ratio=0.787 converging is=1 it=7 ser= 1.23E+00 fer= 9.85E-07 rms= 1.81E-01 ratio=0.866 converging is=1 it=8 ser= 1.08E+00 fer= 1.10E-06 rms= 1.63E-01 ratio=0.897 converging is=1 it=9 ser= 9.52E-01 fer= 1.25E-06 rms= 1.46E-01 ratio=0.897 converging is=1 it=10 ser=-8.44e-01 fer= 1.07E-06 rms= 1.31E-01 ratio=0.899 converging is=1 it=11 ser=-7.58e-01 fer= 1.08E-06 rms= 1.18E-01 ratio=0.903 converging is=1 it=12 ser=-6.82e-01 fer= 1.25E-06 rms= 1.07E-01 ratio=0.904 converging is=1 it=13 ser=-6.16e-01 fer= 1.05E-06 rms= 9.69E-02 ratio=0.905 converging is=1 it=14 ser=-5.58e-01 fer= 1.20E-06 rms= 8.81E-02 ratio=0.909 converging

130 121 is=1 it=15 ser=-5.06e-01 fer= 1.25E-06 rms= 8.01E-02 ratio=0.909 converging is=1 it=16 ser=-4.60e-01 fer= 1.22E-06 rms= 7.29E-02 ratio=0.911 converging is=1 it=17 ser=-4.19e-01 fer= 1.27E-06 rms= 6.64E-02 ratio=0.911 converging is=1 it=18 ser=-3.82e-01 fer= 1.21E-06 rms= 6.06E-02 ratio=0.913 converging is=1 it=19 ser=-3.49e-01 fer= 1.28E-06 rms= 5.54E-02 ratio=0.913 converging is=1 it=20 ser=-3.19e-01 fer= 1.54E-06 rms= 5.07E-02 ratio=0.915 converging is=1 it=21 ser=-2.93e-01 fer= 1.12E-06 rms= 4.64E-02 ratio=0.916 converging is=1 it=22 ser=-2.68e-01 fer= 1.21E-06 rms= 4.25E-02 ratio=0.916 converging is=1 it=23 ser=-2.46e-01 fer= 1.19E-06 rms= 3.90E-02 ratio=0.917 converging is=1 it=24 ser=-2.26e-01 fer= 1.34E-06 rms= 3.57E-02 ratio=0.917 converging is=1 it=25 ser=-2.08e-01 fer= 1.25E-06 rms= 3.28E-02 ratio=0.918 converging is=1 it=26 ser=-1.92e-01 fer= 1.43E-06 rms= 3.02E-02 ratio=0.919 converging is=1 it=27 ser=-1.76e-01 fer= 1.21E-06 rms= 2.77E-02 ratio=0.920 converging is=1 it=28 ser=-1.62e-01 fer= 1.51E-06 rms= 2.55E-02 ratio=0.920 converging is=1 it=29 ser=-1.50e-01 fer= 1.19E-06 rms= 2.35E-02 ratio=0.921 converging is=1 it=30 ser=-1.38e-01 fer= 1.06E-06 rms= 2.17E-02 ratio=0.921 converging is=1 it=31 ser=-1.28e-01 fer= 1.32E-06 rms= 2.00E-02 ratio=0.922 converging is=1 it=32 ser=-1.18e-01 fer= 1.19E-06 rms= 1.84E-02 ratio=0.921 converging is=1 it=33 ser=-1.09e-01 fer= 1.17E-06 rms= 1.69E-02 ratio=0.922 converging is=1 it=34 ser=-1.01e-01 fer= 1.22E-06 rms= 1.56E-02 ratio=0.922 converging is=1 it=35 ser=-9.32e-02 fer= 1.32E-06 rms= 1.44E-02 ratio=0.923 converging is=1 it=36 ser=-8.62e-02 fer= 1.38E-06 rms= 1.33E-02 ratio=0.922 converging is=2 it=1 ser=-7.99e-02 fer= 8.18E-07 rms= 1.23E-02 ratio=0.922 converging is=2 it=2 ser=-7.27e-02 fer= 8.86E-07 rms= 1.12E-02 ratio=0.916 converging Matrix convergence achieved Load step convergence achieved Total iterations 108 Time factor F seconds Matrix solution hours INFO: Matrix solution INFO: Pre-conditioning matrix INFO: Building accelerator is=1 it=1 ser=-1.53e+02 fer= 8.54E-07 rms= 7.88E+00 ratio=1.000 converging is=1 it=2 ser=-3.59e+01 fer= 1.11E-06 rms= 2.13E+00 ratio=0.270 converging is=1 it=3 ser=-6.96e+00 fer= 9.52E-07 rms= 6.33E-01 ratio=0.297 converging is=1 it=4 ser= 3.74E+00 fer= 8.93E-07 rms= 3.90E-01 ratio=0.617 converging is=1 it=5 ser= 2.97E+00 fer= 9.80E-07 rms= 2.90E-01 ratio=0.743 converging is=1 it=6 ser= 2.43E+00 fer= 9.70E-07 rms= 2.38E-01 ratio=0.821 converging is=1 it=7 ser= 2.01E+00 fer= 1.03E-06 rms= 2.01E-01 ratio=0.845 converging is=1 it=8 ser= 1.68E+00 fer= 1.45E-06 rms= 1.73E-01 ratio=0.858 converging is=1 it=9 ser= 1.41E+00 fer= 9.87E-07 rms= 1.49E-01 ratio=0.864 converging is=1 it=10 ser= 1.19E+00 fer= 1.12E-06 rms= 1.30E-01 ratio=0.869 converging is=1 it=11 ser= 1.02E+00 fer= 1.12E-06 rms= 1.14E-01 ratio=0.877 converging is=1 it=12 ser= 8.78E-01 fer= 1.26E-06 rms= 9.96E-02 ratio=0.876 converging is=1 it=13 ser= 7.58E-01 fer= 1.69E-06 rms= 8.79E-02 ratio=0.882 converging is=1 it=14 ser= 6.58E-01 fer= 1.36E-06 rms= 7.76E-02 ratio=0.883 converging is=1 it=15 ser= 5.74E-01 fer= 1.55E-06 rms= 6.89E-02 ratio=0.888 converging is=1 it=16 ser= 5.01E-01 fer= 1.51E-06 rms= 6.13E-02 ratio=0.890 converging is=1 it=17 ser= 4.40E-01 fer= 1.19E-06 rms= 5.48E-02 ratio=0.894 converging is=1 it=18 ser= 3.87E-01 fer= 1.41E-06 rms= 4.91E-02 ratio=0.895 converging is=1 it=19 ser= 3.41E-01 fer= 1.51E-06 rms= 4.41E-02 ratio=0.899 converging is=1 it=20 ser= 3.01E-01 fer= 1.17E-06 rms= 3.97E-02 ratio=0.901 converging is=1 it=21 ser= 2.67E-01 fer= 1.36E-06 rms= 3.59E-02 ratio=0.904 converging is=1 it=22 ser= 2.37E-01 fer= 1.89E-06 rms= 3.25E-02 ratio=0.905 converging is=1 it=23 ser= 2.11E-01 fer= 1.49E-06 rms= 2.96E-02 ratio=0.909 converging is=1 it=24 ser= 1.88E-01 fer= 1.40E-06 rms= 2.69E-02 ratio=0.911 converging is=1 it=25 ser= 1.69E-01 fer= 1.46E-06 rms= 2.46E-02 ratio=0.913 converging is=1 it=26 ser= 1.51E-01 fer= 1.62E-06 rms= 2.25E-02 ratio=0.914 converging is=1 it=27 ser= 1.36E-01 fer= 1.87E-06 rms= 2.06E-02 ratio=0.916 converging is=1 it=28 ser= 1.22E-01 fer= 1.55E-06 rms= 1.89E-02 ratio=0.918 converging is=1 it=29 ser= 1.10E-01 fer= 1.61E-06 rms= 1.73E-02 ratio=0.919 converging is=1 it=30 ser= 9.98E-02 fer= 1.34E-06 rms= 1.60E-02 ratio=0.920 converging is=1 it=31 ser= 9.04E-02 fer= 1.90E-06 rms= 1.47E-02 ratio=0.921 converging is=2 it=1 ser= 8.20E-02 fer= 1.11E-06 rms= 1.35E-02 ratio=0.921 converging is=2 it=2 ser= 7.58E-02 fer= 9.40E-07 rms= 1.24E-02 ratio=0.914 converging Matrix convergence achieved Load step convergence achieved Total iterations 141 Time factor F seconds Matrix solution hours INFO: Matrix solution

131 122 INFO: Pre-conditioning matrix INFO: Building accelerator is=1 it=1 ser=-5.48e+02 fer= 3.79E-07 rms= 2.07E+01 ratio=1.000 converging is=1 it=2 ser=-9.33e+01 fer= 8.89E-07 rms= 2.33E+00 ratio=0.113 converging is=1 it=3 ser=-7.01e+00 fer= 8.21E-07 rms= 3.52E-01 ratio=0.151 converging is=1 it=4 ser=-1.27e+00 fer= 1.00E-06 rms= 1.02E-01 ratio=0.291 converging is=1 it=5 ser= 4.05E-01 fer= 8.63E-07 rms= 4.77E-02 ratio=0.466 converging is=1 it=6 ser= 3.50E-01 fer= 9.33E-07 rms= 3.63E-02 ratio=0.762 converging is=1 it=7 ser= 2.95E-01 fer= 8.82E-07 rms= 3.13E-02 ratio=0.861 converging is=1 it=8 ser= 2.54E-01 fer= 8.32E-07 rms= 2.80E-02 ratio=0.894 converging is=1 it=9 ser= 2.18E-01 fer= 9.80E-07 rms= 2.51E-02 ratio=0.898 converging is=1 it=10 ser= 1.89E-01 fer= 8.77E-07 rms= 2.27E-02 ratio=0.902 converging is=1 it=11 ser= 1.65E-01 fer= 8.85E-07 rms= 2.05E-02 ratio=0.903 converging is=1 it=12 ser= 1.45E-01 fer= 8.84E-07 rms= 1.86E-02 ratio=0.908 converging is=1 it=13 ser= 1.28E-01 fer= 8.59E-07 rms= 1.69E-02 ratio=0.908 converging is=1 it=14 ser= 1.14E-01 fer= 9.36E-07 rms= 1.54E-02 ratio=0.912 converging is=1 it=15 ser= 1.02E-01 fer= 8.56E-07 rms= 1.41E-02 ratio=0.913 converging is=1 it=16 ser= 9.07E-02 fer= 8.99E-07 rms= 1.29E-02 ratio=0.915 converging is=1 it=17 ser= 8.15E-02 fer= 9.59E-07 rms= 1.18E-02 ratio=0.916 converging is=2 it=1 ser= 7.35E-02 fer= 8.51E-07 rms= 1.08E-02 ratio=0.916 converging is=2 it=2 ser= 6.68E-02 fer= 8.98E-07 rms= 9.92E-03 ratio=0.918 converging Matrix convergence achieved Load step convergence achieved Total iterations 160 Time factor F seconds Matrix solution hours Total cpu time hours Total clock time hours Disk read time hours 66% of total time INFO: asynchronous I/O was achieved INFO: asynchronous I/O was achieved INFO: asynchronous I/O was achieved Map3D analysis complete INFO: Map3D analysis completed

132 123 APPENDIX C Influence of the control parameter DOC in the accuracy of the Map3D model solution

133 124 The parameter DOC controls the way in which the boundary elements are lumped during matrix assembly. Small values of DOC provide maximum lumping but stresses near excavation surfaces deteriorate in accuracy and matrix conditioning is reduced. Larger values of DOC provide less lumping but accuracy and matrix conditioning are maintained (Wiles 2002b). The parameter DOC was found to have a significant impact on the accuracy of the model solution. Figures C.1, C.2 and C.3 illustrate the distribution of shear stress upon the second graphitic shear as at mining step 4 for DOC = 1, DOC = 2 and DOC = 4 respectively. The results varied from checkered (Figure C.1) to smooth (Figure C.3). To maximize the accuracy of the model solution, DOC was therefore set to 4 in this study. Figure C.1. Distribution of shear stress upon the second graphitic shear as at mining step 4 for DOC = 1

134 125 Figure C.2. Distribution of shear stress upon the second graphitic shear as at mining step 4 for DOC = 2 Figure C.3. Distribution of shear stress upon the second graphitic shear as at mining step 4 for DOC = 4