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LABORATORY SIMULATION OF
RESERVOIR-INDUCED SEISMICITY
by
Winnie (Wai Lai) Ying
A thesis submitted in conformity with the requirements
for the degree of Doctor of Philosophy
Graduate Department of Civil Engineering
University of Toronto
© Copyright by Winnie (Wai Lai) Ying 2010
ii
LABORATORY SIMULATION OF RESERVOIR-INDUCED SEISMICITY
Winnie (Wai Lai) Ying
Doctor of Philosophy
Graduate Department of Civil Engineering
University of Toronto
2010
Abstract
Pore pressure exists ubiquitously in the Earth’s subsurface and very often exhibits a
cyclic loading on pre-existing faults due to seasonal and tidal changes, as well as the
impoundment and discharge of surface reservoirs. The effect of oscillating pore pressure on
induced seismicity is not fully understood. This effect exhibits a dynamic variation in
effective stresses in space and time. The redistribution of pore pressure as a result of fluid
flow and pressure oscillations can cause spatial and temporal changes in the shear strength of
fault zones, which may result in delayed and protracted slips on pre-existing fractures.
This research uses an experimental approach to investigate the effects of oscillating pore
pressure on induced seismicity. With the aid of geophysical techniques, the spatial and
temporal distribution of seismic events was reconstructed and analysed. Triaxial experiments
were conducted on two types of sandstone, one with low permeability (Fontainebleau
sandstone) and the other with high permeability (Darley Dale sandstone). Cyclic pore
pressures were applied to the naturally-fractured samples to activate and reactivate the
existing faults. The results indicate that the mechanical properties of the sample and the
heterogeneity of the fault zone can influence the seismic response. Initial seismicity was
iii
induced by applying pore pressures that exceeded the previous maximum attained during the
experiment. The reactivation of faults and foreshock sequences was found in the
Fontainebleau sandstone experiment, a finding which indicates that oscillating pore pressure
can induce seismicity for a longer period of time than a single-step increase in pore pressure.
The corresponding strain change due to cyclic pore pressure changes suggests that
progressive shearing occurred during the pore pressure cycles. This shearing progressively
damaged the existing fault through the wearing of asperities, which in turn reduced the
friction coefficient and, hence, reduced the shear strength of the fault. This ‘slow’ seismic
mechanism contributed to the prolonged period of seismicity. This study also applied a
material forecast model for the estimation of time-to-failure or peak seismicity in
reservoir-induced seismicity, which may provide some general guidelines for short-term field
case estimations.
iv
Acknowledgements
First, I would like to thank Professor R. Paul Young, my thesis supervisor, for his
guidance, advice and the opportunity he granted me to work in the field of rock fracture
dynamics. Special thanks are also due to Dr. Philip Benson (my experiment and thesis
advisor while he was at the UofT as Marie-Curie Research Fellow), who provided technical
assistance, valuable comments, and discussions throughout the course of the research; Dr.
Farzine Nasseri, who provided help during the sample preparation and assembly of
equipment; and Dr. Alex Schubnel, who provided the Fontainebleau sandstone blocks. I
extend my appreciation to Professor Michael King, Dr. Rosanna Smith, Dr. Ben Thompson
and Dr. Dave Collins who provided insightful comments and discussions. In addition, I
would like to thank my external examiner, Professor Bezalel Haimson, and my examination
committee: Professors John Curran, Brent Sleep and Bernd Milkereit for their valuable
comments to improve the quality of the thesis. I also gratefully acknowledge the assistance
of Professor Mark Kortschot and Billy Cheng for their assistance with the X-ray
micro-computed tomography scanner. Technical support was also received from the
technical team of the Civil Engineering Department (Giovanni Buzzeo, Alan McClenaghan,
Olga Perebatova) and from the Geology Department, Shawn McConville, who prepared the
thin sections for optical microscopy studies. Special thanks are due to Laszlo Lombos and
Dylan Roberts who provided technical support on the geophysical imaging cell (triaxial cell)
and Dr. Will Pettitt and his team who provided technical support on the InSite software.
I also gratefully thank my past and present colleagues: Dr. Toivo Wanne, Dr. Tatyana
Katsaga, and Xueping Zhao. They gave moral support throughout the course of the research.
Furthermore, I would like to thank Professor L. S. Chan and friends for their encouragement
and support. I am also very thankful for my parents’ and my sister’s support. Without their
caring, love, and patience, this path would not be possible.
v
Table of Contents
Abstract......................................................................................................................................ii
Acknowledgements...................................................................................................................iv
Table of Contents.......................................................................................................................v
List of Figures........................................................................................................................ viii
List of Tables ..........................................................................................................................xiv
List of Symbols and Abbreviations .........................................................................................xv
Chapter 1 Introduction...............................................................................................................1
1.1 Fluid-induced seismicity....................................................................................1
1.2 Literature review................................................................................................3
1.2.1 Classification of reservoir-induced seismicity.......................................... 8
1.2.2 Modelling RIS ........................................................................................ 10
1.2.3 Acoustic emissions as earthquake proxies...............................................11
1.3 Thesis objectives and overview.......................................................................12
Chapter 2 Theory .....................................................................................................................15
2.1 Fundamentals of porous media........................................................................15
2.1.1 Definition of porosity ............................................................................. 15
2.1.2 Porosity measurement............................................................................. 16
2.1.3 Permeability............................................................................................ 17
2.2 Rock fracture mechanics..................................................................................21
2.2.1 Stress relations and Coulomb failure criterion ....................................... 21
2.2.2 Pore pressure effects ............................................................................... 26
2.2.3 Rock friction ........................................................................................... 33
2.3 Seismicity patterns...........................................................................................37
2.3.1 Aftershock sequence............................................................................... 38
2.3.2 Foreshock sequence ................................................................................ 41
Chapter 3 Techniques: The Use of Rock Physics and Laboratory Tools ................................42
3.1 Sample materials and preparation....................................................................44
3.1.1 Darley Dale sandstone ............................................................................ 45
3.1.2 Fontainebleau sandstone......................................................................... 45
3.2 Equipment........................................................................................................45
3.2.1 Triaxial deformation cell and triaxial compression loading machine..... 45
3.2.2 Servo-controlled permeameter system ................................................... 48
3.2.3 Confining pressure pump........................................................................ 50
vi
3.2.4 Linear variable differential transformer (LVDT).................................... 51
3.2.5 Data acquisition (DAQ) hardware .......................................................... 51
3.3 Geophysical techniques ...................................................................................53
3.3.1 Ultrasonic-wave velocity survey and AE techniques ............................. 53
3.3.2 AE methods ............................................................................................ 62
3.4 Source of experimental error ...........................................................................72
3.5 X-ray micro-computed tomography ................................................................73
3.6 Optical microscopy..........................................................................................73
Chapter 4 Laboratory Simulation of RIS due to Oscillating Pore Pressures...........................75
4.1 Behaviour under compressive load tests..........................................................75
4.2 Behaviour under pore pressure reduction and subsequent increase ................79
4.3 Behaviour under cyclic pore pressure..............................................................80
4.4 Conclusions from Initial Testing......................................................................84
4.5 Modified Cyclic Pore Pressure Experiments...................................................86
4.6 Experiment setup and procedures ....................................................................91
4.7 Velocity survey ................................................................................................92
4.8 Results .............................................................................................................95
4.8.1 Fontainebleau sandstone intact sample experiment (F5 and F8)............ 95
4.8.2 Fontainebleau sandstone control experiment (F7)................................ 102
4.8.3 Fontainebleau sandstone saw-cut experiment (F6)............................... 105
4.8.4 Darley Dale sandstone experiment (DDS7) ......................................... 108
Chapter 5 Analysis and Discussion................................................................................112
5.1 Experiment F5 ...............................................................................................112
5.1.1 b-value analysis .....................................................................................118
5.1.2 AE source mechanism ...........................................................................119
5.2 Experiment F8 ...............................................................................................120
5.3 Control experiment on Fontainebleau sandstone...........................................122
5.4 Darley Dale sandstone experiment ................................................................126
5.4.1 b-values................................................................................................. 128
5.4.2 AE source mechanism .......................................................................... 130
5.5 Comparison between Fontainebleau sandstone and Darley Dale sandstone
experiments....................................................................................................132
5.6 Saw-cut experiment .......................................................................................133
5.6.1 Migration trends.................................................................................... 135
5.7 Post-experimental analysis ............................................................................135
5.7.1 X-ray micro-computed tomography analysis ....................................... 136
vii
5.7.2 Optical microscopy............................................................................... 138
5.8 Conclusions ...................................................................................................144
Chapter 6 Forecasts of Reservoir-induced Seismicity ...................................................148
6.1 Material failure forecast method....................................................................149
6.2 Forecast of main slip......................................................................................150
6.3 Application to the Koyna reservoir (Protracted seismicity forecast).............154
6.4 Application to the Monticello reservoir (Initial peak seismicity forecast) ....156
6.5 Conclusions ...................................................................................................158
Chapter 7 Conclusions and Recommendations ..............................................................160
7.1 Conclusions ...................................................................................................160
7.2 Recommendations..........................................................................................163
References..............................................................................................................................165
APPENDIX I – Calibration Charts........................................................................................181
APPENDIX II – Sensor location and sensor file...................................................................191
APPENDIX III – Details of the F2 experiment.....................................................................194
APPENDIX IV – Response to Different Frequencies of Oscillation and Rate of Increase in
Pore Pressure………………………………………………………….195
APPENDIX V – Glossary .....................................................................................................196
APPENDIX VI – Information of Paper Published in GRL...................................................198
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List of Figures
Figure 1.1 Worldwide distribution of reservoir-induced seismicity, with M ≥ 4.0………6
Figure 2.1 Schematic diagram of Darcy’s law…………….…………………………….18
Figure 2.2 Schematic figure of stress field…………..…………………………………..22
Figure 2.3 Mohr diagram for normal shear stresses produced by the principal stresses..22
Figure 2.4 Mohr stress circles for a series of tests showing failure according to Coulomb
failure criteria………..……..………………………………………………...23
Figure 2.5 Mohr circle representing the elastic effect of reservoir loading on the strength
of rock underneath the reservoir..……..……………………………………..24
Figure 2.6 Schematic figure of the change in stability of a fault plane relative to the
position of the reservoir..…………………………………………………….25
Figure 2.7 Mohr circle representing the fluid pressure effect on the strength of rock.…26
Figure 2.8 Pore pressure and shear stress at a faulted surface………………………….28
Figure 2.9 Showing the values of equation 2.17 for different values of z and t and D =
106 m
2/day..………………………………………………………………….31
Figure 2.10 Showing the values of equation 2.17 for different values of D and t, and z = 1
km and 125 mm, respectively…..……………………………………………31
Figure 2.11 Block-slider model demonstrating initiation of frictional instability……......35
Figure 2.12 Force displacement diagram showing a hypothetical case…………...….…..35
Figure 2.13 Shear stress plotted as a function of normal stress at the initial friction for a
variety of rock types………………………………………………………....36
Figure 2.14 Mogi’s classification of foreshock-aftershock patterns and their relationship to
the structures of materials and applied stresses…..…..……………………...38
Figure 3.1 Schematic diagram of the flow line from the experimental setup to data
acquisition to data processing to output and analysis..………………………44
Figure 3.2 Compression loading machine and triaxial deformation cell…………….….46
Figure 3.3 Cross section of the triaxial deformation apparatus showing the top and
bottom axial platens………………………………………………………….47
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Figure 3.4 Rubber jacket holding lateral transducers and stacks in position……….…...48
Figure 3.5 North-East-Down (NED) coordinate system………..……..………………...48
Figure 3.6 Schematic diagram of the experiment setup…………..……………………..50
Figure 3.7 NI6255 data acquisition board……..………………………………………...52
Figure 3.8 Flow chart showing the LabVIEW data acquisition program………….……53
Figure 3.9 PAD pre-amplifiers used for amplifying signals by 60 dB…………….……57
Figure 3.10 Continuous waveform of a Darley Dale sandstone experiment and a discrete
acoustic emission waveform extracted from continuous waveform data at
different zoom levels…………………………………………………...……60
Figure 3.11 Flow chart showing the various AE data acquisition units for recording
passive and active AE data……..…………….……………………………...62
Figure 3.12 Showing typical P-wave arrivals received from each channel………...…….64
Figure 3.13 Examples of focal sphere and equivalent forces……………………………..67
Figure 3.14 The nine elementary force couples…………………………………………..68
Figure 3.15 Vector force representation of some source models…………………………70
Figure 4.1 Stress-strain curves of the Darley Dale sandstone samples under 10, 20, and
40 MPa confining pressures…...……………………………………………..77
Figure 4.2 Typical stress-strain curve of Fontainebleau sandstone with 20 MPa confining
pressure………………………………………………………………………78
Figure 4.3 Experiment F2 – Pore pressure cycles introduced after the rupture of the
specimen……………………………………………………………………..82
Figure 4.4 Activation of fault begins when the pore pressure reaches ~4.3 MPa (~87% of
the previous maximum)………………..……………………….……………82
Figure 4.5 a) The fractured F2 Fontainebleau sandstone sample; b) spatially and
temporally scattered seismic events induced by pore pressure cycles occurred
along the pre-existing faults……………………………………………..…..83
Figure 4.6 Showing the reference distance for the measurement of hypocenter locations
during initial tests…..………………………..………………………………84
x
Figure 4.7 The number of events located at different ranges of hypocenter. The trend
indicated during the cyclic pore pressure period is similar to that during the
pre-peak period………………..…...………………………………..……….84
Figure 4.8 The three groups of initial testing and the output used for the design of cyclic
pore pressure experiments..………………………………………...………..86
Figure 4.9 The effect of different pore pressure oscillating frequencies…….….………89
Figure 4.10 An example of a Fontainebleau sandstone experiment in which the phase shift
could not be established…..……….………….……………………………..90
Figure 4.11 Typical velocity-time curve of Fontainebleau sandstone oscillating pore
pressure experiment………..…………………………...………………..…..94
Figure 4.12 Typical velocity-time curve of the Darley Dale sandstone oscillating pore
pressure experiment.……...……………………………….…………………94
Figure 4.13 Stress-time curve of the F5 experiment under the constant confining pressure
of 20 MPa.…………………………………………….………………..…..95
Figure 4.14 Stress-time plot of the F8 experiment under the constant confining pressure of
20 MPa...……………………………………………………………….….....96
Figure 4.15 Strain-time plot of the F5 experiment……………………………..…………96
Figure 4.16 Strain-time plot of the F8 experiment……………..…………………………97
Figure 4.17 Seismic rate-time plot of the F5 experiment…………………..…………….97
Figure 4.18 Seismic rate-time plot of the F8 experiment……………………………..….98
Figure 4.19 Upstream and downstream pore pressures during the post-peak stage of the F5
experiment…...………………………………………………………………99
Figure 4.20 Upstream and downstream pore pressures during the post-peak stage of the F8
experiment…………………………………………………………………..99
Figure 4.21 AEs occurred during the 5 cycles with sinusoidal pore pressure oscillated
between 2.5 and 18 MPa at 2-minute periods of the F5, mimicking a main
shock-aftershock sequence…….……………..………………..…………...100
Figure 4.22 AEs occurred during the 16 cycles with sinusoidal pore pressure oscillated
between 2.5 and 17 MPa at 2-minute periods of the F5, mimicking a
foreshock-main shock-aftershock sequence……….………………….…....101
Figure 4.23 AE locations of the F5 Fontainebleau sandstone experiment………………102
xi
Figure 4.24 Stress-time plot of the F7 experiment under the constant confining pressure of
20 MPa...………………………………………………………..…….…….103
Figure 4.25 Strain-time plot of the F7 experiment………………………..……………103
Figure 4.26 Upstream and downstream pore pressures during the post-peak stage of the F7
experiment……………………………………………………………….....104
Figure 4.27 Seismic rate-time plot of the F7 experiment…..….......................................104
Figure 4.28 Stress-time plot of the F6 experiment under the constant confining pressure of
5 MPa….………………………………………………………………..…105
Figure 4.29 Strain-time plot of the F6 experiment………………………………………106
Figure 4.30 Upstream and downstream pore pressures during the post-peak stage of the F6
experiment…....…………………………………………………………….106
Figure 4.31 Seismic rate-time plot of the F6 experiment………………………………..107
Figure 4.32 AE source location showing the events that occurred during each set of pore
pressure cycles………..…..…………..…………………………………….107
Figure 4.33 Stress-time plot of the DDS7 experiment under the constant confining
pressure of 20 MPa.…………………………………………..……………109
Figure 4.34 Strain-time plot of the DDS7 experiment……………………..……………109
Figure 4.35 Upstream and downstream pore pressures during the post-peak stage of the
DDS7 experiment….……..……..………………………………………….110
Figure 4.36 Seismic rate-time plot of the DDS7 experiment…………………………....110
Figure 4.37 AE source location showing the events that occurred during each set of pore
pressure cycles…………………………………….………………………..111
Figure 5.1 The seismic rate, pore pressure cycles, and axial strain change of the F5
experiment………………………………………………………………….114
Figure 5.2 Phase shift and average pore pressure at each cycle for the F5 experiment..115
Figure 5.3 Showing the reference distance for measurement of hypocenter locations...117
Figure 5.4 Population distribution of the seismic events occurred during pore pressure
oscillations……………………………………………………………….…117
Figure 5.5 Fontainebleau sandstone experiment: a) b-value analysis for the formation of
fault; b) b-value analysis for the aftershock and foreshock sequences......…119
xii
Figure 5.6 Focal mechanism solutions indicating the failure mechanisms during
oscillating pore pressure…...……………………………………………….120
Figure 5.7 The seismic rate, pore pressure cycles, and axial strain change of the F8
experiment………………………………………………………………… 122
Figure 5.8 The control experiment indicates pore pressure steps at 18 MPa for 10
minutes and 17 MPa for 32 minutes.……………………………………….124
Figure 5.9 Schematic diagram indicating the reduction of shear strength with cycles a to
d………………………………………………………………………….…126
Figure 5.10 The seismic rate and axial strain change of the Darley Dale sandstone
experiment……………………………………………………….…………127
Figure 5.11 Showing seismic rate, pore pressure cycles, and axial strain change of the
Darley Dale sandstone experiment, with pore pressure oscillated between a 18
and 2.5 MPa simulated aftershock sequence…………………………..…...128
Figure 5.12 b-value analysis of the Darley Dale sandstone experiment…………...........129
Figure 5.13 The distribution of seismic events that occurred during the oscillation of pore
pressure………………………………………………………………….….130
Figure 5.14 Focal mechanism solutions of the Darley Dale sandstone experiment,
indicating that the dominant failure mechanism during the cyclic pore
pressure stage is shear, with the corresponding double couple percentage...131
Figure 5.15 The F6 experiment indicated stable sliding along the saw-cut at a later stage,
when the average pore pressure was about 3.5 MPa…………………….…134
Figure 5.16 Typical X-ray micro-CT images along the vertical axis……...……..…...…137
Figure 5.17 Normalised crack area is calculated as crack area/minimum crack area of the
plots…..………………………………...……………………………….…..138
Figure 5.18 Optical microscopic views of the Fontainebleau sandstone…….………….141
Figure 5.19 Thin section of the Darley Dale sandstone tested sample……….…………142
Figure 5.20 Optical microscopy of the Darley Dale sandstone with sheared material in the
fractured zone……......…..…………………………………………………143
Figure 6.1 Fitting Ac equals 0.03 and γ equals 2 into failure forecast model………….151
xiii
Figure 6.2 Application of failure forecast model to the experimental foreshock sequence
obtained from the F5 experiment...………………………………………...152
Figure 6.3 Application of failure forecast model to short-term forecast of main slip #2 in
the F5 experiment……..…………………...…………………………….…153
Figure 6.4 Long-term forecast of the Koyna RIS……………….……………………..155
Figure 6.5 Short-term forecast of the Monticello RIS……………...………………….157
Figure A1 Calibration of the two LVDTs: A and B......….…………………..…………182
Figure A2 Calibration of the pore pressure transducers: Pa and Pb……………..…….183
Figure A3 Calibration of the permeameter cylinder volume: Pa and Pb………………184
Figure A4 Calibration of the lateral strain measurement device.……………………...185
Figure A5 Calibration of the axial load transducers, Z1 and Z2……………………..186
Figure A6 Calibration of velocity models during different periods of the Darley Dale
sandstone experiment…………………………………...………………..…188
Figure A7 Calibration of velocity models during different periods of the Fontainebleau
sandstone experiment…………………………………...………………..…189
Figure A8 Locating a synthetic acoustic emission to calibrate source location………190
Figure A9 Locations of the lateral sensors……….………..….………………………..191
Figure A10 Locations of the platen sensors……….………..….………………………..192
xiv
List of Tables
Table 3.1 Calibration for ultrasonic wave arrival time measurements…………………55
Table 3.2 Summary of experimental error sources and accuracy………..…….……….72
Table 4.1 List of experiments…………………………………………………………..87
Table 5.1 b-values during different periods of the F5 experiment……………………118
Table 5.2 Corresponding vertical movements implied by axial strain measurements..125
Table 5.3 b-values during different periods of the DDS7 experiment….…….……….130
Table 5.4 Comparison of the results of the two cyclic pore pressure experiments…...133
Table 6.1 Sensitivity analysis for the ‘long-term’ forecast of the F5 experimental
data…………………………………………………………………………151
Table 6.2 Sensitivity analysis for the forecast of peak seismicity of the RIS at the
Monticello reservoir………………………………………………………...158
Table A1 Summary of calibration parameters………………………………………...186
Table A2 Absolute errors in source location…………………………………………190
Table A3 Sensor file……………...……………………...……………………………193
Table A4 F2 experiment: Peak AE hits and the time delayed in response to the peak
pore pressure magnitude……………………………..…………………..…194
Table A5 AE response corresponding to different rate of increase in pore pressure…195
xv
List of Symbols and Abbreviations
The symbols and abbreviations are listed in alphabetical order, first in the Latin, then the
Greek alphabets. The point of first appearance is given in parenthesis, which refers to an
equation, figure or section. In Figure 3.16, the symbols P (pressure), B (null), T (tension) are
used for different meanings from the ones listed below. They represent minimum,
intermediate and maximum eigenvalues respectively; however those meanings are clear
within the context used.
Symbol/Abbreviation Description
A Anisotropy factor [Equation 4.1]
Ac Constant [Equation 7.1]
a Constant [Equation 2.19]
[ak] Vectoe containing k number of amplitudes [Equation 3.5]
AE Acoustic emission [Section 1.2.3]
B Skempton’s coefficient [Equation 2.13]
b The slope of the line measured from the linear descending portion
of the frequency-magnitude scaling relation [Equation 2.19]
CLVD Compensated linear vector dipole [Figure 3.16]
CT Micro-computed tomography [Section 3.5]
c The time offset parameter [Equation 2.20]
D Hydraulic diffusivity [Equation 2.11]
Ds Sample distance or sample diameter [Equation 3.1]
DAQ Data acquisition [Section 3.2.5]
DC Double couple [Section 3.3.2]
d Diameter of the sample [Equation 2.4]
dm Distance between receiver and the AE location [Equation 3.6]
dT Diameter of transducer [Equation 3.4]
F Applied force [Equation 2.11]
FN Normal force [Equation 2.16]
[Gki,j] Green’s function indicating the propagation effects [Equation 3.5]
xvi
g Gravitational constant [Equation 2.4]
H(t) Heaviside unit step function [Equation 2.13]
K Spring stiffness [Figure 2.16]
k Permeability [Equation 2.2]
L Length of the near field [Equation 3.4]
LVD Linear vector dipole [Figure 3.16]
LVDT Linear variable differential transformer [Section 3.2.4]
M Magnitude of seismic event [Equation 2.19]
Mamax
The largest magnitude of the main shock [Equation 2.21]
Mm Magnitude of the main shock [Equation 2.21]
[M] Vector containing moment tensor components [Equation 3.5]
m Constant [Equation 2.22]
mi Eigenvalues of moment tensor [Section 3.3.2]
mL Location magnitude of an AE between a set of events [Equation 3.6]
N Number of seismic events [Figure 2.14]
P Pore pressure [Figure 2.1]
P’ Pore pressure at the other end of the sample [Equation 2.1]
p The exponent that modifies the rate of change in seismic
frequency [Equation 2.20]
q Darcy velocity [Equation 2.1]
RIS Reservoir-induced seismicity [Chapter1]
S Cross-sectional area of sample [Figure 2.1]
S1, S2 Shear waves [Section 3.2.1]
Sn Number of sensors [Equation 3.6]
T The time difference between sending a pulse and receiving signal
[Equation 3.1]
To The travel time between pulsing and receiving a signal with no
sample present between receiver and pulser [Equation 3.1]
t Time period [Equation 2.10]
tc Time of the main shock occurrence [Section 2.3.2]
u Slip [Figure 2.12]
xvii
V Elastic wave velocity [Equation 3.1]
Vr Total volume/bulk sample volume [Equation 2.1]
Vf Volume of flow rate [Equation 2.4]
Vmax Maximum P-wave velocity [Equation 3.3]
Vmin Minimum P-wave velocity [Equation 3.3]
Vpore Pore volume [Equation 2.1]
Vsolid Volume of solid within the rock [Equation 2.1]
VI Virtual instrument [Chapter 3]
vu Poisson’s ratio [Equation 2.13]
W Amplitude [Equation 2.20]
Wi Waveform amplitude [Equation 3.7]
Win Input amplitude [Equation 3.2]
Wout Output amplitude [Equation 3.2]
X Sample length [Figure 2.1]
x Number of data points in waveform [Equation 3.7]
z Depth [Equation 2.10]
α Angle between the σ1 plane and the fault plane [Equation 2.5]
β Bulk compressibility of fluid-filled rock [Equation 2.11]
∆τ The change in shear stress [Equation 2.9]
∆S Incremental shear strength [Equation 2.9]
∆σn The change in compressive normal stress [Equation 2.9]
∆P The change in pore pressure [Equation 2.9]
Φ Porosity [Equation 2.1]
φ Angle of internal friction [Equation 2.7]
γ An exponent that measures the degree of non-linearity [Equation
7.1]
η Fluid viscosity [Equation 2.2]
λ Wavelength [Equation 3.4]
µ, tanφ Coefficient of internal friction angle [Equation 2.7]
θ Ray-path angle [Equation 3.3]
xviii
ρ Density of the fluid [Equation 2.4]
σ Stress [Equation 2.8]
σ' Effective stress [Equation 2.8]
σ1 Maximum principal stress [Equation 2.6]
σ3 Minimum principal stress [Equation 2.6]
σn Normal stress [Equation 2.6]
τ Shear stress [Equation 2.5]
τ0 Cohesion [Equation 2.7]
Ω Precursory strain [Equation 7.1]
ω Angular frequency of water level changes [Equation 2.14]
1
Chapter 1 Introduction
1.1 Fluid-induced seismicity
Pore fluids exists ubiquitously in the Earth’s subsurface and, in many cases, exhibit a
cyclical loading on pre-existing faults due to seasonal and tidal changes. It has been
speculated that non-volcanic tremor and low-frequency earthquake swarms are generated by
high fluid pressure, which enabled shear slip at plate interface asperities (Shelly et al., 2007).
These types of slow earthquakes exhibit episodic tremors and slips over a wide range of time
scales and with slow rupture propagation (Obara and Hirose; 2006; Obara, 2002; Linde and
Sacks, 2002). Studies have indicated that these earthquakes have low frequencies ranging
from 0.5 to 5 Hz (Obara, 2002; Rogers and Dragert, 2007). Ariyoshi et al. (2009) suggest that
interaction between asperities may cause the low-frequency nature of the earthquakes. In
addition, human activities, such as the impoundment and discharge of surface reservoirs, the
creation of underground reservoirs and the subsequent extraction of geothermal energy from
enhanced geothermal systems (Majer et al., 2007) and, injections in deep oil and gas wells
can generate fluctuating fluid pressures on fault zones (Zhao et al., 1995) and induce
seismicity. The study of fluid-induced seismicity provides a good context within which to
understand the physics of fundamental processes such as stress rotation (Faulkner et al., 2006;
Fitzenz and Miller, 2004), high pressure pulse induced aftershocks (Miller, 2004), and the
generation of seismic swarms (Yamashita, 1999; Kilburn, 2003; Benson et al., 2008).
Although the importance of pore fluids in induced seismicity is well known (Miller, 2004;
Richardson and Marone, 2008), the precise relationship between pore fluid pressure and the
mechanics of faulting in shallow crustal conditions is not fully understood, in particular, the
mechanism of fluid-induced protracted seismicity. Recent work has been focused on
2
fluid-induced micro-seismicity (Benson et al., 2008; Miyazawa et al., 2008) and aseismic
fault movement (Rubenstein et al., 2007; Rogers and Dragert, 2007) in order to establish a
relationship between fault nucleation and slip, and the determination of observable foreshock
sequences (Lin, 2009; Umino et al., 2002).
The study of RIS provides an exceptionally good opportunity to understand the
mechanics of natural earthquakes and the hydraulic properties of the crust (Bell and Nur,
1978; Talwani and Acree, 1984/85; Roeloffs, 1988; Talwani, 1997). Furthermore, RIS can be
a step forward in earthquake forecast, as it provides identifiable foreshock–aftershock
sequences for the verification of various forecasting models (Gupta, 2002).
Since the causal association of seismicity with the reservoir impoundment of Lake
Mead, formed by the Hoover Dam on the Colorado River in the late 1930’s,
reservoir-induced seismicity (RIS) has been reported, due not only to the impoundment of
artificial surface reservoirs, but also to the injection of fluids into the ground (Evans, 1966)
and seasonal water level changes (Saar and Manga, 2003; Roeloffs, 1988). Since then, RIS
has drawn the attention of scientists, as it can cause property damage as well as the loss of
human life. The focus of this thesis is the effect of oscillating pore pressure of artificial
surface water on reservoir-induced seismicity.
The effect of oscillating pore pressure on fractured surfaces is highly complex, with
effects ranging from a transient reduction in grain-contact stress (Iverson and LaHusen, 1989)
to the localised nucleation of the pre-existing fault, resulting in periodic movement on a ‘slip
3
patch’ (Richardson and Marone, 2008). Although the shallow crustal environment is under
less overall stress than at deep subduction zone, the damage can still be considerable due to
stress release at shallow focus. Several such earthquakes have occurred due to the
impoundment of large dams, such as the M 6.3 earthquake at the Koyna reservoir (India)
(Gupta, 2002 and 2005) and the numerous swarms at the Aswan reservoir (Egypt) (Selim,
2002).
1.2 Literature review
As the cases of artificial reservoir-induced seismicity accumulated, studies (Snow, 1972;
Bell and Nur, 1978; Talwani and Acree, 1984/85; Simpson, 1976, 1986; Simpson et al., 1988;
Roeloffs, 1988; Rajendran and Talwani, 1992) have been carried out to identify the effect of
reservoir loading on the existing stress field. Very often, the induced seismicity is associated
with the initial impoundment of the reservoir, which changes the effective stress conditions
of the fault zone due to the increase in pore pressure. However, in some cases, RIS has been
observed several years after the initial impoundment, while others have lasted for several
decades after the initial increase in pore pressure (Gupta, 1985; Simpson, 1976). For instance,
the RIS at the Koyna reservoir in India has continued since 1960s (Rastogi, 2003; Rao and
Singh, 2008). Four years after the initial impoundment of the reservoir, a devastating M 6.3
earthquake occurred in 1967 (Gupta, 2002). The earthquake caused over 200 deaths and
1,500 injuries (Gupta, 1992). There have been over 100,000 earthquakes of M ≥ 0 reported in
Koyna since 1963, of which over 150 were M ≥ 4 and over 17 were M ≥ 5 (Rastogi, 2003).
Protracted seismicity has prompted the need for a more rigorous understanding of the
mechanism of RIS. Some research, such as Roeloffs (1988), has suggested that cyclic
4
variation in pore pressure may induce protracted seismicity, while others have attributed the
protracted phenomenon to the pore diffusion effect (Talwani and Acree, 1984/85; Simpson et
al., 1988; Talwani, 1997; do Nascimento, 2002).
There are four major factors that control RIS (Talwani, 1997): i) Reservoir water depth,
ii) Geological and tectonic settings of the area, iii) Availability of fractures in the substrata
and, iv) Hydromechanical properties of the underlying rocks. Among these factors, the first
three are useful considerations for future reservoir sites. However, for existing artificial
reservoirs with records of continued seismicity, only the last factor can be controlled for
mitigation measures. Stuart-Alexander and Mark (1976) studied the influence of reservoir
water depths in RIS. They found that as the water depth increases, the percentage of RIS
cases increases rapidly. Baecher and Keeney (1982) also found significant correlation
between RIS and reservoir depth, while the correlation of RIS with in situ stress and geology
was less significant.
The influence of reservoir water loading on induced seismicity can be subdivided into
three main effects (Bell and Nur, 1978):
i) Elastic stress increase due to filling of reservoir.
ii) The increase in pore fluid pressure in the saturated rocks, influenced by fluid diffusion
and the compaction of the water-saturated rock due to the weight of the reservoir.
iii) Variation in pore pressure, which varies with mechanical parameters, geology of the
substratum, and the frequency and amplitude of pore pressure fluctuation (inferred by
Roeloffs, 1988).
5
Some studies classify RIS as ‘induced’ or ‘triggered’ according to the stress conditions
(McGarr and Simpson, 1997). ‘Induced’ seismicity involves a substantial change in crustal
stress or pore pressure with respect to its ambient state. This usually relates to the initial
reservoir impoundment or substantial water recharge/discharge. If the crust is sufficiently
close to a failure state due to natural tectonic processes (and only a small change in stress or
pore pressure is required to induce seismicity) this is referred to as ‘triggered’ seismicity. In
other words, the seismicity would have occurred due to the natural tectonic settings and the
impoundment of the reservoir caused it to happen earlier. However, discriminating between
the two types of seismicity can be difficult because it is impossible to prove that earthquakes
would have occurred without reservoir impoundment (Talwani, 2000). Therefore, in this
thesis ‘triggered’ and ‘induced’ seismicity are considered to be the same.
Up to 2000, RIS has been reported for 95 artificial reservoir sites (Figure 1.1). These
sites can be grouped according to the maximum seismic magnitude (Gupta 2002):
i) 4 sites with M ≥ 6, including the Xinfengjiang reservoir in China, the Kariba
reservoir in Zambia-Zimbabwe, the Koyna reservoir in India, and the Kremasta
reservoir in Greece.
ii) 10 sites with M 5 – 5.9.
iii) 28 sites with M 4.0 – 4.9.
iv) 53 sites with M < 4.0.
It should be noted that there are more sites of induced seismicity which have not been
recognized because of the lack of proper seismic surveillance, particularly in third world
countries (Gupta, 1992).
6
Figure 1.1 Worldwide distribution of reservoir-induced seismicity, with M ≥ 4.0 (Gupta, 1992 & 2005).
As the tectonic stress in the Earth’s crust at some locations is often sufficiently close to
a critical stress, a small perturbation in the in situ stress field due to pore pressure variation at
critical locations can trigger seismicity (Talwani and Acree, 1984/85; Shapiro et al., 2006;
Roeloffs et al., 1979). Therefore, RIS sites very often coincide with these critical locations.
King et al. (1994) calculated the Coulomb stress change due to the main shock of the
Landers earthquake, which occurred on the 28th
June, 1992. They found that a stress increase
of less than 0.05 MPa could trigger earthquakes, which suggests that the stress conditions in
the areas must be very close to failure. Similarly, Grasso and Sornette (1998) analysed
induced seismicity cases and reported that both pore pressure change and mass transfer
leading to incremental deviatoric stresses of less than 1 MPa were sufficient to trigger
seismic events. Furthermore, Shapiro et al. (2006) stated that fluid-induced seismicity can be
triggered by pressure perturbations as low as 1 – 100 kPa at the hypocenters.
7
In some countries, the occurrence of RIS has resulted in the major modification of civil
and engineering projects. For instance, the injection of waste fluid into the crust at the Rocky
Mountain Arsenal was discontinued due to induced seismicity (Evans, 1966). In addition, the
construction of the Auburn Dam in California was terminated in view of the potential
hazards (Allen, 1978), and later constructed with a modified design. In other countries, the
construction of large artificial water reservoirs (≥ 100 m high) has thrived for decades. This
is driven by the beneficial effects of large reservoirs, such as the generation of hydroelectric
power, flood control, irrigation and human consumption, etc. This rapid development of
large reservoirs manifests particularly in the developing countries. For instance, the Three
Gorges Dam on the Yangtze River in China was completed in 2008 and is the world’s largest
artificial reservoir, with a capacity of 39.3 km3 and a water level of 175 m. There are
hundreds of other artificial reservoirs under construction in China as of 2008. Many of these
reservoirs are large-scale and are located in seismogenic zones. Similarly, in other
developing countries such as India, the increasing demand for hydroelectric power has
sustained the increasing number of large artificial reservoirs.
After the May 2008 M 7.9 earthquake in Sichuan, China, there was debate about
whether the earthquake was a reservoir-induced (by the nearby Zipingpu reservoir) or natural.
After the completion of the initial impoundment of the Zipingpu reservoir in December 2006,
the water level was increased by 120 m. A week before the great earthquake, the reservoir
water level was rapidly reduced by ~58 m (Wang, 2008), which might have caused stress
perturbation. According to case histories, such as the Aswan reservoir in Egypt, RIS has been
reported during the reduction of surface water level. Furthermore, the Zipingpu reservoir is
8
located 20 km from the epicentre of the M 7.9 earthquake (Ge et al., 2009; Kerr and Stone,
2009). Whether the M 7.9 earthquake was reservoir-induced remains questionable; however,
in view of the increasing number of large reservoirs, their potential hazards, and protracted
effects, it is essential to understand the mechanism of RIS and perhaps develop some reliable
RIS forecast models in order to mitigate or prevent induced earthquakes.
1.2.1 Classification of reservoir-induced seismicity
There are three main classifications of RIS, all of which are divided into temporal
categories. They include:
i) Rapid and delayed seismic responses. Rapid seismicity response follows immediately
after the initial loading of the reservoir or after a rapid change in reservoir water level.
According to Simpson et al. (1988), rapid response consists primarily of low magnitude,
swarm-like activity and is confined to the immediate reservoir area. They also suggest that
this type of RIS is caused by changes in elastic stresses or pore pressure change coupled to
the elastic stress and that pore pressure diffusion is not a major factor for inducing rapid
seismicity. Classic examples of rapid responses include the Nurek and Kariba reservoirs
(Gupta, 2002). Simpson et al. (1988) associate delayed responses with relatively larger
earthquakes and suggest that seismicity might extend significantly beyond the confines of the
reservoir. They suggest that diffusion of pore pressure is the mechanism responsible for these
spatial and temporal effects of RIS. Depending on the permeability and the fracture network
in the rock, it may take months or years for the pore pressure effect to spread into the crust.
When the pore pressure pulse finally reaches a zone of microcracks, it may force water into
the cracks and reduce the normal stress that holds the strained faults, consequently triggering
9
delayed seismicity (Rastogi, 2003). Classic examples of this category are the Aswan and
Koyna reservoirs. The delayed response occurred seventeen years after the initial
impoundment at the Aswan reservoir (Simpson et al., 1988; Selim et al., 2002) and four years
after the initial impoundment at the Koyna reservoir (Talwani, 2000; Gupta, 2002; Gupta,
2005).
ii) Initial and protracted seismicity. Initial seismicity is associated with initial reservoir
impoundment or a large water level change. This applies to seismicity associated with water
level increases above the previous maximum attained. It results from the almost
instantaneous effect of loading (or unloading), as well as the delayed effect of pore pressure
diffusion (Talwani, 1997). The delay between the start of impoundment and the increase in
frequency and magnitude of seismicity varies from months to years and is associated with the
reservoir characteristics, local geology, and mechanical conditions. According to this initial
seismicity definition, both the rapid and delayed responses by Simpson et al. (1998) are an
integral component of initial seismicity. The initial increase in the frequency and magnitude
of earthquakes will reduce progressively, indicating the cessation of the coupled poroelastic
response to the impoundment (Talwani, 1997). Protracted seismicity occurs after the effect of
initial filling has diminished. It is often associated with the frequency and amplitude of water
level changes (Roeloffs, 1988), particularly with lower frequencies (longer periods). This
seismicity is observed both beneath the deepest part of the reservoir and in the surrounding
areas. This seismicity can persist for many years without decrease in frequency and
magnitude (Talwani, 1997). Classic examples of protracted RIS are the Koyna reservoir in
India, the Aswan reservoir in Egypt, and the Xinfengjiang reservoir (also known as the
10
Hsinfengkiang reservoir in some references) in China.
iii) The third RIS classification is an integration of the previous two classifications. It is
divided into rapid response, delayed response, and continued seismicity by Gupta (2002), in
which the term ‘protracted seismicity’ is replaced by ‘continued seismicity’.
Although the classification by Gupta (2002) is the most descriptive of RIS, the one
suggested by Talwani (1997), i.e., initial seismicity and protracted seismicity, is used in this
thesis. This is because this research puts more emphasis on the protracted seismic effects of
pore pressure oscillations and, to a lesser extent, on the differences between the two initial
seismic responses: rapid and delayed.
1.2.2 Modelling RIS
Many analytical and numerical models have been developed to explain the phenomena
of RIS. Roeloffs (1988) classified the effects of RIS into three poroelastic approximations:
coupled effect (in which elastic stresses influence pore pressure and vice-versa), uncoupled
effect (in which the elastic stresses and pore pressure are independent), and decoupled effect
(in which the elastic stresses influence pore pressure, but not vice-versa). She concluded that
two-dimensional (2-D) uncoupled and coupled steady-state pore pressure solutions were
close for a large range of medium properties, while decoupled and coupled pressure solutions
were quite close for all medium properties. She suggests that the cyclic variation of water
level may induce seismic events. Other researchers such as Bell and Nur (1978), Simpson
and Narasimhan (1992), and Lee and Wolf (1998) have proposed different 2-D models to
11
explain the cause of initial and ongoing seismicity in RIS, while Talwani (1997) uses a pore
pressure diffusion model to explain this phenomenon. Kalpna (2000) developed a
three-dimensional (3-D) model using the formulation suggested by Rice and Cleary (1976)
and assuming decoupled responses in RIS. Furthermore, do Nascimento (2002) and do
Nascimento et al., (2004, 2005a & 2005b) present a 3-D numerical model of the field case of
the Açu reservoir, Brazil. They incorporated hydrogeological aspects in the model and
simulated the spatial and temporal seismicity of the region due to the pore diffusion effect.
These hydrogeological factors included the heterogeneous hydraulic properties in the fault,
hydraulic conductivity variation with depth, specific storage coefficients, hydraulic
diffusivity and transmissivity. However, there is a severe lack of laboratory studies to
investigate the mechanism of protracted seismicity of RIS. One laboratory study of the effect
of cyclic pore pressure loading on saw-cut sandstone indicates that pore pressure oscillations
can induce stick-slip failures (Roeloffs et al., 1979).
1.2.3 Acoustic emissions as earthquake proxies
Many studies have shown that laboratory rock deformation experiments generate
behaviours similar to natural earthquakes and have used acoustic emissions as earthquake
proxies. An acoustic emission (AE) is a transient stress wave caused by the sudden release of
the impulsive strain energy of a material (Lockner, 1993), which travels as spherical
wavefronts in the material under stress. Kendall and Tabor (1971) suggest the use of acoustic
methods for monitoring the mechanical properties of rough interfaces. When a rock sample is
subject to deviatoric stress, AE is generated due to the formation of micro-fractures, the
opening or closing of fractures, or the shearing and sliding of pre-existing fractures.
12
Brace and Byerlee (1966) and Dieterich (1979) illustrated that laboratory stick-slip
experiments are mechanically similar to crustal behaviours during earthquakes. In addition,
Scholz (1968) found that the microcracking events (AEs) generated during rock deformation
experiments radiate elastic waves in a manner similar to earthquakes and that these radiations
obey the Gutenberg and Richter frequency-magnitude relation. Furthermore, Lockner (1993)
found an analogy between AE produced by the brittle failure of rock at laboratory scale and
seismic waves generated by earthquakes. McGarr (1999) studied over 14 orders of
magnitude in seismic moment and found that stick-slip friction experiments provide insights
for interpreting earthquake energy-budget data over a broad range of hypocentral
environments. In addition, Thompson et al. (2009) demonstrated that stick-slip behaviour on
a pre-faulted sample shares similarities with large-scale complex fault zones. All these
studies indicate that AE laboratory experiments can be used to study large-scale earthquake
phenomena. This thesis applies observations from laboratory simulations of fluid-induced
seismicity experiments with the aid of the AE techniques to provide insights on the processes
and mechanics of field scale RIS.
1.3 Thesis objectives and overview
Many theoretical and numerical models have been developed to show the spatial and
temporal distribution of reservoir-induced seismicity (do Nascimento, 2002; do Nascimento
et al., 2004, 2005a & 2005b) and fluid-injection induced seismicity. Most of these models
address mechanical factors and focus mainly on explaining the rapid and delayed responses
of seismicity due to pore pressure variation. They do not model the seismic frequency and
13
magnitude responses, which are both useful for RIS and/or earthquake forecasts.
Furthermore, the pore diffusion effect cannot fully explain the mechanism of protracted
seismicity with hypocenters that do not necessarily migrate greater distances. I hypothesize
that protracted seismicity can be influenced by the frequency and amplitude of pore pressure
oscillation, as inferred by Roeloffs (1988), to a greater extent than the mechanical properties
of the subsurface. In view of this, my research aims to use laboratory triaxial experiments
with the aid of acoustic emission techniques to study the effect of oscillating pore pressure on
RIS, in particular the effect on protracted seismicity. There are four main objectives of this
research:
i) To identify whether pore pressure fluctuation can reactivate pre-existing faults and
induce protracted seismicity.
ii) To investigate any evolution of the rate and magnitude of seismic events.
iii) To identify any spatial and/or temporal distribution trends of seismic events.
iv) To investigate the applicability of an existing failure forecast model to RIS.
Chapters 2 and 3 provide an account of the theories of reservoir-induced seismicity and
research techniques, respectively. Compressive loading tests were carried out for the
investigation using a triaxial deformation cell, which allows the formation of natural
fractures in the samples prior to cyclic pore pressure loading. Both mechanical and
continuous acoustic emission data were acquired during the experiments so that the spatial
and temporal distribution of acoustic emissions (AE) could be reconstructed for different
stages of the experiments. Initial testing was conducted to characterise the behaviour of
Darley Dale and Fontainebleau sandstone samples, as detailed in Chapter 4. These initial
14
findings provided information for the design of the subsequent cyclic pore pressure
experiments, which simulate the effects of initial and protracted seismicity. The experimental
results are also presented in Chapter 4. Furthermore, discussions and analyses are provided in
Chapter 5. Two post-experimental analyses were also carried out to provide additional
evidence of the influence of cyclic pore pressure on induced seismicity (Chapter 5). These
include:
i) X-ray micro-computed tomography analysis, which yields an overview of the fracture
behaviour of the tested samples.
ii) Optical microscopy analysis, which aims to understand the microscopic-scale
phenomenon of the influence of cyclic pore pressure on the fractured zone.
The F5 Fontainebleau sandstone experimental data and two RIS field cases were used to
demonstrate the validity of a failure forecast model in Chapter 6. Lastly, the conclusions and
recommendations of the research are stated in Chapter 7. The calibration data and the sensor
files are listed in Appendixes I and II, respectively. The details of the F2 initial experiment
are contained in Appendix III, AE response to different rate of increase in pore pressure is
illustrated in Appendix IV, glossary of terms is listed in Appendix V and, the information of
the paper published in Geophysical Research Letters is enclosed in Appendix VI.
15
Chapter 2 Theory
The study of RIS phenomena involves the interaction between fluid and rock, and hence
it is essential to understand the physics of porous media, and basic rock fracture mechanics.
Furthermore, the understanding of the seismic patterns of the two types of RIS: initial and
protracted RIS is also important for the study of RIS. Thus, this chapter is divided into three
sections to address the fundamentals of porous media, rock fracture mechanics, and
seismicity patterns.
2.1 Fundamentals of porous media
2.1.1 Definition of porosity
Porosity, Φ, is the measure of the pore volume within the rock. It is defined as the
fraction of rock volume Vr that is not occupied by solid matter. If the volume of solids within
the rock is denoted by Vsolid and the pore volume as Vpore = Vr – Vsolid, then porosity can be
defined as:
VolumeTotal
VolumePore
V
V
V
VV
r
pore
r
solidr ==−
=Φ Equation 2.1
There are two main groups of porosity: primary and secondary. Primary porosity is the
main or original porosity system in a rock or unconfined alluvial deposit. Secondary porosity
is a subsequent or separate porosity system in a rock, which often enhances the overall
porosity of a rock. This can result from the chemical leaching of minerals or the generation
of a fracture system. Secondary porosity can either replace the primary porosity or coexist
with it.
16
Fracture porosity is the secondary porosity associated with a fracture system or faulting,
while vuggy porosity is the secondary porosity generated by the dissolution of large features
(such as macrofossils) in carbonate rocks, leaving large holes, vugs, or caves (Guéguen and
Palciauskas, 1994). When primary and secondary porosities overlap and interact, dual
porosity is formed. Dual porosity can be found in fractured rock aquifers where the rock
mass consists of primary porosity and the fractured system contributes to secondary porosity.
However, not all the pores or fractures in a system are interconnected and allow the passage
of fluids. For instance, dead-end pores and non-connected cavities do not allow fluid flow.
Only interconnected pores or cavities which allow fluid flow contribute to effective porosity.
2.1.2 Porosity measurement
There are several ways to estimate the porosity of a given material. The more common
methods include the direct method and the imbibition method. The direct method measures
the two volumes, Vr and Vsolid directly and, the porosity is given as 1-(Vsolid/Vr). This gives
the average porosity of the rock, because Vr-Vsolid includes all the pore spaces, both the
continuous pore network and pores that are not connected to the rock exterior.
For the imbibition method, a porous sample is immersed in a wetting fluid such as
distilled water, for a sufficiently long period of time, which allows the fluid to enter into all
the pore spaces that are connected to the rock exterior. The saturated weight of the sample is
then taken. The dry weight of the sample is measured after the sample is oven-dried for over
a sufficiently long period of time, such that the weight of the sample remains unchanged. The
temperature of the oven is limited to 80 oC to avoid inducing thermal cracks in the sample.
17
The difference in weight will be ρVpore where ρ is the known density of the fluid and Vpore is
the pore volume. A volumetric displacement measurement of the saturated sample will give
the bulk volume, Vr, of the sample. Porosity is therefore determined by Vpore/Vr. This method
will yield the best values for the connected (effective) porosity.
In this study, porosity was determined using the standard ISRM water saturation
porosity technique. The samples were oven-dried for 72 hours at 80 oC before the dry
weights were taken. Then the samples were saturated with distilled water for more than 24
hours before the 100% saturated weights were taken. The difference between the dry and
saturated weights of the samples was used to calculate the effective porosity of the samples
using equation 2.1. The porosities of every sample used in the experiments were measured.
2.1.3 Permeability
Permeability describes the ability of a medium to transmit fluid and is greatly
influenced by the porosity of the medium. There are several ways of measuring the
permeability of a rock sample. The most common method is the steady state flow method,
which is based on Darcy’s law. This can be explained by considering the fluid volume which
crosses perpendicular to a cross-sectional area ‘S’ per unit area per unit time (Figure 2.1).
18
Figure 2.1 Schematic diagram of Darcy’s law: elemental sample length X and surface area S.
A porous material that possesses a permeability of 1 Darcy under a pressure gradient of
1 atmosphere per centimetre produces a flow rate of 1 c.c./second for a fluid viscosity of 0.01
Poise through a 1 cm sided cube (Dullien, 1979; Guéguen and Palciauskas, 1994). One
Darcy is equivalent to 9.7 x 10-13
m2. However, Darcy’s law breaks down with turbulent flow
(with high Reynolds number). This suggests that the volume flow rate during the
measurement of permeability must be kept low. Typically, Darcy’s law applies when the flow
rate is less than 1 m/s (Guéguen and Palciauskas, 1994).
The Darcy’s law for horizontal flow is given as:
dX
kdPq
η−= Equation 2.2
where q is the Darcy velocity (volume/time/area) of the fluid, k is the permeability, η is fluid
viscosity (which is constant at a given temperature), and dP/dX is the pressure gradient over
the sample length.
X
P P’
S
q
19
Equation 2.2 can be rearranged to calculate permeability k by substituting (P-P’) for the
differential pressure, where P is the pressure at one end of the sample and P’ the pressure at
the other end:
)'(/ PP
Xq
dXdP
qk
−≈=
ηη Equation 2.3
The Darcy fluid velocity, q, is defined as the fluid volume that passes through a
sectional area, S, over a period, t. This velocity can also be expressed as Vf/S, where Vf is the
volume flow rate (m3/second). For an experimental setup with a vertical flow through a
cylindrical sample of length X and diameter d, S can be expressed as πd2/4; consequently,
equation 2.3 can be written as:
2
4
)'( d
X
gXPP
Vk
f
πη
ρ±−= Equation 2.4
where g is the gravitational constant, and ρ is the density of the fluid.
This constant pore pressure method allows the determination of continuous changes in
permeability as the pressure changes and is likely to be the situation in nature. However, as
the name suggests, this method is not suitable for environments with variable pore pressure
conditions and very low-permeability rock will take a long time to achieve a steady-state
flow.
In the case of very low permeability rocks, the pulse decay method suggested by Brace
et al. (1968) is more efficient. This method measures the change in pressure through time at
one end of a sample due to a sharp pressure pulse, which is introduced at the other end
20
(Hsieh et al., 1981; Trimmer, 1981). The disadvantage of this method is the interpretation of
the exponential pressure decay versus time curve, which requires processing after stable
experimental conditions occur after a few minutes. This method, therefore, disregards the
first few minutes of good quality data and relies on the latter data segment.
Another technique for measuring the permeability of rock samples is the oscillating
flow method. This technique requires the introduction of a well-controlled sinusoidal
pressure fluctuation upstream of the sample under test. The pore pressure oscillation is
superimposed upon the ambient pore pressure at one end of the rock sample. This method
allows continuous measurements during gradual changes in the state of the rock-environment
system. When both the amplitude ratio and the phase difference of the upstream and
downstream reservoir pressures are measured, permeability and hydraulic diffusivity can be
calculated. This allows the calculation of the magnitude and changes of the effective rock
porosity (Kranz et al., 1990; Fischer, 1992; Bernabé et al., 2006; Song and Renner, 2007).
However, there are several drawbacks to the oscillating flow method. First, the optimum
frequency of oscillation and the ratio of downstream-to-upstream pore pressures depend
upon sample size and the magnitude of permeability. For high porosity sandstones, the
oscillating period can be seconds, while for low porosity rocks such as granites, the pore
pressure oscillation period can be about an hour (Kranz et al., 1990). This imposes a limit on
the range of measurable permeability and hydraulic diffusivities. As for samples with very
high or very low porosities, the required oscillation period may either be unachievable or is
too time consuming. Second, the time required for the measurement of low porosity samples
may increase drastically; as in a typical laboratory setting, several tens of downstream
21
pressure oscillations are required in order to perform a Fourier analysis of the signals in
moving time windows of at least several cycles (Bernabé et al., 2006). Third, the storativity
measurements usually suffer very large uncertainties, which greatly influence the accuracy of
the permeability calculation. The optimization method used for solving the non-linear
coupled equations are extremely sensitive to noise in the recorded data and, hence, may lead
to erroneous calculations. Finally, systematic errors may occur owing to early time transients,
pressure leaks, or long-term temperature variations (Bernabé et al., 2006). In view of these
limitations, the simple steady-state flow method was used in all the permeability
measurements performed in this research.
2.2 Rock fracture mechanics
2.2.1 Stress relations and Coulomb failure criterion
Figure 2.2 shows a two-dimensional stress field applied to a cylindrical rock specimen.
The normal stress σn and shear stress τ components are taken as the axes of abscissa and
ordinate, respectively. Normal stress lies perpendicular to the failure plane, while shear stress
lies along the failure plane. The angle between the σ1 plane and the fault plane is denoted as
α. Shear stress and normal stress can be expressed by equations 2.5 and 2.6, respectively.
τ = ( σ1 – σ3 ) sin2α / 2 Equation 2.5
and
σn = ( σ1 + σ3 ) / 2 – ( σ1 – σ3 ) cos2α / 2 Equation 2.6
where σ1 and σ3 are the principal stresses.
22
Figure 2.2 Schematic figure of the stress field.
The relation between τ and σn with principal stresses σ1 and σ3 is represented in Figure
2.3.
Figure 2.3 Mohr diagram for normal shear stresses produced by the principal stresses.
In a triaxial test, σ1 and σ3 can be presented by a Mohr circle at any point in time. A
family of Mohr circles can be obtained from a series of failure tests with increasing values of
σ1 and σ3. From these circles, a failure envelope can be defined, with the combination of τ
and σn for which failure is reached (Figure 2.4). The failure envelope can be expressed by
σ1
σ3
σ1
σ3
τ
σn
α
σ
σ3
σ1
τ σn = (σ1+σ3) / 2 - (σ1-σ3) cos2α / 2
(σ1+σ3)/2 (σ1-σ3)/2
τ = (σ1-σ3) sin2α / 2
2α
23
equation 2.7:
τ = τ0 + σn tanφ Equation 2.7
where τ0 is cohesion, tanφ is the coefficient of internal friction (often showed as µ), and φ is
the angle of internal friction.
σn
Failure Envelope
σ1
τ0
τ
φ
Region of Stability
0
τ=τ0+σntanφ
σ3
Figure 2.4 Mohr stress circles for a series of tests showing failure according to Coulomb failure criteria.
The Coulomb failure criterion with the consideration of effective stress relates the
normal and shear stresses, which is effective in describing macroscopic-scale failure. It
describes the instantaneous condition of the material and is expressed independently of time.
Furthermore, it does not consider the contribution of rough rock joints and their surface
morphology. This simple criterion may provide a rough interpretation of initial or rapid RIS,
which is represented by a shift of the Mohr circle toward the failure envelope. However, in
the case of protracted RIS, variation in subsurface condition due to pore pressure oscillation,
mineral dissolution, etc. can vary the strength of the pre-existing faults with time and space.
This spatial and temporal variation in the strength of the fault zone cannot be addressed by
this macroscopic failure criterion.
24
During initial reservoir impoundment or large water level change, shear failure may
occur on pre-existing fault planes or fractures. Studies by Gough et al. (1970) and Snow
(1972) focus on the elastic loading effects of reservoir impoundment and elastic stress
changes. The elastic response of the subsurface to reservoir loading causes changes in normal
and shear stress underneath the fault plane. This can be shown by Mohr circles in Figure 2.5,
where the loading of reservoir causes σ1 to increase and, hence, pushes the Mohr circle
towards the failure envelope.
σn
τ
σ3 σ1 (after)σ1 (before)
Figure 2.5 Mohr circle representing the elastic effect of reservoir loading on the strength of rock underneath the
reservoir. The dashed semi-circle represents the strength before loading and the solid line semi-circle represents
the strength after loading.
If an increase in elastic loading is the dominant mechanism for RIS, seismicity would be
triggered soon after reservoir impoundment and the seismicity would soon be stabilized
when the additional strain has been released. The elastic loading effect of water
impoundment would only be effective in thrust fault and normal fault settings and would not
be effective in strike-slip fault settings, as the increase in vertical load would not influence σ1
and σ3 of strike-slip faults. Figure 2.6 shows the change in stability of a fault plane relative to
the position of the reservoir in thrust fault and normal fault settings. In the case of a
25
strike-slip fault, there is no change in ∆τ; therefore, the elastic theory would suggest that this
fault setting is not prone to RIS. However, many RIS case histories have been found in
strike-slip fault setting, for instance, the earthquakes at the Açu reservoir in Brazil (do
Nascimento, 2002), the Koyna reservoir in India (Gupta, 2002), the Xinfengjiang reservoir in
China (Talwani and Chen, 1998), and the Hoover dam in the USA (Guha, 2000) are all
located on strike-slip faults. This suggests that the net increase in impoundment load is not
the dominant mechanism in these RIS cases. Furthermore, numerous case histories of
protracted RIS have continued for decades, such as that at the Koyna reservoir (Gupta, 2002)
and the Xinfengjiang reservoir (Talwani and Chen, 1998). This seismicity cannot be
explained by the elastic loading effect of reservoir impoundment. Other protracted RIS cases
such as that at the Aswan reservoir, Egypt, had protracted RIS recorded during the period
when the surface water level was lowered (Selim et al., 2002). This further suggests that the
increase in elastic loads is not the dominant mechanism for RIS.
Figure 2.6 Schematic figure of the change in stability of a fault plane relative to the position of the reservoir (do
Nascimento, 2002).
Hanging
wall
Foot
wall
Hanging
wall
Foot
wall
reservoir reservoir reservoir reservoir
σ1
σ1 σ3
σ3
a) Normal fault b) Thrust fault
Legend:
unstable
stable
26
2.2.2 Pore pressure effects
Pore fluid has both mechanical and chemical effects on induced seismicity. However,
the current understanding of the nature of RIS places emphasis on the physical effect of pore
pressure enhancement due to the increase in surface water levels. Mechanically, pore
pressure can reduce the effective normal stress that acts on the existing faults or fractures via
the law of effective pressure (Equation 2.8) and, hence induce seismicity. If the medium is
porous and contains fluid with pore pressure P, the principal stresses are reduced to the
effective values:
σ’ = σ – P Equation 2.8
where σ’ is the effective stress. In a Mohr diagram, an increase in pore pressure (with σ1 and
σ3 being constant) moves the Mohr circle toward failure (Figure 2.7).
σn
τ
P
σ3-P σ1σ1-Pσ3
Figure 2.7 Mohr circle representing the fluid pressure effect on the strength of rock. The dashed semi-circle is
the stress before fluid pressure is applied and the solid line semi-circle is the stress after the fluid pressure is
applied.
27
For RIS, the instantaneous increase in pore pressure in the substratum is due to the
increase in impoundment load at the surface. This increase in pore pressure will decrease the
normal stress that holds the fault and, thereby, induce slips along the pre-existing faults.
The long-term chemical effect of water may change the strength of fractured rocks by
decreasing the coefficient of friction (Shen et al., 1974; Kisslinger, 1976; Talwani and Acree,
1984/85; Chen and Talwani, 1998; and Chen, 2001). The chemical interactions of pore fluid
with the rock matrix are discussed by Chen (2001) and will not be discussed in this thesis, as
the focus of the research is on the mechanical effects of pore fluid. In addition, no chemical
effects of pore fluid would have taken place during the relatively short period of experiment.
According to Coulomb failure criterion, the incremental shear strength, ∆S, along a
pre-existing fault plane due to reservoir impoundment, is given by Bell and Nur (1978) and
Talwani (2000):
∆S = µ ( ∆σn – ∆P ) – ∆τ Equation 2.9
where ∆τ is the changes in shear stress on the fault, ∆σn is the change in compressive normal
stress across the fault, µ is the coefficient of internal friction, and ∆P is the change in pore
pressure. Negative values of ∆S indicate fault weakening, while positive values imply fault
strengthening. A decrease in ∆S is due to a decrease in ∆σn, or an increase in pore pressure or
∆τ (Figure 2.8). The calculation of ∆S as a means of assessing the stability of a fault depends
on knowledge of the geometry of the fault, the assumed magnitude and orientation of the
regional stress, and the assumed value of the friction coefficient.
28
shear stress = τ = τ0 + µ ( σn – P )
Figure 2.8 Pore pressure and shear stress at a faulted surface (Simpson and Narasimhan, 1992).
Pore pressure acts in two different deformation regimes: drained and undrained
(Detournay and Cheng, 1993; Guéguen and Palciauskas, 1994). Each regime has a different
effect on RIS.
i) Undrained Response (Rapid Response of Initial Seismicity)
Due to the increase in water level at the surface, there will be an instantaneous increase
in pore pressure in the substratum. This increase in pore pressure due to elastic compression
leads to an undrained response, which weakens the fault and may cause failure. If this
mechanism is dominant, the corresponding RIS will be instantaneous and only minimal delay
between the peak of the water level and the maximum seismic activity will be observed (do
Nascimento, 2002).
Simpson (1976) considered the effects of elastic stress changes and pore pressure
changes due to reservoir impoundment. He showed that elastic stress changes decreased
quickly away from a reservoir in the case of finite reservoir length, while the increased pore
pressure did not dissipate as quickly with distance from the reservoir. This increase in pore
τ
σn P
29
pressure, due to the undrained response, can persist until pore pressure slowly dissipates into
the surrounding fractures. As a result, the reduction in effective pressure can last for a period
of time depending on the mechanical properties of the environment. Simpson and
Narasimhan (1992) proposed that heterogeneities in rock properties can also cause a
localised pore pressure increase due to the undrained response. Consequently, this causes a
rapid seismic response due to reservoir impoundment.
ii) Drained Response (Delayed Response of Initial Seismicity and Protracted RIS)
When sufficient time is allowed for fluid to move through the rock mass, pore pressure
can decrease to the original value; hence, the drained response is associated with delayed RIS.
In most RIS cases, there is a time lag between reservoir impoundment and the onset of
seismicity. Howells (1974), Talwani (1976), and Talwani and Acree (1984/85) suggest that
the pore pressure diffusion effect is a possible mechanism for delayed RIS. Simpson (1976),
Bell and Nur (1978), Roeloffs (1988), and Rajendran and Talwani (1992) use the coupled
elastic effect and pore pressure diffusion effect to explain the phenomenon of RIS. The
change in pore pressure is governed by the basic diffusion equation given by Jaeger et al.
(2007):
t
P
Dz
P
∂∂
=∂∂ 1
2
2
Equation 2.10
where t is the time and D is the hydraulic diffusivity, which can be expressed as follows:
ηβk
D= Equation 2.11
30
where k is the permeability of the rock, η is the viscosity of the pore fluid, and β is the bulk
compressibility of fluid-filled rocks.
Analytically, the delay can be expressed in terms of the distance below the ground
surface and the hydraulic diffusivity, which is a function of permeability, k. If a pressure P(z
= 0, t = 0) is imposed at the surface and retained for t > 0, and D is a constant, the solution to
equation 2.10 is given by Carslaw and Jaeger (1959):
)2
(1)0,0(
),(
Dt
zerf
P
tzP−= Equation 2.12
where P(0, 0) is the original pore pressure change at the bottom of a reservoir due to
reservoir impoundment, P(z, t) is the pore pressure with depth z at time t after the
impoundment, and erf is the standard error function.
By assuming D = 106 m
2/day and that distance z varies from sample distance of 125 mm
to field distance of 0.4 to 5 km, a set of curves can be plotted by using equation 2.12 (Figure
2.9). The plot indicates that the pressure front arrives at shallow depths first and the time
required for the pressure front to reach greater depths increases significantly. In the case of
the laboratory experiment with 125 mm long sample, it takes less than a few seconds for the
pore pressure front to arrive from the upstream (applied pore pressure end) to the
downstream at the other end of the sample. The effect of D, at a depth of 1 km and at sample
depth of 125 mm is illustrated and compared in Figure 2.10, which shows that the time
required for the pressure front to reach a certain depth increases with decrease in D and,
decreases with decrease in distance.
31
Figure 2.9 Showing the values of equation 2.12 for different values of z and t and D = 106 m
2/day.
Figure 2.10 Showing the values of equation 2.12 for different values of D and t, and with z = 1 km and 125 mm,
respectively.
32
Roeloffs (1988) discussed the fault stability changes induced beneath a reservoir with
cyclic variations in water level, with consideration of the fully coupled effect of pore
pressure and elastic stresses, i.e., the elastic stresses influence pore pressure and vice-versa.
She calculated stress and strength changes produced by a steady periodic variation of the
water level on the surface of a uniform porous elastic half-space and modified equation 2.12
to include the effect of undrained response. For a unit step increase in pore pressure at the
surface, P(0, t) = H(t), she calculated the pore pressure at a depth z after time t, P(z, t). For a
one-dimensional case, the pore pressure at depth z and time t becomes:
))((2
)1(),( tHDt
zerfctzP δδ +
−= Equation 2.13
where erfc is the complementary error function, H(t) is the Heaviside unit step function, δ =
B(1+vu)/3(1-vu) for isotropic conditions, B is the Skempton’s coefficient, and vu is the
Poisson’s ratio measured under undrained condition. The coupled response may be
dominated by the undrained response immediately on impoundment and be primarily caused
by diffusion at a later stage.
Roeloffs (1988) also showed that in the case of periodic reservoir water level change,
the magnitude of pore pressure change due to diffusion at any depth depended on the
frequency of water level changes, i.e., the higher the frequency of water level changes, the
lower the magnitude of pore pressure change. She showed that at depths below z, there was
almost no change in pore pressure due to diffusion:
z = 2 π (2D/ω)1/2 Equation 2.14
33
where ω is the angular frequency of water level changes. This concept of the fully coupled
effect of pore pressure and elastic stresses has been used to explain the seismicity at Lake
Mead, the Nurek reservoir (Roeloffs, 1988), the Koyna reservoir, the Oroville reservoir
(Rajendran, 1992), the Monticello reservoir (Rajendran, 1992; Rajendran and Talwani, 1992),
and the Xinfengjiang Reservoir (Shen and Chang, 1995).
Under drained conditions (long-term), other factors such as the hydrochemical
properties of the substratum, the chemical composition of the fluid, the nature of gouge and
clay that clogged the fractures, etc. can influence the permeability of the fractured rock and,
hence, affect the rate of pore fluid diffusion and the time lag in seismic response (Chen,
2001).
2.2.3 Rock friction
Friction is of great importance in rock fracture mechanics. Its effects can be observed on
all scales: ranging from the microscopic scale, in which friction occurs between contact
surfaces; to larger scales such as interaction between grains, aggregates, or surfaces of joints
and fractures; and to even larger scales on the order of square meters or square kilometres,
where friction acts between fault surfaces. The frictional resistance of two surfaces in contact
is defined as the ratio of shear resistance to the normal stress. This concept is referred to as
Amontons’ law, which is similar to but predates the Coulomb friction model by almost a
century (Lockner and Beeler, 2002):
τ = µσn Equation 2.15
34
where τ is the shear stress, σn is the normal stress, and µ is the static friction coefficient.
If there is any variation of frictional resistance during sliding, a dynamic instability can
occur, resulting in a sudden slip associated with stress drop. This dynamic instability is
followed by a period of no motion during which the stress is recharged, followed by
instability. This variation of frictional resistance can be caused by the presence of pore fluid,
which can mechanically affect friction by pore pressure, and/or the chemomechanically
weakening of the solid (Scholz, 2002). Under saturated conditions, the basic friction
coefficient is reduced to an apparent friction coefficient.
The mechanism of dynamic instabilities can be demonstrated using a spring with
stiffness K, pulling a block subject to a normal force FN (Figure 2.11). When the applied
force reaches the frictional resistance of the block, the block is free to slide on the rigid
surface. The hypothetical case in Figure 2.12 shows a maximum resistance followed by a
decrease with continued slip. During the slip, the spring unloads and follows the line with
slope K. After a tangent point B is reached, the frictional resistance F decreases at a rate
greater than K. Instability therefore occurs due to a force imbalance, which causes
acceleration of the block. Beyond point C, resistance becomes greater that the force in the
spring and the block decelerates and come to rest at point D. The shaded area between points
B and C is equal to that between points C and D (Scholz, 2002). The condition for instability
is given by:
Kdu
dFN > Equation 2.16
35
Figure 2.11 Block-slider model demonstrating initiation of frictional instability, where FN is the normal force
acting on the block, K is the spring stiffness, and F is the applied force. When the force reaches the frictional
resistance of the block, the block is free to slide on the surface (Scholz, 2002).
Figure 2.12 Force displacement diagram showing a hypothetical case in which frictional resistance falls with
displacement at a faster rate than the system responds (Scholz, 2002).
Byerlee (1978) conducted laboratory measurements of frictional strengths for silicate
and carbonate rocks and proposed linear relationships to distinguish their frictional behaviour
under low normal stresses (σn < 200 MPa) and high normal stresses (200 MPa < σn < 2000
MPa) (Figure 2.13).
τ = 0.85 σn for σn < 200 MPa Equation 2.17
and
F
Slip, u
B
C
D
Slope = K
F
FN
K
36
τ = 50 + 0.6 σn for 200 MPa < σn < 2000 MPa Equation 2.18
This relationship is known as Byerlee’s law, which indicates that rock types including
silicates and carbonates have friction coefficients that vary from 0.6 to 0.85. However, the
surface energy of silicates can be reduced by the presence of water (Scholz, 2002).
Figure 2.13 Shear stress plotted as a function of normal stress at the initial friction for a variety of rock types.
For crustal faults, the friction coefficients may vary from ~0.5 to 1.0 (Zoback et al.,
1987; Townend and Zoback, 2000), which is a wider range of friction coefficients than that
given by Byerlee’s law. The lower-end friction coefficients are caused by the presence of a
fault gouge with hydrated mineral phases which weaken the fault, while the upper-end
friction coefficients are caused by time-dependent fault healing and the presence of
heterogeneities. Byerlee’s law is limited to certain rock types and does not account for
dynamic instabilities which depend on second-order friction properties such as roughness
Initial Friction
0
200
400
600
800
1000
1200
1400
0 500 1000 1500 2000
Normal Stress (MPa)
Sh
ear
Str
ess
(M
Pa)
τ = 0.85σn
τ = 50 + 0.6σn
37
and sliding velocity. Despite the differences in scales, there has been extensive evidence that
the strength of the continental crust is governed by Byerlee’s law. However, the laboratory
values of the rate and state variables that control stability must be extrapolated cautiously to
larger scales (Scholz, 2002).
2.3 Seismicity patterns
Earthquakes seldom occur as isolated events, but as part of a sequence. Before large
earthquakes occur, local seismicity rates often show a significant increase in number. This
seismicity is referred to as foreshocks, while smaller earthquakes that follow main shocks are
termed aftershocks. This earthquake sequence has well-defined characteristics. Earlier
laboratory experiments by Mogi (1963) found that homogeneous media are characterised by
seismicity with no foreshocks, slightly heterogeneous media have a number of foreshocks
preceding the main shock, and that extremely heterogeneous media are characterised by a
swarm type of earthquake activity. Extremely heterogeneous media are often defined as
media with variations in material type as well as materials created by previous deformations
(Couples and Lewis, 2007), while slightly heterogeneous material can be interpreted as
originally homogeneous material that has undergone deformation and has formed
heterogeneous faulting. These three types of foreshock–aftershock sequences are also
exhibited by natural earthquake sequences (Figure 2.14). Mogi (1963) inferred that the
mechanical structure of the media and the nature of the applied stresses could be responsible
for these patterns. Since the stresses could be regarded as nearly uniform for tectonic
earthquakes, the pattern of the earthquake sequences would be mostly influenced by the
degree of heterogeneity of the media.
38
Figure 2.14 Mogi’s (1963) classification of foreshock-aftershock patterns and their relationship to the structures
of materials and applied stresses. N is the number of seismic events and t is the time. Type I: in the case of
homogeneous material and uniformly applied stress, a main shock occurs without any foreshock and is followed
by numerous elastic aftershocks. Type II: when the material has a rather heterogeneous structure and/or the
applied stress is not uniform, small elastic shocks occur prior to a main shock and many aftershocks occur
following the main shock. Type III: when the structure of the material is extremely heterogeneous and/or the
applied stress has a considerable concentration, a swarm type of activity occurs consisting of a number of
elastic shocks with magnitudes increase gradually and then decrease after some time.
2.3.1 Aftershock sequence
There are three empirical scaling relations that describe earthquake aftershock
sequences: i) the Gutenberg-Richter frequency-magnitude scaling, ii) the modified Omori
39
law for the temporal decay of aftershock rates, and iii) Båth’s law for the difference in the
magnitude of a main shock and its largest aftershock (Shcherbakov et al., 2004). The first
two relations were used in Chapter 5 for analysing the aftershock sequences of the pore
fluid-induced seismcitity.
i) Gutenberg-Richter scaling
The Gutenberg-Richter scaling is the frequency-magnitude scaling for aftershocks.
Under a wide variety of conditions, the number of earthquakes in a specified region and time
window with magnitudes greater than M is given by the relation:
log N(≥ M) = a – bM Equation 2.19
where N is the number of events with magnitudes greater than M on the Richter scale, and a
and b are constants, in which b is the slope of the line measured from the linear descending
portion of the graph.
This relation is valid for earthquakes both regionally and globally, with b-values
typically between 0.5 and 1.5 (Von Seggern, 1980), while the constant, a, gives the logarithm
of the number of earthquakes with a magnitude greater than zero. Studies have shown that
aftershocks correspond to the Gutenberg-Richter scaling relation with b-values similar to
those for main shocks (Kisslinger, 1976). The physical meaning of b-value equals unity is
that there are 10 times more events of a smaller magnitude than that of a magnitude which is
greater by 1. The change in b-value indicates the change in frequency and magnitude of
earthquakes over time. Because precursors often indicate an increase in frequency and
40
magnitude prior to a main shock, the corresponding b-value is expected to decrease with the
growth of larger magnitude events.
Laboratory experiments of brittle rock deformation have been carried out to study the
fracture mechanism of micro-cracking events (Scholz, 1968; Main et al., 1988). These
studies show that rock deformation experiments in the laboratory and deformation of the
crust exhibit similar mechanisms. In addition, the fluctuations in b-value are consistent with
the intermediate and short-term earthquake precursors (Main et al., 1988).
ii) Modified Omori law
The decay of aftershock sequences follows the Omori law. The modified Omori law is
defined as (Utsu, 1961):
ptc
WtN
)()(
+= Equation 2.20
where N(t) is the number of aftershocks in an interval of time t, W is the amplitude, c is the
time offset parameter, and p is the exponent that modifies the decay rate, typically found to
be very close to 1 (Scholz, 2002).
iii) Båth’s law
Båth’s law states that the differences in magnitude between a main shock and its largest
aftershock are approximately constant, typically about 1.2 (Båth, 1965) for large, shallow
earthquakes. This relationship is independent of the magnitude of the main shock. The
relationship is given by:
41
∆M = Mm – Mamax
Equation 2.21
where Mm is the magnitude of the main shock and Mamax is the largest magnitude aftershock.
2.3.2 Foreshock sequence
Jones and Molnar (1979) found that foreshock sequence can be fit with an empirical
relation:
N = at–m
Equation 2.22
where t is the time before the origin time of the main shock, N is the frequency of foreshocks,
and a and m are constants. Papazachos (1975) and Kagan and Knopoff (1978) found that the
exponent m is close to 1. Later, Helmsetter et al. (2003) found that foreshocks obey the
inverse Omori law, which states that the rate of earthquakes prior to a main shock increases
on average as a power law proportional to 1/(tc-t)p of the time to the main shock occurring at
time, tc and p is the exponent that modifies the rate of change of the foreshocks.
42
Chapter 3 Techniques: The Use of Rock Physics and Laboratory Tools
This chapter describes sample preparation, triaxial loading equipment configuration,
and a data acquisition system. An account of the acoustic emission (AE) processing
techniques, including the procedures for extracting discrete AE from continuous AE records
and the methods of calculating source locations and source mechanisms, is illustrated.
Furthermore, descriptions of X-ray micro-computed tomography (CT) techniques and optical
microscopy are provided.
A schematic flow line diagram of the experiment and analysis is indicated in Figure 3.1,
and the author’s contributions are highlighted below. The sketch is divided into five sections,
as follows:
i) Triaxial experiment: the experiment involves the fracturing of a rock sample followed
by pore pressure oscillations to induce AEs that simulates RIS. These experiments were
designed by the author. However, the addition of an intermediate step was suggested by Dr.
Phil Benson to separate AEs obtained during the formation of fault from that obtained during
cyclic pore pressure stage. Furthermore, all the samples were prepared by the author, i.e.
coring, cutting and polishing.
ii) Data acquisition: this is divided into ultrasonic data acquisition and mechanical data
acquisition. Mechanical data are acquired by an NI data acquisition unit. The ultrasonic data
are divided into velocity data, triggered data, and continuous data. The author was involved
in the initial setting up of data acquisition units and trouble-shooting of the interfacial
problems of mechanical and electronic systems.
iii) Data processing: this involves the use of the InSite program for the processing of both
43
velocity survey data and discrete AE data. Continuous data recorded by a Giga RAM
recorder are processed by a SeisAcq event harvester, while continuous data recorded by a
‘Richter’ system are processed by a Streamer harvester. All data processing and analysis were
carried out by the author.
iv) Output: this includes the velocity structure of the sample over time, AE source locations
and mechanisms, and the evolution of b-values. The mechanical data output (which includes
permeability, stress, strain, flow volume, and pore pressure) are automatically logged,
converted, and displayed by a LabVIEW Virtual Instrument (VI) program, which the author
took part in writing the program for this purpose.
v) Analysis of fractured sample: this includes X-ray tomography and optical microscopy.
The X-ray tomography scanning was carried out by the Department of Chemical Engineering
and Applied Chemistry, while the thin sections were prepared by the Department of Geology.
However, the thin section photo captures and both X-ray tomorgraphy and optical
microscopy analyses were performed by the author.
44
Figure 3.1 Schematic diagram of the flow line from the experimental setup to data acquisition to data
processing to output and analysis. Post-experimental analysis includes X-ray tomography and optical
microscopy.
3.1 Sample materials and preparation
The rock types featured in this thesis are Darley Dale and Fontainebleau sandstones.
Cylindrical samples 125 mm in length by 50 mm in diameter were prepared, conforming to
the 2.5 length/diameter ratio recommended by the ISRM (International Society of Rock
Mechanics). The samples were prepared using a hollow coring drill, with the end faces
ground and polished to within 0.01 mm parallelism using a diamond grinding wheel. Prior to
experimentation, the samples were vacuum-saturated with distilled water for at least 72
hours.
Passive data
by AE DAQs
Active data by
velocity survey
Triggered data
Continuous data
Velocity data
InSite Processor
SeisAcq / Streamer event harvester
Discrete AE
Ultrasonic data
Mechanical data (stress, strain, volume, pore pressure)
NI data
acquisition
Permeability, strain, stress, flow volume, pore pressures
Sample
Velocity structure
AE source location AE source mechanism
b-values
Triaxial Experiment Data Acquisition Data Processor Output
Experiment Section
Analysis on fractured sample: i) X-ray tomography, ii) Optical microscopy
45
3.1.1 Darley Dale sandstone
Darley Dale sandstone is a poorly sorted, well-indurated felspathic sandstone from the
North of England, with grain sizes ranging from 0.08 mm to 0.8 mm (Ayling et al., 1995), an
average length of 0.22 mm, and a porosity of 13%. The cementing material is predominantly
silicious (Baud and Meredith, 1997). It was chosen for its relatively homogeneous nature and
highly reproducible stress-strain behaviour, which is ideal for the study of frictional sliding
along natural fractures. The intact samples used in this research have a permeability of 5.7 x
10-15
m2 under 5 MPa hydrostatic pressures.
3.1.2 Fontainebleau sandstone
Fontainebleau sandstone is found in the Ile-de-France region South of Paris. It is
composed of more than 98% quartz, with small quantities of accessory clay minerals. It is a
well-sorted sandstone (David and Darot, 1993), with an average grain size of approximately
0.25 mm. However, as the degree of silicification differs from one sample to another, the
bulk porosities and the characteristics of the porous networks show a wide range of variation
(Bourbié and Zinzner, 1985). In this research, the Fontainebleau sandstone samples typically
have a low porosity of about 4% and the permeability of the intact samples is 1.3 x 10-17
m2
under 5 MPa hydrostatic pressures.
3.2 Equipment
3.2.1 Triaxial deformation cell and triaxial compression loading machine
During a triaxial experiment, the axial load is applied by an external hydraulic actuator
operated under a displacement-rate control mode (Figure 3.2). The axial load is controlled by
46
a fast-acting hydraulic valve and measured by an internal load cell to an accuracy of ±0.005
MPa (or ±10 Pa). The actuators are equipped with a servo-controlled feedback system such
that a complete stress-strain curve can be recorded. Under constant strain rate loading, a
feedback signal is sent from the displacement transducer and is compared to the programmed
signal. If a discrepancy occurs between the two values, the hydraulic pressure is adjusted
until the feedback signal matches the programmed value. The raw signals are recorded in
volts and are converted to stresses in MPa by an automated LabVIEW program.
Figure 3.2 Compression loading machine and triaxial deformation cell.
The triaxial deformation cell is equipped with 18 piezoelectric transducer crystals (12
lateral and 6 axial transducers) for acoustic emission (AE) detection and three pairs of
ultrasonic wave transducers (stacks) for contemporaneous elastic velocity measurement
Triaxial
deformation
cell
Loading
Machine
47
along the three axes of the sample, for P-, S1- and S2-waves. The lateral piezoelectric
transducers, as well as the lateral velocity stacks, are held in position by the rubber jacket,
which separates the saturated sample from the confining oil (Figures 3.3, 3.4). The face of
these lateral transducers and velocity stacks are curved to fit the surface of cylindrical
samples. A North-East-Down (NED) coordinate system is used to describe the position of the
transducers with respect to the sample (Figure 3.5). Prior to the experiment, pencil-lead break
testing is performed at the face of each transducer to identify the sensitivity of the
transducers. A detailed sensor location file is attached in Appendix II.
Figure 3.3 Cross section of the triaxial deformation apparatus showing the top and bottom axial platens. The
apparatus is equipped with 6 axial transducers positioned in the faceplate of the platens and an ultrasonic
velocity measurement system made of piezo-ceramic stacks comprise of three channels (P-S1-S2).
Naturally fractured
sample
48
Figure 3.4 Rubber jacket holding lateral transducers and stacks in position.
Figure 3.5 North-East-Down (NED) coordinate system.
3.2.2 Servo-controlled permeameter system
The servo-control permeameter system consists of two identical hydraulic intensifiers,
which provide high-pressure pore fluid to each end of the sample (Figure 3.6). Each
intensifier has a maximum internal volume of 75 ml and is filled with distilled water. The
N
D
E
Lateral transducers
inserted in rubber
jacket
Lateral strain
measurement device
Lateral
stack
Rubber
jacket
49
intensifiers are servo-controlled using analogue electrical feedback from an external pressure
transducer to maintain any pressures up to 100 MPa, to an accuracy of +/-0.005 MPa. The
intensifiers are fitted with integral displacement transducers which monitor the position of
the high-pressure pistons, thus enabling the intensifiers to be used as volumometers. For
steady-state flow permeability measurements, the upstream (pore pressure port at the bottom
platen) and downstream (pore pressure port at the top platen) intensifiers are set to slightly
different control pressures in order to maintain a small, constant pressure gradient across the
sample (typically a 0.5 MPa difference). During the pre-peak stress constant pore pressure
stage of an experiment, the pore pressure is kept at a constant value (average of 5 MPa) and
the two intensifiers is controlled independently. As a result, permeability is not measured
continuously during pore pressure oscillation. Steady-state flow measurement of
permeability was measured at intervals that would not affect the oscillations of pore
pressures. Thus, they were measured prior to the oscillations and after the completion of
oscillations. Figure 3.6 indicates the schematic diagram of the permeameter and the
connection to the triaxial deformation cell. Another pair of pressure transducers is located in
close proximity to the triaxial deformation cell for the detection of upstream and downstream
pressures. This minimises the head loss along the pipelines and can provide more accurate
measurements. Raw signals are recorded as voltages and are converted into pressures in MPa
by the LabVIEW program.
50
Figure 3.6 Schematic diagram of the experiment setup. Showing a pair of servo-controlled intensifiers
connected to the downstream (top platen) and upstream (bottom platen) of the triaxial deformation cell.
3.2.3 Confining pressure pump
Confining pressure is also controlled by a pair of servo-controlled pressure pumps. Each
51
intensifier has a maximum internal volume of 68 ml and is filled with hydraulic oil. The two
intensifiers are controlled in tandem, using analogue electrical feedback from two external
pressure transducers. The confining pressure pump can maintain any pressure up to 100 MPa,
with an accuracy of +/-0.05 MPa. Another confining pressure transducer is attached close to
the triaxial deformation cell, which monitors confining pressure in the triaxial deformation
cell and provides accurate measurements. The signals are recorded by a data acquisition
board in voltages, which are then converted to pressures in MPa by the LabVIEW program.
3.2.4 Linear variable differential transformer (LVDT)
The corresponding axial shortening of the sample due to axial loading is measured by
two linear variable differential transformers (LVDTs). This LVDT is a common type of
electromechanical transducer that converts mechanical rectilinear motion into a
corresponding electrical signal. They are used for monitoring the axial displacement of the
sample due to compression and during cyclic pore pressure loads and are spaced radially
from the triaxial deformation cell (Figure 3.3), such that the measurements are not affected
by the elastic shortening of the entire loading train. The measured signals are in voltages and
are converted to strain by the LabVIEW program.
3.2.5 Data acquisition (DAQ) hardware
All mechanical experimental data are logged as a function of time using a National
Instrument (NI 6255) high-speed multifunction data acquisition (DAQ) board (Figure 3.7),
running on a computer equipped with LabVIEW 8.3 data acquisition software. This
high-speed device allows 16-bit accuracy with measurements of all channels operating at
52
maximum speeds. During the experiments, data is acquired at a rate of 100 kHz and an
average of 100 points. The acquisition board is equipped with 40 differential analog input
ports or 80 single-ended input ports, referenced to the ground. Differential inputs provide
higher resolution data than single-ended inputs, as the differential amplifier amplifies the
difference in voltage between the two inputs, which influences the output voltage in opposite
ways. During an experiment, the differential input settings are used for readings that require
high accuracy, such as pore pressures and LVDT measurements. Other measurements such as
axial loads and confining pressures are acquired through the single-ended ports.
Figure 3.7 NI6255 data acquisition board.
All raw data acquired by the DAQ are in voltages and are imported into the LabVIEW
data acquisition program, also known as a virtual instrument (VI), for data conversion, data
53
storage, as well as for displaying various real-time plots and values during experiments.
Equipment is calibrated prior to the experiments. By applying linear regression, the gradients
and intercepts of each transducer calibration line can be obtained. These regression results
(gradients and intercepts) are plotted in section 3.7. The calibration parameters are imported
into the logging software so that all measurements are converted into the appropriate
physical quantities (e.g., transducer pressures in MPa, volumometer volume in ml, and
LVDT measurements in strain). The converted measurements are then collectively stored in a
data file and displayed in the program panels. The schematic block diagram of the LabVIEW
VI program is illustrated in Figure 3.8.
Figure 3.8 Flow chart showing the LabVIEW data acquisition program.
3.3 Geophysical techniques
3.3.1 Ultrasonic-wave velocity survey and AE techniques
During an experiment, AE are received by an array of 16 receiver channels, while
ultrasonic-wave velocity surveys are performed at regular time intervals during the pre-peak
stress stage and between each set of pore pressure cycles during the post-peak stage.
54
a) Ultrasonic-wave velocity survey
Ultrasonic-wave velocity measurements are particularly valuable when used in
conjunction with active AE measurements because the surveys provide data on the change in
the elastic properties of the material associated with rapid strain release. An ultrasonic wave
is generated by a synthetic source with a known location. By processing these waveform data,
the change of seismic wave velocities and amplitudes over time can be determined. This
information also implies the evolution of transport properties and the damage of the sample
over time.
To assess the velocity structure of a rock sample during an experiment, active 3-D
velocity surveys were performed at ten minute intervals prior to the rupture of the sample,
using the three pairs of designated transducers along the three axes. The signal-to-noise ratios
were improved by stacking the signals 50 times. During the subsequent pore pressure
oscillation stage, velocity surveys were acquired prior to or after the completion of a cyclic
pore pressure sequence, in order to avoid disturbing the pore pressure oscillations.
During a velocity survey, an electrical pulse is generated by a pulse generator, which
excites the piezoelectric transducer to produce a mechanical signal. The signal then
propagates through the rock sample and is detected by a receiver (transducer) at the other end,
which transforms this mechanical signal into an electrical signal. As the piezoelectric
material is located some distance behind the end cap metal of the transducers, the P- and
S-wave arrival times through a specimen have to be calibrated. This can be done by
performing a face-to-face test of the end platens or by inserting a specimen (e.g., aluminium
55
cylinder) with known elastic properties between two lateral stacks. With a known
dimension/diameter and the elastic wave velocities of the specimen, the times-of-flight can
be back-calculated. These times-of-flight are subtracted from the arrival times acquired for
velocity surveys to calculate accurate velocities (Equation 3.1).
V = Ds/(T-To) Equation 3.1
where Ds is the sample distance or sample diameter; T is the time difference between sending
a pulse and receiving a signal via a high-frequency data-acquisition system (Cecchi digital
storage oscilloscope), with the presence of a sample; To is the travel time between pulsing
and receiving a signal with no sample present between the receiver and pulser; and V is the
elastic wave velocity. The calibration table of To values of P-, S1- and S2-wave
measurements in the three axes are tabulated in Table 3.1. The automatic and/or manual
picking of elastic wave arrivals is performed by finding the first break signal which deviated
from an amplitude level of 0 volts. The manual picking of elastic wave arrival times requires
some level of experience and the picking of all channels and events needs to be consistent.
Table 3.1 Calibration for ultrasonic wave arrival time measurements.
To along X-axis (µs) To along Y-axis (µs) To along Z-axis (µs)
P S1 S2 P S1 S2 P S1 S2
23.155 25.455 26.765 23.185 25.505 26.935 16.997 34.605 35.255
A Milne AE recorder allows 3-D ultrasonic velocity surveys to be performed at regular
time intervals. During a survey, each of the 16 selected transducers is excited sequentially by
an electrical pulse to produce a mechanical signal. This signal is recorded by the other 15
56
transducers in the array. Consequently, a maximum of 240 potential ray paths can be
generated.
b) Passive acoustic techniques
In this research, AE were detected using transducers consist of lead-zirconate-titanate
piezoelectric ceramic material (PZT-5A, Navy Type II) with a frequency range of
approximately 20 kHz to 2 MHz. Each transducer has PZT element with diameter of 2 mm
by 1.4 mm thick. These methods can describe the localisation and extent of induced
seismicity and monitor the propagation of events. Elastic waves emitted from the initiation
and propagation of cracks during the formation of a natural fracture and shearing or sliding
on existing fractures during the pore pressure oscillations are recorded across an array of
transducers, which consists of 16 transducers (typically 12 from the lateral, 2 from the top
platen, and 2 from the bottom platen). Each transducer/receiver is assigned as a channel for
the recording of elastic waves (Appendix II). Each receiver is connected to a Physical
Acoustics Corporation (PAC) pre-amplifier (model 1220 A) or a Pulser-Amplifier Desktop
Units (PAD) (Figure 3.9), which has a filter range of 10 kHz to 1.0 MHz. The signals
received are amplified by 60 dB. The relationship between decibel and amplification is
shown in Equation 3.2, which indicates that 60 dB is equivalent to 1000-times amplification
in amplitude. The subsequent inversion of the elastic waves’ arrival times for each event
provides a localisation of the source of the waves.
dB = 20 log (Wout/Win) Equation 3.2
where Wout is the output amplitude and Win is the input amplitude.
57
Figure 3.9 PAD pre-amplifiers used for amplifying signals by 60 dB
During an experiment, two types of passive data are recorded, namely discrete data and
continuous data. Both sets of data are acquired by two different monitoring systems. Discrete
AE data are monitored by a Milne AE recorder (ASC, 2007) and a Hyperion Ultrasonic Giga
RAM Recorder (ESG, 2002a), while continuous data are recorded by the Hyperion
Ultrasonic Giga RAM Recorder and a recently developed ‘Richter’ system. The Milne AE
recorder is part of the OMNIBUS acoustic emission and ultrasonic monitoring system (ASC,
2007), which is used for collecting discrete data of more than 50 events-per-second. This unit
provides 10 MHz 12-bit full-waveform acquisition. Signals received by sensors are
pre-amplified by a PAD pre-amplifier system (Figure 3.9). It also records the number of hit
counts (number of AEs) per channel. A ‘hit’ is recorded when the waveform signal voltage
exceeds a pre-defined threshold within a pre-defined time window. The threshold voltage
depends upon the experiment. In this research, this threshold is typically set to 60 mv, which
was about 3 to 4 times the peak noise level, and events with amplitudes of less than 60 mv
would not meet the triggering criterion.
58
The Hyperion Ultrasonic Giga RAM Recorder (ESG, 2002a) was used as a secondary
system for acquiring discrete data. During experiments, triggered AE waveform data were
recorded with a maximum capacity of 16 events per second. A minimum of 5 channels was
set as the triggering criteria and each channel is assigned an individual channel threshold.
When at least 5 channels record trigger threshold crossings with a 5 ms time window, an AE
‘hit’ is recorded (ESG, 2002a). These triggered data were sampled at a rate of 10 MHz and
recorded by First-In-First-Out memories.
Conventional AE recorders have limited capacity for recording triggered events during
high AE activity, as ‘mask-time’ occurs during the transfer of data from volatile memory to
permanent storage (Thompson, 2006). However, this inadequacy was overcome by the
Hyperion Giga RAM recorder developed by Young and Bowes (2002), which allows
continuous data acquisition and reconstruction of a complete AE catalogue by eliminating
AE system saturation. Data were digitized at 14-bit resolution, with an input voltage range of
±2.5 V, continuously streamed to a 40 GB RAM buffer, and sequentially copied to hard drive.
The experiments described in this thesis used sampling frequency of 10 MHz, resulting in a
segment of 134.8 s continuous waveform on 16 channels, which can be viewed at various
resolutions (Figure 3.10).
Discrete AE events were extracted from the continuous ultrasonic record using the
SeisAcq program developed by ESG (2002a). This program essentially replays the
continuous record after the test and applies a trigger logic to extract events. In this thesis,
events were extracted when the amplitude of at least five channels exceeded a trigger
59
threshold of 60 mv in a 100 µs window. These events were then processed as conventional,
discrete AE events for source location and source mechanism analysis.
60
Figure 3.10 Continuous waveform of a Darley Dale sandstone experiment and a discrete acoustic emission
waveform extracted from continuous waveform data at different zoom levels.
61
Similar to the Giga RAM Recorder, the ‘Richter’ system was recently developed for
continuous AE data acquisition. The limitation of its capacity is the storage capacity of the
hard drives. During an experiment, the most critical AE data are those that occurred during
pore pressure oscillation; consequently, this system is only activated for a 2-hour period
during pore pressure oscillation. The system consists of 8 individual computer systems,
designated B0052 to B0058. Each computer is responsible for recording continuous
ultrasonic waveforms to the allocated channels. System B0052 is assigned as the ‘master’
computer and linked to the other seven ‘slave’ computers. In order to activate all eight
computers for data recording, a signal is sent from the B0052 to the ‘slave’ computers, which
are all synchronised prior to an experiment. Similarly, by reconstructing and ‘re-harvesting’
the continuous data, discrete events of AE can be restored. These events can then be used for
AE source location for the study of migration trends or the nucleation of events. The
software program used for the ‘re-harvesting’ of events is called Streamer, which is another
subset of the InSite software (ASC, 2007). Figure 3.11 indicates a flow chart which
illustrates the acquisition of passive and active AE data by different monitoring and recorder
systems.
62
Figure 3.11 Flow chart showing the various AE data acquisition units for recording passive and active AE data.
3.3.2 AE methods
AE waveform data are processed to provide information on the micromechanics
involved in the evolution of damage, including nucleation and propagation processes, and in
rock mass structure and competence (Young et al., 2004). These methods include:
i) Source location and parameter analysis: Analysis of spatial and temporal trends of AE
activity due to pore pressure oscillation.
AE source locations or hypocentres were calculated using first arrival times recorded by
an array of transducers. This technique enables the mapping of the temporal and spatial
63
evolution of microcracks. First arrival times were picked by an automatic picking routine
using the InSite waveform processor (ASC, 2007), or manually picked to enhanced accuracy
(Figure 3.12). In order for the auto-picking routine to work effectively, different velocity
models were assumed in the different time periods of an experiment. The velocity model was
expected to change as with changes in differential stress. Microcracks were expected to
orient parallel to the maximum compressive force at the beginning and change the sample
from an initially isotropic to transversely isotropic structure. A transversely isotropic (TI)
structure generally develops with the fast axis parallel to the maximum compressive stress,
due to cracks opening parallel to the maximum loading axis. The velocity data was fitted to a
model in the form:
V(θ) = (Vmax + Vmin)/2 - (Vmax-Vmin)/2 cos (180-2θ) Equation 3.3
where V is the modelled P-wave velocity as a function of the ray-path angle, θ, and Vmax and
Vmin are the maximum and minimum P-wave velocities, respectively.
64
Figure 3.12 Showing typical P-wave arrivals received from each channel. The solid blue line indicates the first
arrival of the P-wave. The dotted pale blue line indicates the peak amplitude of the first arrival of the P-wave.
65
There are four unknowns in a source location equation. The first three describe the
location of the event, which includes x0, y0 and z0, while the fourth is t0, which is the time of
the AE. The unknowns were solved using a Simplex algorithm, which is an iterative
procedure that minimises errors between the measured and calculated arrival times (Nelder
and Mead, 1965; Press et al., 1994). The procedure uses a geometrical shape known as
Simplex, which has one extra vertex as compared to the number of dimensions of the defined
geometry. The error distance for each vertex is minimised through an iterative process. At
least seven arrival times are required for solving the source location in order to minimise the
AE location error.
There are three major errors in source location. First is the error associated with picking
the first arrival times; second is the uncertainty in the velocity model; and third is the ±2 to
±4 mm uncertainty in the location of transducers. In order to reduce the location error, travel
time residuals between the calculated and measured arrival times for a channel are limited to
two sample points; if the residual exceeds the limit, the channel is omitted from the location
algorithm. The most accurate method of assessing location errors is by locating a synthetic
source, i.e. locate the transmitters during ultrasonic wave-velocity surveys and then calculate
a residual between the actual location and the calculated location. This allows fine tuning of
the source location velocity structure. This source location calibration is illustrated in
Appendix I, which indicates that absolute source location error ranged from ±2 to ±4 mm.
According to Pettitt (1998), the error at the centre of the sample was approximately half that
at the edge. Therefore, for the experiments conducted in this thesis, a source location error of
approximately ±1 to ±2 mm was expected near the centre of the sample. Subsequently, AEs
66
closer to the centre of the samples were chosen for source mechanism analysis due to their
relatively higher location accuracy, as compared to events occurred near the edge of the
sample.
ii) Source mechanism studies: Analysis of the failure mechanics of AEs as a function of the
compression and tension forces acting at the source and the orientation of failure, giving
information about movement on existing microstructures and new crack and damage zone
creation.
Source mechanism analysis determines the modes of failure operating in terms of how
the sample is reacting to external forces. The simplest method to determine the source
mechanism of an AE is to calculate a fault plane solution as described by Gibowicz and
Kijko (1994). This method requires the polarity of P-wave arrivals to be identified at a
number of sensors in an array. The polarity recorded at a sensor indicates whether the first
motion at the source is dilation (positive) or compression (negative) for a particular ray path.
The polarities are plotted on a lower hemisphere stereograph representing the focal sphere of
the source. If a shear type event is assumed, then the equivalent forces are modelled as a
double couple (DC). Orthogonal nodal planes are drawn to separate regions of dilation and
compression. One of the planes is the fault plane, while the other is an auxiliary plan. The
differentiation of the two planes requires additional information.
The source mechanisms of AE are often characterised using a ratio of first arrival
polarities, with a tensile event having all positive values and a compression event having all
67
negative values (Figure 3.13). For an event with mixed polarity data, the success of fitting a
fault plane solution can define the event source as either shear or complex.
Figure 3.13 Examples of focal sphere and equivalent forces. Shaded regions represent dilation and white
regions represent compression (modified from Aki and Richards, 2002).
Another method for analysis source mechanism was developed by Pettitt (1998) based
on a time invariant moment tensor approach. The error quantification routine was improved
by Collins et al., (2002). This approach consists of two main stages, namely the inversion of
moment tensor and its composition into a source model. A brief account of moment tensor
approach is summarized in the following.
A seismic source can be described by 9 elemental force couples (a couple being a pair of
equal and oppositely oriented forces, and the moment of each, Mij, comprises the moment
68
tensor of the source. Conservation of angular momentum for the equivalent force couples
means the moment tensor is a symmetric second order tensor (3 x 3 matrix) requires only 6
components (Figure 3.14).
Figure 3.14 The nine elementary force couples which describe general source mechanism when combined in
moment tensor. The matrix notation of subscripts 1, 2, 3 correspond to x, y, z in Cartesian axes at the source
(Aki and Richard 2002).
By assuming a point source, the procedure can be simplified to a time invariant process.
Only channels receiving far-field signals will be considered in the moment tensor analysis,
while those receiving near-field signals will be disregarded. This further simplifies the source
radiation pattern. The near-field distance can be calculated by Equation 3.4 (Savage and
Aronson, 2005).
69
L = dT2/4λ Equation 3.4
where L is the length of the near field; dT is the diameter of the transducer; and λ is the
wavelength, which equals velocity divided by frequency.
The moment tensor is calculated by the inversion of P-wave first arrival amplitudes
recorded by the receiver array (Equation 3.5). The Green’s function matrix inversion is
performed using Singular Value decomposition after De Natale and Zollo (1989). As the
particle response of the sensors is not known, the procedure performs a relative amplitude
inversion, and calculates a relative event magnitude. At least 7 first motion P-wave
amplitudes are used in the moment tensor analysis, and the residual between the modeled and
observed amplitudes is used for checking the quality of the inversion. Since good focal
coverage is important for the accuracy of MT analysis, events are selected only from the
central third of the sample for this analysis. Furthermore, these selected events are processed
manually to enhance the accuracy. Finally, the stability of each inversion is tested by
dropping random arrivals (Thompson et al., 2009).
[ak] = [Gki,j][Mij], or
where [ak] is a vector containing n number of amplitudes, [Gki,j] is the Green’s function
=
a1
:
:
:
:
ak
G11,1 G11,2 G11,3 G12,2 G12,3 G13,3
: : : : : :
: : : : : :
: : : : : :
: : : : : :
Gk1,1 Gk1,2 Gk1,3 Gk2,2 Gk2,3 Gk3,3
M11
M12
M13
M22
M23
M33
Equation 3.5
70
indicating the propagation effects between the source and the receiver, and [Mij] is a vector
containing the 6 moment tensor components.
The physical mechanism of moment tensor can be interpreted using 3 eigenvectors, ai,
and 3 eigenvalues mi. The eigenvectors are mutually orthogonal in space, representing the
principal stress axes of the source; while the eigenvalues represent the magnitude and
polarity of the forces. The convention used for the principle stress axes are pressure (P), null
(B) and tension (T), representing minimum, intermediate and maximum eigenvalues
respectively. The forces can be represented in linear vector dipoles in Figure 3.15.
Figure 3.15 Vector force representation of some source models: a) negative Linear Vector Dipole (LVD), b)
Double Couple (DC), c) pure implosion, d) pure explosion, e) positive Compensated Linear Vector Dipole
(CLVD), and f) negative Compensated Linear Vector Dipole (CLVD) (Pettitt, 1998).
iii) Magnitude-frequency (b-value) trends for the identification of spatial and temporal
changes in rock mass response.
a) b) c)
d) e) f)
-1
-1
-1
1
1
1
-0.5
-0.5 0.5
0.5
-1 1
1 -1 -1
71
Previous studies have shown that AE hits have a power law frequency-magnitude
relationship similar to the Gutenberg-Richter b-value relationship (Equation 2.19) for
earthquakes. It was found that the b-values depend primarily on stress, and are much higher
in ductile rock than that observed in brittle rock (Scholz, 1968). For AE, magnitude is
calculated as location magnitude mL using equation 3.6.
=∑
=
n
n
m
mRMS
LS
dW
m
)(
log 1 Equation 3.6
where mL is an estimate of relative magnitude between a set of events, Sn is the number of
sensors and dm is the distance between receiver m and the AE location and WRMS is
calculated according to equation 3.7.
x
W
W
x
i
i
RMS
∑== 1
2
Equation 3.7
where Wi is the waveform amplitude and x is the number of data points in waveform.
The power law frequency-magnitude relationship for AE is the same as the
Gutenberg-Richter relationship for earthquakes, except that the magnitude M is replaced by
mL. Thus, equation 2.19 can be written as:
LL bmamN −=)(log Equation 3.8
where N is the number of events with magnitudes greater than mL, and a and b are constants,
72
in which b is the slope of the line measured from the linear descending portion of the graph.
3.4 Source of experimental error
There are two main categories of experimental error: physical experimental
measurement errors and human errors involved in the interpretation of physical results (Table
3.2). Physical errors can be minimised through standard good practices such as averaging
physical measurements and performing accurate calibrations. Human errors are often a
greater source of error. These errors involving the interpretation of physical results are
inevitable, but can be minimised by interpreting the results using consistent criteria, such as
during the picking of the first arrivals of elastic waves.
Table 3.2 Summary of experimental error sources and accuracy
Experimental Errors Absolute Accuracy
Sample length/diameter ±0.01 mm
Sample surface ±0.01 mm
Sample parallelism ±0.01 mm
Sample mass ±0.001 g
Axial load ±0.005 MPa
Displacement ±0.0005 mm
Confining pressure ±0.05 MPa
Pore pressure ±0.005 MPa
P-wave arrival time ±0.2 µs
73
3.5 X-ray micro-computed tomography
A three-dimensional X-ray micro-computed tomography (CT) technique has been
applied to geomaterials to provide 3-D information on fault zones (Mees, 2003; Benson et al.,
2003; Salvo et al., 2003; Thompson et al., 2009). This 3-D information is obtained from a
series of 2-D measurements. The basis of X-ray micro-CT is X-ray radiography: an X-ray
beam is sent through a sample and the transmitted beam is recorded on a CCD-based detector
(Salvo et al., 2003). In this study, the 3-D X-ray micro-CT technique is adopted to understand
the variation of flow path along the vertical axis of the sample. In order to achieve a higher
resolution of X-ray tomography (34.89 µm x 34.89 µm x 34.89 µm), the volume of scanning
is limited to the central most representative range of the sample. The reconstructed 3-D
images can indicate the complexity of the fractured network within the samples and provide
an account of the homogeneity or heterogeneity of the fractured zone. A representative area
is chosen from the scanned image (slice), which is then used for the calculation of the
relative crack area. The resulting areas are normalised by the minimum crack area of all the
slices of the sample. These normalised crack areas are plotted according to the sequence of
the slice. The resulting profiles illustrate the relative ease of fluid flow along the vertical axis
during oscillation of pore pressure. This analysis can indicate zones with relatively narrow
flow paths, in which transient pore pressure accumulation is expected during pore pressure
cycles.
3.6 Optical microscopy
One sample each of tested Fontainebleau and Darley Dale sandstone is imbibed with
epoxy to stabilize the fractures prior to obtaining optical microscopy specimens. Three thin
74
section specimens are prepared for each sample: one on the xy-plane, one on the xz-plane,
and one on the yz-plane. Precise microscopic information regarding the microstructure of the
porous networks can be related to the variations of the measured transport properties.
Microscopy photos are taken with a CMOS colour microscopy camera, with 1.3 mega-pixel
resolution. The analysis of the microscopy can provide an account of the difference between
the fractured zone and the far-field area. In addition, the comparison of the microscopy of the
two rock types (Darley Dale sandstone and Fontainebleau sandstone) can illustrate the
difference in the behaviour of the samples under cyclic pore pressures.
75
Chapter 4 Laboratory Simulation of RIS due to Oscillating Pore Pressures
In RIS, the variation of surface water level affects the pore pressure at the bottom of the
reservoir. It is appropriate to assume that the water level cycles are equivalent to the pore
pressure cycles at the bottom of the reservoir (Talwani, 1997). Furthermore, do Nascimento
et al. (2005) numerically show that the use of sinusoidal water level variation has only a
minor effect on the resulted diffusivity, as opposed to the use of real seasonal water level data.
Therefore, in the experiments, sinusoidal pore pressure variation was used as a proxy of
surface water level change.
Initial tests were carried out to identify three important parameters for the design of
cyclic pore pressure experiments: first, to identify the compressive strength and behaviour of
samples under different confining pressures; second, to identify the behaviour of the sample
during reduction in pore pressure and the different rate of increase of pore pressure; and third,
to investigate the behaviour of samples under different frequencies of pore pressure
oscillations. The findings from these initial sets were used as inputs for the design of the
subsequent cyclic pore pressure experiments. The peak value of the compressive strength of
the samples determined which pair of axial platens to be used during the cyclic pore pressure
experiment. Titanium platens were designed to deform samples with compressive strength
less than 500 MPa, while hardened stainless steel platens were designed to deform samples
with compressive strength up to about 600 MPa.
4.1 Behaviour under compressive load tests
Three triaxial compressive loading experiments were carried out on the saturated Darley
76
Dale sandstone under a strain rate of 2 x 10-6
s-1
and confining pressures of 10, 20, and 40
MPa, respectively, to provide the parameters used for the cyclic pore pressure experiments.
The behaviour of the rock became more ductile and the failure angle range reduced from 71o
to 66o, as higher confining pressures were used. Figure 4.1 shows the loading curves of three
initial tests. Although only three initial tests, each at different confining pressure was
conducted to provide the strength and behaviour of the samples, the number of initial tests
were considered adequate because Darley Dale sandstone has been widely studied and is
known to have consistent behaviour under deformation tests (e.g. Baud and Meredith, 1997).
In addition, the failure behaviour of the samples (ductile or brittle failure) was of a greater
importance than the absolute value of the peak strength in the case of cyclic pore pressure
experiments in the post-peak regime. Furthermore, the stress-time plots of the Darley Dale
sandstone illustrated in section 4.8 showed that the failure behaviour of the sandstone was
consistent with that indicated in the initial testing.
The experimental results suggest that 40 MPa confining pressure creates ductile
deformation, in which the stress-strain curve does not provide the clear stress drop and
rupture occurrence essential for indicating the end of stage 1 of the experiment. Conjugate
sets of faults were formed during the experiment, which enhance the difficulty in the study of
the migration trends of seismic events. Therefore, 40 MPa confining pressure was not used in
the cyclic pore pressure experiment.
77
Figure 4.1 Stress-strain curves of Darley Dale sandstone samples under 10, 20, and 40 MPa confining pressures.
The behaviour of Fontainebleau sandstone was very brittle. Samples subjected to 15 and
20 MPa confining pressure both failed with a brittle ruptured, which provided a clear mark
for the beginning of the post-peak regime. However, under these confining pressures, the
samples did not generate a clear shear failure plane. Axial splitting and complex shear
conjugates were developed (Figure 4.2). Although only two initial tests, each at different
confining pressure was conducted to provide the strength and behaviour of the samples, the
number of initial tests were considered adequate because Fontainebleau sandstone has been
widely studied and is known to have consistent behaviour under deformation tests (e.g.
Bourbié and Zinzner, 1985). Similarly, the failure behaviour of the samples (ductile or brittle
failure) was of a greater importance than the absolute value of the peak strength in the case
of cyclic pore pressure experiments in the post-peak regime. In addition, the stress-time plots
78
of the Fontainebleau sandstone experiments illustrated in section 4.8 showed that the failure
behaviour of the sandstone was consistent with that indicated in the initial testing.
With the information from these initial compressive load tests of the two sandstone
types, it was decided that a confining pressure of 20 MPa, which represents conditions at 800
m in the crust, would be used for cyclic pore pressure experiments for both types of
sandstone for comparison purposes. This confining pressure not only allows the development
of a clear sample rupture mark (i.e., a sharp stress reduction) for both sandstone types, but
also allows a larger variation in pore pressure, which has to be kept below the confining
pressure at all times during the experiment to avoid damaging the rubber jacket.
Figure 4.2 Typical stress-strain curve of the Fontainebleau sandstone with 20 MPa confining pressure.
79
4.2 Behaviour under pore pressure reduction and subsequent increase
Furthermore, trial experiments were carried out to investigate the responses of fractured
Darley Dale sandstone due to pore pressure variations. After the failure of the sample, the
strain rate was paused. The pore pressure was then reduced to half of that used during the
loading stage to observe the acoustic behaviour of the sample. During this stage, the
quiescence period was obtained with the seismic rate reduced to background levels. This is
due to the increase in the effective stresses that hold the faults together, which then lock the
faults. This quiescence period is essential for the separation of residual events caused by
sample failure from those caused by pore pressure variation.
After quiescence has been observed, the pore pressure was then ramped up beyond the
previous maximum to investigate the possibility of the activation of faults due to pore
pressure increase. Three experiments (DDS4, DDS5 and DDS6) were carried out to
investigate this possibility. A list of the rate of increase in pore pressure that has been used in
various experiments is illustrated in Table A5 (Appendix IV). Two of the experiments
(DDS4 and DDS5) used a constant pore pressure of 1 MPa in the pre-peak stage, and then
lowered to 0.5 MPa during the quiescence period. The subsequent targeted pore pressure was
1.5 MPa, which exceeded the previous maximum. The rates of increase of pore pressure were
0.2 MPa/minute and 0.5 MPa/minute, respectively. In both experiments, no activation of
fault was observed, i.e., there was no distinguishable increase in AE due to the increase in
pore pressure. Consequently, the third experiment (DDS6) was modified to use a higher rate
of increase and a higher amplitude of pore pressure in order to investigate the activation of
faults. During the pre-peak stage, a constant pore pressure of 5 MPa was used, which was
80
then lowered to 2.5 MPa during the post-peak for quiescence purposes. The pore pressure
was then increased at a rate of 5 MPa/minute to reach a designated pore pressure of 7.5 MPa.
The result suggests that the activation of faults by pore pressure increase is possible and that
the rate of increase in pore pressure used in the subsequent cyclic pore pressure experiments
could be kept at ≥ 5 MPa/minute.
4.3 Behaviour under cyclic pore pressure
Roeloffs (1988) inferred that the frequency of the cyclic pore pressure can play an
important role in RIS. Thus, a third set of initial testing was conducted primarily to identify
the seismic response of faulted samples due to the different frequencies and/or amplitudes of
pore pressure cycles. Because the number of AE responses of Fontainebleau sandstone
during the post-peak regime surpass those recorded in the Darley Dale sandstone
experiments, the third set of initial testing was carried out on the saturated Fontainebleau
sandstone. During the experiment, the sample was loaded to rupture under a constant
confining pressure, a constant strain rate of 2 x 10-6
s-1
and a constant pore pressure of 5 MPa.
The strain rate was then paused and pore pressure was reduced to 2.5 MPa for the locking of
faults and quiescence. For the ease of pore pressure control during this stage, the two pore
pressure ports were linked to perform as a pair, i.e., both ports received the same command
of pore pressure change during the variation in frequency and amplitude of pore pressure.
The details of the pore pressure cycles used in the F2 experiment are tabulated in Appendix
III.
The results of the F2 experiment indicate that seismicity can be activated when the pore
81
pressures reach or exceed the previous maximum. However, seismicity reduced rapidly
during the subsequent cycles with the same amplitudes. No significant seismicity was
observed when the pore pressure was lower than the previous maximum (Figure 4.3).
However, it is noted that the activation of seismicity began when the pore pressure was lower
than the previous maximum (Figure 4.4). Consequently, it is speculated that if cyclic pore
pressure peaks could be maintained at a higher percentage of the previous maximum, faults
might be reactivated after a greater number of cycles. This postulation was then
demonstrated by the subsequent cyclic pore pressure experiments (F5 and F8).
The AEs generated due to cyclic pore pressure were spatially and temporally scattered
along the pre-existing fault (Figure 4.5). There were no clusters of events or migration trends
observed from the reconstructed temporal seismicity distribution. This behaviour may be
explained by the existence of a heterogeneously faulted structure, consisting of axial splitting
and shear fractures, which causes anisotropy in diffusivity within the sample and, hence the
scattered locality of the pore pressure development that induced the seismic events.
82
Figure 4.3 Experiment F2 – Pore pressure cycles introduced after the rupture of the specimen.
Figure 4.4 Activation of fault begins when the pore pressure reaches ~4.3 MPa, which is lower than the
previous maximum.
83
a) b)
Figure 4.5 a) The fractured F2 Fontainebleau sandstone sample; b) spatially and temporally scattered seismic
events induced by pore pressure cycles occurred along the pre-existing faults.
The seismic data of this initial testing was also used for the investigation of the
distribution of seismicity along the sample. With the reference points set at both ends of the
sample where pore pressure was applied (Figure 4.6), the hypocenter distances were then
grouped into 10 mm bins. The results indicate that the number of events tends to increase
toward the middle of the sample (Figure 4.7).
Figure 4.6 Showing the reference distance for the measurement of hypocenter locations during initial tests.
62.5
0
0
84
Figure 4.7 The number of events located at different ranges of hypocenter. The trend indicated during the cyclic
pore pressure period is similar to that during the pre-peak period.
It was speculated that by applying pore pressure at one end of the sample and recording
the pore pressure response at the other end, more information about the pore pressure
gradient along the fractured sample could be provided. In addition, this procedure provided
longer distances for the migration of events, if any, and hence eased the study of migration
trends. Consequently, this modified procedure would be used in the subsequent cyclic pore
pressure experiments.
4.4 Conclusions from Initial Testing
Initial testing indicates that the amplitude and rate of increase of pore pressure and the
frequency of pore pressure oscillations can influence the activation of RIS. The effect of
cyclic pore pressure frequency on seismicity is demonstrated in Figure 4.9. The specific
frequency range that influence seismicity depends on the mechanical properties of the sample
and would not be determined in this thesis, as it is beyond the scope of this research. The
findings and modifications of the cyclic pore pressure experimental procedures are
summarized in Figure 4.8. The initial experiments indicate that the procedures can be divided
85
into three stages:
i) Loading of an intact rock sample under a strain rate of 2 x 10-6
s-1
, constant pore
pressure of 5 MPa, and confining pressure of 20 MPa, which replicates shallow crustal
condition of 800 m.
ii) After the failure of the sample, a period of quiescence must be introduced by pausing
the strain rate and reducing the pore pressure to 2.5 MPa. This provides a clear separation of
the residual events caused by the rupture of sample and the events caused by pore pressure
variation.
iii) Oscillating pore pressure with a rate of increase of pore pressure greater than 5
MPa/minute would be used. The peak pore pressures should exceed the previous maximum
for the activation of faults, while peaks at ~95% of the previous maximum would be used for
the investigation of the reactivation of faults due to oscillating pore pressures. The pore
pressure would be applied at the bottom of the sample (upstream port) and measured at the
top of the sample (downstream port). This method is similar to that used for measuring
permeability of intact rock samples (Kranz et al., 1990; Fischer, 1992; Bernabé et al., 2006;
Song and Renner, 2007), which has been discussed in section 2.1.3.
86
Figure 4.8 The three groups of initial testing and the output used for the design of cyclic pore pressure
experiments.
4.5 Modified Cyclic Pore Pressure Experiments
Two different sandstones: i) Fontainebleau sandstone with a relatively low porosity of
4%, and an initial permeability of ~1.3 x 10-17 m2 and ii) Darley Dale sandstone with a
relatively high porosity of 13%, and an initial permeability of ~5.7 x 10-15
m2 were used in
the cyclic pore pressure experiments. This provides a good comparison of the effect of pore
pressure oscillation on different permeability samples. Furthermore, one control and one
saw-cut experiment were carried out on Fontainebleau sandstone samples. The purpose of the
87
control experiment was to distinguish the significance of cyclic pore pressure on induced
protracted seismicity and the reactivation of pre-existing faults from that of a step increase in
pore pressure, while the saw-cut Fontainebleau sandstone experiment provided a clear single
fracture for the investigation of any migration trends of AEs. The list of experiments is
tabulated in Table 4.1:
Table 4.1 List of experiments
Fontainebleau sandstone experiments Description
F5 Naturally-fractured sample underwent
oscillating pore pressure
F6 Saw-cut sample underwent oscillating pore
pressure
F7 Naturally-fractured sample with pore pressure
step changes, as a control
F8 Naturally-fractured sample underwent
oscillating pore pressure
Darley Dale sandstone experiment
DDS7 Naturally-fractured sample underwent
oscillating pore pressure
Sinusoidal pore pressure cycles were applied from one end of the sample and recorded
at the other in all the experiments except the control experiment. This procedure required
trial-and-error to identify the oscillation frequency or oscillation period that could be used in
the fault activation and reactivation experiment. The upstream and downstream pore
pressures in Figure 4.9 indicate that the response of the downstream pore pressure was
affected by the frequency of the applied pore pressure. When the frequency was too high, the
downstream pore pressure might not respond according to the applied pore pressure
88
frequency. In addition, seismicity was not induced when the average pore pressure of the
sample did not exceed the previous average; nevertheless, the applied pore pressure was set
beyond the previous peak values. In this case, existing faults were not activated unless
sufficient time was allowed for the downstream pore pressure to develop. If the oscillating
frequency was too low (or the rate of increase in pore pressure was too low), the downstream
pore pressure synchronised with the upstream pore pressure (Figure 4.9). The optimal pore
pressure frequency for the reactivation experiment was obtained by several trials, such that a
phase shift between the upstream and downstream pore pressures was observed. This phase
shift corresponds to an observable repositioning between the applied upstream pore pressure
and the measured downstream pore pressure. However, a phase shift is not always achievable.
It depends on two main factors. First, the permeability of the sample: when the permeability
is too high, the upstream and downstream pore pressures can equilibrate almost
instantaneously. Second, the structure of the faulted sample: if the naturally-generated fault
exhibits a through connection between the upstream and downstream (i.e., a major axial
splitting through the sample as indicated in Figure 4.10), then the upstream and downstream
pore pressures can also be equilibrated almost instantaneously, without phase shifts.
89
Figure 4.9 The effect of different pore pressure oscillating frequencies. Left: In a Fontainebleau sandstone
experiment in which the oscillating frequency was too high, the downstream pore pressure (Pressure A) did not
respond according to the applied cyclic signals at the upstream (Pressure B). Although the upstream pore
pressure peaks exceeded the previous maximum, the sample seemed to not experience the effect of the increase
in pore pressure due to the high oscillation frequency. There was no seismicity during this period, as the
downstream pore pressure did not exceed the previous maximum of 5 MPa. Right: In another Fontainebleau
sandstone experiment in which the oscillating frequency was too low, the downstream pressure synchronised
with the upstream pore pressure almost instantaneously.
90
a) b)
Figure 4.10 An example of a Fontainebleau sandstone experiment in which the phase shift could not be
established. The sample failed with a major axial splitting fault. a) Top view of a failed Fontainebleau sandstone;
b) side view of a failed Fontainebleau sandstone.
The laboratory experiments involve an approximate size-frequency scaling relationship
that has been established in the literature for analysing millimetre-scale laboratory
experiments as compared to field observations in kilometre-scale (e.g. Burlini et al., 2007;
Benson et al., 2008). This size ratio is ~106. In addition, a relatively high frequency of pore
pressure oscillation is required for inducing seismicity in the laboratory. However, in the
field case, when the distance between the upstream and the downstream is large, a much
lower pore pressure oscillation frequency (e.g., seasonal pore pressure oscillations) may
induce seismicity (Saar and Manga, 2003; Roeloff, 1988). Therefore, the laboratory cyclic
pore pressure frequency is in the order of 10-2
Hz, whilst in the field scale, the seasonal water
level oscillation generates a corresponding cyclic pore pressure frequency in the order of
~10-8
Hz; giving an approximate frequency ratio of ~10-2
/10-8
= 106. Similarly, the frequency
of the P-waves of the acoustic emissions in the laboratory experiments is in the range of 500
kHz to 800 kHz, while in the field the frequency of the waveform is in the order of 0.5 Hz to
91
5 Hz, resulting in an approximate scaling of ~105 to 10
6. Furthermore, the rate of increase of
pore pressure in the laboratory scale to that of the field is also in the order of 106. The details
of the ratio of the rate of increase in pore pressure are indicated in Appendix IV.
4.6 Experiment setup and procedures
In the cyclic pore pressure experiments, initial RIS were investigated by introducing
cyclic pore pressure peaks that exceeded previous maxima, while the investigation of the
reactivation of pre-existing faults used cyclic pore pressures peaks at ~95 % of the previous
maximum (e.g., when the previous set used 18 MPa peak pore pressure, the subsequent set
should use 95% x 18 = ~17 MPa peak pore pressure). Each experiment was divided into
three parts. The first part was the preparation of a ‘naturally’ faulted sample, during which an
intact sample was loaded under a constant strain rate (2 x 10-6 s-1), a constant confining
pressure (20 MPa) and a constant pore pressure (5 MPa) until failure occurred. The second
stage started after the rupture of a sample in which strain rate was paused and pore pressure
was lowered to 2.5 MPa to allow the locking of faults and to obtain quiescence for the clear
observation of fault reactivation in the subsequent stage. The last part of the experiment
began with a series of cyclic pore pressure loading on the fractured sample, to simulate
induced seismic events along the pre-existing fractures. The seismic responses were recorded
by a streaming system, which allows continuous data acquisition for the reconstruction of the
spatial and temporal distribution of seismic events. Different amplitudes of sinusoidal cyclic
pore pressure were used for the study. The most suitable frequency of the sinusoidal cyclic
pore pressure was obtained by testing the response of the fractured sample during the
experiment.
92
A control experiment was carried out to identify the effect of pore pressure without
oscillation. This experiment used the same procedures as in stages 1 and 2. However,
constant pore pressure steps were applied in stage 3, instead of pore pressure oscillations.
The pore pressure steps were 18 MPa for 10 minutes and 17 MPa for 32 minutes, which were
the equivalent durations of the 5 cycles of main shock-aftershock sequence and the 16 cycles
of foreshock-main shock-aftershock sequence, respectively, in the F5 experiment.
A saw-cut Fontainebleau sandstone sample was prepared for the F6 experiment to
investigate the migration trends of the AE events during the oscillation of pore pressure. The
sample was pre-cut at 60o and it was expected that all the AEs would occur along the cut. The
experimental procedures were slightly modified. During the experiment, the sample was first
loaded at 5 MPa hydrostatic pressure, with a constant pore pressure of 1 MPa. An axial strain
rate of 2 x 10-6
/s was then applied until the sample was close to failure (i.e., when the sample
began to indicate ductile behaviour with a reduction in the rate of increase of axial stress in
response to the applied constant axial strain. The strain was then stopped and the pore
pressure was reduced to 0.5 MPa for the quiescence period. After that, a series of pore
pressure oscillations was introduced to reactivate the fault.
4.7 Velocity survey
Velocity surveys were conducted periodically during each experiment, and each
consisting of 9 velocity components, namely: P-, S1- and S2-waves each along x-, y-, and
z-axes. Initially, the sample was isotropic with velocities in all three axes similar to each
other; however, as the differential stress increased, so did the percentage of anisotropy. This
93
anisotropy, A, can be calculated as follows:
100max
minmax xV
VVA
−= Equation 4.1
where Vmax and Vmin are the maximum and minimum velocities. These anisotropy factors
and P-wave velocities provide the velocity structures of the sample during the experiment,
which are essential for the auto-picking algorithm of P-wave arrivals. Only a few velocity
surveys were performed after the failure of the sample. These surveys were taken either prior
to or after the completion of pore pressure oscillations, to avoid disturbing the oscillation
effects.
The plots of the evolution of elastic-wave velocities (Figure 4.11 and 4.12) show that a
maximum reduction in velocities occurred during the sample rupture and that the change
during the post-peak stage was relatively small compared to that of the pre-peak to rupture
stage. This significant reduction in velocities was due to the creation and coalescence of
microcracks during the failure stage. The velocity changes along the horizontal axes were
greater than that along the vertical axis during the rupture stage, which indicated that there
were more cracks oriented parallel to the vertical or sub-vertical axis than parallel to the
horizontal axis. This anisotropy in the velocity structure was taken into account for accurate
source locations (Equation 4.2). The details of the velocity models are listed in Appendix I.
94
Figure 4.11 Typical velocity-time curve of Fontainebleau sandstone oscillating pore pressure experiment. The
development of transverse anisotropy indicates cracks were preferentially oriented in the direction parallel to
the vertical or sub-vertical axis (i.e., axial splitting).
Figure 4.12 Typical velocity-time curve of Darley Dale sandstone oscillating pore pressure experiment. There
was a greater reduction in velocity in the horizontal axis than in the vertical axis during the sample failure (i.e.,
transverse anisotropy).
95
4.8 Results
4.8.1 Fontainebleau sandstone intact sample experiment (F5 and F8)
Two sets of cyclic pore pressure were applied in the Fontainebleau sandstone F5 and F8
experiments during the post-failure stage. These experiments simulated fluid-induced initial
seismicity by increasing pore pressure amplitude to a level higher than the previous
maximum. The applied pore pressure at upstream oscillated between 2.5 and 18 MPa at
2-minute periods, while the downstream pore pressure was measured. Figures 4.13 and 4.14
show the axial stress-time plots of the F5 and F8, respectively, while Figures 4.15 and 4.16
show the strain-time plots of the F5 and F8, respectively. During the post-peak period, the
fractured sample responded with an increase in seismicity, when the average pore pressure
exceeded the previous maximum (5 MPa) (Figure 4.17 and 4.18).
Figure 4.13 Stress-time curve of the F5 experiment under constant confining pressure of 20 MPa.
96
Figure 4.14 Stress-time plot of the F8 experiment under constant confining pressure of 20 MPa.
Figure 4.15 Strain-time plot of the F5 experiment.
97
Figure 4.16 Strain-time plot of the F8 experiment.
Figure 4.17 Seismic rate-time plot of the F5 experiment.
98
Figure 4.18 Seismic rate-time plot of the F8 experiment.
The oscillating pore pressure of the two stages (the first stage with a peak pore pressure
of 18 MPa and the second stage with a peak pore pressure of 17 MPa) of the F5 and F8
experiments were plotted in Figures 4.19 and 4.20, respectively. Depending on the
naturally-fractured network of the sample, the downstream pore pressure of the F8
experiment tended to catch up with the applied upstream pore pressure faster than in the F5
experiment.
99
Figure 4.19 Upstream and downstream pore pressures during the post-peak stage of the F5 experiment (Ying et
al., 2009).
Figure 4.20 Upstream and downstream pore pressures during the post-peak stage of the F8 experiment.
100
With the aid of non-destructive acoustic techniques, seismicity that occurred during the
cyclic pore pressure could be located. Figures 4.21 and 4.22 show the AE events that
occurred during each pore pressure cycle during the main shock-aftershock and
foreshock-main shock-aftershock sequences, respectively. Figure 4.23 indicate the collective
events that occurred in the two sequences of the F5 experiment. The InSite software (ASC,
2007) allows the replay of events over time, from which no trends of event migration or
magnitude growth over time was observed. The pore pressure induced seismicity occurred
mostly along the pre-existing fractures and most of these events have relatively small
location magnitudes, ranging from -3 to -2. Similar results were found in the F8 experiment
and there were no trends of event migration found in either experiment.
Cycle 1 Cycle 2 Cycle 3 Cycle 4 Cycle 5
Figure 4.21 AEs occurred during the 5 cycles with sinusoidal pore pressure oscillated between 2.5 and 18 MPa
at 2-minute periods of the F5, mimicking a main shock-aftershock sequence.
101
Cycle 1 Cycle 2 Cycle 3 Cycle 4 Cycle 5
Cycle 6 Cycle 7 Cycle 8 Cycle 9 Cycle 10
Cycle 11 Cycle 12 Cycle 13 Cycle 14 Cycle 15 Cycle 16
Figure 4.22 AEs occurred during the 16 cycles with sinusoidal pore pressure oscillated between 2.5 and 17 MPa
at 2-minute periods of the F5, mimicking a foreshock-main shock-aftershock sequence.
102
Fractured sample Set 1 Set 2
Figure 4.23 AE locations of the F5 Fontainebleau sandstone experiment. Set 1: Cumulative seismic events
occurred during the 5 cycles of the main shock-aftershock sequence. Set 2: Cumulative seismic events occurred
during the 16 cycles of the foreshock-main shock-aftershock sequence. Each seismic event is represented by a
dot and the colour of the dots indicates different magnitude of events.
4.8.2 Fontainebleau sandstone control experiment (F7)
Figures 4.24 and 4.25 show the stress-time and strain-time plots of the F7 experiment,
while Figure 4.27 indicates the seismic rate-time plot of the experiment. The pore pressure
steps used in the experiment are illustrated in Figure 4.26.
103
Figure 4.24 Stress-time plot of the F7 experiment under constant confining pressure of 20 MPa.
Figure 4.25 Strain-time plot of the F7 experiment.
104
Figure 4.26 Upstream and downstream pore pressures during the post-peak stage of the F7 experiment. The
upstream and downstream pore pressures equilibrate almost instantaneously (Ying et al., 2009).
Figure 4.27 Seismic rate-time plot of the F7 experiment.
105
4.8.3 Fontainebleau sandstone saw-cut experiment (F6)
The stress curve began to show ductile behaviour at about 16 MPa (Figure 4.28). The
strain rate was paused and subsequent pore pressure oscillation was applied (Figure 4.29).
However, due to the high permeability zone of the saw-cut, the upstream and downstream
pore pressures equilibrated almost instantaneously (Figure 4.30). The seismic rate-time plot
is illustrated in Figure 4.31.
Figure 4.28 Stress-time plot of the F6 experiment under constant confining pressure of 5 MPa.
106
Figure 4.29 Strain-time plot of the F6 experiment.
Figure 4.30 Upstream and downstream pore pressures during the post-peak stage of the F6 experiment. The
upstream and downstream pore pressures equilibrated almost instantaneously.
107
Figure 4.31. Seismic rate-time plot of the F6 experiment.
The source location, with location error of about 4 mm, showed that the events occurred
along the pre-cut during pore pressure oscillation and that the relative location magnitudes of
the events were small, ranging between -3.3 and -2.2 (Figure 4.32).
Figure 4.32 AE source location showing the events that occurred during each set of pore pressure cycles.
108
4.8.4 Darley Dale sandstone experiment (DDS7)
Experiment DDS7 (Darley Dale sandstone), provides a good comparison to the
low-permeability Fontainebleau sandstone experiment, as Darley Dale sandstone has
relatively high porosity (~13%) and high initial permeability (~5.7 x 10-15 m2). Due to this
high permeability, phase shift could not be achieved even when the period of cycles was
reduced to half of that used in the Fontainebleau sandstone experiment (i.e. 1-minute period).
This suggests that the pore pressure of the entire system was almost at equilibrium. A total of
eight sets of pore pressure cycles were performed in this experiment. These sets involve pore
pressures cycled between a minimum of 2.5 MPa and a maximum of 7.5, 7.0, 10.0, 9.5, 12.5,
12.0, 18.0, and 17.0 MPa, respectively. The 7.5, 10.0, 12.5, and 18.0 MPa peak pore
pressures are the sets with increases in pore pressure that exceed the previous maximum. The
7.0, 9.5, 12.0, and 17.0 MPa pressure sets are those with lowered peaks as compared to the
preceding sets, i.e., at approximately 95 % of the previous maximum. These sets were used
for investigating fault reactivation and foreshock–main shock–aftershock sequences. Figure
4.35 shows the period in which the pore pressure oscillations were peaked at 18.0 and 17.0
MPa. This partial plot of the pore pressure oscillating stage indicates that the upstream and
downstream pore pressures equilibrated almost instantaneously. The results indicate that an
existing fault was activated at the four step increase in pore pressure peak that exceeded the
previous applied maximum. The activations were accompanied by significant axial strain
change. The seismic rate in the subsequent oscillations reduced more rapidly than that in the
Fontainebleau sandstone experiments (F5 and F8). Although there was occasional seismicity
during the reduced peak pore pressure sets, no significant axial strain change was observed.
As a result, no reactivation of faults was identified during these periods. The stress-time and
109
strain-time plots (Figures 4.33 and 4.34) indicate the four stages of fault activation, when the
pore pressure exceeds the previous applied maximum. These four stages of activation were
accompanied by an increase in AEs, as indicated in Figure 4.36.
Figure 4.33 Stress-time plot of the DDS7 experiment under constant confining pressure of 20 MPa.
Figure 4.34 Strain-time plot of the DDS7 experiment.
110
Figure 4.35 Upstream and downstream pore pressures during the post-peak stage of the DDS7 experiment.
Partial plot of the oscillating pore pressure stage, showing the upstream and downstream pore pressures
equilibrate almost instantaneously.
Figure 4.36 Seismic rate-time plot of the DDS7 experiment.
111
The AEs generated during the post-peak cyclic pore pressure regime occurred along the
pre-existing fault. In this experiment, no trends of event migration or magnitude increase
with time were observed. Figure 4.37 shows the collective seismic events that occurred
during the eight cyclic pore pressures sets.
Figure 4.37 AE source location showing the events that occurred during each set of pore pressure cycles. Sets 1
to 8 correspond to pore pressure cycles with peak pressures at 7.5, 7.0, 10.0, 9.5, 12.5, 12.0, 18.0, and 17.0 MPa,
respectively. Most of the events occurred during the sets with pore pressure peaks exceeding the previous
maximum. Few events occurred during the sets with pore pressure peaks lower than the previous maximum.
112
Chapter 5 Analysis and Discussion
5.1 Experiment F5
By plotting the strain, seismic rate, and pore pressure oscillation on the same graph
(Figure 5.1), a clear picture of the seismic response with respect to the oscillating pore
pressure can be observed. During the first set of applied pore pressures with oscillation
between 2.5 and 18 MPa, there was a corresponding cyclic axial strain change (Figure 5.1)
with the cumulative axial strain change during the 5 cycles equivalent to a sample shortening
of ~0.019 mm. The strain changes in the first three cycles were greater than the last two
cycles. In Roeloffs et al. (1979), where cyclic pore pressure experiment was carried out on
saw-cut sandstone samples, a greater sliding along the pre-cut was also found to be greater
during the first few cycles than the subsequent cycles.
The aftershock peak seismicity of the cycles decayed according to the modified Omori
law (Utsu, 1961) with p-value about 0.0039, but at a slower rate compared to tectonic events.
This is a common characteristic in fluid-induced seismicity (Gupta, 1972 & 2005). After
main slip 1 in the aftershock sequence, the seismic rate continued in the subsequent cycles,
but reduced gradually in cycles 2 to 5. Due to the relatively low permeability of the fractured
sample (~5.7 x 10-17
m2), there was a phase shift between the applied pore pressures and the
responding pressures downstream. This phase shift decreased with the increase in the number
of oscillations (Figure 5.2). This is due to the permeability increase due to cumulative
damage. The permeability measured after the completion of the cycles was ~5.0 x 10-16
m2,
which is an increase of one order of magnitude, as compared to the initial permeability of
~1.3 x 10-17
m2.
113
After the first set of pore pressure cycles, a period of quiescence was introduced by
reducing the pore pressure to 2.5 MPa until the seismic rate fell to a background level. A
second set of pore pressures was then applied, oscillating between 2.5 and 17 MPa, with a
period of 2 minutes. The lower pore pressure amplitude set was introduced, with an objective
to investigate whether pore pressure oscillation can reactivate a fault and generate a
foreshock–main shock–aftershock sequence. It is observed that during this set of pore
pressure oscillation, the fault was reactivated and the seismic rate intensified after the 6th
cycle, when the average peak pore pressure amplitude exceeded the previous maximum
attained (Figure 5.2). During each pore pressure cycle, the corresponding axial strain change
indicated a relative shortening and extension of the sample, which suggests a back-and-forth
sliding movement along the pre-existing fault. This cumulative axial strain change
corresponds to a total of ~0.061 mm vertical movement (comprised of ~0.021 mm extension
movement and ~0.04 mm shortening movement). The amount of movement due to each pore
pressure cycle was small, but hysteretic (i.e., when the pore pressure is reduced to the
minimum amplitude of each cycle, the corresponding axial strain change cannot be
recoverable completely).
114
Figure 5.1 The seismic rate, pore pressure cycles, and the axial strain change of the F5 experiment. The first 5
cycles simulate an aftershock sequence in which pore pressure was oscillated sinusoidally between 18 and 2.5
MPa, with a period of 2 minutes. The subsequent 16 cycles simulate a foreshock–main shock–aftershock
sequence, when pore pressure was oscillated between 17 and 2.5 MPa. Fault reactivation intensified after the
6th cycle, when the change in strain increased and the main slip 2 occurred at the 11th cycle. Downstream pore
pressure cycles exhibited phase shifts and remained at a transient state in response to the applied upstream pore
pressure cycles (Ying et al., 2009).
115
Figure 5.2 Phase shift and average pore pressure at each cycle for the F5 experiment. The phase shift decreased
with the increasing oscillation number. The reactivation of faults begins when the average pore pressure
exceeds the previous maximum, i.e., beyond the 6th cycle. A main slip occurs at the 11th cycle, with a reduction
in phase shift.
The increase in average peak pressure was accompanied by a reduction in the phase
shift (Figure 5.2). The largest slip in the foreshock sequence (denoted as main slip 2 in
Figure 5.1) occurred in the 11th cycle, which was denoted with an anomalous reduction in
phase shift. After this slip, the period of phase shift rebounded to the previous trend, with a
reduction in the seismic rate in the aftershock sequence (cycles 12 to 16). The
116
foreshock–aftershock sequence exhibits a Mogi (1963) Type II model (Figure 2.14), which
reflects the heterogeneity of the sample after the formation of ‘natural’ fractures during the
rupture. This heterogeneity causes an uneven distribution of stress during the transient state
of pore pressure, which is reflected by the irregular distribution of induced seismicity, as
indicated by the AE locations.
It is inferred that the number of pore pressure cycles required for reactivation depends
on the fracture network which controls the mechanical properties of the fractured sample,
which in turn control the development of pore pressures within the system. As the average
pore pressure (average of upstream and downstream) reached the previous maximum average,
the seismic rate began to accelerate and subsequently developed into the reactivation slip (2),
accompanied by a significant axial strain increase (Figure 5.1). The downstream pore
pressure oscillation and the periods of phase shift are good indicators of whether the system
has reached steady-state or remained transient. If the downstream pore pressure peaks
continued to grow, it is likely that faults would be reactivated and further main slips might
occur with an increase in the number of pore pressure cycles. The results suggest that cyclic
pore pressure can induce protracted seismicity during the period in which pore pressure
amplitudes are lower than the previous applied maximum. This effect has been observed in
the Aswan reservoir when the seismicity continued and enhanced between 1982 and 1987,
during which the water level of the reservoir was reduced.
The vertical distances of the hypocentres are measured from the upstream of the
samples (Figure 5.3). The population distribution charts indicate that the seismic events
117
occurred during the pore pressure oscillation distributed over a wide range; however, there
were fewer events located at the top third of the downstream of the sample (Figure 5.4),
possibly affected by the permeability of the fractured sample.
Figure 5.3 Showing the reference distance for measurement of hypocenter locations.
Figure 5.4 Population distribution of the seismic events occurred during pore pressure oscillations.
125
0
Upstream
Downstream
118
5.1.1 b-value analysis
The AE samples were grouped into four different periods: i) before the failure of sample,
ii) aftershock sequence of main slip 1, iii) foreshock sequence of main slip 2 and, iv)
aftershock sequence of main slip 2. For each period, log N values were calculated for
location magnitudes ranging from -2.0 to -2.9 at 0.1 intervals. The equation for obtaining
b-values is indicated in Equation 3.8. The b-values were obtained from the slope of the line
measured from the linear descending portion of the frequency-magnitude plots. In the
experiment, there was a slight variation between the b-values. The b-value analyses of the
two aftershock sequences are very similar (< 4% difference). However, the b-value of the
foreshock sequence is ~1.93, which is about 22% lower than that of the aftershock sequence
(Table 5.1, Figure 5.5). This indicates that there are more large-magnitude events occurring
during the foreshock period than during the aftershock period.
Table 5.1 b-values during different periods of the F5 experiment.
Period b-value
Before the failure of sample 2.069
Aftershock sequence of main slip 1 2.385
Foreshock sequence of main slip 2 1.927
Aftershock sequence of main slip 2 2.474
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Figure 5.5 Fontainebleau sandstone experiment: a) b-value analysis for the formation of fault; b) b-value
analysis for the aftershock and foreshock sequences.
5.1.2 AE source mechanism
Typical AEs generated during the pore pressure oscillation period were analysed using
focal mechanism solutions. Representative AE data with large magnitudes were chosen for
the analysis. These events have high signal-to-noise ratios which provide high confidence
mechanism solutions. The results indicate that shear or a complex mechanism dominated
during the oscillation pore pressure stage (Figure 5.6).
120
Figure 5.6 Focal mechanism solutions indicating the failure mechanisms during oscillating pore pressure.
5.2 Experiment F8
The results of the F8 experiment are similar to those of F5 that seismic sequences can be
activated during the period when pore pressure peaks were lowered to 95% of the previous
maximum. However, due to the difference in the mechanical properties of the
naturally-fractured samples, the foreshock development was not as obvious as that showed in
the F5 experiment (Figure 5.1). The main slip caused by the increase in pore pressure
generated significant numbers of AEs (Figure 5.7), which reduced rapidly from about 200
events in the first cycle to about 30 events in the subsequent cycles. The decay is according
to modified Omori law (Utsu, 1961), with p-value about 0.0036. During the foreshock
sequence, the number of AEs gradually increased in the first 4 cycles. After cycle 4, the AE
rate of each cycle was similar and persisted during the aftershock sequence. Starting from the
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cycle 4 of the foreshock sequence, the downstream pore pressure reached a ‘steady-state’, i.e.,
the peak pore pressures remained unchanged. It was observed that the seismicity
development was influenced by the downstream pore pressure or the average pore pressure
of the system, instead of the upstream pore pressure. However, in the field, often only the
upstream pore pressures are readily available. The response of the downstream pore pressure
is often unknown, unless monitoring wells are installed in the downstream.
In the F8 experiment the development of the downstream pore pressure was not as rapid
as that of the F5 experiment (Figure 5.1). This, in turn, influenced the strain development, as
well as the seismic rate. This difference was likely caused by the variation in the mechanical
properties between the F5 and F8 samples, when the fracture networks of the two
naturally-fractured samples were not identical.
122
Figure 5.7 The seismic rate, pore pressure cycles, and axial strain change of the F8 experiment. The first 5
cycles simulated an aftershock sequence in which pore pressure was oscillated sinusoidally between 18 and 2.5
MPa, with a period of 2 minutes. The subsequent 16 cycles simulated a foreshock–main shock–aftershock
sequence when pore pressure was oscillated between 17 and 2.5 MPa. The seismic rate developed slightly in the
first 4 cycles of the foreshock sequence; however, due to the limited increase in downstream pore pressure, the
corresponding strain did not change significantly.
5.3 Control experiment on Fontainebleau sandstone
The strain, seismic rate, and pore pressure change plots are indicated in Figure 5.8. The
plot shows that without the cyclic effect, seismicity due to pore pressure enhancement is
123
reduced, as compared to the F5 experiment. Aftershocks decay according to the Omori law
(Utsu, 1961) with p-value about 0.0108, about 2.8-3.0 times faster than that of the
aftershocks in the F5 and F8 experiments. This suggests that the rate of reduction in
aftershock sequence was reduced due to oscillating pore pressure. The cumulative number of
seismic events was significantly less than that recorded in the cyclic pore pressure
experiment. The seismicity dissipated in ~6.6 minutes in the control experiment, while the
seismicity continued throughout the 5 cycles of 18 MPa peak pressure in the F5 and F8
cyclic pore pressure experiments. In addition, no reactivation of fault was observed in the
control experiment when the pore pressure is at ~95 % of the previous maximum (i.e., 17
MPa). However, in the control experiment, seismicity was reactivated during the periods
when a significant reduction of pore pressure took place (i.e., reduced to 2.5 MPa). The two
periods of constant pore pressure could be viewed as two trapezoidal pore pressure cycles.
During each decrease and/or increase in pore pressure, seismicity was induced. The
experimental results confirm that cyclic pore pressure has greater influence on seismicity
than a constant step increase of pore pressures.
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Figure 5.8 The control experiment indicates pore pressure steps at 18 MPa for 10 minutes and 17 MPa for 32
minutes. The seismicity due to enhancement in pore pressure reduced rapidly. In addition, there was no
reactivation of fault when the pore pressure was at ~95 % of the previous maximum (17 MPa). Seismicity was
reactivated during the reduction of pore pressure (Ying et al., 2009).
Due to the pore pressure step change to 18 MPa for 10 minutes and the subsequent
reduction back to 2.5 MPa, the corresponding shortening of the sample totalled ~0.019 mm,
which is comparable to the total vertical movement measured during the 5 cycles of 18 MPa
peaks in the F5 oscillating pore pressure experiment (Table 5.2). However, during the
subsequent 17 MPa step change, the axial strain change in the control experiment
corresponded to 0.006 mm vertical movement, which is much less than that measured in the
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cyclic pore pressure experiment. This suggests that oscillating pore pressure can cause
oscillating movements along the fault, which can continue over a long period of time. The
cumulative wearing of asperities not only reduce the roughness of the fault, but also prolongs
the period of seismicity. This phenomenon can be seen as a ‘slow’ mechanism of oscillating
pore pressure, characterised by a protracted but discontinuous seismicity over a long period,
rather than continuous seismicity within a relatively short period of time, as per a typical
seismic sequence due to a pore pressure step increase. This slow seismicity is also signified
by asperity-controlled stick-slip-like movements. Implications of such phenomenon may be
seen in natural slow earthquakes occur at the intermediate crustal levels of subduction zones
such as SW Japan (Obara, 2002; Ariyoshi et al., 2009) and Cascadia, Chile (Rogers and
Dragert, 2007), in which the subduction zones dip shallowly and are accompanied by fluid
flow and related tremors with relatively low frequencies (typically in 1-5 Hz band).
Table 5.2 Corresponding vertical movements inferred by axial strain measurements.
Pore
pressure
peaks
F5 cyclic pore pressure experiment
(cumulative relative movement due
to oscillating pore pressure)
Control experiment (cumulative
relative movement due to step
change in pore pressure)
18 MPa ~0.019 mm ~0.019 mm
17 MPa ~0.061 mm ~0.006 mm
As suggested by the comparison between the control experiment (F7) and the F5
experiment, cyclic pore pressure can cause a longer period of progressive sliding and
seismicity, as compared to a step increase in pore pressure. Most of the seismic events due to
cyclic pore pressure occurred over a longer period of time, while for the pore pressure step
increase the seismicity reduced rapidly to its background level within a shorter period of time.
126
This effect of oscillating pore pressure versus step increase in pore pressure can be illustrated
by Figure 5.9.
Figure 5.9 Schematic diagram indicating the reduction of shear strength with cycles a to d. Left: showing the
reduction is progressive with the number of cycles. The time required for the strength to get to stage d is longer
because the duration of each cycle peak is short and requires several cycles to accumulate the same effect as
that of a step change in pore pressure. Right: showing a schematic result of a step increase in pore pressure
where the reduction in the friction angle occurs within a shorter period.
5.4 Darley Dale sandstone experiment
Figure 5.10 shows the strain and seismic rate during the oscillating pore pressure stage.
There are 4 activation and aftershock sequences in which the pore pressure exceeded the
previous maximum. The pattern of the four seismic sequences corresponds to the Type I
Mogi model (1963), which suggests that the structure of the sample is homogeneous. Figure
5.11 indicates the typical set of the main shock-aftershock sequence; there was no
reactivation of fault when the pore pressure peaks were reduced to ~95% of the previous
maximum. The aftershocks decayed according to the modified Omori law (Utsu, 1961), with
p-value about 0.158, which is a much faster rate than that of the F5 and F8 experiments. The
permeability of the fractured sample prior to pore pressure oscillation was relatively high,
127
~3.6 x 10-13
m2, which is two orders of magnitude increase as compared to the initial
permeability of ~5.7 x 10-15
m2.
Figure 5.10 Induced seismicity due to oscillatory pore pressures in Daley Dale sandstone. Eight sets of pore
pressure cycles were performed: with pore pressures cycled between a minimum of 2.5 MPa and a maximum of
7.5, 7.0, 10.0, 9.5, 12.5, 12.0, 18.0 and 17.0 MPa, respectively. The 7.5, 10.0, 12.5 and 18.0 MPa peak pore
pressures sets simulated activation of fault, with increase in pore pressure exceeding the previous maximum,
while the rest were at ~95% of the previous maximum, aiming to investigate reactivation of fault (Note: For
clarity, only the peaks and troughs of the cyclic pore pressures were plotted for the sinusoidal pore pressure
cycles). The upstream and downstream pore pressure equilibrated almost instantaneously (Ying et al., 2009).
128
Figure 5.11 Showing seismic rate, pore pressure cycles and axial strain change of the Darley Dale sandstone
experiment, with pore pressure oscillated between a 18 and 2.5 MPa simulated aftershock sequence. The
subsequent cycles oscillated between 17 and 2.5 MPa, accompanied by insignificant seismicity, which implies
that the pre-existing fault was not reactivated when the peak pore pressure was lower than the previous
maximum.
5.4.1 b-values
There are more seismic events during the peak pore pressure enhancement periods
(aftershock sequence) (sets 1, 3, 5, and 7 in Figure 5.10) than during the peak pore pressure
reduced periods (sets 2, 4, 6, 8 in Figure 5.10). The frequency-magnitude analyses of the 4
aftershock sequences indicate that there were more low magnitude events than high
magnitude events and that the range of magnitude varied narrowly between -2.5 and -2.9.
129
This magnitude range is lower than those observed during the formation of the fault (between
-2.2 and -2.9) (Table 5.3, Figure 5.12). In addition, the seismic events that occurred in the
Darley Dale sandstone were generally of lower magnitude than those recorded in the
Fontainebleau sandstone experiment. The larger number of low magnitude events than high
magnitude events cause the b-value to be lower than those obtained in the Fontainebleau
sandstone experiment. This difference is due to the material property difference between the
two sandstones. Darley Dale sandstone behaves more ductile while the Fontainebleau
sandstone is more brittle in nature. According to Scholz (1968), it was found that the
b-values are much higher in ductile rock than that observed in brittle rock.
Figure 5.12 b-value analysis of the Darley Dale sandstone experiment: a) During the formation of the fault; b)
during the aftershock sequences.
130
Table 5.3 b-values during different periods of the DDS7 experiment.
Period b-value
Before the failure of sample 4.48
Aftershock sequence 1 4.50
Aftershock sequence 2 5.20
Aftershock sequence 3 5.44
Aftershock sequence 4 4.06
The population distribution of the seismic events measured along the vertical distance
indicates that most of the events occurred in the middle portion of the sample, i.e., where the
main fault was located (Figure 5.13), which is also influenced by the event accuracy.
Figure 5.13 The distribution of seismic events that occurred during the oscillation of pore pressure.
5.4.2 AE source mechanism
Typical AEs generated during the oscillating pore pressure periods were analysed using
131
focal mechanism solutions. Representative AE data with large magnitudes were chosen for
the analysis. These events have high signal-to-noise ratios which provide high confidence
solutions. The results show that shear or complex mechanisms are the main mechanisms
during the pore pressure oscillation period (Figure 5.14). The representative mechanisms
occurring during the increase in pore pressure typically have compression (white) in the
central portion of the focal sphere and dilation (shaded) on both sides of the sphere, indicated
by sphere 2, 3, 4 and 6, which are related to crack opening events; while the representative
mechanisms occurred during the decrease in pore pressure typically have dilation (shaded) in
the central portion of the focal sphere and compression (white) on both sides of the sphere,
indicate by sphere 1 and 5 (Figure 5.14), which are related to crack closing events. This was
observed in the Darley Dale experiment due to the relatively simple fault zone and the
absence of phase shifts between the upstream and downstream pore pressures.
Figure 5.14 Focal mechanism solutions of the Darley Dale sandstone experiment, indicating that the dominant
failure mechanism during the cyclic pore pressure stage is shear or complex.
132
5.5 Comparison between Fontainebleau sandstone and Darley Dale sandstone
experiments
A comparison between the two cyclic pore pressure experiments is shown in Table 5.4.
The results show that the mechanical properties of the sample influence the decay of
aftershocks, fault reactivation, as well as the development of foreshock and main slip events.
When faults are reactivated, the progressive swarms develop into a main slip after a number
of pore pressure oscillations. However, this reactivation requires a faulted sample with a
heterogeneous structure, as well as low permeability, which in turn allows a phase shift to
develop.
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Table 5.4 Comparison of the results of the two cyclic pore pressure experiments.
Fontainebleau Sandstone
(relatively low permeability,
~1.3 x 10-17
m2)
Darley Dale Sandstone
(relatively high permeability
~5.7 x 10-15
m2)
Phase Shift
Between Upstream
and Downstream
Pore Pressure
Present, reduction in phase shift with
increase in the number of cycles,
sharp reduction during the
occurrence of main slip
Downstream pore pressure
caught up with the applied
upstream pore pressure almost
instantaneously
Steady-state Pore
Pressure
Oscillations
The downstream pore pressure peaks
gradually increase, indicating that the
system was at transient state
Equilibrium of the upstream and
downstream pore pressure cycles
suggests steady-state oscillation
was achieved
Characteristics of
Aftershock
Sequence
Reduction in seismic rate is relatively
gradual, thus seismicity can continue
for a longer period
Reduction in seismic rate is
relatively rapid
Fault Reactivation Marked by a significant axial strain
change and increase in seismic rate
No distinguishable axial strain
change; occasional increase in
seismic rate
Characteristics of
Foreshock– Main
Shock–Aftershock
Sequence
Foreshocks gradually developed and
when the average pore pressure
exceeds the previous maximum, the
seismic rate increased and developed
until a main slip occurred, followed
by the aftershock sequence
No observable sequence
5.6 Saw-cut experiment
The main purpose of the saw-cut experiment was to identify any trends of event
migration. However, due to the formation of the high permeability continuous fracture, the
upstream and downstream pore pressure equilibrated almost instantaneously and
pore-pressure-induced AEs occurred along the fractured path almost without delays.
Migration trends were therefore not observed. Due to the low stress level, relatively fewer
134
AE events were recorded during the oscillating pore pressure period. When the pore pressure
oscillated between 3.25 to 3.75 MPa, the saw-cut sample started to creep and underwent
stable sliding. This is signified by the measured strain indicated in Figure 5.15.
Figure 5.15 The F6 experiment indicated stable sliding along the saw-cut at a later stage, when the average pore
pressure was about 3.5 MPa.
135
5.6.1 Migration trends
Some researchers (Talwani, 1997; Talwani et al., 2007; do Nascimento et al., 2004; Rao
and Singh, 2008) suggest that protracted RIS has a migration trend, as seismic events with
higher magnitudes and deeper hypocentres were observed at a later stage after the reservoir
impoundment. This migration trend may be possible to recognize in the field because the
diffused distance is longer. However, there were no such patterns found in the laboratory
experiments. This can be due to two reasons. The first is the limited size of the sample, in
which the entire sample can be viewed as a single fractured zone and so any pore pressure
diffusion effect can occur within a relatively short period of time, which inhibits the
observation of the migration of events and trends in the event magnitude change. However,
in the field, migration of events can be observed as hypocentres occurred at deeper depth and
further distance from the initial seismic region due to pore-fluid diffusion (do Nascimento et
al., 2004; Rao and Singh, 2008). The second reason is that the acoustic emissions in the
Fontainebleau sandstone experiments were located in the irregular fractured network. The
heterogeneity of the fractured zone and the progressive shearing effect of the cyclic pore
pressure both contribute to flow anisotropy, which also inhibits the observation of migration
trends in the sample.
5.7 Post-experimental analysis
There were two post-experimental analyses carried out to provide additional
information regarding the characteristics of the tested samples that underwent cyclic pore
pressures. These analyses included X-ray micro-computed tomography analysis and optical
microscopy analysis. These analyses were carried out on the Fontainebleau (F5) and Darley
136
Dale (DDS7) sandstone samples, which were used in the experiments described in Chapter 5.
5.7.1 X-ray micro-computed tomography analysis
In order to understand the structure of the faulted samples, high-resolution X-ray
micro-computed tomography (CT) was carried out for both the Fontainebleau and Darley
Dale sandstone samples. Prior to scanning, the samples were preserved with epoxy to avoid
movement of faults during handling. The samples were then trimmed into a smaller size to
suit the requirement of the high-resolution SkyScan 1172 scanner. The most representative
middle portions of the samples were retained for the micro-CT scan. The images produced
by the scanner correspond to a series of 34.89 µm thick slices throughout the specimens. The
reconstructed images of the Fontainebleau sandstone sample indicate that the faulting system
is comprised of heterogeneous shear fractures and axial splitting, while that of the Darley
Dale sandstone sample consists of a single shear fracture. Figure 5.16 indicates the typical
micro-CT images of the Fontainebleau and Darley Dale sandstones. These images align with
the fact that slightly heterogeneous medium (F5) has a number of foreshocks preceding the
main shock, while homogeneous medium (DDS7) is characterised by seismicity with no
foreshocks (Mogi, 1963). Slightly heterogeneous medium is defined by the presence of
heterogeneous type of fractures within in a homogeneous sample.
137
a) b)
Figure 5.16 Typical X-ray micro-CT images along the vertical axis. a) Showing a complex faulted system with
shear fractures and axial splitting within the naturally fractured Fontainebleau sandstone sample; b) showing
that a shear fracture was formed in the Darley Dale sandstone.
The 489 slices of xy-plane scanned images of each specimen were changed to binary
colour for the calculation of normalised crack area with depth (z-direction), i.e., normalised
by the smallest crack area among the 489 slices. This normalised area indicates the relative
ease of fluid flow along the vertical axis during the oscillation of pore pressure (Figure 5.17).
The flow areas or crack areas changed significantly along the vertical axis, which suggests
the variation of local permeability and local transient pore pressure development along the
path. This increase in pore pressures reduced the local contact stress and release as an AE or
stress redistribution within the material.
138
Figure 5.17 Normalised crack area is calculated as crack area/minimum crack area of the plots. This indicates
the change in flow path in the z-direction. a) For Fontainebleau sandstone; b) for Darley Dale sandstone.
5.7.2 Optical microscopy
During initial rupture, the grains along the fracture zone were crushed into smaller sizes.
The subsequent pore fluid increase may transiently reduce grain-contact stresses to zero, and
induce failure along the existing fault (Iverson and LaHusen, 1989). This fluctuation can
propagate outside the shear zone and promotes shear-zone growth. As the pore fluid
oscillation continues, cumulative damage due to progressive shearing can occur in the
fractured zone. This shearing involves the grinding and over-riding of grains along the
fractured surface, which may extend the shear zone outward. The cumulative axial strain
change during the pore pressure oscillations can be used to infer the relative grinding
movement along the fractured zone. As the number of cycles increase, more grains are worn
off or ground into smaller sizes, which exposes more surface area for wetting, and enhances
the lubricating effect. The wearing of asperities eventually reduces the friction coefficient
139
and, hence, leads to protracted slips. The amount of progressive wearing due to cyclic pore
pressure cannot be distinguished by optical microscopy. However, optical microscopy can
provide an overall indication of the shearing that has occurred in the fractured zone, due to
the initial rupture and subsequent pore pressure oscillations. Optical microscopy analysis was
carried out on the tested Fontainebleau (F5) and Darley Dale (DDS7) sandstones after the
completion of the X-ray micro-CT scan. Three thin sections along the xy-plane, xz-plane,
and yz-plane were taken from each tested sample. The comparison between the thin sections
of the two types of sandstone can provide some indication of the corresponding differences
in seismic responses.
Fontainebleau sandstone is composed of more than 98% quartz, which is a brittle
mineral. Due to the hardness contrast between the quartz grains and the adjacent softer gouge
material, abrasive wearing could be the dominant process during progressive shearing.
During abrasive wearing, the harder material can plough through the softer material (Scholz,
2002). Optical microscopy indicates that large loose-wear particles with angular forms were
embedded in the gouge material (Figure 5.18b), while for the Darley Dale sandstone, which
is more ductile in nature, the wearing could be adhesive, in which junctions shear off part of
the adjoining asperity, resulting in transfer of material from one surface to the other (Scholz,
2002; Rabinowicz, 1965). Deposits of ground material were found in the fractured zone of
the Darley Dale sandstone (Figures 5.19 and 5.20). The optical microscopy of both
sandstones indicates larger grain sizes further away from the shear zone (Figures 5.18 to
5.20). However, the thin sections of Fontainebleau sandstone exhibit two types of
phenomena. It was found that no significant shearing occurred in areas where the crack
140
widths were relatively wide (Figure 5.18c), while in other areas excessive shearing has
occurred and the grain size was reduced significantly (Figure 5.18b). This might cause
permeability contrast between the different zones. In regions with relatively large cracks,
pore pressure might dissipate at a faster rate than that within the sheared zone.
The shear zone of the Darley Dale sandstone was relatively loosely packed, which
indicates a relatively high permeability and allowed pore pressure dissipation. This
permeability contrast between the two sandstones may explain why almost instantaneous
pore pressure equilibrium was established in the Darley Dale sandstone during the pore
pressure oscillations, while the phase shift between the upstream and downstream pore
pressure persisted in the Fontainebleau sandstone.
141
(a) (b) (c)
Figure 5.18 Optical microscopic views of the Fontainebleau sandstone that has been subjected to oscillating
pore pressures. a) Larger grain sizes can be found in areas further away from the sheared zone; b) gouge
material found within the shear zone that has undergone grinding and progressive shearing. The grain size of
the gouge material was reduced significantly and was closely packed, influencing the permeability of the
sample. It is noted that larger grains were embedded in the sheared zone; c) areas with relatively larger cracks
that enhance the local permeability. Consequently, less gouge material was found, which implies that less
progressive shearing has occurred in the area.
142
Figure 5.19 Thin section of the Darley Dale sandstone tested sample. Left: Typical grain size found in the area
further away from the shear zone. Right: Grains in the sheared zone have significantly smaller grain sizes due to
shearing. There is no embedment of larger, angular grains in the sheared zone and the shear zone is not as
closely packed as compared to that of the Fontainebleau sandstone thin sections.
143
Figure 5.20 Optical microscopy of the Darley Dale sandstone with sheared material in the fractured zone. The
grain size of the sheared material is reduced significantly. The sheared zone is not as closely packed as that of
the Fontainebleau sandstone, suggesting that the permeability of the sheared zone is relatively high and can
permit almost instantaneous equilibrium in pore pressure between the upstream and downstream.
144
The relative axial strain change implies that oscillating pore pressure can progressively
wear off asperities at the pre-existing fractured surfaces, which in turn reduce the friction
coefficient and the frictional strength of the material and, subsequently, cause the fractured
sample to be more susceptible to sliding or shearing. As the shear displacement due to each
cycle of pore pressure is relatively small, a large number of cycles is required to wear or
smooth the fractured surface. This increase in shear displacement along the existing fractures
can cause the sample to become heterogeneous and anisotropic (Yeo et al., 1998),
subsequently altering the pore network and easing pore pressure development at different
areas. This alteration has no specific trend and, therefore, the seismic events that occurred
during the pore pressure oscillation have no identifiable migration patterns. This oscillating
pore pressure induced protracted seismicity is expected to last for a long period of time and
the magnitude of the seismic events are often relatively small.
5.8 Conclusions
Many researchers have attributed protracted RIS to the pore diffusion effect. This may
explain the phenomenon of delayed RIS and the migration of RIS to deeper crust over time.
However, in many RIS cases, protracted seismic events at shallow depths continued to
dominate after a prolonged period of time. This suggests that effect due to oscillating pore
pressure other than pore diffusion may be taking place to allow continuous shallow crustal
seismicity.
The experimental results indicate that cyclic pore pressure can cause a progressive
shearing effect, which was validated by the AE source mechanism and implied by the small
145
strain change due to each cycle. The shearing and corresponding seismicity due to cyclic
pore pressure can last for a longer period of time, as compared to that of a step increase in
pore pressure. This shearing and wearing of asperities at the fractured surface can influence
the flow anisotropy and, hence, affect the pore pressure distribution in the subsequent cycles,
which then induce seismicity at different regions along the existing fractured surface.
The results illustrate that initial seismicity can be activated when the peak pore pressure
exceeds the previous maximum experienced by the system. The decline in the number of
aftershocks occurred more rapidly for the Darley Dale sandstone than for the Fontainebleau
sandstone, which was influenced by the mechanical properties of the samples.
The comparison between the control experiment and that of the cyclic pore pressure
experiment on the Fontainebleau sandstone indicates that pore pressure oscillations can
significantly extend the period of seismicity, i.e., can induce protracted seismicity. The
reactivation of fault and protracted seismicity were found in the heterogeneously-faulted
Fontainebleau sandstone, but not in the Darley Dale sandstone experiment. The relatively
low permeability Fontainebleau sandstone exhibited phase shifts and transient-state pore
pressure cycles, which then gradually developed and reactivated the pre-existing faults.
However, no foreshock sequence was developed in the relatively high-permeability Darley
Dale sandstone, which allowed an equilibrium state of pore pressure oscillation to be reached
almost instantaneously. This finding is in line with the observation that homogeneous media
are characterised by seismicity with no foreshocks, while slightly heterogeneous media are
characterised by a number of foreshocks preceding the main shock. The experimental results
146
suggest that two main factors influence the protracted seismic response of the samples: i) the
presence of pore pressure oscillation, and ii) the mechanical properties and the heterogeneity
of the fault zone.
The effect of cyclic pore pressure loading can reduce the effective stress and cause
sliding between the fracture surfaces. During each sliding, the amount of movement is small,
as implied by the relatively small changes in axial strain. The movement of each cycle is
hysteretic, as shearing along the interlocked asperities at the fractured surfaces is irreversible.
The progressive changes in phase shifts between the upstream and downstream pore
pressures, as well as the transient changes in downstream pore pressure, can provide useful
information for mitigation measures of reservoir-induced seismicity caused by the
exploitation of underground fluid reservoirs and cyclic variation in the water levels of surface
reservoirs. When a cyclic pore pressure system is at equilibrium, the phase shift between the
upstream and downstream would be steady. In addition, the downstream pore pressure cycles
would generate steady-state oscillations. Therefore, by monitoring the phase shifts and
downstream pore pressure variations in the field, the progression of pore-pressure-induced
seismicity and the state of the pore pressure in the substratum can be monitored. This
provides some information about the susceptibility of the area to protracted RIS and, hence,
appropriate mitigation measures can be carried out when necessary. When controlling the
upstream water levels or pore pressures as a means of reducing reservoir-induced seismicity,
it is essential that the extent of the reduction be large enough to lower the downstream pore
pressures and that the rate of the reduction must be gradual to prevent seismicity induced by
147
rapid reduction. It should be noted that the response of the downstream pore pressure may
take months or longer, depending on the mechanical properties of the substratum, as well as
the natural seasonal variations.
As the wearing damages accumulate with the increase in the number of pore pressure
cycles, the friction coefficient reduces and, subsequently, induces protracted seismicity. The
X-ray micro-CT scans indicate irregular flow paths within the samples. Optical microscopy
shows a contrast in permeability in different areas of the Fontainebleau sandstone specimen,
which suggests that during the experiment the development of pore pressures might be
different in different regions. In some regions where grains were closely packed together,
progressive shearing could be developed. The permeability contrast between the Darley Dale
and Fontainebleau sandstones can explain the difference in their pore pressure and seismic
responses. In the case of high-permeability Darley Dale sandstone, almost instantaneous
equilibrium could be established between the upstream and downstream pore pressures and
no protracted seismicity or reactivation of fault occurred due to this equilibrium state. For the
low permeability Fontainebleau sandstone, phase shifts between the upstream and
downstream pore pressures persisted and, due to the gradual pore pressure development
within the system, fault reactivation and foreshock sequence was able to develop.
148
Chapter 6 Forecasts of Reservoir-induced Seismicity
The foreshocks of an earthquake can only be recognised after the main shock has
occurred (Gupta, 1992). Recognition of foreshocks soon after their occurrence is one of the
most important issues in earthquake prediction studies. Although many earthquake forecast
methods have been proposed in the past (e.g., Scholz, 2002; Mogi, 1985), many of these
methods suffer from a lack of reliable data in the run-up to failure, i.e., recording foreshock
sequences and how they can be identified as distinct from a ‘regular’ shock before the event
(Helmstetter, 2003). However, the classification of RIS into foreshocks, main shock, and
aftershocks is much easier due to their localisation within the reservoir region and their
correlation with pore pressure changes. As a result, the study of RIS provides an
exceptionally good opportunity to understand the mechanics of natural earthquakes (Bell and
Nur, 1978; Talwani and Acree, 1984/85; Roeloffs, 1988; Talwani, 1997). The ultimate goal
of both field and laboratory studies of RIS is to forecast the acceleration of seismicity and
earthquakes ahead of time (Umino, 2002; Lin, 2009). The identifiable foreshock–aftershock
sequences of RIS can be used for the verification of various forecasting models, thus
providing a step forward in the long-term goal of earthquake prediction (Gupta, 2002).
In other disciplines, in particular volcanology (Kilburn and Voight, 1998; Reyes-Dávila
et al., 2002; Kilburn 2003; Lavallée et al., 2008), foreshock sequences are also well defined,
which permits the used of the materials failure forecast method for the prediction of volcanic
eruptions (Voight, 1988; McGuire and Kilburn, 1997; Kilburn and Voight, 1998;
Reyes-Dávila and Cruz-Reyna, 2002; Kilburn, 2003; Lavallée et al., 2008). The repeated
pressurization of a volcanic edifice is cyclical in nature and is governed by the same
149
mechanical and physical rock processes as those govern tectonic deformation. Prior to a
major volcanic eruption, the daily rate of earthquakes often indicates substantial increase
(Kilburn and Voight, 1998). This increase is accompanied by accelerating rates of ground
deformation (Jackson et al., 1998), and is clearly related to the propagation of a magma
conduit through the volcanic edifice. Similarly, in the case of RIS, prior to a major
earthquake, the daily rate of seismicity often indicates a substantial increase due to crack
propagation and/or coalescence. Therefore, the forecast method used in volcanology may be
applicable to the forecasts of RIS.
6.1 Material failure forecast method
In the case of volcanology, eruptions are commonly preceded by self-accelerating
processes such as earthquake frequency and rates of ground deformation (Scarpa and Tilling,
1996; McGuire and Kilburn, 1997). Such acceleration is described by an empirical relation
known as Voight-Fukuzono (VF) relation, proposed for modelling pre-eruption rates of
volcanic deformation (Voight, 1988, 1989; Main, 1999):
γ)(2
2
dt
dA
dt
dc
Ω=
Ω Equation 7.1
where t is time, Ac is a constant, γ is an exponent that measures the degree of non-linearity
(Voight, 1988 & 1989) and lies between 1 and 2 (Kilburn, 2003), and Ω is related to
precursory strain. This equation has been applied retrospectively to predict the time of
volcanic eruptions (Voight, 1988; Kilburn and Voight, 1998) and to predict earthquake failure
times, often based on the observation of accelerating strain (e.g., Bufe and Varnes, 1993;
Bowman et al., 1998).
150
When approaching the final stages of ground deformation, crack growth becomes
uncontrolled propagation and is described by the condition γ = 2. This failure forecast
method uses the concept that the time-to-failure or the occurrence of peak seismicity depends
on the cumulative damages on the weak zones and, hence, the inverse of the seismic rate or
the inverse of the peak energy rate is used to forecast the time-to-failure. A plot of inverse
seismic rate or inverse of peak energy rate against time follows a negative linear trend, so
that the time at which the inverse rate is zero corresponds to the uncontrolled crack
propagation when dΩ/dt tends to infinity. This specific time can be obtained by a simple
linear extrapolation of the measured trend to the time axis.
6.2 Forecast of main slip
The material failure forecast model (Kilburn and Voight, 1998; Kilburn, 2003; Lavallée
et al., 2008) was adopted for the forecast of peak seismicity for the foreshock sequence data
obtained from the Fontainebleau sandstone F5 experiment. The data set was fit to Equation
7.1, with Ac equals 0.03 and γ equals 2 (Figure 6.1). By plotting the inverse of peak acoustic
emission rate of each pore pressure cycle with time, the extrapolation of the inverses crossing
the lowest points was drawn (Figure 6.2). A best-fit line crossing a minimum of at least four
lowest points on a moving time window was used based on Kilburn and Voight (1998). When
the extrapolated line intercepts the time axis, the expected time-to-failure or expected peak
seismic rate occurrence was defined. Using this method, a main slip was forecasted at cycle
10, while the actual peak seismicity occurred at cycle 11. A sensitivity analysis was also
conducted by using different number of lowest data points for the extrapolation (Table 6.1).
The analysis indicates that the use of the first four data points for the extrapolation would
151
have generated a higher forecast error (25%).
Figure 6.1 Fitting Ac equals 0.03 and γ equals 2 into failure forecast model: γ)(2
2
dt
dA
dt
dc
Ω=
Ω .
Table 6.1 Sensitivity analysis for the ‘long-term’ forecast of the F5 experimental data, using different number of
points in moving window and different number of points for extrapolation.
Data points within
moving window
Points used for
extrapolation
Estimated
Error %
4 4 25%
7 4 7.6%
8 4 8.3%
8 5 9.5%
8 6 12.2%
152
Figure 6.2 Application of failure forecast model to the experimental foreshock sequence obtained from the F5
experiment. The method is based on the extrapolation of the inverse of peak seismic rate. The dots indicate the
inverse of the peak seismic rate of each pore pressure cycle, while the solid line indicates the extrapolation from
the four lowest points. The expected time-to-failure is when the line hits the x-axis, which indicates that peak
seismicity occurred in the 10th pore pressure cycle, while the actual main slip and peak seismicity occurred in
the 11th
pore pressure cycle (Ying et al., 2009).
Using this same data set, a ‘short-term’ forecast based on the seismic rate at cycle 11,
prior to the main slip #2 (Figure 6.3) was also performed. The estimated time-to-failure was
just 2 seconds earlier than the actual main slip. This failure forecast model provides more
accurate forecasts for the ‘short-term’ data than the ‘long-term’ data.
153
Figure 6.3 Application of failure forecast model to short-term forecast of main slip #2 in the F5 experiment.
Seismic rate recorded during cycle 11, prior to the main slip (Ying et al., 2009).
With the approximate size-frequency scaling relationship that has been established in
the literature for analysing millimetre-scale laboratory experiments as compared to field
observations in kilometre-scale (e.g. Burlini et al., 2007; Benson et al., 2008), and the
promising estimated results of the failure forecast model on experimental data, the next step
would be to apply this forecast method to field data. The field-to-experiment size ratio is
kilometre-to-millimetre, i.e. ~106. While the cyclic pore pressure frequency ratio between the
experiment and the field is also in the order of ~106, i.e. experimental frequency of 10
-2 Hz (1
to 2-minute periods) to seasonal oscillation in the order of ~10-8
Hz (annual period). Two
field cases would be chosen for the purpose, one for long-term forecast and the other for
short-term forecast, as described in sections 6.3 and 6.4, respectively.
154
6.3 Application to the Koyna reservoir (Protracted seismicity forecast)
One classic example of protracted seismicity related to seasonal water level change is
the Koyna reservoir (India), which is one of the longest known sequences of RIS (Gupta,
2002). The impoundment of the Koyna reservoir started in 1961 and the seismicity of the
region has been monitored and observed since 1963. There was a lack of data during the
early stage of reservoir impoundment. After the devastating M6.3 earthquake occurred on 10
December 1967, a seismological network consisting of seven stations was established from
1967 to 1972.
The Koyna reservoir is situated near the west coast of India in the Deccan volcanic
province that covers one-third of the peninsular shield and is known as the Deccan traps
terrain. These basalts are of Palaeocene age (65 Ma), with numerous fractures and tensional
joints underlain by Archean granite and gneiss (Jain et al., 2004). The Deccan trap rocks have
a low permeability and the migration of water occurs through fractures and faults. As
suggested by Gupta (2005) that the Koyna reservoir RIS is an ideal site for earthquake
forecast studies; the failure forecast model was applied to the Koyna RIS data. The aim was
to forecast the peak seismicity that occurred in December 1967. The starting data of the
analysis is in January 1963, with a moving time window of 30 data points. At least 4 data
points were used for the extrapolation of the linear regression line of the inverse seismic rate
trend. The retrospective forecast based on the extrapolation line suggests that peak seismicity
would be expected in January 1968 (Figure 6.4). However, the actual peak seismicity
occurred in December 1967, which is one month earlier. In this case, the application of the
forecast method to long-term RIS data (in months) provides fairly accurate forecast of the
155
occurrence of peak seismicity.
Figure 6.4 Long-term forecast of the Koyna RIS: Seasonal water level changes and seismicity of M > 2.0
occurred between 1963 and 1970 at the Koyna reservoir (Talwani, 1995) (using seismic data starting in January
1963, with a moving time window with 30 data points). The 4 red square points were used for the extrapolation
of the forecast model. The model suggests an expected peak seismicity occurred in January 1968, which is one
month later than the actual peak seismicity month (December 1967).
156
6.4 Application to the Monticello reservoir (Initial peak seismicity forecast)
The second example of field application is related to the peak seismicity forecast due to
initial impoundment. The effect of fluid pressure development due to reservoir impoundment
is similar to the fluid pressure development in a magma chamber toward the final stage of
ground deformation, crack growth and propagation. Prior to a major volcanic eruption, the
daily rate of earthquakes often increases substantially. Similarly, the daily seismicity in RIS
related to initial reservoir impoundment or substantial water level changes is also
accompanied with accelerated rates of seismicity. Thus, the same failure forecast method that
has provided reasonable volcanic eruption forecast (Kilburn and Voight, 1998; Kilburn, 2003;
Lavallée et al., 2008) can be applied to estimate the time-to-peak seismicity in the RIS.
Monticello Reservoir is located in South Carolina, U.S.A. The region consists of a thick
stratified sequence of Cambrian meta-sedimentary and meta-volcanic rocks (Secor, et al.,
1982). The South Carolina seismic network was deployed before reservoir impoundment,
which enabled the detection and accurate location of the seismicity events due to the
reservoir impoundment. Induced seismicity has been observed in the Monticello Reservoir
region since the impoundment of the reservoir in December 1977. This seismicity was
attributed to the undrained elastic response due to impoundment of the reservoir (Talwani,
1997). The failure forecast method was applied to forecast the peak initial RIS. The forecast
indicates that the expected date of peak seismicity is 6th February 1978, while the actual peak
seismicity did occur in February 1978 (Figure 6.5) (Talwani, 1997). However, the exact date
of peak seismic rate is not available in the literature.
157
Figure 6.5 Short-term forecast of the Monticello RIS for peak initial seismicity due to filling of the Monticello
reservoir, from December 1977 to January 1978 (seismic data started on 25 December 1977, with a moving
time window with 30 data points). Seismicity began about three weeks after the beginning of initial
impoundment (Chen and Talwani, 2001; Talwani, 1997). Based on the limited data, the forecast model suggests
peak seismicity is 6th February 1978 (Ying et al., 2009).
A sensitivity analysis was conducted using different number of data points for the
extrapolation of failure forecast (Table 6.2). The results indicate that although the estimated
time-to-failure was different using different number of points for extrapolation, the failure
forecasts fell within a narrow range between early to mid-February 1978.
158
Table 6.2 Sensitivity analysis for the forecast of peak seismicity of the RIS at the Monticello reservoir using
different number of data points for the extrapolation.
No. of data points used for extrapolation Estimated time-to-failure/peak seismicity
4
5
6
7
8
9
10
11
12
13
6-Feb-78
10-Feb-78
11-Feb-78
9-Feb-78
11-Feb-78
15-Feb-78
14-Feb-78
16-Feb-78
19-Feb-78
18-Feb-78
6.5 Conclusions
It is observed that the fluid pressure development in initial impoundment in reservoir
has similar effects as that in volcanic eruption, in particular the acceleration of seismicity
toward the final failure or peak seismic rate when crack communication and linkage
processes become significant (Ying et al. 2009). In addition, the repeated pressurization of a
volcanic edifice is cyclical in nature, while the seasonal water level change in protracted RIS
sites are also cyclical in nature. The application of the failure forecast model that has
provided reasonable estimates in volcanic eruption forecast may therefore be applicable to
the forecasts in RIS. This forecast model provides reasonable retrospective estimates to the
laboratory data as well as the field data of Monticello reservoir. This is because the failure
159
forecast method was developed for short-term forecast close to the final stages prior to
volcanic eruption when ground deformation and crack coalescence starts to be significant,
and when the acceleration of the seismic rate or seismic energy becomes rapid. Although the
short-term field case forecasts showed preliminary success, further investigation is required.
The application of this method to longer-term forecasts also requires further justification. It is
advisable that detailed seismic monitoring of RIS should be carried out starting from the
pre-impoundment stage, so that RIS can be distinguished from the local background
seismicity and reliable RIS data can be obtained for accurate failure forecasts. It is suggested
that the failure forecast model developed by Kilburn and Voight (1998) may provide some
general guideline for peak seismic rate estimates in short-term forecasts of RIS.
160
Chapter 7 Conclusions and Recommendations
7.1 Conclusions
Fluids play an important role in the triggering of seismicity in various areas such as
initial reservoir impoundment, long-term lake level fluctuation, fluid injections in deep
boreholes, geothermal operations, and volcanic activity. This research studies the mechanical
influence of oscillating pore fluid on naturally-fractured sandstones. With the aid of
non-destructive acoustic emission techniques, the acoustic emissions due to pore pressure
oscillations were recorded and analysed. The experimental results provide insights on the
failure mechanism of RIS:
a) Pore pressure variation can induce initial seismicity as well as protracted seismicity. In
the case of initial seismicity, an increase in pore pressure amplitude that exceeds the previous
maximum experienced by the system can induce rapid responses. In the case of protracted
seismicity, existing faults can still be reactivated when the applied pore pressure amplitude is
lower than the previous maximum. This is because the average pore pressure within the
system may continue to increase during the subsequent cycles despite the lowered oscillation
pore pressure peaks at the upstream.
b) This research suggests a number of factors which are important in protracted RIS and,
can influence the growth of seismicity, namely the mechanical properties of material, the
frequency of oscillation and the rate of increase of pore pressure. When the rate of change of
pore pressure is rapid, the seismic rate increases rapidly; when the rate of change of pore
pressure is gradual, the acceleration in seismic rate is also gradual and the number of seismic
161
events greatly reduces. When the frequency of pore pressure oscillation is too high, the
system may not respond to the peak amplitude of the applied pore pressure. However, when
the frequency of pore pressure oscillation is too low (i.e., the rate of change of pore pressure
is gradual) the acceleration in seismic rate in response to pore pressure oscillation is also
gradual, and fewer seismic events are expected. Furthermore, it is found that the effect of the
amplitude of the applied pore pressure is influencing the seismic response to a less extent.
These factors imply that in the field if the rate of increase in initial reservoir impoundment
can be controlled at a slower rate, then seismicity is less likely to occur. Similarly, in theory,
the control of protracted seismicity can be achieved by reducing the rate of increase of the
seasonal water level change by discharging.
c) The comparison between the RIS responses of the Darley Dale and Fontainebleau
sandstones suggest that the mechanical properties of the sample can influence the
reactivation of fault and induce protracted seismicity. The factors that affect the protracted
seismic response include:
i) Interconnected porosity and permeability of the fractured sample. Fractured samples
with low porosity and permeability allow the pore pressure to be at a transient state for a long
period of time, which is indicated by transient downstream pore pressure peaks and phase
shifts between the upstream and downstream pore pressures.
ii) The heterogeneity of the fractured sample, which also influences the development of the
foreshock sequence. Foreshocks are not found in homogeneous media (in the case of DDS7
experiment), but precede the main shock in slightly heterogeneous media (in the case of F5
experiment).
162
d) No recognisable event migration trends were observed due to the heterogeneity of the
faulted system and the relatively short distance between the existing fractures within the
sample. However, in the field when the distances are measured in kilometre-scale,
observations of migration trends are more probable.
e) Monitoring of phase shifts and pore pressure variations at both upstream and
downstream may provide guidelines for effective mitigation measures for reservoir-induced
seismicity.
f) The material failure forecast model, which has been widely used in volcanic eruption
forecast, provides promising retrospective forecasts for both the experimental data, and the
short-term field data (seismic data in days). However, the forecast for long-term field data
(seismic data in months) may not be reliable, and would require further investigation. As the
forecast model was developed based on the exponential trend of seismicity close to failure, a
more accurate fit for short-term forecasting than for long-term forecasting is justifiable.
g) Oscillating pore pressure can induce progressive shearing that prolongs the period of
protracted seismicity. This progressive shearing can gradually smooth the asperities at the
fractured contact surface and reduce the friction coefficient, consequently reducing the shear
strength of the fault and causing protracted failures.
h) Oscillating pore pressure also slows down the pore pressure development in the system
and, hence, extends the period of seismicity, as compared to a step increase in pore pressure.
163
The progressive wearing of asperities smoothes the fractured surfaces as the number of pore
pressure cycles increase. This is a ‘slow’ mechanism due to pore pressure oscillation. The
damage can accumulate and develop into a main slip when a sufficient number of pore
pressure cycles is allowed.
7.2 Recommendations
Thorough investigation of the sites, including the geology and mechanical properties of
the region prior to the construction of surface reservoirs is advisable. The selection of
aseismic zones as locations for reservoirs is crucial; however, if surface reservoirs are
inevitably located in seismogenic zones, proper surveillance of the region’s seismic activity,
as well as the upstream and downstream pore pressure changes, must be carried out in order
to observe any trends of seismic growth or pore pressure enhancement within the region that
may develop into a main slip. It is recommended that seismic monitoring stations should be
set up prior to any man-made pore pressure fluctuations to monitor the background seismic
level as well. This information is particularly important for the study of foreshock sequences,
which can be used for failure forecasts. Furthermore, the material failure forecast model can
be employed for short-term failure estimates and any episodic fault reactivation.
This research provides valuable insights into the effect of oscillating pore pressure on
induced seismicity. It also addresses the gradual change in shear strength due to oscillating
pore pressure. Future laboratory studies on fluid-induced seismicity may focus on the
relationship between the number of pore pressure cycles and the surface roughness in a
controlled environment. These experiments can be done on replicas of naturally-fractured
164
rock. Furthermore, according to the field statistics by Talwani et al. (2007), there is a
seismogenic permeability range that plays an important role in RIS. In order to identify the
possibility of such a seismogenic permeability range in a laboratory-controlled environment,
a series of rock samples that cover a wide range of permeability can be tested to stipulate the
range. Further research on the seismogenic permeability range of up-scaled model can also
be done by numerical modelling.
165
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APPENDIX I – Calibration Charts
This section provides the relationship of transducer output (in volts) and the
corresponding measurement of pressure (in MPa), axial displacement (in mm), and volume
(in ml). By applying linear regression, the gradients and intercepts of each transducer
calibration line can be obtained. The more important parameters are illustrated in Figures A1
to A5, while a comprehensive list of parameters are tabulated in Table A1. In addition, the
calibration of source location is provided.
182
Figure A1 Calibration of the two LVDTs: A and B
183
Pa (Pressure)
y = 20.112x + 0.0114
0
5
10
15
20
25
0 0.2 0.4 0.6 0.8 1 1.2
Volts
Pore Pressure A
Pb (Pressure)
y = 20.077x + 0.0279
0
5
10
15
20
25
0 0.2 0.4 0.6 0.8 1 1.2
Volts
Pore Pressure B
Figure A2 Calibration of the pore pressure transducers: Pa and Pb.
184
Pa (Volume)
y = 7.4947x + 37.532
0
10
20
30
40
50
60
70
-4 -2 0 2 4 6
Volts
Volume A (ml)
Pb (Volume)
y = 7.5014x + 37.529
0
10
20
30
40
50
60
70
-6 -4 -2 0 2 4
Volts
Volume B (ml)
Figure A3 Calibration of the permeameter cylinder volume: Pa and Pb.
185
Cantilever A
y = 0.5844x + 0.0048
0
1
2
3
4
5
0 2 4 6 8
Volts
Deflection (mm)
Cantilever B
y = 2.3313x - 0.0008
0
1
2
3
4
5
6
7
0 0.5 1 1.5 2 2.5 3
Volts
Deflection (mm)
Figure A4 Calibration of the lateral strain measurement device.
186
Figure A5 Calibration of the axial load transducers, Z1 and Z2.
Table A1 Summary of calibration parameters. The gradient, m, is the key parameter, representing the voltage
change per measurement change.
m, gradient c, intercept Description
1.5151 1.8967 LVDT A
0.5844 0.0048 Cantilever A
1.3009 2.9033 LVDT B
2.3313 -0.0008 Cantilever B
53.813 -26.38 Confining Pressure
27.581 1.0032 Pressure A
27.572 -1.1146 Pressure B
680.14 1.4159 Z1 Load
23.0675 -0.07 Z1 Displacement
680.14 1.4159 Z2 Load
10.1899 -0.025 Z2 Displacement
6.97 67.97 ISCO Vol A
6.97 67.97 ISCO Vol B
20.112 0.0114 Pa Pressure
7.4947 37.532 Pa Volume
20.077 0.0279 Pb Pressure
7.5014 37.529 Pb Volume
187
Velocity models and source location calibration:
Different velocity models and anisotropy factors were being used at different stage of
the experiments to account for the development of transverse isotropic structure so that the
accuracy of automatic P-wave picking could be enhanced. Figure A6 and A7 show the
velocity models at the start of the experiment and after the failure of sample for typical
Darley Dale sandstone experiment and Fontainebleau sandstone experiment, respectively.
188
a)
b)
Figure A6 Calibration of velocity models during different periods of the Darley Dale sandstone experiment. a)
The P-wave velocity change. b) Velocity model at the start of the experiment and after the sample failure.
189
a)
b)
Figure A7 Calibration of velocity models during different periods of the Fontainebleau sandstone experiment. a)
The P-wave velocity change. b) Velocity model at the start of the experiment and after the sample failure.
190
The absolute error in source location can be calculated by locating the synthetic AE
generated by each individual transmitter. The following example used a P-wave velocity
model of 5300 m/s and anisotropy of 31% for locating the synthetic AE during F5
experiment.
Figure A8 Locating a synthetic acoustic emission to calibrate source location.
Table A2 Absolute errors in source location.
Sensor ID Actual location of sensor Located sensor
Northing Easting Depth Northing Easting Depth
Absolute error
(mm)
Channel 1 23.47 9.72 -42.33 22.5 9.37 -40.1 2.44
Channel 2 9.72 -23.47 -42.33 8.78 -22.5 -40.1 2.56
Channel 3 25.4 0 -21.17 22.3 1.25 -20 3.08
Channel 4 0 25.4 -21.17 2.12 22.01 -21 2.57
Channel 5 -25.4 0 -21.17 -25.99 -0.57 -24.55 -2.69
Channel 6 0 -25.4 -21.17 3.02 -28 -23.8 -3.81
Channel 7 17.96 -17.96 21.17 20.2 -19.23 21.5 -2.15
Channel 8 17.96 17.96 21.17 17.05 16.78 19.48 2.21
Channel 9 -17.96 17.96 21.17 -16.8 16.8 19.81 2.13
Channel 10 -17.96 -17.96 21.17 -18.99 -19.52 -23.11 -2.65
Channel 11 -23.47 9.72 42.33 -21.01 8.78 40.11 3.24
Channel 12 9.72 23.47 42.33 9.67 23.01 40.23 2.02
The maximum absolute error in source location is 3.81 mm.
191
APPENDIX II – Sensor location and sensor file
Figure A9 Locations of the lateral sensors
192
Figure A10 Locations of the platen sensors
193
194
APPENDIX III – Details of the F2 experiment
Table A4 F2 experiment: Peak AE hits and the time delayed in response to the peak pore pressure magnitude.
Stage Cycle Range of pore
pressure (MPa)
Peak mean AE hits
per second
Delay in response
(s)
1 71 -
2 3.25 -
3 1.875 - 1
4
2.5 – 7.5
1.875 -
1
2
3 2
4
2.5 – 5
No significant AE has been recorded as the
maximum magnitude of pore pressure is less
than the previous peak value
1 1 -
2 0.875 -
3 0.75 - 3
4
2.5 – 7.5
0.5 -
1 23 11
2 2.4 54
3 1.8 70 4
4
2.5 – 10
1.3 49
1
2
3 5
4
2.5 – 7.5
No significant AE has been recorded as the
maximum magnitude of pore pressure is less
than the previous peak value
1 4.3 19
2 4.6 20
3 4 22 6
4
2.5 – 10
4.3 23
1
2
3 7
4
2.5 – 7.5
No significant AE has been recorded as the
maximum magnitude of pore pressure is less
than the previous peak value
1 3.75 28
2 4.6 22
3 3.56 21 8
4
2.5 – 10
4 20
1
2
3 9
4
2.5 – 7.5
No significant AE has been recorded as the
maximum magnitude of pore pressure is less
than the previous peak value
10 1 2.5 – 7.5
No significant AE has been recorded as the
maximum magnitude of pore pressure is less
than the previous peak value
Most of the AE were generated during the first cycle of a maximum pore pressure. Subsequent pore pressure
cycles also induce seismicity provided that the maximum experierenced pore pressure has been reached;
however, the number of AE reduced substantially. Delayed seismic response is also observed.
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APPENDIX IV – Response to Different Frequencies of Oscillation and
Rate of Increase in Pore Pressure
The rate of increase in seasonal water level change of artificial reservoir is about 40 m in 3
months time, which is equivalent to a rate of increase of 3 X 10-6 MPa/min. The experimental
results indicate that when the ratio of the rate of increase in laboratory experiment to that of
the field was in the order of 106, there were AE responses during the experiment.
Table A5 AE response corresponding to different frequencies and rate of increase in pore pressure.
Experiment
ID
Frequency
(Hz)
Rate of Increase
(MPA/min)
Change in Pore
pressure (MPa)
Ratio of rate of
increase (lab : field)
AE
Response
F5 0.2 72 3 2.E+07 N.G.
F5 0.1 36 3 1.E+07 N.G.
F5 0.1 48 4 2.E+07 N.G.
F5 0.1 60 5 2.E+07 N.G.
F5 0.1 72 6 2.E+07 N.G.
F5 0.1 84 7 3.E+07 N.G.
F5 0.1 96 8 3.E+07 N.G.
F5 0.1 108 9 3.E+07 N.G.
F5 0.05 54 9 2.E+07 N.G.
F5 0.0083 15 15 5.E+06 Yes
F2 0.0056 3.3 5 1.E+06 Yes
F2 0.0083 5 5 2.E+06 Yes
F2 0.0056 5 7.5 2.E+06 Yes
F2 0.0111 10 7.5 3.E+06 Yes
F3 0.0083 3.5 3.5 1.E+06 Yes
F3 0.0083 4.5 4.5 1.E+06 Yes
F3 0.0083 5.5 5.5 2.E+06 Yes
F3 0.0083 6.5 6.5 2.E+06 Yes
F3 0.0083 7.5 7.5 2.E+06 Yes
F4 0.0020 0.84 3.5 3.E+05 N.G.
F4 0.0014 0.94 5.5 3.E+05 N.G.
F4 0.0010 0.9 7.5 3.E+05 N.G.
DDS4 - 0.2 1 6.E+04 N.G.
DDS5 - 0.5 1 2.E+05 N.G.
DDS6 - 5 5 2.E+06 Yes
DDS7 0.0167 10 5 3.E+06 Yes
DDS7 0.0167 15 7.5 5.E+06 Yes
DDS7 0.0167 19 9.5 6.E+06 Yes
DDS7 0.0167 29 14.5 9.E+06 Yes
Note: Various oscillation frequencies have been used in Fontainebleau sandstone experiments
and it was found that when the frequency ranged between 0.0056 to 0.0111 Hz, seismicity
was induced; however, frequencies higher than 0.05 Hz or lower than 0.002 Hz did not
induce seismicity. More systematic investigation is required to determine the effective range
of frequencies of oscillation for inducing seismicity for different materials; however, it is
outside the scope of this research.
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APPENDIX V – Glossary
Abrasive wearing – occurs when a hard rough surface plough through a softer material.
Adhesive wearing – wearing that occurs with junctions shear off part of the adjoining
asperity, resulting in transfer of material from one surface to the other.
Acoustic Emission – a transient stress wave caused by the sudden release of the impulsive
strain energy of a material (Lockner, 1993), which travels as spherical wavefronts in the
material under stress.
Aftershock – an earthquake that occurs after a main shock.
b-value – the slope of the frequency-magnitude scaling relation i.e. log N(≥ M) = a – bM.
Continuous waveform – a stream of ultrasonic waveforms that is recorded in real-time by
the continuous data acquisition units, by each channel. It allows a complete AE catalogue to
be recorded for processing.
Far field – observation of seismic waveforms at distances from the source much larger than
the dominant wavelengths being generated at the source; i.e., several wavelengths away from
the source (ESG, 2002b).
Foreshock – an earthquake that occurs before a main shock.
Fracture – formation of new surfaces in material by breaking the material bonds, and
present in the form of cracks.
Hit count -- A ‘hit’ that is recorded when the waveform signal voltage exceeds a pre-defined
threshold within a pre-defined time window.
197
Permeability - describes the ability of a medium to transmit fluid and is greatly influenced
by the porosity of the medium.
Phase shift – an observable repositioning between the applied upstream pore pressure and
the measured downstream pore pressure.
Porosity – the measure of the pore volume within the rock. It is defined as the fraction of
rock volume V that is not occupied by solid matter.
P-wave – a primary or compressional seismic wave generated by elastic energy release in
material.
S-wave – a secondary or shear seismic wave that has a comparatively low velocity rotational
vibrations (waves), which propagate through the rock mass.
Seismic event – instability within a rock mass often caused by rock fracturing or slip on
pre-existing features (ESG, 2002b).
Simplex method – an iterative location method that uses a geometric pattern (Simplex) to
minimise errors between the measured and calculated arrival times, and rapidly reduce the
search volume.
Source location – the point or location where crack initiates.
Sensor – a device (transducer) that converts vibrations of one quantity into those of another
(e.g. pressure to voltage or vice versa) (ESG, 2002a).
Triggered data – AE data that is recorded when the waveform signal voltage exceeds a
pre-defined threshold within a pre-defined time window.
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APPENDIX VI – Information of Paper Published in GRL
Ying, W. L., Benson, P. M. and Young, R. P. 2009. Laboratory Simulation of Fluid-Driven
Seismic Sequences in Shallow Crustal Conditions. Geophys. Res. Lett. 36, L20301,
doi:10.1029/2009GL040230.
Link: http://www.agu.org/pubs/crossref/2009/2009GL040230.shtml
Contributions to the paper:
Winnie (Wai-lai) Ying carried out the experiments, analysed the data and wrote the
paper.
Philip M. Benson assisted in preparation of experiments and provided valuable
discussions and comments on the paper.
R. Paul Young received NSERC discovery grant which was used for the development of
the Rock Fracture Dynamics Laboratory at the University of Toronto, in which the
experiments were carried out.
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