shear-slip induced seismic activity in underground mines: a case … · shear-slip induced seismic...
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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 1999. Several seismic events were recorded around the second graphitic
shear between April 2000 and February 2002. 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-
ii
dimensional boundary element code of Map3D. The shear structure was physically
incorporated into the model in order to simulate inelastic shear deformation. An elasto-
plastic 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.
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AACCKKNNOOWWLLEEDDGGEEMMEENNTTSS
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.
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TTAABBLLEE OOFF CCOONNTTEENNTTSS
Abstract ..............................................................................................................................i Acknowledgements ..........................................................................................................iii Table of Contents .............................................................................................................iv List of Figures ..................................................................................................................vi List of Tables .................................................................................................................viii 1. Introduction...................................................................................................................1
1.1. Background ............................................................................................................1 1.2. Problem statement..................................................................................................5 1.3. Research objectives................................................................................................6 1.4. Thesis structure ......................................................................................................6 1.5. Deviation................................................................................................................8
2. Literature review ...........................................................................................................9
2.1. Introduction............................................................................................................9 2.2. Shear strength of planes of weakness.....................................................................9 2.3. Elasto-plastic Mohr-Coulomb model...................................................................13 2.4. Asperity and barrier models .................................................................................15 2.5. Shear instability model.........................................................................................16
2.5.1. Loading system stiffness versus source stiffness ..........................................17 2.5.2. Shear instability mechanical model ..............................................................18
2.6. Seismic monitoring ..............................................................................................21 2.6.1. Description of a seismic event ......................................................................21
2.6.1.1. Source location.......................................................................................21 2.6.1.2. Source parameters ..................................................................................22 2.6.1.3. Source mechanism .................................................................................27
2.6.2. Description of seismic activity......................................................................30 2.6.2.1. Seismicity parameters ............................................................................30 2.6.2.2. Energy-moment relation ........................................................................31 2.6.2.3. Frequency-magnitude distribution .........................................................31 2.6.2.4. Clustering of seismic activity.................................................................32
2.7. Numerical modelling............................................................................................34 2.7.1. Numerical modelling methods ......................................................................34 2.7.2. Numerical modelling program selected - Map3D.........................................35 2.7.3. Modelling shear-slip seismicity using Excess Shear Stress..........................35 2.7.4. Modelling shear-slip mechanisms using Map3D..........................................37
2.8. Previous studies on shear-slip induced seismic activity ......................................39 2.9. Summary ..............................................................................................................40
3. Incremental Work Density ..........................................................................................42
3.1. Introduction..........................................................................................................42 3.2. Description of Incremental Work Density ...........................................................43 3.3. Numerical modelling of Incremental Work Density............................................43 3.4. Conclusion ...........................................................................................................45
4. Big Bell Gold mine .....................................................................................................46
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5. Exposures of the second graphitic shear .....................................................................51 5.1. Introduction..........................................................................................................51 5.2. Characteristics of the second graphitic shear .......................................................51 5.3. Model of the second graphitic shear ....................................................................53 5.4. Summary ..............................................................................................................55
6. Numerical modelling...................................................................................................56
6.1. Introduction..........................................................................................................56 6.2. Description of the Map3D model.........................................................................56 6.3. Map3D results ......................................................................................................65 6.4. Numerical modelling limitations and uncertainties .............................................70 6.5. Summary ..............................................................................................................70
7. Seismic monitoring .....................................................................................................72
7.1. Introduction..........................................................................................................72 7.2. Selected seismic events ........................................................................................72 7.3. Gridding and smoothing of the selected seismic data..........................................82 7.4. Seismic monitoring limitations and uncertainties ................................................88 7.5. Summary ..............................................................................................................89
8. Comparison of the modelled and seismic data............................................................90
8.1. Introduction..........................................................................................................90 8.2. Spatial distribution of the modelled and seismic data..........................................90 8.3. State of Incremental Work Density versus interpreted seismic activity ..............93 8.4. Statistical relationship between the modelled and seismic data...........................95 8.5. Summary ..............................................................................................................97
9. Conclusions and recommendations.............................................................................98 References .....................................................................................................................101 Appendix A ...................................................................................................................107 Appendix B ...................................................................................................................117 Appendix C ...................................................................................................................123
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LLIISSTT OOFF FFIIGGUURREESS
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 2.10. P-wave first motion distribution generated by a shear-slip event...............28 Figure 2.11. Six models for mine seismicity in Canada (Hasegawa et al 1989).............28 Figure 2.12. Four models of radiation patterns (Hasegawa et al 1989) ..........................29 Figure 2.13. Energy-moment relation .............................................................................31 Figure 2.14. Frequency-magnitude distribution..............................................................32 Figure 2.15. Conceptual stress and strength conditions along a plane (Ryder 1988) .....36 Figure 2.16. 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 1. ...........67
Figure 6.8. View looking east showing the distribution of normal stress upon the second graphitic shear as at mining step 4. .........................................................................68
Figure 6.9. View looking east showing the distribution of shear stress upon the second graphitic shear as at mining step 4. .........................................................................68
Figure 6.10. 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. ......................................................69
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
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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 1. .....................................77
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 7.10. Smoothing of gridded data .........................................................................84 Figure 7.11. 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. .................86
Figure 7.12. 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. .................87
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). ....................................91
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). ....................................92
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. .......94
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. .......94
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...............................................................................................................................96
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...............................................................................................................................96
Figure C.1. Distribution of shear stress upon the second graphitic shear as at mining step 4 for DOC = 1 .......................................................................................................124
Figure C.2. Distribution of shear stress upon the second graphitic shear as at mining step 4 for DOC = 2 .......................................................................................................125
Figure C.3. Distribution of shear stress upon the second graphitic shear as at mining step 4 for DOC = 4 .......................................................................................................125
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LLIISSTT OOFF TTAABBLLEESS
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 root-
mean-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
1
11.. IINNTTRROODDUUCCTTIIOONN
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.
1.1. 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.
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.
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 post-
peak. 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
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 small-
scale 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 post-
peak 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.
UNSTABLE MOTION
Shear displacement
S h e a r s t r e s s Radiated seismic energy
Loading system response Plane response
Shear displacement
S h e a r s t r e s s
QUASI-STABLE MOTION
Radiated seismic energy Loading system response Plane response
(a)
(b)
Figure 1.1. Conditions for unstable motion (a) and quasi-stable motion (b) on a plane of
weakness
5
1.2. 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 1999. 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
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.
1.3. 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.
1.4. 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.
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 elasto-
plastic 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 2002. 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.
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. It also provides
recommendations for further research.
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.
9
22.. LLIITTEERRAATTUURREE RREEVVIIEEWW
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.
2.2. 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:
10
stressnormalstrengthsheart
ft
n
n
==
=
σ
σ )(
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.
11
Asperity failure component
Geometrical component
Roughness component
Total frictional resistance
Residual frictional component Shear deformation
Shear stress
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
12
strength reduction. Low-friction materials such as chlorite, graphite, talc and
serpentine can markedly decrease friction angles especially when wet.
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 rock-
to-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 low-
friction 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.
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.
2.3. 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) (b)
Shear deformation σn
Inadmissible
Elastic
ττ
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
14
by permanent shear deformation. The constant relating shear stress and shear
deformation in the elastic range is referred to as the shear modulus.
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:
anglefrictionstressnormal
strengthshear
tan
n
n
==
=
=
φστ
φστ
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).
15
2.4. Asperity and barrier models
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.
Asperit ation)y (strong region of stress concentr
After rupture Before rupture
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.
16
Barrier (strong region of stress concentration)
After rupture Before rupture
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.
2.5. 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).
17
Shear deformation
Source strength degradation (source stiffness)
Slip initiation point
Loading system stiffness
Unstable shear deformation
Shear stress drop Radiated
seismic energy
τ
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.
2.5.1. 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 post-
failure 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 post-
failure response of the yielding plane. The strain energy released by the loading system
18
is greater than the energy that can be absorbed by the yielding process and the slip is
sudden and violent.
2.5.2. 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 (σn) 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 (τs) 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 (τd).
σn
k
Spring τs, τd
τ
Figure 2.6. Shear instability mechanical model
Figure 2.7 illustrates the shear displacement history of the block. The stress drop (τs -
τd) is a necessary condition for violent shear instability.
19
Dynamic strength
τ
Shear deformation
Static strength
Stress drop Stress drop
τ
σn
Static strength envelope
Dynamic strength envelope
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 post-
failure 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.
20
(a)
(b) (c)
Shear deformation
τ
τs
τd
k
WK
τ
τs
τd
Shear deformation
WK
τ
τs
τd
Shear deformation
k
k
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 fault-
slip 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.
21
2.6. Seismic monitoring
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.
2.6.1. Description of a seismic event
2.6.1.1. 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
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).
2.6.1.2. 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 (Ωο), the corner frequency (fo)
and the energy flux. The source parameters are calculated separately for the P- and S-
waves on the basis of these spectral parameters.
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):
areasourcetheoverntdisplacemeaverageDareasourceseismicA
sourcetheatulusmodshearGmomentseismicM
DAGM
o
o
===
=
=
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:
24
tcoefficienpatternradiationwaveSorPFlevelspectralfrequencylow
receiverandsourcethebetweencetandisRvelocitywaveSorPV
densityrockmomentseismicM
FRVM
c
o
c
o
c
oco
−−==Ω
=−−=
==
Ω=
ρ
ρπ 34
The total seismic moment is then calculated as:
22
2
)M()M(M
where
MMM
waveSVo
waveSHo
waveSo
waveSo
wavePo
o
−−−
−−
+=
+=
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:
25
tcoefficienpatternradiationwaveSorPFtcoefficienpatternradiationaveragewaveSorPF
fluxenergyJreceiverandsourcethebetweencetandisR
velocitywaveSorPVdensityrock
energyseismicradiatedE
FF
JRVE
c
c
c
c
cc
cc
−−=−−=
==
−−===
=
ρ
ρπ 22
24
The total radiated seismic energy is then calculated as:
waveSVwaveSHwaveS
waveSwaveP
EEEwhere
EEE
−−−
−−
+=
+=
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:
metresNewtoninmomentseismicMmagnitudemomentM
MM
o
o
−=−=
−= 0.6log32
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:
frequencycornerwaveSorPfvelocitywaveSorPV
elmodsourcetheondependsthatttanconsKradiussourcer
fVKr
o
c
c
o
o
cco
−−=−−=
==
=π2
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:
)elmodBrune(radiussourcermomentseismicM
dropstressstatic
rM
o
o
o
o
===∆
=∆
σ
σ 3167
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:
27
momentseismicMenergyseismicradiatedE
sourcetheatulusmodshearGstressapparent
MEG
o
A
oA
====
=
σ
σ
2.6.1.3. 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.
28
Compression First motion up
Dilatation First motion down
Dilatation First motion down
Compression First motion up
Sensor
Source Fault trace
Figure 2.10. 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 2.11. Six models for mine seismicity in Canada (Hasegawa et al 1989)
29
Figure 2.12. 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.
30
2.6.2. Description of seismic activity
2.6.2.1. 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.
31
2.6.2.2. Energy-moment relation
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 moment)
Log ( seismic energy)
) Molog(dc)Elog( +=
Figure 2.13. Energy-moment relation
The relation takes the form of:
relationthedescribingparametersaredandcmomentseismicM
energyseismicestimatedE
)Mlog(dc)Elog(
o
o
==
+=
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).
2.6.2.3. 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).
32
Moment magnitude
Log (cumulative frequency) bma)nlog( −=
Figure 2.14. Frequency-magnitude distribution
Introduced by Gutenberg and Richter (1954), the relation takes the following form:
relationthedescribingparametersarebandamagnitudeeventm
mmagnitudewitheventsofnumbern
bmanlog
==
−=
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).
2.6.2.4. 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).
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.
34
2.7. Numerical modelling
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).
2.7.1. 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
35
overall behaviour of the rockmass but are generally limited to more simple geometry
problems.
2.7.2. 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 three-
dimensional 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.
2.7.3. 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.
36
Figure 2.15 summarizes the ESS concept. Shear stress and strength conditions along
a plane are shown. The static strength (τs = c + σNtanφs) is represented as an irregular
line to show the effects of irregularities or asperities on the plane. The dynamic strength
(τd = σNtanφd) 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:
planeofanglefrictiondyamicrupturebeforeplanetheonstressnormal
planeoffrictiondynamictanrupturebeforeplanetheonstressshear
tanESSplaneofstrengthdyamicsliptopriorstressshearprevailingESS
d
n
dn
dn
==
==
−=−=
φσ
φστ
φστ
Stress drop
ESSDynamic friction
Static strength Shear stress (MPa)
B
Distance along fault/rupture (m)
PA
Shear stress prior to rupture
Figure 2.15. 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.
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.
2.7.4. 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
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 2.16. 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
Stage II
Stage I
Deformation
WK
LSS
WF
Load
Figure 2.16. Loading System Response (Wiles 2002b)
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
1 1 21
i
n
j
Iij
IIij
IIij
Iij uuttWK )
( )( )∑ ∑= =
⎥⎦
⎤⎢⎣
⎡−=
3
1 1i
n
j
Iij
IIij
IIij uutWF
( )(∑ ∑= =
⎥⎦
⎤⎢⎣
⎡−+=+=
3
1 1 21
i
n
j
Iij
IIij
IIij
Iij uuttWFWKWT )
IIstageIIIstageI
surfacetestenergytheonelementsofnumberncomponentsndeformatiou
componentsloadt
i
i
=====
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.
2.8. 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
40
Shear Stress upon the fault and a discontinuum model was used to simulate the non-
elastic 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.
2.9. 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.
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.
42
33.. IINNCCRREEMMEENNTTAALL WWOORRKK DDEENNSSIITTYY
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.
43
3.2. 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:
)ndeformatioshearinelasticinchange()stressshearaverage(IWD ×=
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.
3.3. 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
44
therefore well suited to describe the plane behaviour. IWD is calculated for each
boundary element of the plane.
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 stress-
deformation 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:
( )
IIstepingminIIIstepingminI
componentndeformatioshearinelasticDcomponentstressshearS
DensityWorklIncrementaIWD
DDSSIWD
S
S
)I(S
)II(S
)II(S
)I(S)II(
==
==
=
−×⎟⎟⎠
⎞⎜⎜⎝
⎛ +=
2
Mining Step
41 2 3
IWD(4)IWD(3)IWD(2)
Inelastic shear deformation (DS)
Shear
stress
(SS)
Figure 3.1. Concept of Incremental Work Density
45
3.4. Conclusion
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.
46
44.. BBIIGG BBEELLLL GGOOLLDD MMIINNEE
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 1916. 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
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.
Lode Footwall 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 2002. 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
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.
Mining Step 1
Mining Step 2
Mining Step 3
Mining Step 4
Lower Levels
Upper Levels
- Level 410 - Level 380 - Level 350 - Level 320 - Level 275 - Level 244
- Level 535- Level 510
- Level 435
- Level 485- Level 460
Dec 2001 to
Feb 2002
Dec 2000to
Dec 2001
Apr 2000to
Dec 2000
Up to Apr 2000
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
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 DensityMPa GPa kg/m3
Amphibolite (AMPH) 123 67 0.28 2870Altered Schist (ALSH) 121 45 0.21 2800Biotite Schist (BISH) 103 51 0.23 2900
Cordierite Schist (CRSH) 137 52 0.18 2820
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 Dipm MPa ° °
1 Major (S1) -350 74.3 215 6Intermediate (S2) 38.1 306 7
Minor (S3) 19.3 86 812 Major (S1) -380 52.5 242 16
Intermediate (S2) 29.6 338 19Minor (S3) 22.8 114 65
3 Major (S1) -483 69.1 274 27Intermediate (S2) 34.3 7 6
Minor (S3) 29.9 109 634 Major (S1) -570 86.3 266 10
Intermediate (S2) 37.9 170 29Minor (S3) 31.4 14 59
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 2002. The
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.
Table 4.3. Rockburst history at Big Bell (Barrett and Player 2002)
MStep 3
MStep 4
Date of rockburst Magnitude
(Australian Geological Survey Organization)
Cubic meter fallen/ejected Location
12 February 1999 4 Level 460 – Ore drive
16 June 1999 5 Level 435 – Footwall drive
7 July 1999 2 Level 485 – Footwall drive
9 August 1999 1.9 12 Level 485 – Footwall drive
22 August 1999 2.2 20 Level 460 – Footwall drive
25 November 1999 1.7 8 Level 460 – Footwall drive
25 November 1999 2.4 40 Level 485 – Footwall drive
6 April 2000 3 Level 510 – Footwall drive
11 April 2000 1 Level 485 – Footwall drive
8 May 2000 15 Level 535 – Footwall drive
23 May 2000 0.2 Level 535 – Footwall drive
17 June 2000 2.2 60 Level 535 – Footwall drive
4 July 2000 1.7 2 Level 510 – Footwall drive
9 July 2000 2.1 300 Level 510 – Ore drive
2 September 2000 10 Level 510 – Ore drive
5 May 2001 0.1 - 0.5 Level 410 – Access drive
6 February 2002 3 Level 560
31 March 2002 2 – 3 Level 560
26 May 2002 2 Level 585
MStep 2
MStep 1
51
55.. EEXXPPOOSSUURREESS OOFF TTHHEE SSEECCOONNDD GGRRAAPPHHIITTIICC SSHHEEAARR
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.
5.2. 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
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
53
5.3. 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 Depthm m m
E1 3716 508 -316E2 3411 559 -413E3 3512 557 -431
E4 (Rejected) 3646 598 -507E5 3712 591 -518
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).
54
C4
C3
C1
E1
E2 E3
E4 (Rejected)E5
C2 Second Graphitic shear
E4 E5
E3 E2
E1
Second Graphitic shear
(b)
(a)
Figure 5.2. View looking east (a) and view looking north (b) showing the modelled
plane and exposure locations
55
Corner Northing Easting Depthm m m
C1 4250 423 -150C2 4250 673 -760C3 3150 707 -760C4 3150 457 -150
Dip Direction 88 °Dip 68 °
RMS Value 2 m
Fitted Plane Corner Coordinates
Fitted Plane Orientation
Fitted Plane Root-Mean-Square Value
Table 5.2. Position and orientation of the modelled structure and corresponding root-
mean-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.
56
66.. NNUUMMEERRIICCAALL MMOODDEELLLLIINNGG
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.
6.2. 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
57
shear was physically incorporated within the model in order to simulate its non-linear
behaviour.
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. 0.000001 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.
Underground stopes
Open pit
Second Graphitic Shear (Modelled area = 726000 m2)
Figure 6.1. Isometric view of the Big Bell Map3D model
58
(a) Mining Blocks
504m274m
(b)
68°
Second Graphitic Shear
150m
536m
536m
Mining Blocks
Figure 6.2. View looking west (a) and view looking north (b) showing the physical
dimensions of the Map3D model
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 4
Mining Step 3
Mining Step 2
Mining Step 1
Figure 6.3. Mining sequence used in Map3D
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 pre-
mining stress state used in the model is summarized in Table 6.1. Depth is negative
down.
Principal Stress Magnitude VS Depth
0
10
20
30
40
50
60
70
80
90
100
-600-500-400-300-200-1000
Depth (m)
Prin
cipa
l Str
ess
Mag
nitu
de (M
Pa)
S1S2S3
Rejected
Figure 6.4. Principal stress magnitudes
61
S1
S3
S2
Figure 6.5. Principal stress orientations
Principal Stress Magnitude Dip Direction DipMPa ° °
Major (S1) - 0.146 x Depth 260 18Intermediate (S2) - 0.070 x Depth 170 1
Minor (S3) - 0.058 x Depth 79 72
Pre-mining Stress State
Table 6.1. Pre-mining stress state used in Map3D
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).
Young's Modulus (MPa) 67,100Poisson's Ratio 0.28
Elastic Rockmass Properties
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 elastic-
perfectly plastic constitutive behaviour is only a gross approximation of the actual
structure behaviour.
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:
( )
( )
ratios'Poissonvulusmods'YoungE
wherev
EulusmodShear
vEulusmodNormal
==
−=
−=
12
213
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.
Normal Modulus (MPa) 50,800Shear Modulus (MPa) 26,200Cohesion (MPa) 0Friction Angle (°) 8
Structure Properties
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
64
processes. All the control parameters directly impact on solution accuracy, model
size and run-time.
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.
Maximum Number of Load Steps (NLD) 10,000Maximum Number of Iterations (NIT) 10,000Stress Tolerance (STOL) 0.1Relaxation Parameter (RPAR) 1.2Element Length (AL) 5Grid Spacing (AG) 5Grid Discretize (DOL) 4Element Discretize (DON) 1Matrix Lumping (DOC) 4Element Lumping (DOE) 8Grid Lumping (DOG) 8Aspect Ratio (DOR) 5
Control Parameters
Table 6.4. Control parameters used in Map3D
65
2048 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 0.025 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
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 250000 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.
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.
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.
69
(a)
(b)
(c)
Figure 6.10. 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.
70
6.4. Numerical modelling limitations and uncertainties
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.
6.5. 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
71
deformation was most likely seismic upon the zone below the stopes and most likely
aseismic upon the upper zone of the shear structure.
72
77.. SSEEIISSMMIICC MMOONNIITTOORRIINNGG
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.
7.2. 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
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 - 585 Level
500
550
600
650
700
750
800
850
900
3400350036003700380039004000
Northing (m)
East
ing
(m)
DataBaseGrSh2
Second Graphitic Shear
First Graphitic Shear
30m
30m
Figure 7.1. Seismic events recorded within 30 metres on each side of the second
graphitic shear (585 Level)
74
Number of Events Versus Distance
533
327
234
183
250
616
0
100
200
300
400
500
600
700
0-10 10-20 20-30 30-40 40-50 50-60
Distance (m)
Num
ber o
f Eve
nts
1476 seismic events were recorded within a distance of 30 meters on each side of the
second graphitic shear
Seismic events were predominantly caused by the second graphitic shear
Seismic events were not caused by the second graphitic shear
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.
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.
76
Source Location Error Distribution of Selected Seismic Events
552 563
195
6139 34 27
2 1 20
100
200
300
400
500
600
700
800
0 - 2 2 - 4 4 - 6 6 - 8 8 - 10 10 - 12 12 - 14 14 - 16 16 - 18 18 - 20
Source Location Error (m)
Num
ber o
f Sei
smic
Eve
nts
89% of the seismic events
Source Location Error < 6m
11% of the seismic events
6m < Source Location Error < 20m
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.
77
View Looking West
-800
-700
-600
-500
-400
-300
-200
-100
0
100
2900 3100 3300 3500 3700 3900 4100 4300
Northing (m)
Dep
th (m
)
MoMag < 00 =< MoMag < 1MoMag >= 1
View Looking West
-800
-700
-600
-500
-400
-300
-200
-100
0
100
2900 3100 3300 3500 3700 3900 4100 4300
Northing (m)
Dep
th (m
)
MoMag < 00 =< MoMag < 1MoMag >= 1
View Looking West
-800
-700
-600
-500
-400
-300
-200
-100
0
100
2900 3100 3300 3500 3700 3900 4100 4300
Northing (m)
Dep
th (m
)
MoMag < 00 =< MoMag < 1MoMag >= 1
(a)
(b)
(c)
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.
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
1
10
100
1000
10000
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0
Moment Magnitude
Num
ber o
f Eve
nts
Log (n) = a - b (MoMag)
a = 2.0b = 1.9
The sensitivity of the seismic network began to fall off at
moment magnitude -0.6
Figure 7.5. Frequency-moment magnitude distribution of the selected seismic events
79
Seimic Energy - Seismic Moment Relation
1.00E-02
1.00E-01
1.00E+00
1.00E+01
1.00E+02
1.00E+03
1.00E+04
1.00E+05
1.00E+06
1.00E+07
1.00E+06 1.00E+07 1.00E+08 1.00E+09 1.00E+10 1.00E+11 1.00E+12
Seismic Moment (Nm)
Seis
mic
Ene
rgy
(J)
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
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
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03
S:P Energy ratio
Freq
uenc
y (%
)
80% of the seismic events
S- to P-wave energy
ratio < 10 20% of the seismic
events
S- to P-wave energy ratio > 10
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.
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.
82
Cumulative Number of Events VS Time
0
200
400
600
800
1000
1200
1400
1600
2000/01/25 2000/05/04 2000/08/12 2000/11/20 2001/02/28 2001/06/08 2001/09/16 2001/12/25
Time (YYYY/MM/DD)
Cum
ulat
ive
Num
ber o
f Eve
nts
Blasts - Upper Levels Blasts - Lower Levels
Min
ing
Step
1 Mining Step 21049 Events
4.2 Events/Day
Mining Step 3311 Events
0.8 Events/Day
Mining Step 4116 Events
2.4 Events/Day
Shutdown
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 equal-
area 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 354.3 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.
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:
elementthewithineventsseismicofnumberNEv
EE
MoMo
NEv
ii
Gridded
NEv
ii
Gridded
=
=
=
∑
∑
=
=
1
1
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.
84
Node
Search Radius (R)
Weighting Distance (di)
Figure 7.10. Smoothing of gridded data
The smoothed values were calculated for each node or element as follows:
Rdw
radiussearchthewithinnodesofnumberNNo
w
wEE
w
wMoMo
ii
NNo
ii
NNo
ii
Griddedi
Smoothed
NNo
ii
NNo
ii
Griddedi
Smoothed
−=
=
×=
×=
∑
∑
∑
∑
=
=
=
=
1
1
1
1
1
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
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 7.12. 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.
86
Zone of Low Seismic Activity
(a)
(b)
(c)
Figure 7.11. 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.
87
Zone of Low Seismic Activity
(a)
(b)
(c)
Figure 7.12. 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.
88
7.4. Seismic monitoring limitations and uncertainties
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).
89
Therefore, these uncertainties should not prevent the interpretation and comparison of
seismic data collected by the same seismic system.
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.
7.5. 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.
90
88.. CCOOMMPPAARRIISSOONN OOFF TTHHEE MMOODDEELLLLEEDD AANNDD SSEEIISSMMIICC DDAATTAA
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.
8.2. 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 100000 J/m2 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.
91
IWD > 100 000 J/m2
IWD > 100 000 J/m2
IWD > 100 000 J/m2
(a)
(b)
(c)
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).
92
IWD > 100 000 J/m2
IWD > 100 000 J/m2
IWD > 100 000 J/m2
(a)
(b)
(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).
93
8.3. State of Incremental Work Density versus interpreted seismic activity
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 100000 J/m2 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 100000 J/m2. 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.
94
State of Incremental Work Density VS smoothed seismic moment (MStep 4 - MStep 1)
0.00E+00
2.00E+06
4.00E+06
6.00E+06
8.00E+06
1.00E+07
1.20E+07
1.40E+07
1.60E+07
0.00E+00 5.00E-03 1.00E-02 1.50E-02 2.00E-02 2.50E-02 3.00E-02
Change in Inelastic Shear Deformation (m)
IWD
per
met
er S
hear
Def
orm
atio
n (J
/m2-
m)
Element
IWD = 100000 J/m2
3E07 Nm < Mo < 3E08 Nm
3E08 Nm < Mo < 8E08 Nm
8E08 Nm < Mo < 2E09 Nm
2E09 Nm < Mo < 3E10 Nm
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)
0.00E+00
2.00E+06
4.00E+06
6.00E+06
8.00E+06
1.00E+07
1.20E+07
1.40E+07
1.60E+07
0.00E+00 5.00E-03 1.00E-02 1.50E-02 2.00E-02 2.50E-02 3.00E-02
Change in inelastic Shear Deformation (m)
IWD
per
met
er S
hear
Def
orm
atio
n (J
/m2-
m)
Element
IWD = 100000 J/m2
1E00 J < E < 4E01 J
4E01 J < E < 2E02 J
2E02 J < E < 2E03 J
2E03 J < E < 5E05 J
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.
95
8.4. Statistical relationship between the modelled and seismic data
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.
96
Log of Smoothed Seismic Moment VS Incremental Work Density (MStep4 - MStep1)
R2 = 0.29
0.0
2.0
4.0
6.0
8.0
10.0
12.0
0 50000 100000 150000 200000 250000
IWD (J/m2)
Log1
0 (S
moo
thed
Mo
in N
m)
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)
R2 = 0.24
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0 50000 100000 150000 200000 250000
IWD (J/m2)
Log1
0 (S
moo
thed
E in
J)
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.
97
8.5. Summary
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 non-
seismically 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.
98
99.. CCOONNCCLLUUSSIIOONNSS AANNDD RREECCOOMMMMEENNDDAATTIIOONNSS
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
99
strongly influenced by mining, were predominant when mining was undertaken in the
lower levels and were time-dependant.
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
100
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 (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.
101
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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, 295-298.
Trifu, C.I. and Urbancic, T.I. (1996) Fracture coalescence as a mechanism for
earthquakes: Observations based on mining induced microseismicity. Tectonophysics,
261, 193-207.
Trifu, C.I. and Urbancic, T.I. (1997) Characterization of rock mass behaviour using
mining induced microseismicity. CIM Bulletin, 90, 62-68.
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Queensland, 791-797.
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107
AAPPPPEENNDDIIXX AA
Map3D Input File
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
* ------------------------------------------------------------------------------
10000 10000 0 1.2 0.100000 5.00 5.00 4.0 1.0 4.0 8.0 8.0 5.0
* ------------------------------------------------------------------------------
* 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
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0
* ------------------------------------------------------------------------------
* COORDINATE SPECIFICATION LIST - one line per coordinate - end list with N=0
* ------------------------------------------------------------------------------
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* ------------------------------------------------------------------------------
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314 737.957855 3830.260495 -430.546219
315 753.807941 3839.983157 -457.260246
316 732.620675 3839.982929 -457.260248
317 738.005032 3862.533692 -429.947306
318 753.805350 3855.008535 -457.084078
319 733.975084 3855.008063 -457.084086
320 718.089978 3862.533708 -429.947306
329 693.432218 3270.089111 -402.693567
332 706.886991 3270.088379 -402.693542
333 679.264025 3366.000004 -373.798054
334 689.818481 3366.000000 -405.660736
335 707.256897 3366.000000 -405.660736
336 697.967814 3366.000001 -373.798054
337 686.608582 3216.000000 -372.534149
338 693.981995 3216.000000 -401.545227
339 706.989136 3216.000000 -401.545227
340 697.430054 3216.000000 -372.534149
341 685.583252 3257.554688 -373.045807
344 698.116089 3257.554199 -373.045807
351 687.911802 3355.000002 -343.948382
352 698.196228 3355.000000 -373.785950
353 680.306030 3355.000000 -373.785950
354 669.896610 3354.999992 -343.948382
355 658.566223 3319.000000 -313.089447
356 673.069336 3319.000000 -343.530090
357 687.809204 3319.000000 -343.530090
358 677.712158 3319.000000 -313.089447
359 666.484425 3365.999998 -271.675974
360 643.102378 3365.999997 -271.675975
361 657.044990 3366.000000 -313.150211
362 678.203024 3365.999998 -313.150211
363 630.532803 3447.096700 -237.757647
364 643.061784 3434.312978 -272.881063
114 365 673.313779 3434.312762 -272.881057
366 669.585837 3447.096506 -237.757632
367 631.280412 3358.671140 -236.020117
368 642.886292 3345.776855 -271.446472
369 666.144714 3345.777100 -271.446472
370 657.422305 3358.671385 -236.020110
371 631.467041 3336.000000 -236.667175
373 657.494202 3336.000000 -236.667175
375 631.648453 3314.000000 -237.294662
376 642.547241 3314.000000 -271.085846
377 665.611206 3314.000000 -271.085846
378 657.563896 3314.000000 -237.294662
379 633.304749 3266.000000 -225.558548
380 646.867737 3266.000000 -270.325256
381 665.067383 3266.000000 -270.325256
382 654.930176 3266.000000 -225.558548
383 642.839722 3182.000000 -225.598282
384 654.429321 3182.000000 -268.994385
385 664.116150 3182.000000 -268.994385
386 655.220703 3182.000000 -225.598282
387 625.172974 3336.000000 -218.075867
388 652.264709 3336.000000 -218.075867
389 627.855835 3314.000000 -225.535828
390 654.763550 3314.000000 -225.535828
391 690.140137 3984.000000 -314.440857
392 704.221863 3984.000000 -347.971497
393 689.478943 3984.000000 -347.971497
394 675.644409 3984.000000 -314.440857
395 679.062145 3984.000000 -270.217285
396 662.767558 3984.000000 -270.217285
397 671.216309 3984.000000 -238.896545
398 653.647705 3984.000000 -238.896545
399 639.697083 3960.000000 -199.448273
400 665.645874 3960.000000 -199.448273
401 639.697082 3984.000000 -199.448273
402 665.645874 3984.000000 -199.448273
443 422.615007 4250.000000 -150.000000
444 672.865628 4250.000000 -760.000000
445 707.089890 3150.000000 -760.000000
446 456.839288 3150.000000 -150.000000
0
* ------------------------------------------------------------------------------
* 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
* ------------------------------------------------------------------------------
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
1 0.00E+0 0.00E+0 0.00E+0 -1.46E-1 -7.00E-2 -5.80E-2 260 18 79 0.000000 0.00E+0 0.00E+0
1 6.71E+4 6.71E+4 2.80E-1 2.80E-1 0.00E+0 0.00E+0 1.00E+0 0.00E+0 1.00E+0 1.00E+0 'Host Material '
0 0.00E+0 0.00E+0 0.00E+0 0.00E+0 0.00E+0 0.00E+0 3.00E+1 3.00E+1
2 0.00E+0 0.00E+0 0.00E+0 -1.46E-1 -7.00E-2 -5.80E-2 260 18 79 0.000000 0.00E+0 0.00E+0
4 5.08E+4 5.08E+4 2.62E+4 2.62E+4 0.00E+0 0.00E+0 1.00E+0 0.00E+0 1.00E+0 1.00E+0 'GrSh2 '
1 0.00E+0 0.00E+0 1.00E+6 1.00E+6 0.00E+0 0.00E+0 8.00E+0 8.00E+0 0.00E+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
* ------------------------------------------------------------------------------
0
* ------------------------------------------------------------------------------
* MINING STEP SPECIFICATION LIST - 1 line per block - end list with N=0
* ------------------------------------------------------------------------------
* N - block identification number (1 - 32000)
* 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 '
1 0
2 1
3 1
4 1
102 2
0
'2000-AUG-26 6PM '
2 0
0
'2001-DEC-20 6PM '
3 0
0
116
'2002-FEB-10 6PM '
4 0
0
117
AAPPPPEENNDDIIXX BB
Map3D Log File
118INFO 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 49.595 MFLOPS
Testing disk read rate for this computer
119INFO: asynchronous I/O was achieved
Measured disk rate (DIO) 9.961 MB/second
Number of mining steps 4, maximum number 40
Number of block surfaces 342, maximum number 128000
Number of lump surfaces 977, maximum number 128000
Number of coordinate points 446, maximum number 128000
Number of material types 2, maximum number 100
Number of field point grids 0, maximum number 1000
Number of boundary elements 4020, maximum number 333333
Number of boundary nodes 6150, maximum number 333333
Number of field points 0, maximum number 333333
Number of seismic points 0, maximum number 333333
Estimated space required 71.106, available space 30696.000 MBytes
Estimated analysis time 0.913 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 49397760 bytes, successful
INFO: VirtualAlloc 151000000 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 190.316544 MBytes
Lumping ratio R1 0.245090
Time factor F1 0.000104 seconds
Matrix assembly 0.114701 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
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 F2 0.000004 seconds
Matrix solution 0.342248 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
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 F2 0.000004 seconds
Matrix solution 0.189041 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 F2 0.000004 seconds
Matrix solution 0.166092 hours
INFO: Matrix solution
122INFO: 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 F2 0.000005 seconds
Matrix solution 0.100678 hours
Total cpu time 0.915099 hours
Total clock time 1.313881 hours
Disk read time 0.604509 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
123
AAPPPPEENNDDIIXX CC
Influence of the control parameter DOC in the accuracy of
the Map3D model solution
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
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