Upload
others
View
0
Download
0
Embed Size (px)
Citation preview
In situ stress reconstruction using
rock memory
Chung-min (Ariel), Hsieh
This thesis is presented for the degree of Doctor of Philosophy of The
University of Western Australia
School of Civil & Resource Engineering
June 2013
School of Civil and Resource Engineering The University of Western Australia
(i)
ABSTRACT
Knowledge of in situ stress for underground construction or excavations is important.
With an input of in situ stress magnitude/orientations, one can predict the potential
failure, improve the efficiency of ground support and/or provide the parameters for
numerical modelling/planning to make the design cost effective. In this thesis, two rock
memory-based in situ stress measurement methods, the acoustic emission method and
the Deformation rate analysis method, were studied.
The acoustic emission method utilizes the Kaiser effect to recover the previously
applied maximum stress, which is expected to be the in situ stress. The phenomenon
that Kaiser has found and the usage of the Kaiser effect for the in situ stress
measurement were reviewed, and a series of tests in aluminium, agate, sandstone,
ultramafic and slate samples with different conditions in the sample end was performed.
The result shows that the Kaiser effect method of the in situ stress determination has
severe limitations. Firstly, the asperities/irregularities/residual material at the sample
ends at low stress can manifest themselves as the Kaiser effect. This ‘ghost’ Kaiser
effect created by the sample ends is not related to the rock memory and it is an artefact
of the test preparation. A thin plastic sheet (TML strain gauge) plus silicone gel can be a
buffer material to reduce the noise from end. A multichannel source location system
could also be able to detect the origin of signal.
Secondly, the process of crack generation/growth can create sufficient change in the
stress path in the following loading cycle. Because the Kaiser effect is masked by the
acoustic emission associated with the damage accumulation, the acoustic emission
could start much earlier than the previous maximum stress. In order to prevent the
damage accumulation from imitating the Kaiser effect and misleading the analysis, one
should find the stress range in which the Kaiser effect can be detected, before using the
Kaiser effect as a stress measurement method.
For Deformation rate analysis (DRA) method, the investigation on the change in tangent
modulus under uniaxial load was conducted first, in order to understand the relationship
between inelastic strain and change in stiffness. The nonlinear deformation contributed
to by crack closure, sliding and crack growth could co-exist within the same stress
range, and the increase in stiffness under repeated load is proportional to the residual
School of Civil and Resource Engineering The University of Western Australia
(ii)
strain. This phenomenon is independent from the physical properties of rock or the
stress level subjected to the sample.
The mechanism of deformation rate effect under low stress was proposed as the
frictional sliding over the pre-existing crack, interfaces, and/or grain boundaries. A
basic rheological model was developed to simulate the rock specimen with large
number of interfaces. This new theoretical model explains the phenomena of memory
fading, time gap between pre-stress and DRA tests, and the influence of the holding
time of the preload. The differences between the in situ stress (long term memory) and
the laboratory pre-stress (short term) were shown to be caused by creep. To understand
the mechanism of deformation rate effect further, a series of tests confirmed that the
DRA technique is able to predict the most recent stress, instead of previous maximum
stress, and the DRA method can recover a laboratory pre-stress, which is smaller than
the in situ stress. The results provide experimental evidence to improve the rheological
model in the future study.
In the case of imperfect test conditions, the effect of sample bending caused by the
imperfections of the loading frame and/or sample preparation was examined. The
bending effect was shown to cause considerable scatter in the pre-stress values
reconstructed from the stress-strain curves from the individual strain gauge locations. A
compensation formula, which based on the assumption that the stress/strain non-
uniformity cause by bending can be approximated by assuming that the sample bends as
a classical beam, was proposed to improve the stress prediction.
School of Civil and Resource Engineering The University of Western Australia
(iii)
ACKNOWLEDGEMENTS
I would like to acknowledge the guidance of my supervisors Professor Phil Dight and
Professor Arcady Dyskin. They have assisted me with helpful information/comments
for my research and provided wise suggestions on the social/personal issues. Their
invaluable support has improved my personality and the understanding of my research
field.
I would also like to thank the staff at the civil & resources engineering workshop and
the Australian Centre for Geomechanics (ACG) for their help and efforts. The financial
support provided by the ACG allows me to undertake the research and has been much
appreciated.
Finally, sincere thanks to my family and husband David Yong for their unconditional
support and encouragement.
School of Civil and Resource Engineering The University of Western Australia
(iv)
PUBLICATIONS ARISING FROM THIS THESIS
1. Hsieh A, Dight P, Dyskin AV. Ghost Kaiser effect at low stress: the role of the
sample ends. Int J Rock Mech Min Sci. 2012;submitted (Chapter 2, the contribution
of the student is 60%).
2. Hsieh A, Dight P, Dyskin AV. The Kaiser effect at mid to high stress. Int J Rock
Mech Min Sci. 2013;submitted (Chapter 3, the contribution of the student is 60%)
3. Hsieh A, Dyskin AV, Dight P. The tangent modulus and relationship between
residual strain and increase in bulk modulus in rock after applied stress under
uniaxial compression test. Int J Rock Mech Min Sci. 2013;submitted (Chapter 4, the
contribution of the student is 60%).
4. Wang HJ, Dyskin AV, Hsieh A, Dight P. The mechanism of the deformation
memory effect and the deformation rate analysis in layered rock in the low stress
region. Computers and Geotechnics. 2012;44: 83-92. (Chapter 5, the contribution of
the student is the model and discussion of results, 20%)
5. Wang Hj, Dyskin AV, Hsieh A, Dight P. The mechanism of the deformation memory
effect in the low stress region and the deformation rate analysis. Rock Mech Rock
eng. 2013;submitted (Chapter 6, the contribution of the student is the model and
discussion of results, 20%)
6. Hsieh A, Dyskin AV, Dight P. The influence of sample bending on the DRA stress
reconstruction. Int J Rock Mech Min Sci. 2013;submitted (Chapter 7, the
contribution of the student is 60%)
School of Civil and Resource Engineering The University of Western Australia
(v)
TABLE OF CONTENTS
Abstract ............................................................................................................................. i Acknowledgements ......................................................................................................... iii Publications arising from this thesis ............................................................................. iv Table of Contents ............................................................................................................ v Table of Figures ............................................................................................................ viii Chapter 1. Introduction .................................................................................................. 1
1.1 The in situ stress measurements ......................................................................... 1 1.1.1 The sources of stress in the rock ......................................................... 1 1.1.2 The importance of understanding the stress field ............................... 2 1.1.3 The in situ stress measurement techniques: The stress relief
methods and the stress compensation methods ................................... 3 1.1.4 The in situ stress measurement techniques: The fracture/damage
evolution methods ............................................................................... 4 1.1.5 The in situ stress measurement techniques: Rock memory
methods ............................................................................................... 5 1.2 The Acoustic Emission method of revealing the rock memory ......................... 7
1.2.1 Background ......................................................................................... 7 1.2.2 The origin and original description of the Kaiser effect ..................... 7
1.3 The difficulties of using Kaiser effect for stress measurements ........................ 9 1.3.1 Influence of damage accumulation in high stress region .................... 9 1.3.2 The mechanism of Kaiser effect in low stress region ....................... 10
1.4 AN alternative method of revealing rock memory: the Deformation Rate Analysis ............................................................................................................ 12 1.4.1 Background ....................................................................................... 12 1.4.2 Previous studies and unsolved problems .......................................... 14
1.5 The difficulties in using the DRA method ....................................................... 22 1.5.1 The source of strain difference between two cycles ......................... 22 1.5.2 Effect of sample bending .................................................................. 22 1.5.3 The influence of stress applied earlier than pre-stress ...................... 23
1.6 Research objective, originality and significance .............................................. 23 1.7 Thesis structure ................................................................................................ 25
Chapter 2. The Kaiser effect at low stress: Ghost kaiser effect ................................ 29 2.1 Abstract ............................................................................................................ 29 2.2 Introduction ...................................................................................................... 29 2.3 Experimental apparatus and parameters .......................................................... 32 2.4 Tests and results ............................................................................................... 34
2.4.1 Aluminium ........................................................................................ 34 2.4.2 Agate ................................................................................................. 37 2.4.3 Sandstone .......................................................................................... 39
2.5 conclusion ........................................................................................................ 43
School of Civil and Resource Engineering The University of Western Australia
(vi)
Chapter 3. The kaiser effect at high stress.................................................................. 45 3.1 Abstract ............................................................................................................ 45 3.2 Introduction ...................................................................................................... 46 3.3 Experimental apparatus and parameters .......................................................... 49 3.4 Test results ....................................................................................................... 50 3.5 Conclusion ....................................................................................................... 58
Chapter 4. The tangent modulus and residual strain after applied stress under uniaxial compression test .................................................................................. 59
4.1 Abstract ............................................................................................................ 59 4.2 Introduction ...................................................................................................... 59 4.3 Experimental apparatus and rock properties .................................................... 63 4.4 Test results and discussion ............................................................................... 64
4.4.1 The trend of tangent modulus at 1st cycle ......................................... 64 4.4.2 The overlapping between the regions of crack closure, sliding and
crack growth ...................................................................................... 66 4.4.3 The increase of the modulus from 1st cycle to 2nd cycle ................... 67
4.5 Conclusion ....................................................................................................... 73 Chapter 5. The mechanism of the deformation memory effect and the deformation rate analysis in layered rock in the low stress region .......................... 75
5.1 Abstract ............................................................................................................ 75 5.2 Introduction ...................................................................................................... 75 5.3 Experimental evidence of DRA working in low stress region ........................ 80 5.4 The mechanism of deformation memory effect based on frictional sliding.
The basic element ............................................................................................ 82 5.4.1 Frictional sliding over sliding planes ................................................ 82 5.4.2 The basic element ............................................................................. 84 5.4.3 Behaviour of the basic element ......................................................... 85
5.5 Two basic elements (sliding planes) with different cohesions ........................ 89 5.5.1 Introduction to the model .................................................................. 89 5.5.2 Behaviour of the model with two basic elements ............................. 90
5.6 A model of layered rock with multiple basic elements (sliding planes) .......... 91 5.6.1 Introduction to the model .................................................................. 91 5.6.2 DRA in multi--element model with 500 elements ........................... 92
5.7 Discussion ........................................................................................................ 95 5.7.1 The role of the Maxwell body ........................................................... 96 5.7.2 The role of the St.V body .................................................................. 98
5.8 Conclusions ...................................................................................................... 98 Chapter 6. The mechanism of the deformation memory effect in the low stress region and the deformation rate analysis ....................................................... 101
6.1 Abstract .......................................................................................................... 101 6.2 Introduction .................................................................................................... 101 6.3 The Deformation memory effect and DRA in low stress region ................... 105
School of Civil and Resource Engineering The University of Western Australia
(vii)
6.3.1 The DRA method ............................................................................ 105 6.3.2 Experimental evidence of DRA working in low stress region ........ 107
6.4 Our experiments in low stress region ............................................................. 108 6.5 The mechanism of the deformation memory effect based on frictional
sliding and basic element ............................................................................... 109 6.5.1 Frictional sliding over pre-existing interfaces ................................ 109 6.5.2 The basic element ............................................................................ 110 6.5.3 Behaviour of the basic element ....................................................... 112
6.6 A model of rock with multiple interfaces ...................................................... 120 6.6.1 Introduction to the model ................................................................ 120 6.6.2 DRA in multi-element model with 200 elements ........................... 121
6.7 Discussion ...................................................................................................... 126 6.7.1 Inflection points .............................................................................. 126 6.7.2 Comparisonwith experimental results ............................................. 129
6.8 Conclusions .................................................................................................... 133 Chapter 7. The influence of sample bending on the DRA stress reconstruction .............................................................................................................. 135
7.1 Introduction .................................................................................................... 135 7.2 Experimental apparatus and parameters ........................................................ 138
7.2.1 The influence of bending and rock heterogeneity on volumetric strain ................................................................................................ 138
7.2.2 Compensation of bending in the DRA stress reconstruction .......... 142 7.3 Conclusion ..................................................................................................... 147
Chapter 8. discussion: The influence of stress applied earlier than pre-stress ............................................................................................................................. 149
8.1 Introduction .................................................................................................... 149 8.2 Experimental setup ......................................................................................... 150 8.3 Test result ....................................................................................................... 152
8.3.1 The laboratory pre-stress that is smaller than the in situ stress ....... 152 8.3.2 The number of pre-stress that DRA technique can recorded .......... 152 8.3.3 The most recent stress (lower than PMS) ....................................... 153
8.4 discussion and suggestion .............................................................................. 155 Chapter 9. Conclusions ............................................................................................... 156 Chapter 10. Recommendations for future research................................................. 159
10.1.1 The Kaiser effect ............................................................................. 159 10.1.2 The deformation rate analysis ......................................................... 159
Chapter 11. References ............................................................................................... 161
School of Civil and Resource Engineering The University of Western Australia
(viii)
TABLE OF FIGURES
Figure 1-1 Kaiser effect in materials and rocks under compression: (a) the loading
cycles, (b) cumulative acoustic emission activities corresponding to
these loading cycles [4]. ............................................................................... 7
Figure 1-2 Stress-strain curve and acoustic emission intensity of a soft-annealed
steel probe with 0.15 weight% carbon under tensile stress. The
sample was subjected to tensile stress to cause elongation up to point
Z previously. Then, the sample was reloaded. The ASE intensity
shows the Kaiser effect after the specimen is relaxed followed by re-
applying tensile stress to exceed the previous maximum elongation
(after [2]). ..................................................................................................... 8
Figure 1-3 The elongation area which Kaiser effect exists and was studied by
Tensi and Kaiser (after [2]). ......................................................................... 8
Figure 1-4 Acoustic emission activity patterns in rock. Relative acoustic emission
signal’s rate indicated by spacing of horizontal lines at the
corresponding stress level: (a) AE activity during the first of a series
of tests; (b) AE activity after numerous cycles of loading and
unloading (after [3]). .................................................................................... 9
Figure 1-5 The stress versus acoustic emission signature and possible relationship
to mechanisms of brittle rock fracture (after [56]) ..................................... 12
Figure 1-6 Loading process of pre-stress (1st cycle), 2nd and 3rd cycles. ........................ 13
Figure 1-7 a): Stress and strain curve. A black arrow shows a strain difference
(Δεij) under same stress. b): An inflection point which indicates PMS
(previous maximum stress) is marked with arrow. .................................... 13
Figure 2-1 Kaiser effect in materials and rocks under compression: (a) the loading
cycles, (b) cumulative acoustic emission activities corresponding to
these loading cycles [4]. ............................................................................. 30
Figure 2-2 The concave region of stress-strain curve created by successive crack
closure in compression. The strain energy stored in the sample
increases at a higher rate than that of pure elastic sample, which
excludes the energy excess needed for generating acoustic emission........ 31
School of Civil and Resource Engineering The University of Western Australia
(ix)
Figure 2-3 The continuous process of crack closure: (a) the open crack before
loading; (b) load increase caused a point contact of the opposite faces
of the crack; (c) further load increase enlarges the contact area. ............... 32
Figure 2-4 The loading machine and the sample ............................................................ 33
Figure 2-5 The acoustic emission response of aluminium A from the 1st loading
cycle. ........................................................................................................... 34
Figure 2-6 The axial and lateral stress-strain curves of aluminium sample. The
axial (in black) and lateral strain (in grey) responses are linear. ................ 35
Figure 2-7 The AE bursts around 21 MPa in aluminium A indicate the PMSes that
were applied in the first loading cycles. The sample aluminium B
shows no sign of the Kaiser effect. ............................................................. 35
Figure 2-8 The sample aluminium B from Figure 7 was wiped by finger over the
sample end and reloaded to 20 MPa. The majority of the acoustic
signals are below 5 MPa, which indicates “memory fading”. This
initial “burst” was from the free particles brought from fingers, and
this burst can also be observed in [3]. ........................................................ 36
Figure 2-9 The surface of aluminium sample: (a) with additional cleaning; (b) with
tissue cleaning only. The very fine particles which are indicated by
the black arrows at the right were gathered in the uneven part of
surface in the sample end without additional cleaning (b) and were
absent in the additionally cleaned end (a). ................................................. 36
Figure 2-10 (a) Agate sample with high roughness (marked as Rgh) shows much
higher acoustic emission at low stress, while the sample with low
roughness (marked as Sth) has little acoustic emission. (b) The
sample with higher asperity also exhibits the Kaiser effect, while the
sample with lower asperity does not show the memory of previous
load. ............................................................................................................ 38
Figure 2-11 The number at each column is the roughness before testing. The
sample with low roughness (1 and 2) has minor reduction of
roughness after 2 loading cycles, compared with the sample with high
roughness (3 and 4). ................................................................................... 39
School of Civil and Resource Engineering The University of Western Australia
(x)
Figure 2-12 The total amount of acoustic events of samples with different end
preparation. ................................................................................................. 41
Figure 2-13 (a) The comparison of acoustic emission amount between sandstone
samples with/ without plastic insert. The sample without plastic tape
insert has much higher number of acoustic pulses than the sample
with plastic tapes at both ends. (b) The sample without plastic tape
insert (sample end 5 and 6) has higher reduction of roughness,
compared with the sample with plastic tapes at both ends (surface 7
and 8). ......................................................................................................... 42
Figure 3-1 Kaiser effect in materials and rocks under compression: (a) the loading
cycles, (b) cumulative acoustic emission activities corresponding to
these loading cycles [4]. ............................................................................. 46
Figure 3-2 The cross type strain gauges were glued at the 4 spots shown in the
graph. .......................................................................................................... 50
Figure 3-3. The sandstone sample was loaded to near the failure stress (100MPa as
detected at the 2nd cycle). The tangent modulus reduced its value
dramatically after the applied stress exceeded 99MPa, where the
acoustic emission started bursting. The amount of acoustic emission
did not exceed 1.5 events/MPa before the stress reached 98MPa and
is considered as background noise. ............................................................ 51
Figure 3-4. The response of acoustic emission and the change in the bulk modulus
at the 2nd loading indicates the new cracks were created from 78MPa
(grey arrow) onwards. ................................................................................ 51
Figure 3-5. The sandstone sample shows no sign of dilatancy when the applied
stress reached 90MPa. There were very few acoustic emission
activities (35 events) evenly spreading out in the whole loading cycle
and the “acoustic emission burst” was not observed. ................................. 53
Figure 3-6. The acoustic emission in the 2nd and 3rd loading cycles from sample
WAou B3. The acoustic emission pulses were observed from around
10MPa onwards. The acoustic emission rate increased more
significantly after the load reached 25MPa (black arrow), which is
School of Civil and Resource Engineering The University of Western Australia
(xi)
well below the PMS (41MPa). The volumetric strain shows the
sample is very close to failure. ................................................................... 54
Figure 3-7. The acoustic emission in the 2nd and 3rd loading cycles from sample
WAou B4. The bursting is observed at 40MPa (black arrow), which
is well below the PMS (58MPa). The acoustic emissions at the 2nd
and 3rd cycles do not have the memory of 58MPa. The volumetric
strain shows the sample was loaded to high stress. .................................... 54
Figure 3-8. The top 3 graphs show the tangent modulus, bulk modulus and the
acoustic emission rate at the 1st loading cycle indicate there was a
sudden increase in dilatancy at 14MPa. The acoustic emission rate at
the 2nd loading cycle does not show the memory of the 1st loading
cycle. ........................................................................................................... 57
Figure 3-9. The acoustic emission in the 3rd loading cycle shows a memory of the
PMS. ........................................................................................................... 57
Figure 4-1 The small unloading cycle (white arrow) shows higher modulus than
loading cycle while the tangent modulus increases at whole loading
process (after [108]). .................................................................................. 61
Figure 4-2 The 3 main stages in a theoretical volumetric strain curve: crack
closure, perfect elastic deformation, and fracture propagation [109]. ........ 62
Figure 4-3 (a) An ultramafic rock sample shows maximum 26GPa increase in the
tangent modulus (black line), before reducing its value and failed.
The UCS is 55MPa. The slope of volumetric strain (grey line)
increased its value during loading. (b) The volumetric strain (black
line) shows a similar trend as Figure 4-2. The dash line is a straight
line which could be mistaken as a linear part of the volumetric strain. ..... 65
Figure 4-4 (a) A porphyry sample shows a less than 2GPa increase in the tangent
modulus (black line). The slope of volumetric strain (grey line)
slightly increased its value during loading. (b) Compared with the
dash line (straight line), the volumetric strain is slightly non-linear
during loading. ............................................................................................ 65
Figure 4-5 (a) A sandstone sample shows a 12GPa decrease in the tangent
modulus during loading. The source of decrease is expected to be
School of Civil and Resource Engineering The University of Western Australia
(xii)
sliding, because the decrease started at the beginning of loading. The
slope of volumetric strain (grey line) is unchanged. (b) The
volumetric strain is a straight. .................................................................... 66
Figure 4-6 (a) The sample of decrease type in tangent modulus shows the residual
strain after unloading in the 1st loading. The secant modulus in the 2nd
loading is higher than it in the 1st loading. (b) The sample of decrease
type in tangent modulus also shows certain amount of residual strain.
The secant modulus at the 2nd loading is higher than it at the 1st
loading, although the sample had reached 95% of UCS in the 1st
loading. ....................................................................................................... 68
Figure 4-7 The loading stress-strain curve at 1st and 2nd cycles. σm is the
maximum stress of 1st and 2nd loading cycles, εm is the maximum
strain of the 1st cycle, εr is the residual strain of 1st cycle, and ∆ε is
the difference between maximum strain at 1st cycle and 2nd cycle. ........... 69
Figure 4-8 The relationship between the portion of residual strain and the increase
in secant modulus. Each black dot is the result of each sample. The
equation shown at the top of each graph is the linear trend line (black
line) of all results. The dash line is the calculated value of E2E1
regarding to the value of r shown in each graph. ....................................... 72
Figure 4-9 The relationship between residual strain and the increase in modulus
from [110] is similar to our results in Figure 4-8. ...................................... 73
Figure 4-10 The relationship between the portion of residual strain and the
increase in secant modulus in all samples. ................................................. 73
Figure 5-1 Illustration of the deformation rate analysis (DRA) (a) the definition of
the strain difference function Dei,j(r) and (b) the plot of Dei,j(r)
(DRA curve) and the DRA inflection. ....................................................... 77
Figure 5-2 A rock sample with parallel sliding planes. .................................................. 81
Figure 5-3 The basic rheological element. ...................................................................... 83
Figure 5-4 The loading cycles assumed for the modelling. ............................................ 85
School of Civil and Resource Engineering The University of Western Australia
(xiii)
Figure 5-5 (a) The stress–strain curve and (b) the DRA curve in a test. The values
of dimensionless groups are: g1r/k1co1 = 100, rT/co1 = 10, rp/co1 =
1.6, rm/co1 = 1.8. ....................................................................................... 87
Figure 5-6 The relationship between σdra1/co1, σdra2/co1 and η1r k1co1, rT/co1,
σp/co1 = 1.2, σm/co1 = 1.4. ........................................................................ 89
Figure 5-7 The model with two basic elements. ............................................................. 90
Figure 5-8 DRA curves for the model including 2 elements: (a) σp/co1 = 1.6,
σm/co1 = 1.8; σdra2 > σdra3. (b) σp/co1 = 2.4, σm/co1 = 2.8; σdra2 >
σdra3. The values of dimensionless groups are: η1r k1co1= 100,
rT/co1= 10, co2/co1 = 100. .......................................................................... 91
Figure 5-9 The multi-element model consisting of n basic elements. ............................ 92
Figure 5-10 Stress–strain curve in a test. (a) Uniformly distributed cohesions. (b)
Normally distributed cohesions. The range of cohesions in uniform
distribution is 0.01–5 MPa. The mean value is 2.505 MPa, the
standard deviation is 1.4448 MPa. The loading regime is σp = 8 MPa,
σm = 10 MPa, T = 0. .................................................................................. 94
Figure 5-11 DRA curves for the multi-element model in the case in Fig. 10: (a)
Uniformly distributed cohesions. (b) Normally distributed cohesions. ..... 94
Figure 5-12 The memory fading in the DRA. The loading regime is σp = 2 MPa,
σm = 3 MPa, the cohesion follows the uniform distribution described
in Figure 5-10. ............................................................................................ 95
Figure 5-13 The stress relaxation in a Maxwell body locked by the friction
element. σ0=1MPa, t0=0. ........................................................................... 97
Figure 6-1 Illustration of the DRA method: (a) loading cycles (b) the definition of
the strain difference function Δεi,j(σ), the horizontal bar shows the
differential strain between successive loadings (c) the plot of Δεi,j(σ)
curve (DRA curve) and the DRA inflection(after Yamamoto[113]). ...... 106
Figure 6-2 The sandstone sample and the location of four strain gauges. .................... 108
Figure 6-3 The DRA curves for the sandstone sample. ................................................ 109
Figure 6-4 The basic rheological element. .................................................................... 112
Figure 6-5 Loading regime 1......................................................................................... 113
School of Civil and Resource Engineering The University of Western Australia
(xiv)
Figure 6-6 Loading of the basic element; parameters:π1=1,π2=1,π3=1.6,π4=1.8:(a)
the stress-strain curve and (b) the DRA curve. ........................................ 114
Figure 6-7 Loading of the basic element; parameters: π1=1, π2=1, π3=2.6, π4=2.8:
(a) the stress-strain curve and (b) the DRA curve. ................................... 115
Figure 6-8 The relationship between π01 and π1, π2. ..................................................... 116
Figure 6-9 Loading regime 2. ....................................................................................... 116
Figure 6-10 The relationship between π01, π02 and π5, π6: (a) for π01 (b) for π02. .......... 118
Figure 6-11 Loading regime 3. ..................................................................................... 118
Figure 6-12 The relationship betweenπ01, π02 and π6, π7: (a) for π01 (b) for π02. ........... 119
Figure 6-13 The multi-element model: (a) the multi-element model consisting of n
basic elements (b) a realization of the cohesions in a system with 200
elements with normal distributions. ......................................................... 121
Figure 6-14 Stress-strain curve in a test, parameters: η1r/k1=107, k3/k1=1, σp=1.2
MPa, σm=1.6 MPa: (a) Uniformly distributed cohesions (b) Normally
distributed cohesions. ............................................................................... 121
Figure 6-15 DRA curves for the multi-element model in the case in Figure 6-14:
(a) uniformly distributed cohesions (b) normally distributed
cohesions. ................................................................................................. 122
Figure 6-16 DRA curves for the multi-element model: (a) uniformly distributed
cohesions (b) normally distributed cohesions; η1r/k1=107, k3/k1=1,
σp=2.6 MPa, σm=2.8 MPa. ........................................................................ 123
Figure 6-17 Stress-strain curve: (a) uniformly distributed cohesions (b) normally
distributed cohesions; η1r/k1=106, k3/k1=1, σp=1.2 MPa, σm=1.6 MPa,
Tc=8σp/r, Td=0. ......................................................................................... 123
Figure 6-18 Influence of holding time on the DRA: (a) uniformly distributed
cohesions (b) normally distributed cohesions. The numbers in the
right parts of the plots are the ratios of Tc and σp/r (the time of the
preload); η1r/k1=106, k3/k1=1, σp=1.2 MPa, σm=1.6 MPa, Td=0. ............... 124
Figure 6-19 The memory fading in the DRA: (a) Uniformly distributed cohesions
(b) Normally distributed cohesions. The numbers in the right parts of
School of Civil and Resource Engineering The University of Western Australia
(xv)
the plots are the ratios of Tc and σp/r (the time of the preload).
η1r/k1=5×107, k3/k1=1, σp=1.2 MPa, σm=1.6 MPa, Td=0. .......................... 125
Figure 6-20 Stress-strain curve: (a) Uniformly distributed cohesions (b) normally
distributed cohesions; η1r/k1=106, k3/k1=1, σp=1.2 MPa, σm=1.6 MPa,
m=3, Td=0. ................................................................................................ 125
Figure 6-21 The memory fading effect in the DRA: The numbers in the right parts
of the plots are the ratios of the delay time and the time of the
preload. All parameters except m are the same as that in Figure 6-20. .... 126
Figure 6-22 Examples of MF: (a) the loading regime (b) the DRA curve: σp =
8MPa, τ0 is the holding time equal to 1 minute, τ is the delay time
(based on Ref. [113]). ............................................................................... 129
Figure 6-23 DRA curve for Inada Granite [126]. The upward arrows are labelled
by the authors in this paper. “Strain2-Strain1” presents the
differential strain between the first two measuring loadings. .................. 130
Figure 7-1 Loading process of pre-stress (1st cycle), 2nd and 3rd cycles. ...................... 135
Figure 7-2 Stress and strain curve. A black arrow shows a strain difference (Δεij)
under same stress. b): An inflection point which indicates PMS is
marked with arrow. ................................................................................... 136
Figure 7-3 The strain gauges A and C would have the same strain reading if the
non-parallelness is only in the B-D direction. .......................................... 137
Figure 7-4 Locations of the strain gauges on a sample. ................................................ 138
Figure 7-5 The bending effect created by: (a) unleveled bottom platform, (2) non-
parallelism of the sample ends, and/or (c) eccentric loading. .................. 139
Figure 7-6 The stress-strain plot of the aplite porphyry sample (H782 D2).
Considerable non-uniformity in the stress/strain distribution is seen
(bending level=13%). The axial strain is positive and lateral strain is
negative. ................................................................................................... 141
Figure 7-7 The stress-strain plot for a slate sample (PR2 D1). The axial strain is
positive and lateral strain is negative. ...................................................... 141
Figure 7-8 Sketch of the sample showing the strain gauge locations and orientation
with respect to the direction of foliation. ................................................. 142
School of Civil and Resource Engineering The University of Western Australia
(xvi)
Figure 7-9 The sample with co-ordinate frame (x, y, z). The z-axis is directed along
the axis of the sample, the x-axis runs through the pair of opposite
strain gauges. ............................................................................................ 143
Figure 7-10 The DRA curves with recognisable inflection points from individual
strain gauges located at 0°, 90° and 180° of aplite porphyry sample
H782 D2: (a) the original curves recorded form the strain gauges. The
inflection points are not consistent; (b) the curves corrected using
equation 8; the inflection points now indicate stresses close to the
pre-stresses. .............................................................................................. 144
Figure 7-11 Actual stresses calculated at the measurement locations using
equation 8 vs. the average stress. The pre-stress of 50MPa shall result
in the number of ‘recovered’ stresses from the DRA of strain
measurements at different strain gauges (shown by arrows). .................. 144
Figure 7-12 Actual stresses calculated at the measurement locations using
equation 8 vs. the average stress. The pre-stress of 38MPa shall result
in the number of ‘recovered’ stresses from the DRA of strain
measurements at different strain gauges (shown by arrows). .................. 145
Figure 7-13 The DRA curves of aplite porphyry sample H782 E2: (a) the original
curves recorded form the strain gauges. The inflection point in the
strain curve registered by strain gauge 270° is not identifiable. The
inflection points at other curves are not consistent; (b) the curves
corrected using equation 8; the inflection points now indicate stresses
close to the pre-stresses of 38MPa. .......................................................... 146
Figure 7-14 At the various bending levels, the standard deviation of the inflection
points in each aplite sample is reduced after the bending effect is
eliminated by the equation 8. ................................................................... 146
Figure 7-15 The pre-stress values inferred from identifiable DRA inflection
points: (a) before stress correction and (b) after stress correction. .......... 147
Figure 8-1 Locations of the strain gauges on a sample. ................................................ 150
Figure 8-2 (a) The average axial strain difference between 2nd and 3rd cycles from
an ultramafic rock (WA51B4) shows a memory of maximum stress
applied at 1st cycle. (b) The strain difference between 3rd and 4th
School of Civil and Resource Engineering The University of Western Australia
(xvii)
cycles from the same sample only shows an inflection point at
15MPa, which is the maximum stress at 2nd cycle. The maximum
stress at 1st cycle (5MPa) did not show any sign on the strain
difference curve. ....................................................................................... 152
Figure 8-3 (a) The ultramafic rock sample does not show a memory of most recent
stress (5MPa on 7th cycle), because the most recent stress is lower
than the PMS. (b) The felsic volcanics sample show a memory of the
most recent stress (10MPa on 4th cycle), even the most recent stress is
lower than the PMS. ................................................................................. 153
Figure 8-4 The volcanic sediment sample does not have a detectable memory of
most recent stress (7MPa at (a) and 20MPa at (b)). ................................. 154
School of Civil and Resource Engineering The University of Western Australia
1
CHAPTER 1. INTRODUCTION
1.1 THE IN SITU STRESS MEASUREMENTS
1.1.1 The sources of stress in the rock
The distribution of internal forces, the stress field, can be described by magnitude and
orientation components. The stress field in the underground rock mass is generated
mainly by three sources: gravity, tectonic movement, and the change in
chemical/physical in the material/environment.
The gravity of earth creates gravitational stress through the weight of overburden
(geological materials). The gravitational stress at the vertical direction is usually
calculated by average density and depth of rock mass (Equation 1). It is also called
overburden stress. The gravitational stress at the horizontal direction in an isotropic
elastic rock mass is calculated by density, depth and Poisson’s ratio (Equation 2).
(1)
, (2)
Where is the overburden stress, is density, is the depth below surface, is the
horizontal stress and v is Poisson’s ratio
Because the gravitational stress is usually calculated from the average density of rock
mass, in the highly foliated rock or heterogeneous rock mass the estimated stress could
sometimes be far from the in situ stress. On top of non-homogeneity and discontinuity,
the other two sources of underground stress, tectonic movement, and the change in
chemical/physical in the material/environment, can considerably affect the stress field.
The tectonic stress comes from boundary and body forces of the plates, for example slab
pull, ridge push, trench suction, and/or collisional resistance. At the large (tectonic)
scale, the stress generally is acting on one direction. However, due to the local lithology,
surface topography, geological structure/discontinuity, and geometry of rock formation,
the local tectonic stress can be very different in terms of magnitude or orientation.
School of Civil and Resource Engineering The University of Western Australia
2
The residual stress comes from chemical processes and phase transformations in the
rock. For example, the sedimentary rock was made by the deposition of material at the
earth’s surface. The deposition of material was gathered by wind, water, or gravity; then
it was compressed, cemented or heated and form a sedimentary rock. The process of
forming a sedimentary rock might include the pressure change, temperature change and
the chemical change in the composition of material. The heat-induced stress, mineral
expansion/shrinkage due to chemical alteration, or cementation under stress can create
internal stress, which is stored by the rock. The same process happened in the
metamorphic rock can sometimes cause enormous residual stress, especially in the
mountain building process. The interactions between plates can lift rock from few
kilometres underground to earth’s surface in a very short geological period, and it
results in high residual stress. In the igneous rock the primary source of residual stress is
the phase transformation in the process of rock crystallisation.
Other than the original stresses mentioned above, there is induced stress associated with
stress redistribution. An underground opening can locally disturb the stress field of
original stresses and result in induced stress. The magnitude/orientation of the induced
stress depends on the stress field of original stress and the location/geometry/dimension
of the opening. Blasting can also cause induced stress to the area where the seismic
wave has been. The distribution of blasting-induced stress is also relevant to the original
stress.
1.1.2 The importance of understanding the stress field
Knowledge of the in situ stress is critical for stable design of excavations, slopes,
tunnels, drilling, and underground storage. It is also important to the numerical
modelling where deformation is considered. The high stress field in the rock might
introduce borehole breakouts, rock burst, slope failure or failure in underground
excavations. High stress ratio between three principal stress components could create
very high/low stress concentration on the rock mass near underground opening/pillar
and causes rock failure. Hence, the stress field underground is one of the main
parameters that control the stability of any construction, which requires deep
excavation.
School of Civil and Resource Engineering The University of Western Australia
3
The information about in situ stress is also essential to control the fracturing process. In
the block caving, one needs to consider the magnitude/orientation of the in situ stress to
design an efficient blasting pattern. In the oil and gas industry, in situ stress is a factor
for prediction of the fracture dimension/location in the blasting process.
1.1.3 The in situ stress measurement techniques: The stress relief methods and
the stress compensation methods
The conventional in situ stress measurement techniques can be classified to four groups.
The first group is the stress relief methods. These methods utilise the strains caused by
the stress relief when part of the stressed rock was removed. It includes the Overcoring
method, the Door stopper method, and the Linear variable differential transformer
method.
The second group comprises the stress compensation methods. This method applies
pressure on the opening to restore the position of rock before the opening was made. It
includes the Flat jack method and the Cylindrical jack method.
These methods generally require an underground opening and service of a drilling crew
in the target location. After installing the measuring cell with the strain gauges attached,
a logging machine will record the strain response before removing part of the stressed
rock until there is no change in the strain. It usually takes a day or two to finish one test.
Then, the data will be analysed and the in situ stress will be calculated according to the
modulus of rock. The methods in these two groups have been developed for long time in
the past and they are generally well accepted worldwide.
The disadvantages of these methods are (1) they require underground opening/access;
(2) they are expensive; and (3) possible locations and orientations of the measurement
unit are limited. The installation of the instrument must be carried out on the wall of an
underground opening. The design personnel would not have the in situ stress
information until the opening/access reaches the target depth. Hence, the opening/access
to the target depth has to be designed without the information of current stress field. The
mine planning would not accommodate the potential failure of the infrastructure
associated with current stress field.
School of Civil and Resource Engineering The University of Western Australia
4
In terms of cost, it is expensive to have a drilling crew and a stress measuring crew
together in an underground opening for a day or two. The high cost of stress
measurement makes some small mining companies have their mines designed either
with the stress measurements confined to only few locations or without any
measurements at all.
Since the measurements must be carried out from the wall of an underground opening,
the heterogeneity could introduce errors to the measurement. The reason characteristic
to most mineral resources is that they are located in unusual geological environments
where the local tectonic forces have generated the conditions for mineralization to be
concentrated. As a result, the mining sites have a high chance of encountering a highly
heterogeneous rock mass.
The stress relief methods and stress compensation methods calculate the in situ stress by
recording the magnitude of strain change after overcoring process/applied stress. Then
the rock sample removed from the spot is compressed in a laboratory uniaxially in order
to calculate the modulus of the rock so the change in strain can be converted to stress.
Since the modulus of the rock is one of the key components to analysis in situ stress, the
lack of information on the anisotropy of the moduli might increase the error of in situ
stress reconstruction. Dight and Dyskin [1] showed the effect of rock mass anisotropy in
Hollow Inclusion cell (HI cell, CSIRO, NZ) stress measurement. In our own experience,
it is not unusual that the maximum and minimum moduli of a same rock sample in
different orientation have two times difference in magnitudes. Regardless of the various
moduli to different orientations, crack/ pore closure, crack opening, creeping and/ or
friction also cause the change of modulus under different stress level. Many of our rock
samples show more than 20GPa changes in tangent moduli from low to high stress
level. In this case the modulus of rock would be difficult to determine.
1.1.4 The in situ stress measurement techniques: The fracture/damage
evolution methods
The fracture/damage evolution methods include the Borehole breakouts method, the
Core disking method and the Hydraulic fracture method. They require an observation of
the damage in the opening/hole/core made in stressed rock. The damage is more likely
to be observed in deep boreholes or rock cores from deep boreholes. The borehole
School of Civil and Resource Engineering The University of Western Australia
5
breakout is a phenomenon of spalling or sloughing around the hole caused by the
induced stress on the wall of a borehole. The breakouts are usually oriented towards the
secondary principal stress acting in the plane normal to the borehole axis. It can provide
a good indication of the orientations of in situ stress, rather than a precise magnitude.
However, the heterogeneity/foliation of rock can introduce errors to the interpretation of
stress orientation.
Core disking usually occurs in brittle rocks at great depth. The thickness of the disk
indicates the magnitude of in situ stress. However, the properties of rock and
type/technique of drilling can greatly affect the occurrence and thickness of disks. It is
not a robust method to find the magnitudes of in situ stress.
The Hydraulic fracture method involves pressurising a borehole until rock fractures.
The water (or fracturing fluid) pressure required to break the rock provides one
condition connecting the horizontal components of in situ stress. Another condition is
provided by the shut-in pressure. Vertical boreholes are usually used in this method and
it is assumed that one of the principal stresses should be vertical or parallel to the axis of
the borehole. The borehole is inspected using a television camera after the test, in order
to determine the orientation of the induced fracture and thus the orientation of the
horizontal stress components. The hydraulic fracture method has been studied and
developed since 1960s. It is a well-established method and worldwide accepted for
determining the in situ stress. However, it is expensive and required an experienced
interpreter for good result. It is also more suitable for non-porous rock than for porous
rock, because the pore pressure might influence the stress result.
1.1.5 The in situ stress measurement techniques: Rock memory methods
It is assumed that a rock sample removed from the rock mass would “remember” the
original stress condition and present the memory of in situ stress in its deformation
behaviour or acoustic emission response. The methods of extracting memory of rock are
inelastic strain recovery (ASR) method, differential strain curve analysis (DSCA),
deformation rate analysis (DRA), and acoustic emission (Kaiser effect) method. These
methods utilize the rock cores to determine the in situ stress. Because the cores are
usually bi-products of exploration drilling and an independent access to underground is
School of Civil and Resource Engineering The University of Western Australia
6
not necessary, these methods are generally attractive with respect to the cost and
flexibility.
The ASR method determines the in situ stress by analysing the stress-strain curve
measured from loading an oriented core in the laboratory. The interpretation is difficult
and there are many factors which can affect the accuracy of result [1] and make the
method impractical. The DSCA method tests a cubical sample cut out from an oriented
core. The sample is loaded by hydrostatic stress and the strass-strain curves are used to
determine the stress when all crack closure processes were finished. The method has not
been widely used and the interpretation/quality of the result is dependant to the
experience of the interpreter.
Acoustic emission (AE) method and deformation rate analysis (DRA) method were
proposed and started using for the in situ stress measurements in early 1990s. The main
advantage of AE method is that it does not require the information on strain or any
deformation property; hence, it is free from the influence of heterogeneity. An
additional bonus is that AE method is relatively cheap as it does not require the use of
disposable strain gauges.
DRA method only requires the strain data from two uniaxial loading cycles in order to
utilize the inelastic properties of rock, and the rock sample can be tested in any
orientation in laboratory. DRA technique avoids the error introduced by limitation of
test orientation and the varied moduli. It has a potential to be an alternative in situ stress
measurement in anisotropic environments.
Although the acoustic emission method and DRA method are attractive in terms of cost
and flexibility, they are new compared with other well-established methods and a lot of
research is still required to improve the understanding of the methods. We have chosen
these two methods as potential methods for in situ stress measurement and conducted a
series of study to understand the mechanism/limitation behind these two methods. The
experiments in this thesis were designed to examine the reliability of DRA and acoustic
emission methods on recovering both laboratory applied stress and in situ stress.
School of Civil and Resource Engineering The University of Western Australia
7
1.2 THE ACOUSTIC EMISSION METHOD OF REVEALING
THE ROCK MEMORY
1.2.1 Background
The phenomenon associated with the Kaiser effect in uniaxial compression test is
illustrated in Figure 1-1. It was experimentally demonstrated that the acoustic emission
produced in the material under repeated loading has a specific feature whereby the
acoustic emission activity is zero or close to background level when the stress
magnitude of the repeated load remains below the previously attained maximum stress.
This is the nature of so-called Kaiser effect, firstly discovered by Kaiser [2] in metals
(tested under tension) and then confirmed in rocks [3] (tested under compression).
Figure 1-1 Kaiser effect in materials and rocks under compression: (a) the loading cycles, (b)
cumulative acoustic emission activities corresponding to these loading cycles [4].
1.2.2 The origin and original description of the Kaiser effect
Kaiser [2] had tested metal specimens in order to study the behaviours of metal
materials under mechanical tensile stress. His most important finding is his acoustic
sound emission-measurements (ASE-measurement) in the area of non-destructive
material tests and the core of the Kaiser effect. In 1957, Kaiser officially handed his
work to Tensi. In Tensi’s doctoral thesis which he included in [2], he described: the
ASE and the stress as functions against the elongation for a tensile test specimen, which
School of Civil and Resource Engineering The University of Western Australia
8
has already been loaded up to point “Z” shows a sudden ASE increasing upon passing
the previous load can be recognised (Figure 1-2). The regions in the stress vs.
elongation diagram where the Kaiser effect is used are shown in Figure 1-3.
Figure 1-2 Stress-strain curve and acoustic emission intensity of a soft-annealed steel probe with
0.15 weight% carbon under tensile stress. The sample was subjected to tensile stress to cause
elongation up to point Z previously. Then, the sample was reloaded. The ASE intensity shows the
Kaiser effect after the specimen is relaxed followed by re-applying tensile stress to exceed the
previous maximum elongation (after [2]).
Figure 1-3 The elongation area which Kaiser effect exists and was studied by Tensi and Kaiser
(after [2]).
School of Civil and Resource Engineering The University of Western Australia
9
1.3 THE DIFFICULTIES OF USING KAISER EFFECT FOR
STRESS MEASUREMENTS
1.3.1 Influence of damage accumulation in high stress region
Although the Kaiser effect was originally found in metal during “necking” deformation
under tension that is under the ultimate tensile strength but higher than the yield
strength, Kurita [5] believed this phenomenon was appealed in Goodman’s test results
(Figure 1-4) under uniaxial compression test. Kurita tested cored granite samples under
compressive stress and concluded the Kaiser effect is an indicator of previous maximum
stress (PMS) if the PMS is lower than the onset of dilatancy. He pointed out that once
the applied stress is higher than the onset of dilatancy, the acoustic emission activities
increase dramatically, regardless to the magnitude of PMS. The differences in the
observation of Kaiser effect between Kurita and Tensi are listed in Table 1.
Figure 1-4 Acoustic emission activity patterns in rock. Relative acoustic emission signal’s rate
indicated by spacing of horizontal lines at the corresponding stress level: (a) AE activity during the
first of a series of tests; (b) AE activity after numerous cycles of loading and unloading (after [3]).
(a) (b)
School of Civil and Resource Engineering The University of Western Australia
10
Table 1 The differences of test condition when observing the Kaiser effect
Tensi [2] Kurita [5] Loading type Tensile test Compression test Area of Kaiser effect can be found
Above yield stress
Lower than the onset of dilatancy
Material Metal Rock
Table 1 shows that regardless of the type of test (tensile or compressive), the most
methods of finding PMS by the acoustic emission, including the ISRM suggested
method [6] do not consider whether PMS is lower than the onset of dilatancy. Hence, in
order to understand the Kiser effect at high stress, we studied the influence of damage
accumulation to the observation of Kaiser effect in Chapter 3.
1.3.2 The mechanism of Kaiser effect in low stress region
Other than the influence of damage accumulation, there are other factors that could
affect the stress determination by the Kaiser effect. These are: the time gap between
applied stress (in laboratory)/recovering sample (in situ) and conducting the AE test, the
heat generated by drilling, the water contain, the loading rate, the stress memory under
triaxial stress state and the rock type. One of these issues on which we concentrate here
is the background noise [4] causing the appearance of acoustic emission at low stress to
strength levels.
The source of acoustic emission under compression is traditionally assumed to be either
the generation of new cracks or the extension of pre-existing cracks [3, 5, 7-42]. It is
believed that the onset of this mechanism coincides with the onset of dilatancy [43-47],
which corresponds to the compressive stress magnitudes above 20% (20-30% [48], 40%
[43-45, 47, 49-54], or 50-70% [54] ) of the UCS. However, this hypothesis contradicts
Kurita’s claim: the Kaiser effect cannot indicate the PMS when PMS is higher than the
onset of dilatancy. And there is experimental evidence suggesting that the acoustic
emission starts earlier, at much lower stress to strength levels.
For example Table 2 shows the results from Seto et al [55]. The sandstone samples were
rectangular with dimensions of 30 x 30x 60mm (length), and were tested at a loading
rate of 0.6MPa/min. The coal samples were 105 x 105 x 110mm and were tested at a
School of Civil and Resource Engineering The University of Western Australia
11
loading rate of 0.1mm/min. Seto et al [55] compared test results with either lab pre-
stress or in situ stress and believed the Kaiser effect is a good indicator for in situ stress
measurement. According to the percentage of PMS/UCS we have calculated and listed
in Table 2, the Kaiser effect is able to predict the lab pre-stress at the stress range from
5% to 18% of UCS, where the stress is insufficient to create/extend cracks. It is also
able to predict the in situ stress at the stress range of 1% to 33%.
Table 2 The result of [55] using the Kaiser effect to find PMS by four acoustic emission sensors
(5mm in diameter and 200k - 550k gain). The numbers estimated by us from the graphs in the
paper were marked in red. The numbers mentioned in the descriptions or tables in the paper were
marked in black. The in situ stress was calculated from overburden stress, HI cell or hydraulic
fracture result.
No. Material and sample ID
UCS (MPa)
Sample depth below
surface (m)
Pre-stress (P) or In situ Stress (I)
(MPa)
Estimated stress by the AE method
(MPa)
PMS/UCS (%)
1 Granite -Inada 185 N/A P 10 10 5
2 Sandstone Coal 32 10-360 P 5.7 5.6 18
3 Granite -Inada 185 N/A P 20.44 20.3 11
4 Sandstone Shirahama (6 samples)
60 N/A P 10 Claimed close to 10
17
7 Sandstone Coal A 32 356 I 8.5 9.2 27
8 Sandstone Coal A 32 Around 100
I 2.8 Around 3 9
9 Sandstone Coal A 32 Around 200
I 5.6 Around 5.6 18
10 Sandstone Coal B 32 301 I 7.4 9 23
11 Sandstone Coal B 32 310 I 7.7 9.5 24
12 Sandstone Coal B 32 Around 100
I 2.8 Around 2.4 9
13 Sandstone Coal B 32 Around 200
I 5.6 Around 4.8 18
15 Granite C G4-1 185 159 I 2.73 1.96 1
16 Granite C 185 117-173 I 2-3 Claimed close to in situ stress
1
17 Core D 32 N/A I 10.5 9.3 33
Besides Seto’s et al [55] results, there is also experimental evidence suggesting that the
acoustic emission starts at the stress less than 20% of the UCS or less than 20% of
School of Civil and Resource Engineering The University of Western Australia
12
maximum applied stress when the UCS is unknown. Boyce et al [56] hypothesised that
the early acoustic emission signals in the low stress region was created by the crack
closure in compression, Figure 1-5. In order to understand the mechanism that produce
the Kaiser effect at the stress lower than the onset of dilatancy, We analysed and
conducted a series of tests to clarify the source of acoustic pulse at low stress, and the
detectability of Kaiser effect when crack growth is absent in the Chapter 2.
Figure 1-5 The stress versus acoustic emission signature and possible relationship to mechanisms of
brittle rock fracture (after [56])
1.4 AN ALTERNATIVE METHOD OF REVEALING ROCK
MEMORY: THE DEFORMATION RATE ANALYSIS
1.4.1 Background
In 1990, Yamamoto et al. [57] demonstrated the approach of DRA technique detected
the previous applied stress. The approach is based on examining the inelastic strain
between two successive loading cycles in a uniaxial test. The loading process is shown
School of Civil and Resource Engineering The University of Western Australia
13
in Figure 1-6. The pre-stress (1st cycle) is the maximum previous stress that the
specimen has been subjected (PMS). The 2nd and 3rd cycles are the loading cycles
applied after the pre-stress, in order to produce the DRA graph. The time gap between
the 1st (pre-stress) and 2nd cycle is the delay time. The difference of strain between 2nd
and 3rd cycles is shown in Figure 1-7a. The difference of strain can be expressed by
equation 3. In Figure 1-7b, the maximum gradient change in the strain difference versus
stress graph is called the inflection point. The inflection point is corresponding to the
maximum previous stress.
ijijij (3)
Figure 1-6 Loading process of pre-stress (1st cycle), 2nd and 3rd cycles.
Figure 1-7 a): Stress and strain curve. A black arrow shows a strain difference (Δεij) under same
stress. b): An inflection point which indicates PMS (previous maximum stress) is marked with
arrow.
stre
ss
time
Loading process prestress
1st cycle
2nd cycle
stre
ss
strain
Stress-strain curve
prestress
1st cycle
2nd cycle stra
in d
iffe
renc
e
stress
DRA
School of Civil and Resource Engineering The University of Western Australia
14
1.4.2 Previous studies and unsolved problems
In 1991 and 1992, Tamaki et al. [58] and Tamaki and Yamamoto [59] proposed a
hypothesis for stress memory in rock. Rocks are aggregate of different minerals, which
have different elastic modulus. Due to varying modulus properties of each mineral
component in rocks, uniform deformation applied over rocks will not result in a uniform
stress distribution. Tamaki et al. [58] and Tamaki and Yamamoto [59] assumed that the
non-uniform deformation between each mineral eases after long time under in situ
stress. After recovering a sample from borehole, the inelastic strain caused by non-
uniform stress is still small until the applied stress becomes larger than in situ stress.
Therefore, the gradient change in stress-strain curve will take place at the level of in situ
stress. They had concluded that DRA technique is able to estimate in situ stress.
However, rock with weak strength might develop inelastic strain which is unrelated to
in situ stress. This unwanted inelastic strain contaminates the measurement. They did
not address whether the inelastic strain is from enlarging of the cracks, new cracks
generating or other reasons.
In 1994, Yamshchikov and Shkuratnik [60] reviewed the deformation memory effect
which can be interpreted from stress-strain curves, including DRA. They concluded that
majority of the investigators considered the occurrence and development of defects in
various scales in rock are the mechanisms of deformation memory. However, they
suggested that occurrence and development of cracks cannot fully explain all
phenomena, because of the loss of memory.
In 1995, Shin and Kanagawa [61] had conducted experiment which showed the
relationship between the change amount of P-wave velocity and the DRA. The result
shows that P-wave velocity changes more after pre-stress during loading, while the
DRA also shows inflection point at the pre-stress level. The results of testing samples
with lateral pressure show that the lateral stress/confinement has no or little influence to
the axial pre-stress detected by DRA.
Also in 1995, Yamamoto [62] proposed a new hypothesis of mechanism based on the
crack porosity/volume. The crack porosity increases with an increase of sampling depth,
because the non-uniform expansion produced by the mineral components occurs when
rock core was drilled out. The rock expands after stress releases and the crack porosity
School of Civil and Resource Engineering The University of Western Australia
15
increases. The rate of inelastic strain increase from crack porosity will rise when applied
stress exceeds the in situ stress and stress non-uniformity increases. In this hypothesis
the increase in the existing crack volume is the mechanism of stress memory, while new
crack generation is not mentioned. Although a possible mechanism was proposed,
Yamamoto [62] suggested this hypothesis could not explain the rock memory
repeatedly observed by repeating loading.
In 1997, Utagawa et al. [63] had conducted some DRA experiment in order to
investigate the influence of delay time, loading rate and stress in orthogonal direction.
He concluded that memory becomes less pronounced or lost altogether with longer
delay time. The influence of loading rate is insignificant. In contrast with Shin and
Kanagawa [61] , Utagawa et al. [63] believed that both axial pre-stress and lateral pre-
stress can be recovered from the DRA results when sample was subjected to stress
uniaxially. From their conclusion, they considered DRA as a useful technique to
estimate the initial stress, such as the in situ stress.
We should note however that if the magnitude of in-situ stress estimated through DRA
is not just derived solely from the sample’s axial loading direction, but is also
influenced by stresses in the orthogonal direction, DRA will be unreliable. Indeed, the
stress at orthogonal direction (the lateral confinement) influences the stress-strain curve,
therefore the stress value indicated by the inflection point can be influenced as well.
Another difficulty comes from the fact that the lateral stress in situ might not be known
beforehand.Furthermore, we cannot find the inflection point in the stress-strain curves
with the stress that Utagawa et al. [63] applied at the orthogonal direction.
In 1999, Seto et al. [31] supported the idea that DRA method is similar to acoustic
emission method in the way that both methods utilize the Kaiser effect. They believed
the growth of pre-existing cracks and new crack generation should happen particularly
when the applied stress exceeds the peak value of the previous stress. Therefore,
changes in density and/or size of cracks are the source of irreversible inelastic strain.
Seto et al. [31] also claimed that the confining stress – the stress in orthogonal direction
– is hard to determine from the results obtained from loading sample uniaxially. This
can be confirmed from the DRA result graphs they presented. The influence of
orthogonal stress on the DRA result that Utagawa et al. [63] had suggested was not
School of Civil and Resource Engineering The University of Western Australia
16
observed. The influence of delay time between applied pre-stress in lab and measuring
by DRA was also considered as insignificant. The memory lasts for at least 7 years.
This is also different from the observation from Utagawa et al. [63].
The results by Seto et al. [31] suggesting that the memory still holds after 7 years delay
time are from the Inada granite and Shirahama sandstone. The delay time reported is
very long, much longer than reported in other studies.
Furthermore, Seto’s et al. [31] DRA result for granite is from the strain difference
between 5th and 1st cycles, and for sandstone is from the strain difference between 5th
and 2nd cycles. If DRA phenomenon is based on new cracks generating by stress, any
loading to the same stress as the PMS should produce none or very few new cracks.
Therefore there should be no strain difference between 5th and 2nd cycles. Seto et al. [31]
had explained that instead of using the strain difference between 1st and 2nd reloading
cycles, it is sometimes clearer (larger strain difference) to use the strain from 3rd, 4th or
5th cycle. From the crack mechanism point of view, the DRA should be only able to
detect PMS. It is hard to explain why the strain difference between 5th 2nd cycles can
predict lab pre-stress more clearly when 1st to 5th loading cycles were all subjected to
same stress.
In 2001, Yamamoto and Yabe [64] followed the concept that the mechanisms of Kaiser
effect should be different from the mechanism of deformation rate effect, although these
two mechanisms may have some resemblance parts. They applied DRA technique on
some in situ stress measurements near Nojima fault and believed the result is
reasonable.
In 2002, Yamamoto et al. [65] had published the experiment results on measuring in situ
stress by DRA. They confirmed the idea from [62]: the property of in-situ stress
memory is explained by assuming that stress field in rock is mostly uniform in situ.
However, they claimed that the mechanism of in situ stress memory should be
discriminated from the Kaiser effect, which was mainly believed to be due to generation
of cracks.
In 2002, Villaescusa et al. [32] used the DRA for in situ stress measurements in 4
mines. The results of DRA method were compared with the results from HI cell tests in
same mines and it was found that the results correspond to each other. Villaescusa et al.
School of Civil and Resource Engineering The University of Western Australia
17
[32] agreed with Seto et al. [31] that the source of inelastic strain is from the new crack
generation or existing crack growth.
In 2003, Hunt et al., [26] had employed the discrete element package PFC 2D for
creating a synthetic sample and simulated the uniaxial compression tests. They assumed
DRA and acoustic emission is due to the interaction of microcracks and both methods
utilize the Kaiser effect. They compared the numerical results with laboratory
observations and concluded that the link between the Kaiser effect/ DRA and
development of microcracks was established.
There are however two questions Hunt et al., [26] did not answer. First, the memory
fading is observed in experiments, while the microcracks are not likely to heal in such a
short time span. Second, the internal damage is known to occur after at least 20-60% of
UCS. The contact-bond normal strength range in the discrete element method will be
expected to be higher than 20% of UCS instead or random distribution from 1-99% of
UCS.
In the same year, Hunt et al. [27] showed the result of the DRA reconstruction of the
pre-stress of 13% of UCS and confirmed the pre-stress can be detected by DRA method.
It is not clear though how new cracks could occur at only 13% of UCS without
producing dilatancy.
In 2006, Dight [66] pointed out that the results of DRA are free from the influence of
anisotropy and considered the DRA to be a Kaiser effect type phenomenon. He tested
and compared the in situ stress results of DRA method, Hydraulic fracture method and
HI cell method. He indicated that there were two inflection points in DRA graph and
one of the inflection points coincided with the current in situ stress, while another point
coincided with the PMS that was applied previously in the lab tests. Therefore, the rock
has memory of more than one previous stress it has been subjected to. After recovering
stresses in different directions and calculating the stress tensor, Dight [66] found that the
maximum, median and minimum stresses by DRA are similar with results from
Hydraulic fracture and HI cell.
In 2006, Louchnikov et al. [30] considered how the DRA relates to the Kaiser effect. A
discrete element model was built to investigate the influence of confining stress. They
believed that the DRA is caused by new crack generation; therefore, the crack initiation
School of Civil and Resource Engineering The University of Western Australia
18
threshold was set low. They concluded that the confining stress has a significant effect
on DRA. However, from their numerical results, there were microcracks generating
during unloading, and microcrack quantity during loading is directly related to the crack
initiation threshold. We note that the crack initiation thresholds were different in each
test, which affected the results significantly stronger than few microcracks induced by
the confining stress.
In 2007, Cheng [25] conducted experiments on black schist. When the lab-applied stress
was 70% of UCS, he found the delay time would reduce the stress that inflection point
indicates. It had no influence though on the inflection point when the pre-stress was
30% of UCS. It should however be noted that each sample underwent up to 1000 pre-
stressing cycles. Because each cycle involved loading the sample up to 70% UCS, it is
plausible that cumulative damage on the sample may have occurred. If the UCS is
reduced after loading, the unwanted non-elastic deformation might alter the inflection
point. Therefore, inflection points occur at lower stress.
In 2008, Chan [28] studied the rock memory in sandstone. He pre-loaded each sample
500 times. He concluded that if the delay time was within 14 days, its influence on the
DRA result is not significant. From his result graphs, there is no inflection point when
pre-stress is higher than 70% of UCS. This agrees with and explains Cheng’s [25]
observation: cumulative damages from huge amount of repeated pre-stress might erase
the memory due to accumulation of fatigue cracks or damage.
In 2010, Xie et al. [67] estimated the in situ stress in shale by DRA. They agreed that
DRA could indicate in situ stress. However, the results from acoustic emission
measurements they conducted on the same sample (i.e. the sample where they measured
AE and DRA together) show different magnitude of in situ stress. There are no
independent in situ stress measurements to compare the stress predictions of DRA and
acoustic emission. Hence, it is not clear why they believed that DRA could indicate in
situ stress.
In 2010, Fujii and Kondo [68] recovered the previous load using the changes in tangent
moduli instead of DRA inflection points. The change in tangent modulus is the reason
that causes the strain difference measured in the DRA. They loaded sample to 12MPa
for 1 day and then to 16MPa for 1 minute. The results showed that the inflection points
School of Civil and Resource Engineering The University of Western Australia
19
indicated 16MPa when the delay time was less than 1 hour, and 12MPa when delay time
was longer than 1 hour. They suggested this result could support the fact that in situ
stress might create a long term memory in rock, and the memory could be recovered
when the rock core was extracted and left relax for long time before conducting the
DRA test. They assumed the mechanism causing a change in the modulus was the
void/crack closure, since the pre-stress was only 30% and 40% of UCS.
Based on above papers we can conclude that most of the above authors consider the
phenomenon of DRA being caused by the crack growth/extension and one paper
suggests the crack/void closure. Some papers do not discuss the mechanism. The
summary of papers which have mentioned the mechanism/phenomenon of deformation
rate effect is shown in Table 3.
School of Civil and Resource Engineering The University of Western Australia
20
Table 3 The main claims and problems in the literatures.
School of Civil and Resource Engineering The University of Western Australia
21
Time/first
author
Mechanism and/or observation Our/author’s commends
1991, 1992/
Tamaki
Mechanism of deformation rate effect relates to
the stress field in rock in situ/after extracting
from in situ
Require further work to confirm the
hypothesis
1994/
Yamshchikov
The mechanism of deformation rate effect is
the occurrence and development of defects in
various scales
Cannot explain memory fading
1995/
Shin
The orthogonal stress has no or little influence
to the axial pre-stress detected by DRA
Require further work to confirm
1995/
Yamamoto
Mechanism of deformation rate effect is the
change in crack porosity/volume
Cannot explain the memory is
repeatedly observed by repeating
loading
1997/
Utagawa
Both axial and orthogonal stresses can be
predicted by DRA
The graphs does not show his claim
1999/
Seto
The orthogonal stress cannot be seen from
DRA graph. The memory can last at least 7
years
The DRA graph of first two cycles
after pre-stress disagrees his claim
2002/
Yamamoto
Mechanism of deformation rate effect relates to
the stress field in rock in situ/after extracting
from in situ
Require further work to confirm the
hypothesis
2002/
Villaescusa
Mechanism of deformation rate effect is new
crack generation or existing crack enlargements
Cannot explain DRA at low stress
2003/
Hunt
Mechanism of deformation rate effect is the
interaction of microcracks
Cannot explain memory fading
2006/
Dight
DRA can record more than one pre-stress. Require experimental work (i.e. two
laboratory pre-stresses) to confirm
2006/
Louchnikov
Using numerical model to prove the mechanism
of deformation rate effect is crack
growth/extension
DRA would not be able to predict the
pre-stress below crack initiation
thresholds.
2007/
Cheng
The delay time increased the error of DRA
prediction when pre-stress >70% of UCS
The rock structure is possible to
change after 1000 times pre-stress
which is 70% of UCS
2008/
Chan
No DRA when pre-stress >70% of UCS The UCS of fresh sample is expected
to be higher than the same sample
with 500 times of pre-stress.
2010/
Xie
DRA can predict in situ stress The result does not seen to be
successful.
School of Civil and Resource Engineering The University of Western Australia
22
2010/
Fujii
Mechanism of deformation rate effect is
void/crack closure
Void/crack without friction should
re-open during unloading
1.5 THE DIFFICULTIES IN USING THE DRA METHOD
1.5.1 The source of strain difference between two cycles
Despite the phenomenon of memory fading and the influence of confinement, the main
issue of DRA is that crack theory cannot explain the memory happened under 20% of
UCS or before occurrence of dilatancy. Many tests in the literary review were
conducted with the pre-stress less than 20% of UCS, i.e. at the stress levels when the
cracks were not expected to appear/grow, yet the DRA showed no issue with recovering
the pre-stress. There could be only two explanations for that: either stress which is less
than 20% of UCS can still generate new cracks, or there is another mechanism which
can produce memory shown in strain.
Since the onset of dilatancy is believed to correspond to the compressive stress
magnitudes above 20% (20-30% [48], 40% [43-45, 47, 49-54], or 50-70% [54] ) of the
UCS, we believe there is a mechanism other than crack growth/extension can produce
memory shown in DRA method. The cause of strain difference between two cycles is
due to the tangent moduli at two cycles are different from each other at same stress.
Hence, the first step to find the mechanism of deformation rate effect is to understand
the change in tangent moduli after repeated load. In order to study which mechanism
can cause a change in the stiffness after loading, we analysed the occurrence of crack
closure, crack growth/extension, sliding and compaction at different stress level and
discuss the possibility to distinguish the source of inelastic strain from total strain. We
also study the relationship between residual strain and the change in moduli, in order to
find an indicator that is relevant to the change in the moduli after repeated load. The
result is shown in Chapter 4. The mechanism of the deformation rate effect at low stress
is addressed in Chapter 5 and Chapter 6.
1.5.2 Effect of sample bending
Another issue related with the use of the DRA is the quality of data. In the uniaxial
compression tests, when the sample ends are not exactly parallel and the loading is not
perfectly coaxial sample bending can be induced. Because the DRA methods require
School of Civil and Resource Engineering The University of Western Australia
23
applying load to a sample uniaxially, the stress/strain non-uniformity at the scale of the
sample caused by bending can introduce errors to the stress reconstruction. We discuss
the source and the phenomenon of bending, and provide a compensation formula to
reduce the error in DRA prediction in Chapter 7.
1.5.3 The influence of stress applied earlier than pre-stress
It was proposed in [69] that the mechanism of the rock memory detectable by the DRA
is based on frictional sliding. The mechanism of frictional sliding is able to explain the
fact that DRA can predict the pre-stress under 20% of UCS. However, it brings to our
attention that all the proposed mechanisms behind the DRA (i.e. crack activity,
ununiformed stress field, and frictional sliding) can only record the maximum stress the
sample has been subjected to. Hence, if a sample was loaded under a stress of
magnitude of p, the sample would not able to predict any stress smaller than p.
Since all rock samples were under in situ stress when they were underground, a rock
sample is not supposed to show the inflection point of lab pre-stress if the pre-stress is
smaller than the in situ stress. However, we have not seen a case in the literature that
DRA cannot predict the pre-stress applied in laboratory. It might be that: (1) the DRA
method can predict more than one previous stress, (2) the pre-stress applied in
laboratory was higher than the in situ stress, (3) the rock sample loses its memory very
fast, or (4) the mechanism of in situ stress memory recorded by DRA is different from
the mechanism of laboratory pre-stress.
We designed a series of experimental tests on ultramafic rock volcanic sediment and
felsic volcanics samples to investigate whether: (1) the DRA can recover the laboratory
pre-stress which is smaller than the in situ stress, (2) the DRA can predict two previous
stresses. The results are presented in Chapter 8.
1.6 RESEARCH OBJECTIVE, ORIGINALITY AND
SIGNIFICANCE
The in situ state of stress in a rock mass is important for the underground constructions,
for examples mine layouts, stability of slope, underground waste storage etc. With the
information of the in situ stress magnitude and orientation, the risk of failure, the
potential failure location and mining method can be determined to make the design of
School of Civil and Resource Engineering The University of Western Australia
24
ground support/reinforcement safer and more cost effective. The better design/stability
in the underground construction also reduces the chance of failures that may affect the
productivity and cost life.
Currently the measurements of in situ stress are expensive. The worldwide-accepted
stress measurement methods like overcoring and hydraulic fracture methods are not
always affordable to small companies. These methods also require experienced
personnel to analyse the data for better result, and are sensitive to the heterogeneity of
rock. Hence, a low-cost, robust, and easy-operated stress measurement method is
desired by industry and the stress memory method was proposed. The Kaiser effect
method and the DRA method utilize the rock cores which were drilled for other
purposes to predict the previous maximum stress. They are relevantly cheap compared
with other methods and they do not require the information of rock stiffness; hence,
they are free from the error introduced by the heterogeneity. These methods however
have not been sufficiently studied and a number of questions remained unanswered.
The objectives of the Kaiser effect research are to: (1) understand the mechanism of the
Kaiser effect under uniaxial compression test, (2) evaluate the reliability and the
feasibility of the Kaiser effect, and (3) investigate the factors that might influence/mask
the acoustic emission result in stress prediction. The originality of this part of the
research is evidenced by the fact that it seems to be reliable to recover laboratory
prestress by the Kaiser effect, but it is much more difficult to recover the in situ stress.
There is no existing work that discusses why the hypothesis of new crack generation
cannot explain the memory recovered by the Kaiser effect in the low stress to strength
region. There is also lack of information about the source of acoustic pules in the rock at
low stress. Although there is literature observing that the acoustic emission is created by
the new crack generation at the stage of dilatancy, there is no investigation on the
relation of the damage accumulation to the Kaiser effect. The significant benefit of this
research is that the potential factors that mislead the analysis of the Kaiser effect are
investigated and demonstrated. For the industry which considers the Kaiser effect for
their stress measurement work, this thesis provides a comprehensive review and study
on the reliability of the Kaiser effect.
School of Civil and Resource Engineering The University of Western Australia
25
The objectives of the DRA study are to understand the deformation behaviour of rock
and the phenomenon of DRA in different rocks/stress histories. The condition of sample
bending caused by the test frame or sample heterogeneity is also important to the
experimental work in the stress reconstruction. There is no existing work that discusses
the cases when the linear part of deformation in rock does not exist. The increase in the
stiffness of rock under repeated load in our observation also cannot be explained by the
conventional rock mechanics theory. The thesis provides evidence to support the fact
that crack closure, sliding and crack generation of different degrees could co-exist
within the same stress range. The existing approach [50] to find the modulus of
uncracked rock is not feasible. Another significant finding in this part is that the
nonlinear deformation contributed by irreversible sliding, compaction and dilatancy
increases the rock stiffness in the repeated loading. It is important in improving the
numerical modelling which deformation is essential to the analysis.
1.7 THESIS STRUCTURE
Chapter 1: Introduction
We introduce the demand of the in situ stress measurement, the advantage of the
alternative stress measurement methods, the unsolved issue and the methodology we
have applied to improve the understanding of the AE and DRA methods.
Chapter 2: The Kaiser effect at low stress
We firstly review the phenomenon that Kaiser has found and the development of using
Kaiser effect on in situ stress measurement. We describe special experiments we
performed to check the hypothesis of the effect of end conditions at low stresses. We
start with describing artificial samples made of aluminium where the contact surfaces
can be very smoothly machined and polished. We then proceed with samples made of
agate – these have chemical composition somewhat similar to rocks but are amorphous
and very homogeneous and then turn our attention to rock using sandstone as an
example. The analysis shows that the acoustic pulses at low stresses were caused by the
asperities/irregularities/residual material in a rock sample ends.
Chapter 3: The Kaiser effect at mid/high stress
School of Civil and Resource Engineering The University of Western Australia
26
In this chapter we describe a further study of acoustic emission at mid-high stress level.
We performed experiments to check the acoustic emission patterns on different rock
types, UCS, and modulus range when stress reach mid-high stress to strength level. We
then discuss the feasibility of using Kaiser effect when estimated stress is at mid-high
stress level.
Chapter 4: The tangent modulus and residual strain after applied stress under uniaxial
compression test
The DRA method utilises inelastic behaviour of rock deformation. In order to clarify the
foundamentals of the deformation rate analysis, we investigate the change in tangent
modulus under uniaxial load. We have studied the sources of nonlinear deformation in
hard rock under short term uniaxial compression test, and provided evidence to support
the fact that nonlinear deformation contributed by crack closure, sliding and compaction
in different degrees could co-exist within the same stress range. We demonstrate the
change in tangent modulus under different stress levels is attributable to the
combination of crack closure, sliding and dilatancy. Hence, the mechanism that changes
the tangent modulus after repeated load is not limited to the crack growth/extension at
mid/high stress.
Then, we investigate the behavior of rock under repeated uniaxial load. We have
performed a series of test to show the evidence of increased stiffness under repeated
load. The phenomenon of the modulus increase after loading is discussed and compare
with residual strain.
Chapter 5 and Chapter 6: The mechanism of the deformation memory effect and the
deformation rate analysis in the low stress region
In the chapter 5, a frictional sliding model as a new mechanism of the deformation rate
effect in layered rocks at the low stress is proposed. We propose a new theoretical
model which is symmetrical, based on frictional sliding at low stress region. The stress
memory recorded by the deformation that produces by a single basic rheological
element is discussed and the results of the models with two basic elements and multi
element are shown.
School of Civil and Resource Engineering The University of Western Australia
27
In the chapter 6, we firstly review the experimental results to find if the DRA method is
applicable in the low stress region. Then, a rheological and axisymetrical element with a
spring (the Hookean elastic body), Maxwell body and St. Venant (St. V) body is
developed to simulate frictional sliding over a single crack. The results of theoretical
model with multi elements is compared against the experimental results.
Chapter 7: The influence of sample bending on the DRA stress reconstruction
In this chapter we discuss and investigate two potential reasons for bending effect: (1)
the sample heterogeneity, and (2) the non-parallelness of the sample ends and non-
coaxiality of the applied load. The sample heterogeneity leads to the stress/strain non-
uniformity during loading. It can be improved by using larger gauge or more gauges in
different parts of sample. The non-parallelness of the sample ends and non-coaxiality of
the applied loading might not be easily fixed by adjusting the setting of the loading
frame. Hence, we describe the proposed compensation method to reduce the error of
bending effect caused by the non-parallelness of the sample ends and non-coaxiality of
the applied loading.
Chapter 8: The influence of stress applied earlier than pre-stress
We investigate the influence of in situ stress/previous laboratory applied stress to the
DRA method. The first step is to confirm whether the DRA method can recover the
laboratory stress that is lower than the in situ stress in a rock sample. The second step is
to find if the DRA method can recover two previous laboratory applied stress. We have
applied the different magnitudes of stress to the ultramafic rock, felsic volcanics and
volcanic sediment samples in different stress path sequence. The result is
discussed/compared against different rock types.
Chapter 9: Conclusions
Chapter 10: Recommendations for future research
Chapter 11: References
Appendix A
Appendix B
Appendix C
School of Civil and Resource Engineering The University of Western Australia
28
School of Civil and Resource Engineering The University of Western Australia
29
CHAPTER 2. THE KAISER EFFECT AT LOW STRESS:
GHOST KAISER EFFECT
2.1 ABSTRACT
A considerable body of research on determining the in situ stress measurement from
diamond drill core has relied on the Kaiser Effect. It seems to be reliable to recover
laboratory pre-stress however when used as a means of estimation of the in situ stress is
somehow much more difficult to achieve reliably. We have investigated the mechanism
of the Kaiser Effect from the literature and a hypothesis of the source of Kaiser Effect
was created and examined. The sample ends of 2 aluminium samples, 2 agate samples,
and 2 sandstone samples were specially machined and cleaned in order to create
different conditions in the contact surfaces between the sample and the platen. The
result shows that the free particles on the end of an aluminium sample, the asperities in
an agate sample, and the asperities/irregularities/residual material in a rock sample
provide a source of acoustic signals which manifest itself as the Kaiser effect at low
stress. The Kaiser effect created by the sample ends is not related to the rock memory
and it is an artefact of the test preparation.
2.2 INTRODUCTION
It was experimentally demonstrated that the acoustic emission produced in the material
under repeated loading has a specific feature whereby the acoustic emission activity is
zero or close to background level when the stress magnitude of the repeated load
remains below the previously attained maximum stress, Figure 2-1. This is the nature of
so-called Kaiser effect, firstly discovered by Kaiser [2] in metals (tested under tension)
and then confirmed in rocks [3].
School of Civil and Resource Engineering The University of Western Australia
30
Figure 2-1 Kaiser effect in materials and rocks under compression: (a) the loading cycles, (b)
cumulative acoustic emission activities corresponding to these loading cycles [4].
Since then a considerable body of research has been directed towards developing the
method of recovery of the maximum in situ stress using the Kaiser effect by testing
samples made from cores extracted from the locations of interest [4, 5, 7-11, 13-15, 17-
42, 55, 60, 61, 67, 70-96].
This method of in situ stress determination is based on undertaking laboratory tests in
uniaxial compression. In situ this would be equivalent to having rock samples oriented
parallel to the principal directions. Since the principal directions of the in situ stress are
not known a priory, it was proposed that the cores should be sub-sampled in different
directions such that at least three samples will be close to the principal directions [4].
Despite considerable efforts the method still has a number of issues, which makes the in
situ stress determination unreliable. One of these issues on which we concentrate here is
the appearance of acoustic emission at low stress to strength levels. The source of
acoustic emission under compression is believed to be either the generation of new
cracks or the extension of pre-existing cracks [3, 5, 7-42]. Hereafter we will refer to this
mechanism as damage accumulation. It is believed that the onset of this mechanism
coincides with the onset of dilatancy [43-47], which corresponds to the compressive
stress magnitudes above 20% (20-30% [48], 40% [43-45, 47, 49-54], or 50-70% [54] )
of the UCS. There is however experimental evidence suggesting that the acoustic
emission starts earlier, at much lower stress to strength levels. The magnitude of the
School of Civil and Resource Engineering The University of Western Australia
31
early acoustic emission right after applying load is comparably low magnitude as
compared to the magnitude of acoustic emission when the applied stress exceeds the
PMS. Hence it is often considered as a background noise [4].
Other than the early and low magnitude acoustic emission, there have been observations
of high magnitudes of acoustic emission activity at low stress. Boyce et al [56]
hypothesised that the initial “burst” of acoustic emission signals in the low stress region
was caused by the crack closure in compression. We however note that the successive
crack closure creates a concave region in stress-strain curve, Figure 2. Suppose the
sample is loaded to a strain ε1. This leads to the strain energy stored in the sample (the
shaded area under the stress-strain curve) above the energy that would be stored if the
material had experienced a pure elastic increase (the double shaded area). This
additional energy is supplied by the loading machine (due to increase in the stress in the
loading machine). There is however no excess in the energy to be dissipated by the
acoustic emission. Furthermore, the crack closure is a continuous process whereby the
opposite faces first get into contact and then the contact continuously spreads, Figure 3.
It is this continuity and the absence of abrupt changes that exclude the possibility of
formation of acoustic pulses. In addition, to the best of our knowledge, there is no
evidence in the literature to support that crack closure can produce acoustic signals
under quasi-static loading.
Figure 2-2 The concave region of stress-strain curve created by successive crack closure in
compression. The strain energy stored in the sample increases at a higher rate than that of pure
elastic sample, which excludes the energy excess needed for generating acoustic emission.
School of Civil and Resource Engineering The University of Western Australia
32
Figure 2-3 The continuous process of crack closure: (a) the open crack before loading; (b) load
increase caused a point contact of the opposite faces of the crack; (c) further load increase enlarges
the contact area.
The above consideration forces us to look for the low stress acoustic pulses in the areas
of high stress concentration. The first obvious candidate for this is the contacts between
the sample ends and the loading platens where the surface roughness (micro-asperities)
and/or free particles (e. g. dust or residual material at the sample ends after grinding)
considerably reduce the area of actual contact and thus increase the contact stress.
We performed special experiments to check this hypothesis. We start with artificial
samples made of aluminium where the contact surfaces can be very smoothly machined
and polished. We then proceed with samples made of agate – these have chemical
composition somewhat similar to rocks but are amorphous and very homogeneous and
then turn our attention to rock using sandstone as an example.
2.3 EXPERIMENTAL APPARATUS AND PARAMETERS
We tested cylindrical samples of aluminium, agate and sandstone of 18mm -19mm in
diameter and 40mm- 45mm in length, as shown in Table 4. Acoustic signals were
measured by two piezoelectric transducers from Physical Acoustics Corporation
(MISTRAS). The transducers were connected through a 40dB pre-amplifier to the 60dB
front amplifier. The acoustic signals were filtered in the frequency range from 1 kHz to
1 MHz. The signal threshold of the system was set to 47dB. The maximum signal
amplitude was 100dB and the maximum sample rate was 1M samples/per second.
School of Civil and Resource Engineering The University of Western Australia
33
The samples were loaded using a servo-controlled loading machine of 5t capacity. The
load was displacement-controlled, applied by the movement of the upper platform,
while the bottom platform was fixed, Figure 2-4.
The test parameters are listed in Table 4. All samples were prepared in accordance with
ISRM standard for unconfined compressive strength (UCS) [97] and acoustic emission
testing [6].
Figure 2-4 The loading machine and the sample
Table 4 The details of rock samples and test parameters
Material Aluminium Agate Sandstone
Number of samples 2 2 2
UCS (MPa) > 240 > 100 > 100
Elastic (static) modulus (GPa) 70 85 94 - 115
Poisson’s ratio 0.35 0.09 0.27
Sample diameter (mm) 20 17.8 18.8
Sample length (mm) 40 40 40
End planarity < 0.01 mm < 0.01 mm < 0.01 mm
Applied stress (MPa)
1st cycle 20 35 40
2nd cycle 40 45 N/A
Displacement (stress) rate of loading machine: 0.14 mm (7MPa) per minute
Upper platform
Bottom platform
Sample
Acoustic sensor
School of Civil and Resource Engineering The University of Western Australia
34
2.4 TESTS AND RESULTS
2.4.1 Aluminium
We tested two aluminium samples (aluminium A and B) which were made from
aluminium 6000 series, which is a uniformly crystallized metal. It is often used for
calibration of testing equipment. This material has stable physical properties under room
temperature and behaves elastically which makes the results reproducible under
repeated loading. The applied stress was below 48MPa (<20% of UCS) such that,
according to the current understanding we should not be able to detect either acoustic
emission or the Kaiser Effect.
Both aluminium A and B were loaded in two loading-unloading cycles. In the 1st cycle
(the memory inducing load) the sample was loaded to 20 MPa. In the 2nd loading cycle
(the measuring load) the maximum stress was 40 MPa.
In the test result of aluminium A, the acoustic emission starts at a very low stress, less
than 5 MPa; that is below 2% of the UCS (Figure 2-5). As the stress-strain response is
linear at such low stresses (Figure 2-6), the damage produced was minimal (if any) and
hence the AE associated with damage accumulation should not be produced. That
leaves us with the only possible source of low stress acoustic emission – the sample
ends. We hypothesize that the crushing of surface irregularities or free particles at the
contact between the loading platens and the sample ends are responsible for these
acoustic signals.
Figure 2-5 The acoustic emission response of aluminium A from the 1st loading cycle.
0
30
60
0 10 20AE
cum
ulat
ive
even
ts
Stress (MPa)
Aluminium A at 1st cycle
School of Civil and Resource Engineering The University of Western Australia
35
Figure 2-6 The axial and lateral stress-strain curves of aluminium sample. The axial (in black) and
lateral strain (in grey) responses are linear.
In order to check this hypothesis we performed another test on the second sample
(aluminium B) of the same dimensions whose ends were additionally cleaned by
attaching and removing a sticky tape in order to remove as much of the free particles as
possible. We subjected this sample to the same stress path we applied to aluminium A.
Figure 2-7 shows the resulting AE measurements at the 2nd cycle of both samples. The
sample aluminium A shows the Kaiser effect at 21 MPa, which is close to the peak
stress, 20 MPa, of the 1st cycle. There is no acoustic emission activity shown in the
sample aluminium B; hence the Kaiser effect cannot indicate the PMS at 20 MPa. It
suggests that the sticky tape has removed most of the free particles in aluminium B;
therefore, the Kaiser effect cannot exist without free particles on the surface of a sample
end. Conversely, just wiping a finger over the sample ends and reloading it shows
renewed low-stress acoustic emission, Figure 2-8.
Figure 2-7 The AE bursts around 21 MPa in aluminium A indicate the PMSes that were applied in
the first loading cycles. The sample aluminium B shows no sign of the Kaiser effect.
0
10
20
-100 0 100 200 300
Str
ess
(MP
a)
Microstrain
Aluminium A Stress-Strain Plot
0
4
8
12
0 10 20 30 40
AE
Eve
nts
Stress (MPa)
Cumulative Events of 2nd Cycle
Aluminium AAluminium B
School of Civil and Resource Engineering The University of Western Australia
36
Figure 2-8 The sample aluminium B from Figure 7 was wiped by finger over the sample end and
reloaded to 20 MPa. The majority of the acoustic signals are below 5 MPa, which indicates
“memory fading”. This initial “burst” was from the free particles brought from fingers, and this
burst can also be observed in [3].
Figure 2-9 The surface of aluminium sample: (a) with additional cleaning; (b) with tissue cleaning
only. The very fine particles which are indicated by the black arrows at the right were gathered in
the uneven part of surface in the sample end without additional cleaning (b) and were absent in the
additionally cleaned end (a).
0
300
600
0 5 10 15 20
AE
Eve
nts
Stress (MPa)
Cumulative Events
(a)
(b)
School of Civil and Resource Engineering The University of Western Australia
37
The Figure 2-9 shows the aluminium sample surfaces under a scanning electron
microscope. The sample end, cleaned only by a tissue, shows free particles of various
sizes on the surface. The sample end with additional cleaning by a sticky tape shows
significantly less free particles.
The tests on the aluminium samples show the free particles as a source of the initial
“burst” of acoustic emission and the acoustic emission at low stresses. We emphasize
that in the absence of roughness at the well-polished ends of aluminium samples the free
particles are the only material that can be broken. Rocks would have rougher end
surfaces and hence breaking the asperities will play the role of sources of acoustic
emission. In order to check this hypothesis we firstly need to choose a homogeneous
material that allows a different degree of roughness to be induced at its ends and yet has
a rock-like composition.
2.4.2 Agate
The second series of tests was conducted on samples made from agate. Agate is a
strong, uniform, amorphous and isotropic material with very few voids. It is formed by
SiO2, which is the main component of rock. Therefore, it can represent a natural
material, which is similar to rock while the influence of cracks, voids, foliation and
loose mineral grains can be minimal. The ends of the agate sample can be polished and
cleaned to remove most of the free particles.
Without the free particles, the only difference in the end condition between the
aluminium and agate is the mechanical properties. While the aluminium will undergo
plastic deformation under high stress concentration, the brittle agate will break. Thus the
roughness of the end surfaces of agate sample can produce acoustic emission. In order
to investigate the influence of the roughness, we tested two agate samples that were
ground by abrasive material comprising different particle sizes; grit #120 and grit
#1200. Both samples were loaded to 35 MPa (1st loading cycle – the memory inducing
load), followed by 2nd the measuring loading cycles with maximum load of 45 MPa. The
load of 35 MPa in the first loading cycles amounts to less than 35% of the UCS
(seeTable 4), such that the generation of the acoustic emission inside the sample is not
expected. We refer to the sample with its ends ground by grit #120 as sample with high
School of Civil and Resource Engineering The University of Western Australia
38
roughness, and the sample with its ends ground by grit #1200 as sample with low
roughness.
The Figure 2-10a shows that the amount of acoustic emission events in the sample with
high roughness are 193, which is 7.7 times higher than in the sample with low
roughness at the 1st loading cycle. The Figure 2-10b shows that in the 2nd loading cycle,
the sample with high roughness exhibits a memory of the 1st cycle loading, and the
sample with low roughness does not have memory of the 1st cycle loading. At the stress
range 0MPa to 35MPa in the sample with high roughness, the total amount of the
acoustic emission in the 2nd cycle is around 10% of the total amount of acoustic
emission in the 1st cycle. This 10% acoustic emission is commonly considered as close
to zero or a background level [4]. The source of this background noise should be the re-
crushing of the crushed material by the 1st cycle load. The sample with low roughness at
the 2nd cycle also shows a very low magnitude (<10 events) background noise. It is
insufficient to create the Kaiser effect.
Figure 2-10 (a) Agate sample with high roughness (marked as Rgh) shows much higher acoustic
emission at low stress, while the sample with low roughness (marked as Sth) has little acoustic
emission. (b) The sample with higher asperity also exhibits the Kaiser effect, while the sample with
lower asperity does not show the memory of previous load.
The roughness of the sample ends were also changed by crushing the asperities. The
roughness of sample end was measured by a roughness meter (TR 200, manufactured by
TIME high technology Ltd.) before and after testing. There are 10 random spots on each
sample end were picked and the results were averaged and shown in Figure 2-11. The
0
100
200
0 10 20 30 40
AE
Eve
nts
Stress (MPa)
Cumulative events at1st cycle
Sth
Rgh
(a)
0
20
40
0 10 20 30 40 50
AE
Eve
nts
Stress (MPa)
Cumulative events at 2nd cycle
Sth
Rgh
(b)
School of Civil and Resource Engineering The University of Western Australia
39
sample ends 1 and 2 (the sample with low roughness) have no or little change of the
surface roughness after 2 loading cycles, while the sample ends 3 and 4 (the sample
with high roughness) have more reduction of the surface roughness after 2 loading
cycles.
It also brings to our notice that in each sample, the end with higher roughness than the
other one would have more reduction; for example: the reduction in surface 2 is higher
than in surface 1, and the reduction in surface 3 is higher than in surface 4. The
reduction in surface 2 could be the source of background level acoustic emission.
Figure 2-11 The number at each column is the roughness before testing. The sample with low
roughness (1 and 2) has minor reduction of roughness after 2 loading cycles, compared with the
sample with high roughness (3 and 4).
According to the results of the agate tests, it is the roughness of the sample ends that is
the source of acoustic emission at low stress. This acoustic emission exhibits the Kaiser
effect. When the asperities are large, the stress concentration occurs at the “sharp
points” and crushes them, which is registered as acoustic emission. When the asperities
are small, there are very few crushing events, and the energy from crushing events is
smaller than crushing of larger “sharp points”. The acoustic emission is at the
background level, insufficient to show the Kaiser Effect.
2.4.3 Sandstone
According to the agate samplees, the asperities/irregularities/residual material in a rock
sample provides a source of acoustic signals when the samples are compressed and
0.5580.798
2.8612.474
0
1
2
3
1 2 3 4
Rou
ghne
ss
Sample end
The changes of roughness in agate
ReductionAfter loading
School of Civil and Resource Engineering The University of Western Australia
40
some of the particles/asperities are crushed. We now proceed with the issue in rock – a
sandstone from Cadia Hill, Australia. Unlike agate sample, it was impossible to
machine the sample ends of sandstone to low roughness and/or remove all the loose
grains. In order to mitigate the roughness, we had tested cardboard paper, 80gsm
printing paper, graphite powder, cork, plastic tape (Vishay), plastic sheet (TML strain
gauge), plastic tape (3M scotch clear), plastic tape (3M removable), plastic sheet (cling
wrap), silicone gel and the combination of each above material and silicone gel as
buffer materials on 136 rock samples (including blind test). The plastic sheet (TML
strain gauge) plus silicone gel is by far the best choice to reduce the noise from end in
sandstone. Hence, the samples were ground using the grit #1200 and a plastic sheet was
inserted as a buffer material on one sample.
In order to examine the effectiveness of a plastic insert on mitigatint the roughness and
reducing the crushing of loose grains, plastic inserts were placed at 6 out of 36
sandstone samples as a buffer material between sample end and platen.
The basic information (modulus, density, p-wave velocity etc.) and the detailed results
(acoustic emission rate, stress-strain curve) of each sample are shown in appendix A.
The test specification is listed in Table 5. The UCS of samples is estimated to be
between 150-200MPa and the peak stress is between 65-90 MPa (35-60% of UCS). The
samples in group 1 to 4 are the blind tests, which have no plastic insert. The samples in
group 5 have plastic inserts at both end, and samples in group 6 have only one end
covered by plastic insert.
The results are shown in Figure 2-12. All group 5 samples has very few acoustic events
(<20) during whole loading cycle. Because the plastic insert has largely reduced the
acoustic activities in group 5, the amount of acoustic pulse in group 5 is insufficient to
create the Kaiser effect. There are 22 out of 24 samples in the groups 1 to 4 have much
higher number of acoustic events (>100) than group 5. The “initial burst” was also
observed when testing these 22 samples. The samples of group 6, which the plastic
insert was placed on only one side of sample end, have less acoustic pulses than the
samples of groups 1 to 4 but the number of acoustic pules is obviously higher than the
samples of group 5. It shows the plastic insert eliminated the crush of asperities at one
School of Civil and Resource Engineering The University of Western Australia
41
side of sample end, when the crush of asperities at the other side of sample end still
produces acoustic pulses.
Although there are some acoustic pulses in the samples of group 5, the plastic insert can
greatly reduce the number of acoustic pulse and eliminate the Kaiser effect imitated by
the crushed asperities. It also mitigates the initial burst, which indicates that the initial
burst is generated by the same source of the Kaiser effect at low stress.
Table 5 The details of rock samples and test parameters. The sample ID A, B, C… to F represents a
specific orientation of sample in space, which is listed in appendix B.
Sample group 1 2 3 4 5 6
Plastic insert at sample ends
NO NO NO NO At both ends
Only at one end
Number of samples
6 6 6 6 6 6
Core ID VR1 VR2
Sample ID A1 to F1 A2 to F2 A3 to F3 A1 to F1 A2 to F2 A3 to F3
Additional clean No
Peak stress (MPa) 65-90 MPa
Figure 2-12 The total amount of acoustic events of samples with different end preparation.
0
100
200
300
400
500
1 2 3 4 5 6
Tot
al e
vent
am
ount
Sample Group
Acoustic events at 1st cycleA B C
D E F
School of Civil and Resource Engineering The University of Western Australia
42
In order to confirm the change of roughness in sandstone also coincides with the
acoustic activities at low stress, additional two samples were loaded to 40MPa. The
samples were drilled, machined and ground using the grit #1200. Both samples were
cleaned additionally by attaching and removing sticky tapes. A plastic tape was inserted
as a buffer material on both ends of one sample. The other sample has no plastic insert
on both ends.
The results in Figure 2-13 confirm that the acoustic emission of sandstone sample was
greatly reduced by the plastic inserts and can be considered as the background level.
Thus, the acoustic emission which is sufficient to generate the Kaiser Effect in
sandstone at a stress well below 20% of UCS is also due to the end roughness.
Figure 2-13 (a) The comparison of acoustic emission amount between sandstone samples with/
without plastic insert. The sample without plastic tape insert has much higher number of acoustic
pulses than the sample with plastic tapes at both ends. (b) The sample without plastic tape insert
(sample end 5 and 6) has higher reduction of roughness, compared with the sample with plastic
tapes at both ends (surface 7 and 8).
Although the plastic sheet (TML strain gauge) plus silicone gel is by far the best choice
to reduce the noise from the end in sandstone, we are still not able to reduce all acoustic
noise from certain rock types. We recommend a more systematic study on insert
material versus rock types. Also, the source location for acoustic emission will enable
one to distinguish data from the noise. We recommend a study using source location to
confirm the source of Kaiser effect, before using acoustic emission as a stress
measurement method. However, in this case, one should be aware that the error of event
0
150
300
0 10 20 30 40
AE
Eve
nts
Stress (MPa)
Cumulative Events in sandstone
Without plastic insert
With plastic insert
(a)
0.468 0.523 0.504 0.535
0
0.4
0.8
5 6 7 8
Rou
ghne
ss
Sample end
The changes of roughness
ReductionAfter loading
(b)
School of Civil and Resource Engineering The University of Western Australia
43
location has to be less than 1/5 of sample length. Although it is much more difficult to
have source location for acoustic emission on small samples due to the space constraint
and accuracy requirement, small acoustic events are harder to detect in a big sample due
to signal attenuation. To achieve high accuracy when testing a small sample, it is
essential to run a good calibration test and have sufficient number of acoustic sensors.
The sensor calibration test must be carried out on the sample/material of interest. The
diameter of acoustic sensors should be smaller than the target accuracy.
2.5 CONCLUSION
The theory of new crack generation cannot explain the memory in the low stress to
strength region in the aluminium metal. The asperities in an agate sample,
asperities/irregularities/residual material in a rock sample or free particles (e.g. dust) in
aluminium samples provide a source of acoustic signals when the samples are
compressed and some of the particles/asperities are crushed. When the samples were
unloaded to zero stress and reloaded again, the surfaces of sample ends were already
compressed and crushed to the condition which increases the contact area and thus
reduces the stress to below the PMS without crushing any additional material. When the
reloaded stress exceeds the PMS, the asperities at the end are not strong enough to take
higher stress and further crushing occurs. This process keeps the memory of the PMS,
which manifests itself as the Kaiser Effect. By changing the conditions of the sample
ends, one can make the sample to keep or to lose the memory at will. This “end effect”
can be a reason that the laboratory pre-stress is much easer to recover than the in situ
stress.
We emphasize that the Kaiser Effect created by the sample ends is a ghost Kaiser Effect
as it is not related to the rock memory but rather to the failure of free particles or
asperities at the sample ends. This memory is essentially an artefact of the test
preparation and goes a long way to explaining the difficulty laboratories have
experienced in using AE to identify consistently the in-situ stress.
Acknowledgments
School of Civil and Resource Engineering The University of Western Australia
44
The authors would like to thank Australian Centre for Geomechanics for their financial
support, Dr. Joel Sarout (CSIRO) and Sergei Stanchits for their technical help and
advice.
School of Civil and Resource Engineering The University of Western Australia
45
CHAPTER 3. THE KAISER EFFECT AT HIGH STRESS
3.1 ABSTRACT
It has been experimentally demonstrated by many researchers that the acoustic emission
produced in the material under repeated loading has a specific feature whereby the
acoustic emission activity is zero or close to background level when the stress
magnitude of the repeated load remains below the previously attained maximum stress.
This is the nature of so-called Kaiser effect. Using the Kaiser effect one can recover
laboratory pre-stress or in situ stress, however attempts to recover in-situ stress have had
limited success.
In our previous research, we have found the acoustic pulse caused by crushing of
asperities at the sample ends can manifest itself as the Kaiser effect at low to mid stress
level. In this paper, we have focused on the stress higher than the onset of dilatancy to
investigate the dependence of Kaiser effect on the magnitude of the previous load. The
samples of sandstone, ultramafic rock, and slate were specially machined, cleaned, and
loaded to the high stress twice or three times. The results show that the process of crack
generation/growth can create sufficient change in the stress path in the following
loading cycle. Hence the acoustic emission would start much earlier than the PMS and
the Kaiser effect is absent.
Since the Kaiser effect is likely to be masked by the acoustic emission associated with
the damage accumulation, and low/mid stress is not able to generate enough cracks to
produce sufficient amount of acoustic pulse, the Kaiser effect can only be observed
when the previous stress is within a certain stress range. We suggest that one should
find the stress range in which the Kaiser effect can be detected, before using the Kaiser
effect as a stress measurement method. If the “detectable stress range” is unknown, the
acoustic bursting caused by the damage accumulation is likely to imitate the Kaiser
effect and mislead the analysis
School of Civil and Resource Engineering The University of Western Australia
46
3.2 INTRODUCTION
It was experimentally demonstrated that the acoustic emission produced in the material
under repeated loading has a specific feature whereby the acoustic emission activity is
zero or close to background level when the stress magnitude of the repeated load
remains below the previously attained maximum stress, Figure 3-1. This is the nature of
so-called Kaiser effect, firstly discovered by Kaiser [2] in metals (tested under tension)
and then confirmed in rocks [3] (tested under compression). In this paper we regard the
Kaiser effect as a phenomenon observed in rock testing under compression.
Figure 3-1 Kaiser effect in materials and rocks under compression: (a) the loading cycles, (b)
cumulative acoustic emission activities corresponding to these loading cycles [4].
Since Kaiser’s paper a considerable body of research has been directed towards
developing the method of recovery of the maximum in situ stress using the Kaiser effect
by testing samples made from cores extracted from the locations of interest [4, 5, 7-11,
13-15, 17-42, 55, 60, 61, 67, 70-96]. The stress reconstruction method is based on the
assumption that under repeated load, the rock will not generate new cracks or extend the
pre-existing cracks when the stress is lower than the PMS. Therefore, the source of
acoustic emission under compression is believed to be the crack generation/growth [3,
5, 7-42]. Hereafter we will refer to this mechanism as damage accumulation. It is
believed that the onset of damage accumulation coincides with the onset of dilatancy
School of Civil and Resource Engineering The University of Western Australia
47
[43-47], which corresponds to the compressive stress magnitudes above 20% (20-30%
[48], 40% [43-45, 47, 49-54], or 50-70% [54] ) of the UCS.
Since the source of acoustic emission under compression is the process of damage
accumulation, we can conclude that: (1) at the stress lower than the onset of dilatancy,
rock would not generate acoustic emission; and (2) the Kaiser effect can be observed
when the PMS is higher than the onset of dilatancy. However, the experiments
described in the literature and our own experiments suggest that the above two
considerations are not valid. Firstly, there is experimental evidence suggesting that the
acoustic emission starts at the stress less than 20% of the UCS or less than 20% of
maximum applied stress when the UCS is unknown (See Figures 1 and 2 from [3],
Figures 1 and 2 from [5], Figures 3-8 from [71], Figures 2-6 from [73], Figures 2-4 and
6 from [74], Figures 2, 4, 12, 14 and 20 from [31], Figure 1 from [55], Figure 3 from
[76], Figure 9 from [78], Appendixes 1-3 in [23, 79], Figures 5 and 8 from [20], Figures
1, 3 and 4 from [14], Figure 3 from [85], Figures 4, 5, and 7-10 from [61], Figure 4
from [32], Figure 2 from [16]). Secondly, it was suggested in [5] that the Kaiser effect
could not be observed when the PMS is higher than the onset of dilatancy, because
rocks would still generate a sufficient amount of acoustic emission to cover the Kaiser
effect under repeated load at the dilatancy stage.
For the acoustic emission at the stress lower than the onset of dilatancy, we performed
special experiments to check the source of the early acoustic emission and found the
“ghost Kaiser effect” [98]. Our experiments show that the low stress acoustic emission
is produced by the contacts between the sample ends and the loading platens where the
surface roughness (micro-asperities) and/or free particles (e.g., dust or residual material
at the sample ends after grinding) considerably reduce the area of actual contact and
thus produce local contact stress concentration. By changing the conditions of the
sample ends, one can make the sample keep or lose the ‘memory’ at will. The rock
‘memory’ associated with the ghost Kaiser effect is essentially an artefact of the test
preparation.
With regard to the claims that the Kaiser effect cannot be observed at the stress higher
than the onset of dilatancy, we hypothesise that in such cases the structure of rock has
been changed by the previous load. The stress path at the following loading cycle is
School of Civil and Resource Engineering The University of Western Australia
48
different from the previous cycle, and the induced stress at the discontinuity (for
example crack surface and grain boundary) is able to produce further damage
accumulation. Therefore, the acoustic emission and dilatancy can be repeatedly created
under repeated loads.
To check this hypothesis, we performed experiments in sandstone (hard rock),
ultramafic rock (median strength rock), and shale (weak rock) at different stress levels.
Hereafter we refer the stress level which is higher than the onset of dilatancy as high
stress, and the stress level which is lower than the onset of dilatancy as low/mid stress.
Theoretically, rock samples should be subjected to high stress twice. The high stress at
the 1st loading cycle will generate damage accumulation and change the structure of
rock. The acoustic emission from 2nd loading cycle would reveal whether the Kaiser
effect could be observed. However, it is difficult to define the exact onset of dilatancy
by the stress-strain curve or volumetric strain curve in the loading process, because the
non-linear deformation mechanisms associated with the crack closure, crack sliding and
crack propagation can occur simultaneously [99]. Hence, in addition to the sudden
change in the tangent modulus, bulk modulus, and stress-strain curve as an indicator of
dilatancy, we use acoustic emission activity as an additional indicator of dilatancy
[100]. To check the Kaiser effect at high stress, we applied two or three loading cycles
to sandstone and ultramafic rock. Each loading cycle includes loading to maximum
stress followed by unloading to zero stress, and was identical to the other loading cycle.
We had ensured that the dilatancy and acoustic emission produced by damage
accumulation were observed at the 1st loading cycle.
In order to compare with the Kaiser effect in high stress, we had also tested sandstone to
mid stress, where the existing cracks might slide without any damage accumulation.
Then, we tested slate sample which has macro-scale cracks (part of the foliation) to
slide/grow at low/mid stress, to demonstrate the original Kaiser effect theory “crack
grow when the current stress excesses PMS”. Our aim was to evaluate the reliability of
Kaiser effect in high stress region, and to understand the essential criteria of
detectability of the Kaiser effect.
School of Civil and Resource Engineering The University of Western Australia
49
3.3 EXPERIMENTAL APPARATUS AND PARAMETERS
We tested cylindrical samples of sandstone, ultramafic rock, and shale of 18mm -19mm
in diameter and 37mm- 40mm in length, as shown in Table 6. Acoustic signals were
measured by two piezoelectric transducers from Physical Acoustics Corporation
(MISTRAS). The transducers were connected through a 40dB pre-amplifier to the 60dB
front amplifier. The acoustic signals were filtered in the frequency range from 1 kHz to
1 MHz. The signal threshold of the system was set to 47dB. The maximum signal
amplitude was 100dB and the maximum sample rate was 1M samples/per second.
The samples were loaded using a servo-controlled loading machine of 5t capacity. The
load was displacement-controlled, applied by the movement of the upper platform,
while the bottom platform was fixed (Figure 2-4). We used glued cross type strain
gauges (Figure 3-2) that ensure simultaneous measurements of the axial and lateral
strains. All samples were subjected to 2 or 3 loading cycles under a constant
loading/unloading rate of 7~9MPa/min. The average strain was calculated by taking
average of readings of 4 strain gauges. The moduli of each loading cycle were
calculated by the moving average method applying to the average stress-strain curve.
The test parameters are listed in Table 6. All samples were prepared in accordance with
the ISRM standard for unconfined compressive strength (UCS) [97] and acoustic
emission testing [6]. A specific sample end preparation [98] was applied on all samples
in order to eliminate the acoustic emission generated by surface of sample ends.
Figure 2-4 The loading machine and the sample.
Upper platform
Bottom platform
Sample
Acoustic sensor
School of Civil and Resource Engineering The University of Western Australia
50
Figure 3-2 The cross type strain gauges were glued at the 4 spots shown in the graph.
Table 6 The details of rock samples and test parameters
Sample ID/ lithology Modulus (GPa)/ Poisson’s ratio
UCS (MPa)
Peak stress at loading cycle
1st 2nd 3rd
CSA D4 Sandstone 81/ 0.25 ~103 102 100 n/a CSA E3 89/ 0.20 >100 90 90 n/a WAou B3 Ultramafic 27/ 0.13 43 41 41 41 WAou F4 34/0.20 >60 58 58 58 PR2 B3 Shale 46/ 0.31 25 14.5 14.5 25
3.4 TEST RESULTS
We tested two sandstone samples (CSA D4 and CSA E3) which were drilled out from
same core. The sample CSA D4 was loaded to the high stress level first, and then
unloaded to zero stress. Figure 3-3 shows the stress at this cycle (1st cycle) had
generated new cracks/ dilatancy, because a sudden decrease in the tangent modulus, an
increase in the bulk modulus (the slope of volumetric strain), and a sharp increase in
acoustic emission rate at the stress level of 99MPa took place simultaneously.
After the 1st loading cycle, the sample CSA D4 was unloaded, and immediately
reloaded to failure (100MPa). The acoustic emission started bursting at 78MPa, and the
bulk modulus had also largely increased its value at the same stress (Figure 3-4). These
two observations show that at the 2nd loading cycle new cracks were generated when the
stress reached 78MPa, which is lower than the PMS (102MPa).
Strain gauge Sample
School of Civil and Resource Engineering The University of Western Australia
51
Figure 3-3. The sandstone sample was loaded to near the failure stress (100MPa as detected at the
2nd cycle). The tangent modulus reduced its value dramatically after the applied stress exceeded
99MPa, where the acoustic emission started bursting. The amount of acoustic emission did not
exceed 1.5 events/MPa before the stress reached 98MPa and is considered as background noise.
Figure 3-4. The response of acoustic emission and the change in the bulk modulus at the 2nd loading
indicates the new cracks were created from 78MPa (grey arrow) onwards.
50
90
0 50 100
mod
ulus
(G
Pa)
CSA D4
130
330
0 50 100
slop
e of
v-s
trai
n
0
100
0 50 100AE
eve
nts
/MP
a
Stress (MPa)
170
370
0 50 100
bulk
mod
ulus
CSA D4 2nd cycle
0
100
0 50 100
AE
eve
nts/
MP
a
Stress (MPa)
School of Civil and Resource Engineering The University of Western Australia
52
Thus we have demonstrated at the 1st loading cycle a sufficient number of cracks have
been generated to make the stress path at the 2nd loading cycle different from the 1st
loading cycle. As a result, the Kaiser effect cannot be observed. In terms of the in situ
stress reconstruction, if the value of in situ stress is higher than the onset of dilatancy,
the effect discussed would cover and mask the Kaiser effect. Therefore, the Kaiser
effect cannot be used for the in situ stress reconstruction in the high stress area.
Furthermore, although there were some acoustic events (100 events) at the 1st loading
cycle in the low and mid stress regions (1MPa to 77MPa), the events do not show any
bursting characteristic of Kaiser effect. The events were randomly distributed
throughout the low/mid stress level in the 1st loading cycle and were of similar or lower
amount compared with the events at the same stress level in the 2nd loading cycle (117
events). We believe that these events in both cycles might be a part of the acoustic noise
from the environment or from crack sliding, because they had a very low rate (<1.5
events per MPa) and the number of events was similar in reloading. Hence, the
observation is not compatible with the nature of Kaiser effect created by the in situ
stress. One can put forward three reasons for this observation: (1) our equipment is not
sensitive enough to register the Kaiser effect; (2), the Kaiser effect is not able to indicate
the in situ stress when the in situ stress is at low/mid stress level, or (3) the in situ stress
is in the high stress region.
Our experience shows that our equipment does register the Kaiser effect in other rock
samples, so we exclude reason (1). In order to confirm that the Kaiser effect is not
detectable at low/mid stress level in the same rock type, the second sandstone sample
CSA E3 was loaded to 90MPa, which is the stress lower than the onset of dilatancy. The
sample was recovered from the depth of 1530m below the surface and the estimated in
situ stress was 43MPa. The number of acoustic emission pulses was very low and the
acoustic emission rates (event per MPa) were similar before and after the load reached
the 43MPa level (Figure 3-5). There was bursting in AE during the whole loading cycle,
so we conclude that the in situ stress was not detectable by the Kaiser effect in this case.
This excludes case (3).
School of Civil and Resource Engineering The University of Western Australia
53
Figure 3-5. The sandstone sample shows no sign of dilatancy when the applied stress reached
90MPa. There were very few acoustic emission activities (35 events) evenly spreading out in the
whole loading cycle and the “acoustic emission burst” was not observed.
To summarize, the in situ stress in sandstone is not measureable by the Kaiser effect
method due to one of the following reasons: (1) the in situ stress corresponds to the high
stress level, where the dilatancy had covered and masked the Kaiser effect; or (2) the in
situ stress corresponds to the low or mid stress level, where the Kaiser effect (if any) is
not measureable by the equipment.
We have confirmed that the damage accumulation can change the stress path at the
following load and further damage accumulation could occur and produce the acoustic
emission in the sandstone when reloading to same/lower stress. The next step was to
check this hypothesis in other rock types. To this end we loaded 2 ultramafic rock
samples to high stress level repeatedly 3 times, in order to check if there was any crack
generated by the 2nd and 3rd loading cycles. The result for sample WAou B3 is shown in
Figure 3-6. The acoustic emission pulses at the 2nd loading cycle increases significantly
when the stress exceeds 25MPa, which is much lower than the PMS (41MPa). The
difference between the volumetric strain in the 1st and 2nd cycles indicates that a certain
80
100
0 50 100
mod
ulus
(G
Pa)
CSA E3
80
180
0 50 100
bulk
mod
ulus
0
40
0 50 100AE
eve
nts
/MP
a
Stress (MPa)
School of Civil and Resource Engineering The University of Western Australia
54
amount of the dilatancy/lateral strain has been introduced by the 1st cycle. The
difference between the volumetric strain in the 2nd and 3rd cycles shows that even if the
peak stress at the 2nd cycle is the same as it at the 1st cycle, there were still some new
cracks generated or some pre-existing cracks grew in the 2nd cycle. Hence, the acoustic
emission in neither the 2nd nor 3rd loading cycles was indicative of the PMS. The sample
WAou F4 was loaded to 58MPa. The result (Figure 3-7) is similar to WAou B3.
Figure 3-6. The acoustic emission in the 2nd and 3rd loading cycles from sample WAou B3. The
acoustic emission pulses were observed from around 10MPa onwards. The acoustic emission rate
increased more significantly after the load reached 25MPa (black arrow), which is well below the
PMS (41MPa). The volumetric strain shows the sample is very close to failure.
Figure 3-7. The acoustic emission in the 2nd and 3rd loading cycles from sample WAou B4. The
bursting is observed at 40MPa (black arrow), which is well below the PMS (58MPa). The acoustic
emissions at the 2nd and 3rd cycles do not have the memory of 58MPa. The volumetric strain shows
the sample was loaded to high stress.
0
1000
0 20 40AE
eve
nts
/MP
a
Stress (MPa)
WAou B3
23
0
20
40
0 2000
stre
ss (
MP
a)
microstrain
Volumetric strain
123
0
300
0 30 60
AE
eve
nts
/MP
a
Stress (MPa)
WAou F4
23
0
30
60
0 2000
stre
ss (
MP
a)
microstrain
Volumetric strain
123
School of Civil and Resource Engineering The University of Western Australia
55
Since ultramafic samples have also confirmed that the stress is able to generate new
cracks or cause the crack extension at high stress region before the current stress
exceeds the PMS, the Kaiser effect is not able to indicate the PMS. The phenomenon of
creating new cracks or crack extension before reaching the PMS under repeated load
might seem to be controversial. To explain the phenomenon, we have considered the
heterogeneity of rock and proposed two mechanically plausible explanations.
(1) The stress in the previous load has created sufficient amount of cracks to change
the stress path of the following load. The tensile stress (induced stress) which
was created by the heterogeneity at the later load created new cracks before the
applied stress reached the PMS. This scenario is more likely to occur when the
sample was very close to failure at the previous load, because the previous load
needs to create sufficient number of cracks. The possible example for this
scenario is given by the sample whose test results are shown in Figure 3-3.
(2) The rocks are heterogeneous at multiple scales so the rock sample can comprise
several parts which have different stiffnesses. The higher stiffness part (part A)
would take higher stress than the lower stiffness part (part B) when the rock is
deformed. When the applied stress at the previous load was high enough to
damage part A and produce acoustic emission/dilatancy, the new cracks in part
A would reduce its stiffness and part A might become softer than part B after
loading. Hence, the stress in the following loading cycle concentrates on part B
and damages it, just like what the previous load had done to part A. It is not
necessary for the applied stress to be very high for this mechanism to work,
because the stiffness difference could be relatively large enough to create a local
high stress concentration. This scenario explains the acoustic emission in the
ultramafic sample, which occurred repeatedly from pretty low stress.
Since it is possible that the applied stress creates new cracks or crack extension before
reaching the PMS under repeated load, the Kaiser effect would be unreliable in the high
stress region. In additional to the high stress region, the Kaiser effect is not detectable in
the low/mid stress region in sandstone, when crack closure and crack growth are
unnoticeable and the bulk modulus is constant. In this case, the acoustic activity (if any)
School of Civil and Resource Engineering The University of Western Australia
56
is not associated with cracks, and the amount of acoustic emission is too low to show
the bursting nature of Kaiser effect.
We now confirm that the high stress might create “too many” cracks to change the
stress path and mask the Kaiser effect, and low/mid stress might not create cracks or
show the Kaiser effect in sandstone. To create the Kaiser effect, a rock should have few
cracks that are large enough to produce acoustic emission at high stress and the amount
of cracks is not sufficient to change the stress path in the following load. We believe
that slate would be an ideal material because it is uniform and the foliation of slate can
allow the generation of only few macroscale cracks at certain stress. To find the
appropriate maximum stress which creates the “right” amount of cracks, 15 slate
samples were loaded to 14.5MPa, 20MPa, or 23MPa twice, then the samples were
loaded to failure at the 3rd loading cycle. The results show that 9 out of 15 samples were
loaded too high or too low, so the Kaiser effect at 2nd loading cycle was either masked
by the acoustic activity in the dilatancy region, or the amount of acoustic pulses was not
sufficient to produce the Kaiser effect.
Sample PR2 B3 (Figure 3-8) provides an example to show the preferred condition of
Kaiser effect. The cracks had started growing and creating dilatancy from 2MPa in the
sample at the 1st loading cycle and the process of cracking had a sudden increase in
growth at 14MPa. The sample was immediately unloaded to zero stress and reloaded to
the PMS (2nd cycle). The process of crack growth at the 1st loading cycle has changed a
small part of the rock structure so the induced stress at the 2nd loading cycle was able to
create/extend cracks and produce acoustic emission at the stress lower than the peak
stress of 1st loading cycle. However, the number of new cracks generated from 2nd
loading cycle was much smaller than the number of cracks generated from 1st loading
cycle. Hence, the acoustic emission at the 2nd loading cycle was much lower than at the
1st loading cycle. In the 3rd loading cycle, because the number of cracks generated in the
2nd loading cycle was low, the structure/stress path was mostly unchanged. Therefore,
the cracks at the 3rd loading cycle did not grow until the applied stress almost reached
PMS. Consequently, the Kaiser effect was able to indicate the peak stress of 2nd loading
cycle (Figure 3-9).
School of Civil and Resource Engineering The University of Western Australia
57
Figure 3-8. The top 3 graphs show the tangent modulus, bulk modulus and the acoustic emission
rate at the 1st loading cycle indicate there was a sudden increase in dilatancy at 14MPa. The
acoustic emission rate at the 2nd loading cycle does not show the memory of the 1st loading cycle.
Figure 3-9. The acoustic emission in the 3rd loading cycle shows a memory of the PMS.
0
70
0 5 10 15 20 25AE
eve
nts
/MP
a
Stress (MPa)
AE at 3rd cycle
40
50
0 5 10 15
mod
ulus
(G
Pa) PR2 B3
80
200
0 5 10 15
bulk
mod
ulus
0
200
0 5 10 15
AE
eve
nts
/MP
a
Stress (MPa)
1st cycle
0
200
0 5 10 15AE
eve
nts
/MP
a
Stress (MPa)
2nd cycle
School of Civil and Resource Engineering The University of Western Australia
58
3.5 CONCLUSION
We have demonstrated that, in sandstone and ultramafic rocks when the previous stress
reaches a high stress level, the process of crack generation/growth can create sufficient
change in the stress path in the following loading cycle. The acoustic emission would
start much earlier than the PMS and the Kaiser effect is undetectable. Subsequently, the
in situ stress cannot be recovered.
In the low/mid stress level, the stress is not able to generate/propagate enough cracks to
produce sufficient amount of acoustic activities to show the Kaiser effect in sandstone
and some slate samples. We suggest that the Kaiser effect can only be observed under
the condition that the PMS has created the “right amount of cracks” to allow the Kaiser
effect to show the bursting character, while the influence of damage accumulation from
previous load is very minor.
We emphasize that the Kaiser effect is likely to be masked by the acoustic emission
associated with the damage accumulation, and it can only be observed when the
previous stress is within a certain stress range. This stress range could be different in
different samples, even if the samples were from the same rock core. Hence, before
using the Kaiser effect as a stress measurement method, one needs to find the stress
range in which the Kaiser effect can be detected and confirm that for each sample. If the
“detectable stress range” is unknown, the acoustic bursting caused by the damage
accumulation is likely to imitate the Kaiser effect and mislead the analysis.
School of Civil and Resource Engineering The University of Western Australia
59
CHAPTER 4. THE TANGENT MODULUS AND
RESIDUAL STRAIN AFTER APPLIED STRESS UNDER
UNIAXIAL COMPRESSION TEST
4.1 ABSTRACT
The sources of nonlinear deformation in hard rock under short term uniaxial
compression can be attributed to crack closure, sliding, compaction and crack
generation. The common approach to finding the modulus of a “hard rock” is to
determine the linear part of stress-strain curve. However, it is usually a difficult task,
although several methods of resolving it have been proposed in the past. We believe that
in some rock types there is no linear part as such and provide evidence to support the
fact that nonlinear deformation contributed by crack closure, sliding and compaction in
different degrees could co-exist within the same stress range. We demonstrate that the
change in tangent modulus under different stress levels is attributable to the
combination of crack closure, sliding and dilatancy. The difference in tangent modulus
under different stress levels could reach more than 20GPa in some rocks. We have also
found that the nonlinear deformation contributed by irreversible sliding, compaction and
even dilatancy increases the rock stiffness in the second loading. This phenomenon was
found under loads ranging from 15% to 95% of UCS.
4.2 INTRODUCTION
The deformation of a rock samples can be classified to linear elastic and inelastic
deformation. The sources of inelastic deformation are: (1) closure of pre-existing
cracks, (2) sliding of pre-existing cracks, (3) dilatancy caused by wing crack initiation
and propagation, and (4) compaction caused by pore/void collapse. The influence of
creeping and rheology properties is assumed to be very small or undetectable in the
short term (<1hr) loading cycle in the laboratory and will not be discussed in this paper.
The above mechanisms are often described separately as the occurrence of each of them
is attributed to different stress levels, and it is assumed that ranges of stress levels
associated with each mechanism do not intersect [44-52, 54, 101, 102]. It is believed the
School of Civil and Resource Engineering The University of Western Australia
60
sequence of these mechanisms begins with the crack closure when the rock sample was
loaded. It only occurs at the low stress and introduces an increase in modulus, resulting
in a nonlinear region at the beginning of the stress strain curve. It was suggested in [50]
that in hard rock, the stress region of crack closure might be very small or non-existent.
It was assumed that the linear elastic deformation that takes place after the crack closure
process finishes, followed then by the stage of stable crack initiation generating inelastic
strain [44-52, 54, 101, 102]. The wing cracks produced by sliding over pre-existing
cracks produce mainly lateral inelastic deformation.
Following the assumption that the phenomena of crack closure, elastic deformation and
crack growth are attributable to different stress levels, a considerable body of research
has been directed towards identifying the linear part of the stress-strain curve in order to
determine the Young’s modulus and Poisson’s ratio [44, 47-49, 52, 54, 102-105] and to
calculate the values of dilatancy [44, 48, 49, 52, 101, 102]. Since the elastic deformation
modulus represents the solid rock without the influence of crack closure, sliding, and/or
crack propagation, the difference between measured strain and the elastic strain
calculated from the modulus will be the inelastic strain produced by the crack closure at
the low stress or by the dilatancy at the high stress. From here one can delineate
separate mechanisms of non-elastic deformation and identify the stages of crack closure
and growth (e.g., [100, 106, 107]).
However, in many cases the elastic part of deformation might be too small to identify
reliably. For instance, to the best of our knowledge, there is no evidence in the literature
to support that crack closure will only exist in the low stress level before crack sliding.
Hence the elastic part might not exist due to the co-existence of crack closure, crack
sliding and crack propagation mechanisms at the mid stress levels.
The phenomenon of overlapping between crack closure, sliding and propagation can be
found at all stress level by utilising the modulus variations obtained from the unloading
cycle. Because the modulus in a rock without cracks is higher than in a rock with
cracks, the modulus measured at the initial unloading process can represent an
uncracked solid. Indeed, the crack which has slid in the process of loading would not
immediately slide in the opposite direction when the load is reduced due to friction [50,
108]. Therefore, under low stress levels when no crack growth is yet possible, the
School of Civil and Resource Engineering The University of Western Australia
61
difference in the modulus between end of loading and initial unloading process is due to
sliding over pre-existing cracks.
The stress-strain curves [109] show that the modulus of initial unloading process is
always higher than the modulus at same stress in the loading process (Figure 4-1).
Accordingly, the sliding over the pre-existing crack exists in the low stress area (30% of
the maximum strain). The stress-strain curve also showed that the region of sliding co-
exists with the region of crack closure, because the modulus increase was also observed
an this stress level. Therefore, the crack closure and sliding occurred together in this
case.
Figure 4-1 The small unloading cycle (white arrow) shows higher modulus than loading cycle while
the tangent modulus increases at whole loading process (after [109]).
This evaluation of the existence of the linear part in the axial stress-strain curve can be
extended further to the volumetric strain. It was believed that the lateral strain is elastic
at the low stress, followed by an inelastic increase caused by opening of the wings
initiated by sliding over pre-existing cracks [50, 101]. A typical volumetric strain curve
appears to show 3 major regions: (1) crack closure region; (2) elastic deformation; and
(3) crack growth, Figure 4-2.
School of Civil and Resource Engineering The University of Western Australia
62
Figure 4-2 The 3 main stages in a theoretical volumetric strain curve: crack closure, perfect elastic
deformation, and fracture propagation [110].
Based on the previous discussion, the sliding and/or crack closure can occur at any level
of stress. The lateral stress-strain curve will not be linear before the onset of dilatancy
due to the inelastic strain introduced by sliding and crack closure. It is not linear after
the onset of the dilatancy, either. Since both axial and lateral strain could be affected by
crack closure and sliding at all stress level, the volumetric strain could be nonlinear at
all stress level. It would be very difficult to distinguish the elastic part from the inelastic
parts of the deformation by stress-strain curve or volumetric strain curve in the loading
process.
To summarise, the non-linear deformation mechanisms associated with the crack
closure, crack sliding and crack propagation can occur simultaneously resulting in
changes in the overall stiffness of the rock. Before separating inelastic strain from total
strain, the first step is to understand the change in stiffness under stress in different rock
types. We analyse the dependence of the tangent moduli vs. stress in different rock
types in order to establish the trend of moduli in different rock types. Then, we will
evaluate the method of extracting the inelastic strain from the total strain by finding the
elastic part. We also performed a repeated load on all samples to understand the relation
School of Civil and Resource Engineering The University of Western Australia
63
between the modulus increase in the second load and the residual strain (permanent
inelastic strain).
4.3 EXPERIMENTAL APPARATUS AND ROCK PROPERTIES
We tested cylindrical samples of porphyry, slate, sandstone, felsic volcanics,
metasediment, ultramafic, pegmatitic granite and volcanic sediment from 13 locations
(12 boreholes, 205 samples) under uniaxial compression. The samples were 18-19mm
in diameter and 40mm- 45mm in length, as shown in Table 7. All samples were
prepared in accordance with ISRM standard for unconfined compressive strength [97].
The samples were loaded using a servo-controlled loading machine of 5t capacity. The
load was displacement-controlled, applied by the movement of the upper platform,
while the bottom platform was fixed.
Table 7 Details of the tested rock samples.
Location
ID
Rock type Number of
samples
Maximum applied
stress (MPa)
Secant modulus
(GPa)
FE4 Quartz diorite
porphyry complex
14 44-75 24-51
FE5 Quartz diorite
porphyry complex
18 35-75 31-62
WA45 Metasediment 17 55-70 18-58
WA51 Ultramafic rock 17 49-80 86-136
H782 Porphyry 17 81-102 51-66
H784s Porphyry 17 65-95 26-74
H784d Porphyry 18 55-90 53-70
FL Pegmatitic granite 16 45 34-71
CSA Sandstone 18 70-110 59-90
PR2 Slate 13 14-23 30-78
PR3 Slate 13 20-25 36-127
WAsd Metasediment 10 45-70 40-99
WAou Ultramafic rock 17 35-80 10-34
School of Civil and Resource Engineering The University of Western Australia
64
We used glued cross type strain gauges (Figure 3-2), which ensure simultaneous
measurements of the axial and lateral strains. All samples were subjected to 2 loading
cycles under a constant loading/unloading rate of 7~9MPa/min. The average strain was
calculated by taking average of readings of 4 strain gauges. The moduli of 1st loading
cycle were calculated by the moving average method applying to the average stress-
strain curve.
Figure 3-2 The cross type strain gauges were glued at the 4 spots shown in the graph.
4.4 TEST RESULTS AND DISCUSSION
4.4.1 The trend of tangent modulus at 1st cycle
The stress dependence of the tangent modulus can be classified into 3 types: increase,
constant, and decrease. The tangent modulus of the increase type usually reduces its
value at the beginning of loading (the stress of less than 15MPa in our tests). Then the
value of modulus increases steadily until high stress level before it drops and the sample
fails. The increase of modulus could be from 5 to 30MPa and appears to be rock type
dependent. This response (i.e. modulus of increase type) is the most common type in
our experience. The mechanism of modulus increase is believed to be crack closure.
Figure 4-3 shows an increase of 26GPa during loading in an ultramafic rock sample.
The tangent modulus of the constant type is usually unchanged in the region from mid
to high stress, followed by a dramatic drop in the modulus right before failing. The
value of modulus of this type does not represent pure elastic deformation. Figure 4-4
shows a porphyry sample with very little increase (<2GPa) in tangent modulus. The
close-to-constant value of modulus could be a misleading phenomenon, as it seemed to
Strain gauge
A
B D
C
Sample
School of Civil and Resource Engineering The University of Western Australia
65
indicate that there was no crack closure or crack propagation. However, the slope of
volumetric strain shows a slight increase in the value when the stress is increased.
Therefore, the volume change and the crack closure/propagation was taking place in this
case.
Figure 4-3 (a) An ultramafic rock sample shows maximum 26GPa increase in the tangent modulus
(black line), before reducing its value and failed. The UCS is 55MPa. The slope of volumetric strain
(grey line) increased its value during loading. (b) The volumetric strain (black line) shows a similar
trend as Figure 4-2. The dash line is a straight line which could be mistaken as a linear part of the
volumetric strain.
Figure 4-4 (a) A porphyry sample shows a less than 2GPa increase in the tangent modulus (black
line). The slope of volumetric strain (grey line) slightly increased its value during loading. (b)
Compared with the dash line (straight line), the volumetric strain is slightly non-linear during
loading.
0
250
500
15
35
55
0 50 100sl
ope
of v
str
ain
Mod
ulus
(G
Pa)
% of UCS
WA51 A1(a)
0
30
60
0 300 600
Str
ess
(MP
a)Strain (microstrain)
Volumetric strain(b)
80
110
140
40
60
80
0 30 60
slop
e of
v s
trai
n
Mod
ulus
(G
Pa)
Stress (MPa)
H784d C3
0
30
60
0 300 600
Str
ess
(MP
a)
Strain (microstrain)
Volumetric strain
School of Civil and Resource Engineering The University of Western Australia
66
The tangent modulus of the reduce type lowers its value from the beginning of loading
until the sample fails, Figure 4-5. A possible mechanism of this type of behaviour is
sliding over pre-existing cracks; as the stress increases the number of cracks where
sliding is possible increases as well, effecting the modulus reduction. Since the modulus
decreases consistently from the very low stress when no crack growth is yet possible,
the dilatancy-producing crack growth is expected not to be the dominant mechanism.
This conclusion is confirmed by the fact that the volumetric strain vs. stress is a straight
line (the slope of volumetric strain is unchanged by the increase in stress). The modulus
might reduce more steeply when the stress is close to the failure stress (i.e. the UCS). At
this stress level the crack growth is expected to occur and contribute to the modulus
decrease.
Figure 4-5 (a) A sandstone sample shows a 12GPa decrease in the tangent modulus during loading.
The source of decrease is expected to be sliding, because the decrease started at the beginning of
loading. The slope of volumetric strain (grey line) is unchanged. (b) The volumetric strain is a
straight.
4.4.2 The overlapping between the regions of crack closure, sliding and crack
growth
It is a common approach to find the linear part of the volumetric strain by drawing a
straight line to match part of the curve, for example the dash line in Figure 4-3(b).
However, it is not as accurate as it looks. The slope of the volumetric strain does not
show any linear part in the curve. Hence it is not possible to find the elastic deformation
140
170
200
55
75
95
0 50 100
slop
e of
v s
trai
n
Mod
ulus
(G
Pa)
Stress (MPa)
CSA C1
0
50
100
0 300 600
Str
ess
(MP
a)
Strain (microstrain)
Volumetric strain
School of Civil and Resource Engineering The University of Western Australia
67
region by volumetric strain. Furthermore, according to the Figure 4-3, there is no linear
part apparent in the stress-strain curve, because the tangent modulus constantly changes
during the whole loading cycle. Since the linear elastic deformation in the axial stress-
strain curve does not exist independently, but rather in a combination with non-elastic
one, it is possible that the crack closure process is still in place when the sliding and/or
dilatancy have already started.
Figure 4-4 and Figure 4-5 show a similar situation. The tangent modulus in Figure 4-4
remains effectively constant during whole loading cycle. However, the value of
modulus does not represent linear elastic behaviour due to the fact that there is observed
a non-elastic change in the volume. Figure 4-5 shows no change in the volume, but the
crack sliding had to place because of the consistent modulus reduction. Therefore, in
these 2 cases, the modulus of rock unaffected by crack closure, sliding, and growth
cannot be determined.
We have not found any sample with constant modulus but without inelastic volumetric
strain. Subsequently, in all 205 samples the pure elastic modulus of rock was not
measurable.
4.4.3 The increase of the modulus from 1st cycle to 2nd cycle
According to our results from the 205 samples, the residual strain in a completed load-
unload cycle of the 1st cycle is always observed. The amount of residual strain can vary
from less than 1% to more than 50% of the total reversible strain. The sources of
residual strain in our tests could be:
(1) The irreversible sliding in the loading cycle: The friction between the crack
surfaces stops the crack sliding back when the load is removed. The volumetric
strain is unchanged, because there is no increase in volume. The crack might/
might not slide back when a second cycle of load-unload is again applied with
the peak stress higher than the previous peak stress. The stiffness of the rock
increases when the applied load is in the same direction again due to the
irreversible sliding. An example of this case is shown in Figure 4-6(a), which
refers to the same rock type as the sample in Figure 4-5.
School of Civil and Resource Engineering The University of Western Australia
68
(2) The breakage of asperities on the crack surfaces when the crack slides: The
surfaces of an open crack might not be smooth and the sharp points might break
when crack slides. The volumetric strain reduces because the breakage occurs
together with crack closure. Some energy is consumed (dissipated) during the
breakage and the crack would not fully slide back to the original position during
the unloading cycle. Therefore, the volume of the crack reduces and the stiffness
of the rock increases when a second cycle is applied load axially. It might seem
to be controversial that the stiffness of the rock still increases after the load
introduces some damage (i.e. breakage of the asperities) to the rock. However,
the area which was subjected to the load increases after the asperities are broken
and the crack size reduced. The sample is more “compacted” after the breakage.
The possible example of this case is shown in Figure 4-6(b), which refers to the
same sample as Figure 4-3.
(3) Pore collapse: This is similar to case 2 but there is no movement in the lateral
direction in this case. The sample has to be porous and it requires high energy to
collapse the pores. In our samples, which are mostly hard rocks with modulus in
the range of 40-100GPa, it might be less likely to occur than for cases 1 and 2.
Figure 4-6 (a) The sample of decrease type in tangent modulus shows the residual strain after
unloading in the 1st loading. The secant modulus in the 2nd loading is higher than it in the 1st
loading. (b) The sample of decrease type in tangent modulus also shows certain amount of residual
strain. The secant modulus at the 2nd loading is higher than it at the 1st loading, although the sample
had reached 95% of UCS in the 1st loading.
0
60
120
0 800 1600
Str
ess
(MP
a)
Strain (microstrain)
CSA B1 Stress-strain plot
1st loading
2nd loading
0
30
60
0 1000 2000
Str
ess
(MP
a)
microstrain
WA51 A1 Stress-strain Plot
1st loading
School of Civil and Resource Engineering The University of Western Australia
69
We believe cases 1 and 2 are the more likely to be the source of residual strain and both
of them are relevant to the sliding mechanism, which can occur at any level of stress. In
addition, the higher the applied stress, the higher the initial unloading modulus, Figure
4-1, would be. It suggests that different levels of stress could mobilize different cracks
or different amount of cracks to slide. The initial unloading modulus does not represent
the “solid rock” but represents the rock mass with specific part of the cracks “locked”
due to the applied peak stress. Therefore, in the same type of rock, the amount of the
cracks that were locked during loading should have a particular relationship with the
amount of residual strain. The amount of residual strain at the 1st cycle should also have
a particular relationship with the increase in secant modulus at the 2nd cycle. According
to Figure 4-7, the difference between secant moduli at the 1st and 2nd cycles depends on
the amount of ∆ and :
∆
∆
∆ (4)
where is the secant modulus at 1st cycle, is the secant modulus at 2nd cycle. , ,
and ∆ are same as Figure 4-7.
Figure 4-7 The loading stress-strain curve at 1st and 2nd cycles. is the maximum stress of 1st and
2nd loading cycles, is the maximum strain of the 1st cycle, is the residual strain of 1st cycle, and
∆ is the difference between maximum strain at 1st cycle and 2nd cycle.
In all 205 tests, ∆ is much smaller than and it is less than 4% of . We assume
∆ ≪ develop (5) in Taylor series with respect to small parameter ∆ / keeping
Str
ess
Strain
Stress-strain curve at 2 cycles
∆
School of Civil and Resource Engineering The University of Western Australia
70
only the linear term. Assuming that ∆ , where can be different in different rock
types we obtain:
(5)
Equation (5) predicts a linear relationship between the increase in the secant modulus
/ and the portion of residual strain ( ) in each rock type. Figure 4-8 shows the
results of this relationship obtained in our tests and the fitted regressions lines. Similar
observation can be made by looking at the experimental data found in the literature
[111]. We have calculated the portion of residual strain and the secant modulus visually
from the figures in [111]. The results of the determination of are shown in Figure 4-9.
The value of in some locations might not be as accurate as other locations because the
residual strain is very small and the electronic noise can cause more significant errors.
The value of is between 0.1 to 0.2 in 11 out of 13 locations. Figure 4-10 shows that
the average value of for all 205 samples is 0.12.
School of Civil and Resource Engineering The University of Western Australia
71
Figure 4-8 (continue to next page)
y = 0.7835x + 1.0039R² = 0.9619
1.00
1.20
1.40
0.00 0.20 0.40 0.60
E2/
E1
residual/ total reversible strain
WAou residual strain vs E increase
y = 0.7568x + 1.0063R² = 0.8916
1.00
1.10
1.20
0.00 0.10 0.20
E2/
E1
residual/ total reversible strain
WAsd residual strain vs E increase
r = 0.16
y = 0.8055x + 1.0054R² = 0.9705
1.00
1.10
1.20
0.00 0.12 0.24
E2/
E1
residual/ total reversible strain
FE4 residual strain vs E increase
r = 0.14
y = 0.7486x + 1.0011R² = 0.9776
1.00
1.07
1.14
0.00 0.10 0.20
E2/
E1
residual/ total reversible strain
FE5 residual strain vs E increase
r = 0.20
y = 0.833x + 0.9956R² = 0.9497
1.00
1.03
1.06
0.00 0.05 0.10
E2/
E1
residual/ total reversible strain
PR2 residual strain vs E increase
r = 0.16
y = 0.7321x + 1.0001R² = 0.9671
1.00
1.03
1.06
0.00 0.05 0.10
E2/
E1
residual/ total reversible strain
PR3 residual strain vs E increase
r = 0.22
y = 0.8445x + 0.9975R² = 0.9858
1.00
1.20
1.40
0.00 0.20 0.40 0.60
E2/
E1
residual/ total reversible strain
WA45 residual strain vs E increase
r = 0.10
y = 0.8381x + 1.0093R² = 0.7964
1.00
1.07
1.14
0.00 0.09 0.18
E2/
E1
residual/ total reversible strain
WA51 residual strain vs E increase
r = 0.12
School of Civil and Resource Engineering The University of Western Australia
72
Figure 4-8 The relationship between the portion of residual strain and the increase in secant
modulus. Each black dot is the result of each sample. The equation shown at the top of each graph
is the linear trend line (black line) of all results. The dash line is the calculated value of regarding
to the value of shown in each graph.
y = 0.8094x + 1.0004R² = 0.9826
1.00
1.05
1.10
0.00 0.06 0.12
E2/
E1
residual/ total reversible strain
H784s residual strain vs E increase
r = 0.14
y = 0.7061x + 1.0023R² = 0.824
1.00
1.02
1.04
0.00 0.02 0.04
E2/
E1
residual/ total reversible strain
H784d residual strain vs E increase
r = 0.16
y = 0.9367x + 0.9982R² = 0.8898
1.00
1.02
1.04
0.00 0.02 0.04
E2/
E1
residual/ total reversible strain
H782 residual strain vs E increase
r = 0.08
y = 0.7872x + 1.001R² = 0.8795
1.00
1.02
1.04
0.00 0.03 0.06
E2/
E1
residual/ total reversible strain
CSA residual strain vs E increase
r = 0.16
y = 0.8859x + 0.9954R² = 0.9775
1.00
1.10
1.20
0.00 0.10 0.20 0.30
E2/
E1
residual/ total reversible strain
FL residual strain vs E increase
r = 0.10
School of Civil and Resource Engineering The University of Western Australia
73
Figure 4-9 The relationship between residual strain and the increase in modulus from [111] is
similar to our results in Figure 4-8.
Figure 4-10 The relationship between the portion of residual strain and the increase in secant
modulus in all samples.
4.5 CONCLUSION
There are several approaches to separate the inelastic deformation from total strain. It
has always been a difficult task to find the linear elastic part of the stress-strain curve
that represents the behaviour of the solid rock without pre-existing cracks. In order to
evaluate the common approach used on finding the elastic property of a solid rock, we
y = 0.9534x + 1.0009R² = 0.9719
1.00
1.30
1.60
0.00 0.30 0.60E
2/E
1residual/ total reversible strain
Residual strain vs E increase
r = 0.06
y = 0.818x + 1.0002R² = 0.9833
1.0
1.1
1.2
1.3
1.4
1.5
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Residual Strain vs E increase in all samples
all samples
r = 0.12
Linear (all samples)
School of Civil and Resource Engineering The University of Western Australia
74
have tested 205 samples from 12 locations and completed two loading/unloading
uniaxial compressive cycles.
We found that the trend of tangent modulus at the 1st cycle can be expressed by 3 types
of behaviour: increase type, constant type, and reduce type. All 3 types of behaviour
cannot truly represent the modulus of solid material, and we contend there is an
overlapping of crack closure, sliding and crack propagation in the stress-strain curve.
Therefore, the “finding elastic part” from stress-strain curve might mislead the
understanding of real rock behaviour.
We found that contrary to a common belief that the rock reduces its stiffness after
repeated loads it may actually increase. Furthermore, this increase is controlled by the
residual strain of the first unloading. We experimentally showed that the secant modulus
of the 2nd cycle is higher than it at the 1st cycle, and the increase is proportional to a
certain portion of residual strain. This relationship is independent of the maximum
stress level a rock had been subjected to and it seems to be similar for different rock
types.
School of Civil and Resource Engineering The University of Western Australia
75
CHAPTER 5. THE MECHANISM OF THE DEFORMATION
MEMORY EFFECT AND THE DEFORMATION RATE
ANALYSIS IN LAYERED ROCK IN THE LOW STRESS
REGION
5.1 ABSTRACT
We propose a new mechanism to explain the deformation memory effect based on
sliding over pre-existing sliding planes. Sliding resistance can comprise an element of
cohesion and an element of frictional resistance. In this model only the cohesion is
considered. The mechanism is modelled for a particular case of parallel sliding planes
typical for layered rocks. The model consists of a number of identical basic elements
comprising 2 springs, a St. Venant body and a dashpot. The basic elements only differ
in their cohesion. The loading regime incorporating the influence of the delay time was
modelled with one, two and 500 basic elements. The results showed that the recoverable
stress magnitudes were in the range between the minimum and twice the maximum of
cohesion. The model demonstrates the experimentally observed memory fading
whereby the fidelity of stress reconstruction reduces with the increase in the time delay
between the previous load the rock was subjected to and the measuring cycles.
5.2 INTRODUCTION
Knowledge of the in situ stress state is critical for both understanding the basic
geological processes and for safe and economical design of structures in and on rock
masses [112]. There is a large number of stress determination methods, the most
common being the stress relief methods ranging from overcoring and door stopper to
under excavation methods; stress compensation methods such as flat and cylindrical
jack methods; fracture/damage evolution methods such as hydraulic fracturing, borehole
breakouts and core disking methods; structural response methods (seismic wave
velocity and x-ray diffraction). The deformation rate analysis (DRA) method based on
the rock deformation memory effect is attractive because it can utilise oriented diamond
School of Civil and Resource Engineering The University of Western Australia
76
cores that are accumulated in great numbers at the exploration stage. This means the
method is also economical.
The rock has been found to be able to store the information about the stress to which it
was exposed, which is called the rock memory effect [60]. Many manifestations of the
memory effect in the rock have been found, including the deformation memory effect,
the Kaiser effect [2], electrical memory effect, ion emission memory effect and so on
(see the review [60]). These manifestations are observed when the rock is subjected to
several loading-unloading cycles. When the peak stress previously applied is attained in
the following loading cycle, one can observe a change in the slope of the stress-strain
curve (the deformation memory effect). If the load is sufficiently large to produce
internal damage an increase in the AE activity (the Kaiser effect) can be observed.
The most common methods of recovering the maximum stress the rock was previously
subjected to, use either the Kaiser effect or the deformation memory effect. The method
based on the acoustic emission detects the stress the rock was subjected to in the
previous loading by a change of the slope in the curve of “cumulative acoustic emission
hits versus stress” [4]. As for the deformation memory effect, the identification method
involves detecting the gradient change in the stress-strain curve. However, as pointed
out by [57], this method was unreliable as the changes in gradient were often not
distinct. To solve this problem, [57] proposed the DRA method. Firstly, the strain
difference function Δεi,j(σ) is defined for a pair of the ith and the jth loading cycle
on rock sample by
Δεi,j(σ)= εj(σ)- εi(σ), j > i (6)
where, εi(σ) denotes the axial strain in the ith loading stage; σ is the applied stress.
Equation (6) removes the linear and nonlinear components of elastic strain as well as the
invariable components of inelastic stain common to both cycles leaving only the
difference between the inelastic strains attained in the two cycles of loading. Using the
inflection point
exhibited by Δεi,j(σ), the magnitude of the previously attained peak stress can be
determined. Hereafter the inflection is called the “DRA inflection”. According to [60],
School of Civil and Resource Engineering The University of Western Australia
77
[63] and [28], in the course of time, the DRA inflection becomes unclear or even
disappears. This phenomenon is the memory fading.
The DRA method and the strain difference function are illustrated in Figure 5-1.
Figure 5-1 Illustration of the deformation rate analysis (DRA) (a) the definition of the strain
difference function Dei,j(r) and (b) the plot of Dei,j(r) (DRA curve) and the DRA inflection.
The deformation memory effect and the DRA method have been extensively studied
since it was proposed [26, 27, 29, 32, 57, 62, 64, 66, 86, 113]. Yamamoto et al.[57]
conjectured that the appearance of the inflection point in the DRA curve was due to the
same mechanism as the Kaiser effect - the growth of pre-existing cracks in compression
by wing generation. They further suggested that, the growth of pre-existing cracks in a
rock specimen caused non-linear strains that included both reversible strain and
irreversible components. In their opinion, the reversible strain components included
frictional sliding, isolated tensile cracks opening and closure and a change in the density
of the tensile cracks. All this kind of non-linear behaviour in strain was considered to be
reversible during many cycles of loading, as long as the pre-existing cracks did not
change in size. The irreversible stain component resulted from the growth of pre-
existing cracks and from the generation of new cracks when the applied stress exceeded
the peak stress previously applied. The reversible strain was cancelled by the equation
(6), while the irreversible component of the non-linear strain was emphasized by the
strain difference function. This notion was shared by [55] and [32].
School of Civil and Resource Engineering The University of Western Australia
78
Based on the shear micro-fracturing models developed by [114], Tamaki et al. [58]
further pointed out that the inelastic strain increased linearly with the applied stress as
long as the applied stress was smaller than the previous peak stress. However, when the
applied stress was larger than the previous stress, there would be a change in the
gradient of strain dependence upon stress. This change would be detected by the DRA.
From 1991, Tamaki and Yamamoto [59], Yamamoto [62], and Yamamoto and Yabe
[64] adopted a similar explanation for the deformation memory effect as Yamamoto et
al. [57]and Tamaki et al. [58]. Yamamoto [113] developed this concept further, based
on the model from [114]: when the applied stress is smaller than the previous stress, the
strain difference function is approximately linear to the applied stress, while, when the
applied stress is larger than the previous stress, the derivative of the strain difference
function becomes negative. The reasons include two factors: 1) The micro-fractures
began to occur at the point where the applied stress reached the previously applied peak
stress; 2) The occurrence of the microfractures caused the inelastic strain rate to
increase.
Yamshchikov et al. [60] reviewed all the memory effects and the mechanism of the
deformation memory effect. They pointed out that most researchers related the
mechanism of the deformation memory effect to the occurrence and development of
defects in rock at various scale levels – from point and linear lattice defects to micro-
and macrofractures. They also indicated the model developed by Kuwahara, et al. [114]
could not explain a number of features of deformation memory effect, such as the
memory fading.
Hunt et al [26, 27]suggested that the DRA inflection is a manifestation of the Kaiser
effect. By numerical simulation based on a contact bond model in PFC2D (two-
dimensional Particle Flow Code), they confirmed the link between the Kaiser effect and
the development of micro-cracks. What’s more, from the results of numerical
simulation, they also confirmed that, if the loading is below the crack initiation stress
neither the Kaiser effect nor the deformation memory effect would be observed.
As seen from the above, most papers adopted the following approach to explain the
formation of the deformation memory effect suggested by the DRA method: the
compressive load that the rock was subjected to generates new cracks and/or make the
School of Civil and Resource Engineering The University of Western Australia
79
pre-existing crack to grow. When the rock was extracted and hence unloaded and loaded
again, the following happen. While the stress magnitude in the second loading is lower
than the maximum stress achieved in the first one no new cracks can be generated or
grown. When the stress magnitude exceeds that previously attained, new cracks form
and/or grow. This leads to production of new acoustic pulses (Kaiser effect) and the
increase of the inelastic strain. The difference between inelastic strains in the loading
cycles leads to an inflection in DRA curve. Hereafter the model based on this
mechanism is called the “crack model”. Two things are required for this mechanism to
work. Firstly, the new loading is conducted precisely in the direction of the previous
loading. Secondly, the initial loading should be high enough to cause the crack
generation and growth.
There exists however experimental evidence that the rock memory can be detected by
the DRA method in the low stress region as well, where the stress level is much lower
than the crack initiation stress, such that no crack growth can be expected there. The
crack model does not work in this region and therefore another explanation is needed.
Furthermore, the crack model does not explain the memory fading – the reduction of the
detection power of the deformation memory effect with time elapsed between the
extraction of the rock sample from the stressed environment and the actual testing,
unless a sort of crack healing process is assumed.
This paper proposes frictional sliding as a new mechanism of the deformation memory
effect for a particular case of parallel sliding planes typical in layered rocks in the low
stress region. Based on this mechanism, a theoretical model was developed and
analysed. In section 5.3, some existing experimental results are reviewed. The DRA is
shown to be applicable in the low stress region. Section 5.4 describes a basic rheological
element consisting of a spring (the Hookean elastic body), Maxwell body and St.
Venant (St. V) body to simulate frictional sliding over a single interface (crack). The
deformation memory effect produced by two basic elements is discussed in Section 5.5.
Then a multi-element model comprised of many basic elements was developed to
simulate the rock with multiple parallel sliding planes in Section 5.6. Section 5.7
provides discussion of the results obtained.
School of Civil and Resource Engineering The University of Western Australia
80
5.3 EXPERIMENTAL EVIDENCE OF DRA WORKING IN LOW
STRESS REGION
The process of deformation and failure of brittle rock in (uniaxial) compression has
been studied extensively over the last four decades. Generally, five stages are identified
in the stress-strain curve [44, 49, 50, 53].
(1) Concave deformation curve reflecting the closure of pre-existing cracks and
perhaps the crushing of asperities and other imperfections of the sample
ends.
(2) Linear deformation, often modelled as elastic deformation.
(3) Crack initiation and stable crack growth.
(4) Critical energy release and unstable crack growth.
(5) Failure and/or post peak softening.
The demarcation of the second and the third stage is the crack initiation threshold.
When it is exceeded, generation of new and propagation of pre-existing cracks begin.
Prior to the crack initiation threshold is the linear elastic deformation region and the
crack closure stage where no crack production is expected to occur. Previous research
has identified the crack initiation threshold as occurring at 30% to 60% of the
unconfined compressive strength, UCS [43, 44, 49, 53, 54, 115].
Therefore, according to the crack model, both the Kaiser effect and the deformation
memory effect should only apply when the previous peak stress is greater than at least
30% of the UCS. There is however experimental evidence that DRA applies even when
the previous peak is below the crack initiation threshold. Yamamoto et al [57] reported
that for granodiorite core samples the DRA method could detect the in situ stress state
of approximately 1 to 6 MPa. Seto et al. [31] and Hunt et al. [27] showed the DRA
inflection existed when the pre-stresses were less than 15% of the UCS. Chan [28]
showed that the DRA method could determine the pre-stress that was less than 20% of
UCS. Furthermore, according to Yamshchikov et al. [60] the deformation memory
effect existed in both elastic deformation and plastic deformation stages.
School of Civil and Resource Engineering The University of Western Australia
81
If the stress is insufficient to produce micro damage, the only obvious mechanism of
nonlinear deformation left is the frictional sliding over pre-existing planes such as
cracks or intergrain boundaries. This paper attributes the formation of the deformation
memory effect to this mechanism. In principle, the sliding over the pre-existing planes
strongly depends upon their numerous orientations, which complicates the model. There
is however an important case that simplifies the analysis. This is the case of layered or
stratified rock where the sliding is related to the interlayer boundaries. In this situation
all sliding planes have the same orientation, Figure 5-2. An even more important
simplifying factor is that the displacement of sliding interfaces between the layers is
solely controlled by the deformability and rheology of the filler, with deformation of the
layers themselves only contributing to the overall strain of the sample. In particular,
without the filler and friction, the layers would slide indefinitely.
Figure 5-2 A rock sample with parallel sliding planes.
Parallel sliding planes traversing the whole sample are characteristic for layered and
stratified rocks that exist across the spectrum of sedimentary, metamorphic and igneous
rocks. In sedimentary rocks the stratification is often associated with bedding while in
igneous rocks it can be associated with lava flow. In metamorphic rocks it is
predominantly associated with the foliation that aligns normal to the direction of
shortening. The layering can have a profound effect on the behaviour of the rock.
School of Civil and Resource Engineering The University of Western Australia
82
The following sections introduce the model of the deformation memory effect
associated with non-destructive sliding over parallel planes and analyse the accuracy of
stress reconstruction by the DRA.
5.4 THE MECHANISM OF DEFORMATION MEMORY EFFECT
BASED ON FRICTIONAL SLIDING. THE BASIC ELEMENT
5.4.1 Frictional sliding over sliding planes
Frictional sliding with the associated non-linearity, residual strain and hysteresis is a
natural candidate for a mechanism of the deformation memory effect. This mechanism
is modelled to determine whether frictional sliding can produce the deformation
memory effect. Rock is assumed to contain a number of parallel pre-existing interfaces
or interlayer boundaries, referred to as “sliding planes”. The orientation of the sliding
planes is defined in terms of a Cartesian coordinates (x1, x2, x3), Figure 5-2. Consider a
representative volume element (a cube with faces normal to the co-ordinate axes)
containing sufficiently large number of sliding planes, apply uniform tractions at its
boundary and compute the average strain, which is the strain field averaged over the
volume element. Let the volume element be loaded by the external tractions such that in
the absence of the sliding planes it assumed uniform stress . Then the average shear
stress and strain are [116, 117]:
, ∑ (7)
where, is the strain that the surrounding rock would assume under the uniform
tractions without the sliding planes, is the unit normal vector to the surface of the
sliding plane, is the crack ‘volume’ which is the displacement discontinuity
integrated over the surface of sliding plane α. This displacement discontinuity is
controlled by the deformability and rheology of the filler.
The ‘volumes’ of the sliding planes do not have the normal component, ; the
shear components depend upon the applied load and slide with friction and also exhibit
time dependency. The summation is over all the sliding planes in the volume element.
Thus the average strain of the layered rock consists of two parts. One part is the
contribution of the elastic matrix. The other part is the combined contribution of all
School of Civil and Resource Engineering The University of Western Australia
83
sliding planes. In the low stress region below the crack initiation threshold, frictional
sliding would take place over the sliding planes under shear stress without the
production of wings [24]. This paper attributes the inelasticity presented by the DRA
method (or the formation of the deformation memory effect) to the frictional sliding
over the sliding planes.
Further simplifications are required to account for the influence of friction and rheology
on the deformation memory effect. To this end, friction is assumed to be characterised
by cohesion only. In other words, the influence of the compressive stress normal to the
sliding planes was neglected. This is an oversimplification required to reduce the
number of parameters to confirm whether the mechanism considered is capable of
producing detectable deformation memory effect and its core features such as the
memory fading.
Each sliding plane is modelled as a combination of springs, St. V body to model
cohesion and a dashpot to model time dependence, Figure 5-3. This model is referred as
a basic element. The rock is modelled as many sliding planes connecting these elements
in series. The elements are different in the values of their cohesions.
Figure 5-3 The basic rheological element.
School of Civil and Resource Engineering The University of Western Australia
84
5.4.2 The basic element
The basic element, Figure 5-3, consists of two parts that operate in series with each
other. The first part is the top spring (here designated as spring 2). It represents the
deformation of the rock between the sliding planes, which is assumed to be elastic. The
second part comprises the Maxwell body and the St.V body operating in parallel, the
“Maxwell||St.V” part. The strain of the “Maxwell||St.V” part represents the contribution
of the displacement discontinuity over the interfaces to the total strain. Both parts are
connected in series as the average strain in the layered rock is the sum of the average
strain of the matrix and the contribution of the sliding planes. In the “Maxwell||St.V”
part, the St.V body models the frictional sliding. When the stress of the St.V body
exceeds the yield stress (cohesion), it keeps sliding under the cohesion. The Maxwell
body models the elastic-viscous resistance of the interface filler to sliding and shall
describe the memory fading. The parameters of the model are:
(1) k2 is stiffness of spring 2.
(2) k1 is stiffness of spring 1 in the Maxwell body.
(3) η1 is the viscosity of the dashpot.
(4) co1 is the cohesion of the St.V body.
In this model the stress and strain are the shear stress and shear strain in the plane
parallel to the sliding planes. As spring 2 and “Maxwell||St.V” body are connected in
series, the force equilibrium dictates that the stress must be the same in both these
elements. The total strain is the sum of the two strains in each element. Therefore
(8a)
_ _ (8b)
For dashpot 1 and spring 1 in the Maxwell body,
_ _ / (8c)
_ _ (8d)
For the St.V body, there are two states, the state of sliding and the static state.
School of Civil and Resource Engineering The University of Western Australia
85
The sliding state:
| _ | co1 (8e)
The static state:
| _ | co1, (8f)
where, is the applied stress, is the total strain of the basic element, , are the
stress and strain of spring 2, , are the strain and stress of the “Maxwell||St.V” part,
_ , _ are the strain of dashpot 1 and spring 1 in the Maxwell body, _ is the
stress of the St.V body, is the initial strain of the “Maxwell||St.V” body. When
| _ | co1, the “Maxwell||St.V” body is locked by St.V body, thus .
5.4.3 Behaviour of the basic element
Loading regime
The loading sequence applied is shown in Figure 5-4. It starts with linear
loading/unloading characterised by the previous maximum stress . Then after a delay
time T the second and the third loading cycles, so-called measuring loading cycles, are
performed with the peak stress . All loading cycles are characterised by the same
loading/unloading rate r. ∆ , between the two measuring loading cycles are used
as DRA curve.
Figure 5-4 The loading cycles assumed for the modelling.
School of Civil and Resource Engineering The University of Western Australia
86
Numerical simulation of the response of the basic element
Given the above loading sequence, the basic element model contains a total of 8
independent parameters: k1, k2, η1, co1, r, T, and . Spring 2 represents the
elastic part of the strain in the model that does not change in the loading-unloading
cycle. Therefore it will cancel in the DRA curve. For that reason k2 is excluded from the
set of independent parameters as it has no influence on the DRA curve.
Dimensional analysis is used to reduce the number of parameters. The basic variables
co1 (stress) and r (stress over time) are defined. Using Buckingham’s π-theorem, five
independent dimensionless groups, η1r co12, k1 co1, rT/co1, co1, co1 and
three dependent dimensionless groups, co1, , rt co1 are identified. The independent
groups characterise the parameters of the basic element and the loading sequence, the
dependent group characterised the variables measured in the DRA tests. Furthermore,
the results indicated that the DRA curve does not change when the ratios η1r co12 and
k1 co1 are kept unchanged no matter what values the two parameters have. The
following dimensionless groups can be defined by combining the two dimensionless
parameters η1r k1co1:
(1) Independent dimensionless groups: π1= η1r k1co1; π2= rT/co1; π
3= co1; π4= co1.
(2) Dependent dimensionless groups: co1; .
(3) The following values of the dimensionless groups were chosen:
π1: 1, 5, 10, 50, 100, 500, 1000, 5000, 10000
π2: 1, 10, 100
(π3, π4): (1.2, 1.4), (1.6, 1.8), (2.2, 2.4), (2.6, 2.8)
Analysis of the results of numerical simulations
Figure 5-5 shows typical stress-strain curve and DRA curve. Up to two inflection points
can be seen in the DRA curve. Parameters σdra1 and σdra2 can be introduced which are
the stress magnitudes of the first and the second inflection points respectively
corresponding to the following dimensionless groups:
School of Civil and Resource Engineering The University of Western Australia
87
π01= σdra1/co1= f1 (π1, π2, π3, π4)
π02= σdra2/co1= f2 (π1, π2, π3, π4)
Figure 5-5 (a) The stress–strain curve and (b) the DRA curve in a test. The values of dimensionless
groups are: g1r/k1co1 = 100, rT/co1 = 10, rp/co1 = 1.6, rm/co1 = 1.8.
The DRA inflections only exist if previous maximum stress is in the range from one
cohesion to two cohesions, co1< <co2. When π3 and π4 are smaller than 1 (that is,
and are smaller than the cohesion), the “Maxwell||St.V” part of the model does
not permit any sliding. The model therefore behaves purely elastically and the DRA
technique does not recover the previous stress. When π3 is lower than 1 or larger than
2, there are still two inflection points in the DRA curve, however, this kind of inflection
has nothing to do with the memory of the previous loading; it is just the ‘memory’ of
cohesion or two times cohesion. Therefore, only the inflection stresses in the range from
cohesion to two times cohesion are important, which is called the DRA inflection in this
paper. Figure 6 shows the dependence of the two groups upon the dimensionless
parameters π1, π2 when π3 =1.2 and π4 =1.4 such that both of them are fixed in the
range of the previous stress from cohesion to two times cohesion.
The first DRA inflection reflects the memory of the peak stress in the previous loading,
while the second inflection reflects the memory of peak stress in the first measuring
School of Civil and Resource Engineering The University of Western Australia
88
loading cycle. That is to say, σdra1 is the memory of , while the σdra2 is the memory
of . Furthermore, the following characteristics were found:
1. As shown in Figure 5-6 the accuracy of the determination of previous peak stress ( )
using the first inflection point π01 depends upon π1 and π2. At the same value of π
2, with the increase of π1, σdra1 increases its value from the value of cohesion to .
The parameter π2 represents the delay time, at the same value of π1, the σdra1
reduces and thus becomes smaller than with the increase of π2, which is the time
delay between the previous loading and the measuring cycles. This represents the
memory fading in the basic element.
2. The accuracy of the determination of using the second inflection point π02
depends upon π1, while the influence of π2 and π3 is minor. With the increase of π
1, σdra2 increases its value tending to and thus missing , the very stress it is
supposed to reconstruct.
It is seen that the simplest model consisting of a basic element is capable of reproducing
the DRA in some cases. It is the first inflection point that represents the previous load in
the cases when it is measurable. It also reproduces the memory fading; that is the
decrease in the accuracy of stress reconstruction as the time between the previous
loading and the measuring cycle increases. The value of cohesion controls the
measurable values of the initial stress: it should be between the cohesion and two
cohesions. Another basic element with a different cohesion was added to its influence
on the results in the following section.
School of Civil and Resource Engineering The University of Western Australia
89
Figure 5-6 The relationship between σdra1/co1, σdra2/co1 and η1r k1co1, rT/co1, /co1 = 1.2,
/co1 = 1.4.
5.5 TWO BASIC ELEMENTS (SLIDING PLANES) WITH
DIFFERENT COHESIONS
5.5.1 Introduction to the model
The mechanical behaviour of a model with two basic elements was analysed to better
understand the influence of the connection of basic elements in series on the DRA
curve. The model with two basic elements is shown in Figure 5-7. Only the cohesion in
each basic element is different. Let cohesion of the second element be co2. The
equations for this model are as follows:
(9a)
(9b)
where, is the applied stress, is the total strain; , are the stress and strain in the
element 1; , are the stress and strain in the element 2. The behaviour of every
element follows the equations (3a-3f).
School of Civil and Resource Engineering The University of Western Australia
90
Figure 5-7 The model with two basic elements.
5.5.2 Behaviour of the model with two basic elements
The same loading program as that used for the basic element was used to analyse the
model (Figure 5-4). An additional independent dimensionless group, π5=co2/co1 was
included. The results show that:
(1) There are at most four potential inflection points in the DRA curve. This
could be expected, because two elements are connected in series and hence
the total strain is a sum of strains of two basic elements. Therefore, the
resultant DRA curve is also the sum of the DRA curves, each curve having
two different inflections due to different cohesions. Subsequently the
resultant DRA curve can, in principle, have 4 inflection points. σdra1 and σ
dra2 are denoted as the two inflections produced by the element 1, and σdra3
and σdra4 as those produced by the element 2. Similarly to the case of one
basic element, the four inflections are situated in the range from the
minimum cohesion to two times the maximum cohesion.
(2) The shape of the DRA curve depends on the mutual positions of σdra2 and
σdra3. For the case σdra2 > σdra3, the shape of DRA curve is shown in
Figure 8a. For the case σdra2 < σdra3, the shape is shown in Figure 5-8b. In
School of Civil and Resource Engineering The University of Western Australia
91
Figure 5-8b, the inflections for this case can hardly be called the “DRA
inflections”.
Figure 5-8 DRA curves for the model including 2 elements: (a) /co1 = 1.6, /co1 = 1.8; σdra2 > σ
dra3. (b) /co1 = 2.4, /co1 = 2.8; σdra2 > σdra3. The values of dimensionless groups are: η1r
k1co1= 100, rT/co1= 10, co2/co1 = 100.
5.6 A MODEL OF LAYERED ROCK WITH MULTIPLE BASIC
ELEMENTS (SLIDING PLANES)
5.6.1 Introduction to the model
The ultimate goal of modelling the rock with many sliding planes is achieved by using a
multi-element model, consisting of n basic elements (Figure 5-9). The elements are
connected in series reflecting the fact that each sliding plane or interface produces an
additive contribution to the average strain. The equations for the multi-element model
are as follows:
(10a)
∑ (10b)
where, is the applied stress, and are the stress and strain in the ith basic element.
The mechanical behaviour of each element follows the equations (8a) - (8f).
School of Civil and Resource Engineering The University of Western Australia
92
Figure 5-9 The multi-element model consisting of n basic elements.
A total of 500 basic elements (n=500) were used in the numerical simulation. To
simplify the parametric analysis, the elements only differ by their cohesions, since it is
the value of cohesion that provides the yardstick for the stress reconstruction. The
cohesions are generated randomly using the uniform distribution and the truncated
normal distribution. To enable the comparison, the parameters of both distributions are
chosen in such a way that they have the same mean value and standard deviation. The
loading regime is the same as previous, Figure 5-4.
5.6.2 DRA in multi--element model with 500 elements
Numerous numerical tests were performed on the multi-element model. The DRA curve
in the multi-element model is the sum of the DRA curves of the basic elements. A
typical stress-strain curve is shown in Figure 5-10. The results for the multi-element
model with 500 elements are as follows:
(1) The typical DRA curves are shown in Figure 5-11. The first feature which
distinguishes these curves from the curves produced by the two-element
model is that only up to two inflection points can be distinguished. Another
feature is that the line between these two inflection points is non-linear. This
suggests that all intermediate inflection points associated with the various
cohesions in the elements have merged together and are no longer
distinguishable; only the lowest and the highest inflection points survived as
School of Civil and Resource Engineering The University of Western Australia
93
separate features. Two points are denoted as σdra1 and σdra2. The inflections
are situated in the stress range from the minimum cohesion to 2 times the
maximum cohesion in the particular realisation of the set of cohesion values.
This is similar to what was observed in the basic element and in the two-
element model.
(2) There is little difference for the DRA curve between the normal distribution
and uniform distribution, which can be seen from Figure 5-11(a) and Figure
5-11(b). Thus the actual distribution of the cohesions of the sliding planes in
the rock is of secondary importance, as long as the statistical parameters
such as mean value and standard deviation are known. It should be noted,
only two-parametric distributions that are eventually controlled by the mean
value and standard deviation were tested.
(3) Similar to the basic element, the stress value σdra1 at the first DRA
inflection is the one to be used to recover the previous peak stress . The
stress value σdra2 at the second DRA inflection is the memory of , the
peak stress in the first measuring loading cycle.
(4) The accuracy of reconstruction of the previous load from σdra1 and σdra2 in
the DRA curve depends on the parameters and the dependences are similar
to the basic element.
(5) The memory fading in the multi-element model is different from the basic
element, which is another interesting feature. With the increase of delay time
T, the curve became smoother such that the inflection points are more
difficult to identify, Figure 5-12. This is the main manifestation of the
memory fading. Another manifestation is that with the increase in the time
delay, the accuracy of reconstruction decreases even if the inflection point is
identifiable.
School of Civil and Resource Engineering The University of Western Australia
94
Figure 5-10 Stress–strain curve in a test. (a) Uniformly distributed cohesions. (b) Normally
distributed cohesions. The range of cohesions in uniform distribution is 0.01–5 MPa. The mean
value is 2.505 MPa, the standard deviation is 1.4448 MPa. The loading regime is = 8 MPa, =
10 MPa, T = 0.
Figure 5-11 DRA curves for the multi-element model in the case in Fig. 10: (a) Uniformly
distributed cohesions. (b) Normally distributed cohesions.
School of Civil and Resource Engineering The University of Western Australia
95
Figure 5-12 The memory fading in the DRA. The loading regime is = 2 MPa, = 3 MPa, the
cohesion follows the uniform distribution described in Figure 5-10.
5.7 DISCUSSION
Firstly, the mechanism of the inflection points in the DRA curve (Δε2,3(σ)=ε3(σ)-
ε2(σ)) is discussed. After the first loading (called the previous loading) and unloading
is completed, the Maxwell body is locked by St.V body and thus the elastic potential
energy is stored in the spring of the Maxwell body. When the sum of the stress of
Maxwell body and the cohesion is exceeded in the 2nd loading, the St.V body will start
to slide. This action produces a change in the slope of ε2(σ) curve, which causes the
first inflection in the Δε2,3(σ) curve. In the same way, a change in the ε3(σ) will
also cause an inflection in Δε2,3(σ) curve, producing the second DRA inflection. The
stress detected by the DRA method consists of two components, one is the stress stored
in the Maxwell body and the other is the cohesion.
School of Civil and Resource Engineering The University of Western Australia
96
5.7.1 The role of the Maxwell body
When the Maxwell body is locked by the St.V body, stress relaxation occurs, which is
the mechanism of the memory fading. During the stress relaxation, the strain of the
locked Maxwell body is kept constant and the spring releases the elastic potential
energy through the dashpot with time. The stress relaxation is:
(11a)
where, is the initial stress of the Maxwell body. From this equation, the rate of the
Figure 5-13. Stress relaxation in different parts of the loading regime leads to different
phenomena in the DRA curve.
The stress relaxation during the second unloading and initial stage of the third loading,
leads to the second DRA inflection. At the moment when the second loading is
completed, its peak stress value is stored by the “Maxwell||St.V” bodies. However, due
to the stress relaxation, the stress in the Maxwell body decays. When the sum of the
non-intact stress of the Maxwell body and cohesion is attained in the third loading, a
change of the slope of the ε3(σ) curve will happen, which introduces the second
inflection in the Δε2,3(σ) curve. That is why the second DRA inflection is the
memory for the second loading or and why σdra2 is independent of and the delay
time, T.
School of Civil and Resource Engineering The University of Western Australia
97
Figure 5-13 The stress relaxation in a Maxwell body locked by the friction element. =1MPa, t0=0.
The stress relaxation in the first unloading, delay time and the initial stage of the second
loading leads to the accuracy loss of the stress determination form the first DRA
inflection point.
The results of simulations of both the basic element and the multi-element model show
that the accuracy of the DRA method depends upon π01=η1r/k1co1. This result is
related to the fact that the rate of stress relaxation in the Maxwell body is controlled by
η1/k1.
The higher η1r/k1co1, the less will be the loss of the potential energy of spring 1. In the
laboratory, the first DRA inflection occurs nearly at the previous peak stress. It can be
inferred that, the value of η1r/k1co1 is high enough for the second inflection to occur
nearly at the peak measuring stress, where only a very short tail of the DRA curve
exists. As the tail is short, it is difficult to detect the second inflection, see Figure 5-5
and Figure 5-12.
School of Civil and Resource Engineering The University of Western Australia
98
Based on the characteristics of η1r/k1co1, the conclusion can be drawn that, if the
properties of the rock sample do not change, the higher the loading rate r the more
accurate will be the DRA reconstruction.
The stress relaxation during the delay time is a mechanism of the memory fading. For a
basic element, along with the increase of the delay time, the detected stress becomes
farther from the previous peak stress, falling to the cohesion value. In the multi-element
model, the DRA curve becomes smoother due the increase of the delay time, as shown
in Figure 5-12.
5.7.2 The role of the St.V body
The St.V body controls the range where the DRA method can work. When one loading
cycle is finished, the stress stored by the Maxwell body cannot exceed the cohesion,
otherwise, the St.V body would continue to slide keeping the stress of the Maxwell
body equal to the cohesion. That is to say, the stress values that the Maxwell body can
store range from zero to the value of cohesion. What the DRA method can detect is the
sum of the stress in the Maxwell body and the cohesion. Therefore, the stress that the
DRA method can detect is in a limited range from the minimum cohesion to two times
the maximum cohesion.
5.8 CONCLUSIONS
Rocks and some other heterogeneous materials can ‘remember’ the maximum load to
which they have been subjected. One of the methods to read the rock memory and thus
recover the previous maximum load is the deformation rate analysis (DRA) whereby the
sample is subjected to at least two cyclic loads and the strain difference between two
consecutive loads is plotted against stress (the DRA curve). The stress that corresponds
to the inflection point on the DRA curve is believed to represent the maximum stress of
the previous load.
It is traditionally assumed that the DRA can only recover the previous stresses that are
high enough to induce crack initiation or propagation. Some experiments found in the
literature show that the DRA can also detect lower stresses, insufficient to induce any
damage accumulation in rock. The current study puts forward a mechanism of stress
memory based on frictional sliding over internal planes. A model of this mechanism for
School of Civil and Resource Engineering The University of Western Australia
99
a particular case of materials with parallel sliding planes such as for instance layered
rocks was developed.
It is considered a simplified rheological model where friction is reduced to cohesion and
a dashpot element is introduced to account for the time-dependent behaviour of the
interfaces of the sliding planes. In the simulations the cohesions are assumed to be
different on different interfaces, while all other parameters are kept the same. It is
demonstrated that the frictional sliding mechanism does produce inflections in the DRA
curves. Results show that the main controlling parameter is the range between the
minimum and the maximum cohesions; the maximum previous stresses falling in this
range are detectable, all other stress values are not detectible.
The larger the number of the sliding planes the wider the detectible stress interval was
expected. However the increase of their number, essentially the increase in the sample
size, leads to a smoother DRA curve and subsequently to a reduction of accuracy of the
identification of the inflection points. This leads to a reduction of accuracy in the stress
reconstruction. The accuracy of the stress determination also depends upon a
combination of the rheological parameters of the material and interfaces and the loading
rate. Thus the loading rate becomes an important parameter and essentially the only one
parameter that can be controlled. Its reduction leads to decrease in the accuracy of
reconstruction. While it is tempting to take the number of sliding planes, i.e. the sample
size as another controlling parameter, in practice there are considerable restrictions in
the sample size because of the requirement that the samples be subcored from a core in
many different directions in order to locate samples oriented in the principal directions
of the previous loading.
The presence of the dashpots leads to stress relaxation that becomes stronger with the
increase in the time elapsed between the previous loading and the laboratory measuring
cycles. This provides an explanation of the memory fading whereby the fidelity of stress
reconstruction reduces with the (usually uncontrollable) time delay between collecting
the sample from the stress environment and the DRA testing.
Thus the frictional sliding over pre-existing interfaces can serve as a mechanism of
deformation rate effect in the low stress region below the threshold of crack initiation
and production.
School of Civil and Resource Engineering The University of Western Australia
100
Acknowledgements Haijun Wang acknowledges the financial support by China
Scholarship Council, the Fundamental Research Funds for the Central Universities in
China (2010B13914) and Jiangsu 2010 College Graduate Student Research and
Innovation Program Foundation (CX10B_215Z). Arcady Dyskin acknowledges the
financial support from the Australian Research Council through the Discovery Grant
DP0988449 and the support from the West Australian Geothermal Centre of Excellence.
School of Civil and Resource Engineering The University of Western Australia
101
CHAPTER 6. THE MECHANISM OF THE DEFORMATION
MEMORY EFFECT IN THE LOW STRESS REGION AND
THE DEFORMATION RATE ANALYSIS
6.1 ABSTRACT
The deformation rate analysis (DRA) method based on the deformation memory effect
has an inherent advantage in determining the in situ stress. It was initially assumed that
the rock memory was created by crack generation and propagation under the previous
load. However, experimental evidence shows that the deformation memory effect can
also be detected in the low stress region where no new crack generation is expected.
Other unexplained phenomena were the memory fading, the influence of holding time of
preload and preload times. The lack of a theoretical model prevents the correct
interpretation of experimental data and improvement of the DRA method. In this paper,
experimental evidence was reviewed and it was postulated that the frictional sliding
over pre-existing cracks, interfaces and grain boundaries was the controlling factor for
the deformation memory effect in the low stress region. A basic model that consists of
springs, St. Venant body and dashpot in one dimension for simplification was
constructed and then a multi-element model with many basic elements was developed to
simulate the rock specimen with large number of interfaces. The results demonstrate
that the new theoretical model explains the deformation memory effect as well as its
many characteristics, such as the memory fading and the influence of the holding time
of the preload and preload times on the accuracy of the DRA method. The new
theoretical model also provides a potential explanation of why the in situ stress belongs
to long term memory effect and showed the difference between artificial memory and in
situ stress memory.
6.2 INTRODUCTION
The in situ stress state is a critical factor in both the basic geological processes and the
stability of underground structures [118] and open pit excavations [119]. In order to
gain the knowledge of the stress state, a large number of stress determination methods
are used [120], the most common are the stress relief methods (e.g., overcoring and door
School of Civil and Resource Engineering The University of Western Australia
102
stopper methods); stress compensation methods (e.g., flat and cylindrical jack methods);
fracture/damage evolution methods such as hydraulic fracturing, borehole breakouts and
core disking methods and structural response methods (seismic wave velocity methods
and the x-ray diffraction method). In the past two decades another type of stress
reconstruction methods have been gaining attention. These are the rock memory
methods based of the ability of rock to remember some preloads. The information about
the preload can be preserved for some period of time and later revealed via some
physical variables under certain conditions. The rock memory methods have a natural
advantage in that they can use the cores accumulated in great numbers at the exploration
stage and do not require stress recalculation from the strain measurements and hence
avoid the tedious determination of generally anisotropic elastic moduli of the rock
[121]. A number of types of the memory effect have been confirmed [60] including the
deformation memory effect (DME). In the latter case the magnitude of preload
(including in situ stress) can be reconstructed using the deformation rate analysis (DRA)
method.
Yamamoto, et al. [122], Tamaki and Yamamoto [59], Yamamoto [62], Yamamoto and
Yabe [64] conjectured that the deformation memory effect is based on the same
mechanism as the Kaiser effect (KE) – sharp increase in the acoustic emission count
when the applied stress exceeds the preload value – that is the development and growth
of wing cracks from pre-existing cracks in compression. The growth of wing cracks in a
rock specimen caused non-linear strains that included both reversible strain and
irreversible components. In their opinion, the reversible strain components included
isolated tensile cracks opening and closure and change of density of the tensile cracks.
The irreversible stain results from further wing cracks growth when the applied stress
exceeds the peak stress attained in the preload. This description was shared by Seto et
al. [123] and Villaescusa et al. [32].
Based on the shear micro-fracturing models developed by Kuwahara et al. [124],
Tamaki et al. [58] found that, the inelastic strain increased linearly with the applied
stress as long as the applied stress was smaller than the preloaded peak stress. However,
when the applied stress was larger than the preloaded peak stress, there would be a
change in the gradient of strain dependence upon stress. This change would be detected
by the DRA.
School of Civil and Resource Engineering The University of Western Australia
103
Yamamoto [113] developed this concept further, based on the model by Kuwahara et al.
[124]: when the applied stress is smaller than the previous stress, the strain difference
vs. stress dependence is approximately linear, while, when the applied stress is larger
than the preloaded peak stress, the derivative of the strain difference function becomes
negative. The reasons include two factors: 1. The micro-fractures began to occur at the
point where the applied stress reached the preload peak stress and 2. The occurrence of
the micro-fractures caused the inelastic strain rate to increase.
Yamshchikov et al. [60] reviewed the proposed mechanisms of the deformation memory
effect and pointed out that most researchers related the mechanism to the occurrence
and development of defects in rock at various scale levels – from point and linear lattice
defects to micro- and macro-fractures. He also indicated the model developed by
Kuwahara et al. [124] could not explain a number of features of the deformation
memory effect, such as memory fading (MF).
Hunt et al. [26, 125] suggested that the DRA inflection was a manifestation of the KE.
By numerical simulation based on the contact bond model in PFC2D (two-dimensional
Particle Flow Code), they confirmed the link between the KE and the development of
micro-cracks. What’s more, from the results of numerical simulation, they also
concluded that, if the loading was below the crack initiation stress, neither the KE nor
the DRA would be able to reveal the rock memory.
As seen from the above, most of papers adopt the following line to explain the
formation of deformation memory effect suggested by the DRA method: generation of
new cracks and crack propagation in compression lead to increase of the inelastic strain
rate, difference of inelastic strain in cyclic loadings leads to an inflection in DRA curve.
Hereafter this approach is called the “crack model”.
We note however that there exists however experimental evidence [60, 85, 122, 123,
125] that the deformation memory effect can be detected by the DRA method in the low
stress region as well, where the stress level is much lower than the crack initiation
stress, such that no crack growth can be expected there. Since the crack model does not
work in this region, another mechanism of the deformation memory effect is needed.
Wang et al. [69] developed a simplified theoretical model for the layered rock based on
the frictional sliding between interfaces. The formation of the deformation memory
School of Civil and Resource Engineering The University of Western Australia
104
effect and the MF was explained by this model [69]. The main drawback of Wang’s et
al. [69] model is that it assumed that in the rock sample the difference between strains in
the consecutive loading cycles is fully defined by the sliding over interfaces. In other
words, the effect of deformation of rock between the interfaces is neglected. This might
be appropriate for layered rock where the average strain of the rock is the same for all
interfaces and gets cancelled when the difference of strain in different loading cycles is
computed, but can not be used when the interfaces are formed by randomly distributed
small pre-existing cracks or grain boundaries.
Besides the above drawbacks of the "crack model" and Wang's et al. model [69], there
are many other unexplained phenomena of the deformation memory effect and
questions in the application of the DRA method:
(1) Great difficulty in determining the correct DRA inflection, since the DRA curve
has so many different inflections [66] or changed gradually [126].
(2) The difference between the artificial memory effect and in situ stress memory
effect [113] and why in situ stress memory belongs to a long term memory.
(3) The MF observed in some experiments and its absence in the other [86, 127].
(4) Observations that the holding time [26, 123] and repeated preloads [28, 127]
could initiate a better DME without understanding the reasons.
This paper aims to develop a theoretical model for the DME in the low stress region,
based on the viscous frictional sliding over pre-existing cracks and grain boundaries
(called as interfaces hereafter) in the rock. We first introduce the DRA, review the
existing experimental results (Section 6.3) and the results of our own physical
experiments (Section 6.4) showing that the DRA can detect the previous load even if it
is lower than the stress needed to initiate wing cracks. We then proceed with describing
a new theoretical model based on frictional sliding as a mechanism of deformation
memory effect under low stresses. A basic rheological element consisting of springs
(the Hookean elastic body), Maxwell body and St.Venant (St. V) body (Section 6.5)
was constructed to model the frictional sliding over a single interface (crack). The
deformation memory effect produced by a single basic rheological element is also
discussed in this section. Then a multi-element model comprised of many basic
School of Civil and Resource Engineering The University of Western Australia
105
elements is developed to simulate the rock with many pre-existing cracks (Section 6.6).
Section 6.7 presents discussion of the results obtained and comparison with the
experimental results.
6.3 THE DEFORMATION MEMORY EFFECT AND DRA IN
LOW STRESS REGION
6.3.1 The DRA method
The deformation memory effect takes place in the rocks subjected to cyclic loadings.
Take the cyclic uniaxial loadings as an example ( Figure 6-1(a)): when the peak stress
σp in the preload is attained in the following loading (the ith loading), a change in the
slope of the stress-strain curve of the ith loading will happen, called the deformation
memory effect. The preload in Figure 6-1 can be artificial loading in the laboratory or
geological force that forms the in situ stress. If the preload is the artificial loading
(laboratory preload), it is called as "artificial memory effect", while the geological force
corresponds to "in situ stress memory effect". The ith and the jth loadings are called as
measuring loadings.
The direct method to detect the rock memory is to detect the gradient change in the
stress-strain curve. However, the changes in gradient are usually not sufficient for
reliable detection [122]. To solve this problem, Yamamoto et al. [122] proposed the
Deformation Rate Analysis (DRA). Firstly, the strain difference function Δεi,j(σ) is
defined for the ith and the jth loading cycle on rock sample by
Δεi,j(σ)=εj(σ)- εi(σ), j>i (12)
Here, εi(σ) denotes the axial strain in the ith loading stage; σ is the applied stress.The
strain difference function is illustrated in Figure 6-1(b) and (c). Equation (12) presents
the difference between the inelastic strains attained in the two cycles of loading. It is
seen from Figure 6-1 that there is an inflection in the Δεi,j(σ) curve (DRA curve) at σDRA,
called DRA inflection. The magnitude of σp can be determined provided that the cyclic
loading is conducted precisely in the direction of the preload at σDRA (For KE, the
allowable mismatch between the directions was identified as ±10˚ [88, 128]. However,
it is unknown for the DRA).
School of Civil and Resource Engineering The University of Western Australia
106
Figure 6-1 Illustration of the DRA method: (a) loading cycles (b) the definition of the strain
difference function Δεi,j(σ), the horizontal bar shows the differential strain between successive
loadings (c) the plot of Δεi,j(σ) curve (DRA curve) and the DRA inflection(after Yamamoto[113]).
The deformation memory effect has many specific features. The DRA inflection
becomes unclear or even disappears in the course of delay time (Td) [60, 77, 129, 130].
This is called the memory fading(MF). We note however that the rock sample subjected
to the in situ stress can keep the stress information for a considerable period of time
(holding time). It has been observed that the clearness of deformation memory effect
manifestation increases along with the holding time (Tc) of preload acting on the rock
[60, 123, 125]. If the holding time is below a certain threshold, the deformation memory
effect would pick up a lower stress value with the decrease of the holding time [60].
More repeated preloads are suggested and used to initiate successful stress
“memorization” in the laboratory experiments [25, 86, 123, 127].
Generally, the precise in situ stress is unknown, which greatly affects the comparison
between the results by the DRA method and the real in situ stress. Therefore, most
σ
σm
σp
t
Delay time
Td
Preload
Measuring loadings
0
Straingauge
Loading
Sample
i j
Holding time Tc
(a)
σ
ε
Δεi,j
i j
(b)
Preload
σm
σp
Measuring loadings Δε
σ
DRA curve
(c)
DRA inflection
σDRA
School of Civil and Resource Engineering The University of Western Australia
107
researchers [85, 122, 127] investigated the DRA efficiency using so-called artificial
memory effect (laboratory preload) to simulate the in situ stress.
6.3.2 Experimental evidence of DRA working in low stress region
The process of deformation and failure of brittle rock in (uniaxial) compression has
been extensively studied over the last four decades. Generally, five stages are identified
in the stress-strain curve [44, 49, 50, 53]. They are (1) concave deformation curve
reflecting the closure of pre-existing cracks and perhaps the crushing of asperities and
other imperfections of the sample ends, (2) linear deformation, often modelled aselastic
deformation, (3) wing crack initiation followed by its stable growth, (4) critical energy
release and unstable crack growth, (5) failure and/or post peak softening. The
demarcation of the second and the third stage is the wing crack initiation threshold.
When it is exceeded, the generation and propagation of new cracks begin. Below the
crack initiation threshold is the linear elastic deformation region and the crack closure
stage where no crack production is expected to happen. The previous research identified
the crack initiation threshold to fall in the range from 30% to 60% of the unconfined
compressive strength (UCS) [43, 44, 49, 51, 53, 54, 115].
As follows from the literature review above, all existing models of the memory effect
are based on the concept that the memory reflects the crack generation and growth.
Therefore, both the Kaiser effect and DRA should only work when the preloaded peak
stress reached region (3) of the loading that is above at least 30% of UCS. There is
however experimental evidence that the DRA works even if the previous peak stress
was below the crack initiation threshold. Yamamoto et al. [122] verified that the DRA
method could detect the in situ stress value range from about 1 to 5 MPa for
granodiorite core samples. Park et al. [85], Seto et al. [123] and Hunt et al. [125]
showed that the DRA inflection can even be observed after applying pre-stresses less
than 15% of the UCS. Hunt et al. [26], Chang [131] and Chan [28] showed that the
DRA method could be used to determine the pre-stress where the pre-stress was less
than 20% of UCS. Yamshchikov et al. [60] indicated that the deformation memory
effect existed in both elastic deformation and plastic deformation stages.
In order to verify the existence of the deformation memory effect in the low stress
region, we conducted some additional experiments.
School of Civil and Resource Engineering The University of Western Australia
108
6.4 OUR EXPERIMENTS IN LOW STRESS REGION
The sandstone was chosen in the physical experiment to confirm the DRA method can
work in the low stress region. The density of the sample is 2850 kg/m3, the Young’s
Modulus is 44 GPa and the UCS is higher than 80 MPa. The sample is cylindrical with
less than 0.01 mm end planarity. The height is 39.9 mm and the diameter is 18.3 mm.
The sandstone was sub-sampled from a standard 76 mm exploration core recovered
from a depth of 1033 m below surface, from a mine site in northern Australia. The
sandstone sample has been kept in the open air for 7 days before testing. The sample is
shown inFigure 6-2. Four strain gauges were glued axially to the sandstone sample.
Figure 6-2 The sandstone sample and the location of four strain gauges.
Three sequential loading cycles in uniaxial compression were performed on the sample.
The preload is to initiate the stress memory with σp=8.3 MPa, the following two loading
cycles are used as measuring loading cycles in the DRA method with the same σm=75
MPa. There was no delay time between the loading cycles. The sample was loaded by a
servo-control loading frame in the displacement-controlled mode. The displacement rate
was 0.14 mm/min for sandstone sample; the same in loading and unloading.
School of Civil and Resource Engineering The University of Western Australia
109
Figure 6-3 The DRA curves for the sandstone sample.
Figure 6-3 shows the DRA curve for the sandstone sample. The average of four strain
gauges was used in equation (12) to compute the differential strain. It is clear that there
is a kink in the DRA curve at approximately preloaded stress value for sandstone
sample. It is seen that the DRA method allows the reconstruction of stress magnitudes
of below about 10% of the UCS, which is far below the crack initiation threshold.
The fact that the DRA can recover stresses well below the crack initiation threshold
suggests that another mechanism is responsible for the memory effect observed.
6.5 THE MECHANISM OF THE DEFORMATION MEMORY
EFFECT BASED ON FRICTIONAL SLIDING AND BASIC
ELEMENT
6.5.1 Frictional sliding over pre-existing interfaces
An obvious mechanism that produces irreversible non-linear deformation is frictional
sliding with the associated hysteresis. A theoretical model based on this mechanism was
developed in order to determine whether frictional sliding could produce the DRA
detectible memory effects. To this end we consider rock as containing a number of
randomly distributed pre-existing cracks and grain boundaries. Hereafter we call them
interfaces. Consider a representative volume element of rock containing sufficiently
large number of interfaces, apply uniform tractions at its boundary and compute the
average strain, which is the strain field averaged over the volume element. Introduce
School of Civil and Resource Engineering The University of Western Australia
110
Cartesian coordinates (x1, x2, x3). Let the tractions be . Then the average stress and
strain are [116, 117]:
∑ (13)
where, is the strain the surrounding rock would assume under the uniform tractions
without the interfaces, ni is the unit normal vector to the interface, Vi is the crack
‘volume’ which is the jump of the displacement discontinuity integrated over the
interface . The ‘volumes’ of the interfaces do not have the normal component,
0; the shear components depend upon the applied load and slide with friction
and also exhibit time dependency. The summation is over all the interfaces in the
volume element.
According to equation (13), the average strain of the rock consists of two parts, the first
one is the contribution of the elastic matrix, and the other one is the combined
contribution of all interfaces. In the low stress region below the crack initiation
threshold, frictional sliding would take place over the interfaces under shear stress
without production of wings [50, 132].
The behaviour of interfaces is complex as it depends upon many factors such as their
orientations and typical size. Further simplifications are required to account for the
influence of friction and rheology on the deformation memory effect. To this end, we
assume the resistance of the filler as well as the interface roughness and friction is
characterised by cohesion only. Firstly, a basic element was developed to model each
interface in the rock by a combination of springs, St. Venant body to model cohesion
and a dashpot to model time dependence, Figure 6-3. Then the rock with many
interfaces was modelled by connecting these elements in series. The elements are
different in the values of cohesions thus modelling, in a very simplistic manner,
different interface orientations.
6.5.2 The basic element
The basic element, Figure 6-4, consists of two parts connected in series with each other.
The first part is the top spring 2. It represents the deformation of elastic matrix (the rock
between the cracks). The second part comprises spring 3, the Maxwell body (Maxwell)
School of Civil and Resource Engineering The University of Western Australia
111
and the St. V body operating in parallel. For simplicity, hereafter “||” is used to present
“in a parallel way”, then the second part can be presented as “Spr||Maxwell||St. V” part.
The strain of “Spr||Maxwell||St. V” part represents the interface contribution to the total
strain. As the average strain is the sum of the average strain of the matrix and the
interface contribution, both parts are connected in series. In the “Spr||Maxwell||St. V”
part, the St. V body controls the frictional sliding. When the stress of the St. V body
exceeds the yield stress (cohesion), it will keep sliding under the cohesion. The
Maxwell body and spring 3 model the elastic-viscous resistance of the crack to sliding
and shall describe the time effects in the DRA. The parameters include three stiffnesses,
the stiffness of spring 1 in the Maxwell body (k1) representing the elastic resistance of
the interface contact, the stiffness of spring 2 (k2) representing the overall elastic
resistance of the matrix (rock between the cracks) and the stiffness of spring 3 (k3)
representing the elastic resistance of the elastic matrix to sliding over the crack, as well
as the viscosity of the dashpot (η1) and the cohesion of the St. V body (co1).
The following is the constitutive equations with spring 2:
(14)
where, σe, εe are stress and strain in spring 2. Spring 2 and “Spr||Maxwell||St. V” body
are connected in series, the stress is same for them and the total strain is the sum of the
two strains. Therefore
(15)
where, σ, ε are the stress and strain of the model. σc, εc are stress and strain of
"Spr||Maxwell||St. V" part. For the "Spr||Maxwell||St. V" part:
(16)
where, σstv, σspr1, σspr3, σdas are the stresses in the St. V body, springs 1 and 3 and the
dashpot, respectively; εspr1, σspr3, σdas are the strains of springs 1 and 3 and the dashpot,
respectively. For spring 1 and the dashpot in the Maxwell body:
(17)
School of Civil and Resource Engineering The University of Western Australia
112
The St.V body has two states, the state of sliding and the static state:
| | , | |
(18)
where, is the initial strain of "Spr||Maxwell||St. V" part. If |σstv|<co1, the
“Spr||Maxwell||St.V” body is locked by St. V body, keeping the strain unchanged, the
stress relaxation in the Maxwell body will occur if there is elastic potential energy in
spring 1.
Figure 6-4 The basic rheological element.
6.5.3 Behaviour of the basic element
In order to better understand the mechanical behaviour and the deformation memory
effect in the basic element, three kinds of loading regimes were chosen for the
numerical experiments. Each loading regime consists of two parts, the preload with
peak stress σp and two measuring loading cycles with the peak stress σm. The loading
and unloading rates are the same, denoted as r. The corresponding differential strain
Δε2,3(σ) between the two measuring loading cycles is called the DRA curve. The three
loading regimes chosen test different features of the deformation memory effect.
Loading regime 1: The preloading (the first loading cycle) consists of loading and
immediate unloading without a holding time and without any delay between the
preloading and measuring cycles.
Loading regime 2: The preloading includes holding time and a delay between the pre-
loading cycle and the measuring cycles were introduced.
School of Civil and Resource Engineering The University of Western Australia
113
Loading regime 3: Several preloading cycles and the delay time were introduced.
Loading regime 1
Loading regime 1 aims to produce the basic results about the deformation memory
effect, Figure 6-5.
Figure 6-5 Loading regime 1.
The basic element model contains a total of 8 independent parameters: k1, k2, k3, η1, co1,
r, σp and σm. Spring 2, as described in previous section, represents the elastic part of the
strain in the model, which does not change in the loading-unloading cycle. Therefore it
will cancel in the DRA curve. For that reason k2 has no influence on the DRA curve, so
we exclude it from the set of independent parameters. In order to achieve further
reduction of the number of parameters we performed the dimensional analysis. We
choose co1 (stress) and r (stress rate) as the basic variables. Using the Buckingham’s π-
theorem, five independent dimensionless groups η1r/co12, k1/co1, k3/co1, σp/co1, σm/co1
and two dependent dimensionless groups σ/co1, ε were obtained. Furthermore, from the
numerical experiments we found that, the result of the DRA method depends on the
ratio η1r/co12: k1/co1: k3/co1. Dividing by k1/co1, three groups were combined as two new
groups: η1r/k1co1 and k3/k1. Finally, the following dimensionless groups were obtained:
the independent dimensionless groups: π1=η1r/k1co1; π2=k3/k1; π3=σp/co1; π4=σm/co1 and
the dimensionless variables: σ/co1 and ε. The first two dimensionless groups represent
the rock properties; the last two groups represent the parameters of the loading.
School of Civil and Resource Engineering The University of Western Australia
114
For the analysis, the following values of the dimensionless groups were chosen: π1 =5,
10, 30, 50 and π2 =0.01, 0.1, 1, 10, 100. The values of the groups controlling the loading
were: π3 - π4: 1.2-1.4, 1.6-1.8, 2.2- 2.4, 2.6-2.8.
The typical stress-strain curves and DRA curves in loading regime 1 are shown in
Figure 6-6 and Figure 6-7. We can see that there can be up to two inflection points in
the DRA curve. We introduce parameters σdra1 and σdra2, which are the stress
magnitudes of the first and the second inflection points in the strain difference curve
respectively. They correspond to the following dimensionless groups:
π01= σdra1/co1= (π1,π2,π3,π4)
π02= σdra2/co1= (π1,π2,π3,π4)
When π3 and π4 are smaller than 1 (that is, σp and σm are smaller than the cohesion), the
“Spr||Maxwell||St.V” part does not produce any sliding, thus, the model behaves purely
elastic and the DRA does not recover any stress. For the case π3<1<π4 and 2<π3<π4,
there are still two inflection points in the DRA curve, however, this kind of inflection
has nothing to do with the memory of the previous loading; it is just the ‘memory’ of
cohesion or two times cohesion. Therefore, only the inflection stresses in the range of
previous maximum stress from cohesion to two times cohesion are important. We call
them the DRA inflections in the numerical experiments.
Figure 6-6 Loading of the basic element; parameters:π1=1,π2=1,π3=1.6,π4=1.8:(a) the stress-strain
curve and (b) the DRA curve.
0 0.5 1 1.5 2 2.5
x 10-3
0
0.5
1
1.5
2
(a) Strain
Str
ess
(MP
a)
0 0.5 1 1.5 21
2
x 10-4
(b) Stress (MPa)
Dif
fere
ntia
l S
trai
n
1st DRA inflection
2nd DRA inflection
School of Civil and Resource Engineering The University of Western Australia
115
Figure 6-7 Loading of the basic element; parameters: π1=1, π2=1, π3=2.6, π4=2.8: (a) the stress-strain
curve and (b) the DRA curve.
The first DRA inflection point reflects the memory of the peak stress in the preload,
while the second DRA inflection point reflects the memory of peak stress in the first
measuring loading cycle. That is σdra1 is the memory of σp, while σdra2 is the memory of
σm. Furthermore, in the range from cohesion to two times cohesion, the following were
found:
(1) When π2 is kept unchanged, the accuracy of recovery of π01 increases with the
increase of π1. At the same ratio π1, the accuracy of π01 increases with the
increase of π2, Figure 6-8.
(2) The relationship between π02 and π1, π2 is the same as the relationship between
π01 and π1, π2. However, it should be noted that, if the σdra2 is very close or even
equal to σm, the tail from σdra2 to σm in the DRA curve (the part of the curve in
Figure 6-6(b) after the second inflection point) becomes very short or even
disappears. Thus in these cases, the second inflection point in DRA curve will
not be observed. (Imagine the tail after the second inflection in Figure 6-6(b) be
so short that the second inflection point cannot be recognised.)
0 0.005 0.01 0.0150
1
2
3
(a) Strain
Str
ess
(MP
a)
0 1 2 31.2
1.3
1.4
x 10-3
(b) Stress (MPa)
Dif
fere
ntia
l S
trai
n
School of Civil and Resource Engineering The University of Western Australia
116
Figure 6-8 The relationship between π01 and π1, π2.
Loading regime 2
Loading regime 2, Figure 6-9, aims to study the influence of the holding time Tc of the
preload and the delay time Td on the deformation memory effect.
Figure 6-9 Loading regime 2.
As in loading regime 1, co1 and r were chosen as the basic variables. Two additional
dimensionless groups controlling the holding and the delay times, π5=Tcr/co1 and
π6=Tdr/co1 have to be added. . The following values of these new parameters were used:
π5 =1, 10, 20, 30, 40, 50 and π6 =1, 4, 7, 10, 13, 16.
0.01 0.1 1 10 1001.1
1.2
1.3
1.4
1.5
1.6
1.7
2
01
π1=5
π1=10
π1=30
π1=50
- - - 3=1.2,
4=1.4
— 3=1.6,
4=1.8
School of Civil and Resource Engineering The University of Western Australia
117
Similarly to loading regime 1, up to two inflection points can be observed in the DRA
curve, denoted as σdra1 and σdra2. They correspond to the following dimensionless
groups:
π01= σdra1/co1=f12(π1,π2,π3,π4,π5,π6)
π02= σdra2/co1=f22(π1,π2,π3,π4,π5,π6)
The relationship between π01, π02 and π1, π2, π3, π4 and the shape of the DRA curve in
loading regime 2 are the same as those in loading regime 1 and for that reason we do not
repeat them here. The specific results obtained in loading regime 2 are related to the
holding time Tc(π5) and the delay time Td(π6) in the region from cohesion to 2 times
cohesion. These results are:
(1) During the holding time, the creep deformation occurs. If the creep deformation
does not finish during the holding time (π5), the accuracy of determination of π01
decreases with the increase of the delay time (π6). That is to say, the MF occurs
with the increase of the delay time. Error! Reference source not found.a
shows an example. Opposite to what happens to π01, the accuracy of
determination of π02 increases along with the increase of π6, shown in Error!
Reference source not found.b.
(2) When the creep deformation does not finish, at the same delay time π6, the (2) When the creep deformation does not finish, at the same delay time π6, the
accuracy of determination of π01 increases with the increase of the holding time
π5. That is to say, the longer the holding time of preload is, the more accurate the
DRA method would be, see Figure 6-10(a). The relationship between π02 and π5
is the same as that between π01 and π5, shown in Figure 6-10(b).
(3) If the holding time π5 is long enough for the creep deformation to complete, π01
is equal to π3 (σdra1=σp), and keeps unchanged as delay time π6 increases. In
other words, if the holding time is long enough, memory will permanently stay
without fading. Take π5=50 as an example, Figure 6-10(a), π01 is equal to π3 and
keeps unchanged along with increase of delay time π6. Similarly, as for π02, if
holding time π5 is high enough that the creep finishes, π02 keeps unchanged
along with the increase of π6. However, the value of π02 is lower than π4 (σdra2 is
a constant smaller than σm), see the case where π5=50 in Figure 6-10(b).
School of Civil and Resource Engineering The University of Western Australia
118
Figure 6-10 The relationship between π01, π02 and π5, π6: (a) for π01 (b) for π02.
Loading regime 3
Loading regime 3, Figure 6-11, aims to study the influence of preload times (m) and
delay time (Tc) on the deformation memory effect.
Figure 6-11 Loading regime 3.
In this loading regime, the group π7=m was further added to account for the number of
preloads. The following values were chosen for the simulations: π6 =0, 5, 10 and π7 =1,
5, 10, 15, 20, 25.
Similarly to the former loading regimes, there are up to two inflection points in the
DRA curve, denoted by the corresponding stresses as σdra1 and σdra2.
π01= σdra1/co1=f13(π1,π2,π3,π4,π6,π7)
0 10 20 30 40 50
1.3
1.35
1.4
1.45
1.5
1.55
1.6
(a) 5
01
π6=1
π6=4
π6=7
π6=10
π6=13
π6=16
1=5, 2=1
3=1.6, 4=1.8
0 10 20 30 40 50
1.64
1.66
1.68
1.7
1.72
1.74
(b) 5
02
π6=1
π6=4
π6=7
π6=10
π6=13
π6=16
1=5, 2=13=1.6, 4=1.8
School of Civil and Resource Engineering The University of Western Australia
119
π02= σdra2/co1=f23(π1,π2,π3,π4,π6,π7)
The dependences of π01, π02 up on π1, π2, π3, π4 and the DRA curve shape in loading
regime 3 are the same as those in loading regime 1. On top of the similarity with the
results from loading regime 1, the specific results in loading regime 3 related to the
preload times and delay time in the region from cohesion to 2 times cohesion are as
follows:
(1) During the preloads, the creep deformation occurs. If the creep deformation does
not finish during the preloads, the accuracy of determination of π01 and π02
increases with the increase of the number of preloads π7. In other words, the
more times the preload occurred, the more accurate π01 and π02 could be
determined, Figure 6-12.
(2) If creep deformation does not finish during the cycles of the preloads, the
accuracy of determination of π01 decreases with the increase of delay time π6.
This is the MF. Figure 6-12(a) shows an example. On the other hand, the
accuracy of determination of π02 increases with the increase of the delay time π6,
as shown in Figure 6-12(b), which is in agreement with the result in loading
regime 2.
(3) If the number of preloads π7 is high enough for creep deformation to complete
during preloads, there is no MF associated with increase of delay time π6. For
example, from π7=20 to π7=25, π01 keeps unchanged along with increase of π6,
Figure 6-12(a).
Figure 6-12 The relationship betweenπ01, π02 and π6, π7: (a) for π01 (b) for π02.
0 5 10 15 20 251.3
1.4
1.5
1.6
(a) 7
01
π6=0
π6=5
π6=101=5, 2=1
3=1.6, 4=1.8
0 5 10 15 20 25
1.65
1.7
1.75
(b) 7
02
π6=0
π6=5
π6=10
1=5, 2=1
3=1.6, 4=1.8
School of Civil and Resource Engineering The University of Western Australia
120
6.6 A MODEL OF ROCK WITH MULTIPLE INTERFACES
6.6.1 Introduction to the model
The ultimate goal of modelling the rock with many sliding interfaces will be achieved
by using a multi-element model, Figure 6-13, consisting of n basic elements. The
elements are connected in series reflecting the fact that each interface produces additive
contribution to the average strain. The equations for the multi-element model, according
to equation (13):
∑ (19)
where, σ is the applied stress, σα and εα are the stress and strain of basic element α. The
mechanical behaviour of each element in the mulit-element model follows equations
(13) - (18)
The numerical simulations were conducted with n=200 basic elements. In order to
simplify the parametric analysis, the elements were assumed to differ only by their
cohesions, since it is the value of cohesion that provides the yardstick for the stress
reconstruction. We generated the cohesions randomly using two distributions: the
uniform distribution and the normal distribution. (In order to ensure that the cohesions
are positive, the generated negative values were deleted and re-generated.) In order to
enable the comparison, the parameters of both distributions were chosen in such a way
that they have the same mean value and standard deviation. Three loading regimes were
chosen, the same as for the basic element. We have only chosen one example of
uniformly distributed cohesions and one example of normally distributed cohesions.
The range of the uniformly distributed cohesions is from 0.005 MPa to 1 MPa. The
mean value is 0.5025 MPa and the standard deviation is 0.2894 MPa. The
corresponding normal distribution is shown in Figure 6-13(b).
School of Civil and Resource Engineering The University of Western Australia
121
Figure 6-13 The multi-element model: (a) the multi-element model consisting of n basic elements (b)
a realization of the cohesions in a system with 200 elements with normal distributions.
6.6.2 DRA in multi-element model with 200 elements
Loading regime 1
Numerous numerical tests were performed on the multi-element model in loading
regime 1. Typical stress-strain curves in tests are shown in Figure 6-14.
Figure 6-14 Stress-strain curve in a test, parameters: η1r/k1=107, k3/k1=1, σp=1.2 MPa, σm=1.6 MPa:
(a) Uniformly distributed cohesions (b) Normally distributed cohesions.
The results for the multi-element model are as follows:
(1) The typical shape of the DRA curve is shown in Figure 6-15. Up to two
potential inflection points at stresses σdra1 and σdra2 can be observed in the DRA
curve for the multi-element model. The inflection points are situated in the stress
0 0.2 0.4 0.6 0.8 10
10
20
30
(b) Cohesions Range (MPa)
Acc
ount
0 0.1 0.2 0.3 0.4 0.50
0.5
1
1.5
2
(a) Strain
Str
ess
(MPa
)
0 0.1 0.2 0.3 0.4 0.50
0.5
1
1.5
2
(b) Strain
Str
ess
(MPa
)
School of Civil and Resource Engineering The University of Western Australia
122
range from the minimum cohesion to 2 times of the maximum cohesion, which
is similar to that in the basic element. Again, if σdra2 is very close or even equal
to σm, the second inflection in DRA curve will disappear, Figure 6-15. However,
different from the basic element, in the case when σm>σp>two times of
maximum cohesion, there are no DRA inflections, Figure 6-16.
(2) There is little difference for the DRA curve between the normal distribution and
uniform distribution in the range from minimum cohesion to two times of
cohesion, which can be seen from Figure 6-15(a) and Figure 6-15(b). Thus, the
actual shape of the distribution of the cohesions in the rock (multi-element
model) does not affect the shape of the DRA curve.
(3) Similarly to the basic element, the stress value σdra1 at the first DRA inflection
contains the memory of σp, which is the previous peak stress. The stress value
σdra2 at the second DRA inflection is for the memory of σm, the peak stress in
measuring loading cycle.
(4) The accuracy of determination of σdra1 and σdra2 in the DRA curve depends on
the ratios η1r/k1 and k3/k1. Again similarly to the basic element, the relationships
between σdra1, σdra2 and the ratios η1r/k1, k3/k1 are the same as between π01, π02
and π1, π2.
Figure 6-15 DRA curves for the multi-element model in the case in Figure 6-14: (a) uniformly
distributed cohesions (b) normally distributed cohesions.
0 0.5 1 1.5 20.005
0.01
0.015
0.02
0.025
(a) Stress(MPa)
Dif
fere
nt S
trai
n
0 0.5 1 1.5 20.005
0.01
0.015
0.02
0.025
(b) Stress(MPa)
Dif
fere
nt S
trai
n
School of Civil and Resource Engineering The University of Western Australia
123
Figure 6-16 DRA curves for the multi-element model: (a) uniformly distributed cohesions (b)
normally distributed cohesions; η1r/k1=107, k3/k1=1, σp=2.6 MPa, σm=2.8 MPa.
Loading regime 2
Shown in Figure 6-9, loading regime 2 focused on the influence of the holding time of
preload and delay time on the deformation memory effect. Figure 6-17 shows typical
stress-strain curves. The DRA curves can be found in Figure 6-18.
Figure 6-17 Stress-strain curve: (a) uniformly distributed cohesions (b) normally distributed
cohesions; η1r/k1=106, k3/k1=1, σp=1.2 MPa, σm=1.6 MPa, Tc=8σp/r, Td=0.
The results obtained from loading regime 2 include the results from loading regime
1and some specific results related to the holding time and delay time:
(1) During the holding time, creep deformation occurs. If the creep does not finish
during the delay time, σdra1 becomes closer to σp, σdra2 becomes closer to σm with
0 1 2 30.023
0.024
0.025
0.026
0.027
0.028
(a) Stress(MPa)
Dif
fere
nt S
trai
n
0 1 2 30.023
0.024
0.025
0.026
0.027
0.028
(b) Stress(MPa)
Dif
fere
nt S
trai
n
0 0.2 0.4 0.60
0.5
1
1.5
(a) Strain
Str
ess
(MPa
)
0 0.2 0.4 0.60
0.5
1
1.5
(b) Strain
Str
ess
(MPa
)
School of Civil and Resource Engineering The University of Western Australia
124
the increase of preload holding time. That is to say, the longer the holding time
of the preload the more accurate the DRA effect can be seen. Figure 6-18 shows
an example. There are two characteristic features of the MF: σdra1 becomes
farther from σp, and the DRA curve becomes smoother at the inflection point.
(2) If the creep does not finish, during the holding time, σdra1 becomes father from
σp and with the increase of delay time, the MF occurs. However, the influence is
opposite for σdra2, which is same as in the basic element. An example can be
seen in Figure 6-19. It should be noted that, there are two features of the MF, the
DRA curve becomes smoother at the DRA inflection, and the stress value
corresponding to the first DRA inflection becomes lower.
(3) Similarly to the basic element, if the holding time is long enough for the creep to
finish, σdra1 is equal to σp, and keeps unchanged with the increase of delay time.
In this case, there is no MF.
Figure 6-18 Influence of holding time on the DRA: (a) uniformly distributed cohesions (b) normally
distributed cohesions. The numbers in the right parts of the plots are the ratios of Tc and σp/r (the
time of the preload); η1r/k1=106, k3/k1=1, σp=1.2 MPa, σm=1.6 MPa, Td=0.
0 0.5 1 1.2 1.5 20
0.01
0.02
0.03
0.04
0.05
(a) stress(MPa)
Dif
fere
ntia
l Str
ain
0
2
3
6
8
0 0.5 1 1.2 1.5 20
0.01
0.02
0.03
0.04
0.05
(b) stress(MPa)
Dif
fere
ntia
l Str
ain
0
2
3
6
8
School of Civil and Resource Engineering The University of Western Australia
125
Figure 6-19 The memory fading in the DRA: (a) Uniformly distributed cohesions (b) Normally
distributed cohesions. The numbers in the right parts of the plots are the ratios of Tc and σp/r (the
time of the preload). η1r/k1=5×107, k3/k1=1, σp=1.2 MPa, σm=1.6 MPa, Td=0.
Loading regime 3
Loading regime 3 is shown in Figure 6-11. It focuses on the influence of the number of
preloads and the delay time on the deformation memory effect. Figure 6-20 shows the
typical stress-strain curves. The shape of DRA curves in this loading regime is shown in
Figure 6-21.
Figure 6-20 Stress-strain curve: (a) Uniformly distributed cohesions (b) normally distributed
cohesions; η1r/k1=106, k3/k1=1, σp=1.2 MPa, σm=1.6 MPa, m=3, Td=0.
Some of the results are the same as in loading regimes 1 and 2. On top of that there are
the following results related to the preload times in the stress region from minimum
cohesion to two times of maximum cohesion:
0 0.5 1 1.2 1.5 20
0.01
0.02
0.03
(a) stress(MPa)
Dif
fere
ntia
l Str
ain
0
10
20
30
60
100
0 0.5 1 1.2 1.5 20
0.01
0.02
0.03
(b) stress(MPa)
Dif
fere
ntia
l Str
ain
0
10
20
30
60
100
0 0.1 0.2 0.3 0.4 0.50
0.5
1
1.5
(a) Strain
Str
ess
(MPa
)
0 0.1 0.2 0.3 0.4 0.50
0.5
1
1.5
(b) Strain
Str
ess
(MPa
)
School of Civil and Resource Engineering The University of Western Australia
126
(1) During the preloads, the creep deformation occurs. If the creep does not finish,
during the delay time, the accuracy of determination of σdra1 increases with the
increase of preload times (m). In other words, the more cycles of preloads, the
closer of σdra1 to σp. It is also valid for σdra2, but it is not so obvious as that for
σdra1, Figure 6-21.
(2) If the number of preload cycles m is high enough for creep deformation to get
completed, σdra1 will be equal to σp, and no MF will be observed.
Figure 6-21 The memory fading effect in the DRA: The numbers in the right parts of the plots are
the ratios of the delay time and the time of the preload. All parameters except m are the same as
that in Figure 6-20.
6.7 DISCUSSION
6.7.1 Inflection points
The appearance of the inflections in the DRA curve, which is the strain difference
function Δε2,3(σ)=ε3(σ)-ε2(σ), can be explained as follows. After the first loading cycle is
finished, the “Spr3||Maxwell” is locked by St.V body and thus the elastic potential
energy is stored in spring 3 and 1. When the sum of the stress of spring 3, Maxwell
body and cohesion is exceeded in the2nd loading, the St.V body starts sliding, which
produces a change in the slope of ε2(σ) curve. This change will lead to an inflection in
the Δε2,3(σ) curve. In the same way, a change in the ε3(σ) will also lead to an inflection
in Δε2,3(σ) curve, this is why the second DRA inflection occurs. This will be discussed
0 0.5 1 1.2 1.5 20.01
0.02
0.03
0.04
0.05
(a) stress(MPa)
Dif
fere
ntia
l Str
ain
m=1
m=3
m=5
m=10
0 0.5 1 1.2 1.5 20.01
0.02
0.03
0.04
0.05
(b) stress(MPa)
Dif
fere
ntia
l Str
ain
m=1
m=3
m=5
m=10
School of Civil and Resource Engineering The University of Western Australia
127
in the following section in detail. It is important to remember that the stress detected by
the DRA method consists of three components, the stress stored in spring 3, the stress
stored in spring 1 and the cohesion.
Role of the St. V body
The St. V body controls the range where the DRA method works. When one loading
cycle is finished, the stress stored by the “Spr3||Maxwell” part cannot exceed the
cohesion, otherwise, the St. V body would keep sliding until the stress of the
“Spr3||Maxwell” part equals to cohesion. In other words, the stress range that the
“Spr3||Maxwell” part can store ranges from zero to the value of cohesion. What the
DRA method can detect is the sum of the three components mentioned above.
Therefore, the stress that the DRA method can detect is in a limited range from the
minimum cohesion to two times of the maximum cohesion.
Role of the spring 3 and the Maxwell body
Other results relate to the elastic potential energy accumulation, energy loss and energy
exchange due to the stress relaxation of Maxwell body and creep deformation of
“Spr3||Maxwell”part.
Stress relaxation in the Maxwell body
When the “Spr3||Maxwell” part is locked by St.V body, stress relaxation occurs, which
contributes to the accuracy loss of deformation memory effect and MF.
When the Maxwell body is locked by the St. V body, the strain of the Maxwell body is
kept constant and spring 1 releases elastic potential energy through the dashpot with
time. For the Maxwell body in Figure 6-4, the stress relaxation is:
(20)
where, σ0 is the initial stress of the Maxwell body.
Stress relaxation in different parts of the loading regime leads to different phenomena in
the DRA curve. For loading regime 1, the stress relaxation during the unloading in 2nd
loading cycle and initial stage of the 3rd loading, leads to the second DRA inflection. At
the moment when the 2nd loading finishes, its peak stress value is stored by the
“Spr||Maxwell||St. V” bodies. However, due to the stress relaxation, the stress of the
School of Civil and Resource Engineering The University of Western Australia
128
Maxwell bodies decays. When the sum of the non-intact stress of spring 3, Maxwell
body and cohesion is reached in the 3rd loading, the ε3(σ) curve will change its slope,
which introduces the second inflection in the Δε2,3(σ) curve. That is why we say the
second DRA inflection is the memory for the 2nd loading or σm. Similarly, the stress
relaxation in the first unloading and the initial stage of the second loading leads to
accuracy loss of the first DRA inflection. From this point, we can also explain why the
second inflection can’t be detected in the physical experiments. In the laboratory, the
first DRA inflection occurs nearly at the previous peak stress. It indicates that the
memory loss by stress relaxation is very low for the first inflection. In the same loading
conditions, it should be the same to the second inflection to occur nearly at the peak
measuring stress, where only a very short tail of the DRA curve exists. As the tail is
short, it is difficult to detect the second inflection, see Figure 6-6 and Figure 6-15.
The stress relaxation duringthe delay time is a mechanism of the memory effect in
loading regimes 2 and 3. In the multi-element model, the DRA curve becomes smoother
at the inflection, and the detected stress becomes lower, due the increase of the increase
of the delay time, as shown in Figure 6-19.
Creep deformation of the “Spr3||Maxwell” part.
In loading regime with holding time, when the stress applied exceeds the cohesion and
then is kept constant, the creep deformation occurs in “Spr||Maxwell||St. V” part. During
the creep deformation, the stress of spring 3 increases, while the stress in the Maxwell
body decreases, keeping the applied stress unchanged. After the holding time finishes,
σ0 becomes lower than that in loading regime without holding time. From equation (20),
during the same period of time, the stress loss by stress relaxation is low if σ0 is low.
Therefore, the stress loss in the loading regime with the holding time is lower than that
in the loading regime without the holding time. This is the reason why the accuracy of
identifying the DRA inflection increases along with the holding time of preload.
However, if the holding time is so long that the creep finishes (strain stabilization is
reached and σ0 becomes zero), there will be no stress relaxation during loading or
unloading or delay time. In this case, the first DRA inflection can pick up the preloaded
peak stress precisely (σdra1=σp) and MF disappears.
School of Civil and Resource Engineering The University of Western Australia
129
In loading regime 3, when the stress of the consecutive preloads exceeds the sum of the
stress stored in “Spr3||Maxwell” part and cohesion, the St. V body starts to slide, which
leads to the increase of stress stored in spring 3. This process repeats in the following
preload cycles. When m preloads finish, σ0 becomes lower than that in the loading
regime with only one preload, which leads to reduced stress relaxation. This is why the
accuracy of determining σdra1 increases with the increase of the number of preloads
cycles. Similarly to the result of the holding time, if the number of preload cycles is
high enough that creep deformation finishes (σ0 becomes zero), σdra1 will be equal to σp
and no MF will be observed.
6.7.2 Comparisonwith experimental results
Memory fading
MF has been observed in laboratory experiments [60, 77, 85, 129]. Our model explains
it and shows two features: inflection becomes smoother and the stress corresponding to
the inflection becomes lower with the increase of the delay time. The information on
MF in the literature is scarce. Nevertheless, two examples could be found, Figure 6-22
and Figure 6-23.
Figure 6-22 Examples of MF: (a) the loading regime (b) the DRA curve: σp = 8MPa, τ0 is the
holding time equal to 1 minute, τ is the delay time (based on Ref. [113]).
School of Civil and Resource Engineering The University of Western Australia
130
Figure 6-23 DRA curve for Inada Granite [126]. The upward arrows are labelled by the authors in
this paper. “Strain2-Strain1” presents the differential strain between the first two measuring
loadings.
The first feature of MF - smoothing of inflections with the increase of the delay time - is
clearly seen in Figure 6-22(b) [113] from the Δε1,2(σ)curves. The second feature – stress
reduction at the inflection points with the delay time - is also seen in Figure 6-22(b). It
is in agreement with Figure 6-19.
The second feature is more obvious in Figure 6-23, which shows the results of
experiments by Seto et al. [123, 126]. They performed repeated preloads on the Inada
granite with the peak stress 20.44MPa, which is less than 11% of the UCS. Figure 6-23
shows the DRA curve with the delay time of 7 years. The DRA inflection picked by
Seto et al. [126] is about 19.5 MPa, labelled by the downward arrow. They claimed that
up to 7 years did not have any influence on the recollection of the previous peak stress.
However, it is clearly seen that the first DRA inflection occurs at a much lower stress
value, about 16MPa. This is the second feature of the MF. Repeated preloads in their
experiment were not sufficient for initiating the deformation memory effect without
fading.
The shape of DRA curve
The real DRA curves in the experiments always have many different inflections with
different shapes. One of the most important and difficult problems in the application of
School of Civil and Resource Engineering The University of Western Australia
131
the DRA method is to identify the correct DRA inflection. From the results of the model
with many interfaces, DRA curve bends down at the DRA inflection. Four typical
patterns of DRA curves by the axial strain were summarized by Seto et al. [133]. These
four types of DRA curves have one common feature: the DRA curve bends down at the
DRA inflection, which is totally in agreement with the result by our theoretical model.
The shape of the DRA curve (as obtained from the axial strain) was also confirmed by
Figure 6-3 and most experimental DRA curves [32, 58, 122, 129, 134, 135].
The presence of the second DRA inflection depends on the rock type that is on the
combinations of parameters of the model chosen for the simulation. As discussed in
section 6.7.1, generally, when the first DRA inflection is close to the previous
maximum stress, the second inflection should occur at the very end of the DRA curve
and thus cannot be observed in this kind of rock. Most cases considered in the literature
belong to this kind. However, Figure 6-23 shows an example of the existence of the
second DRA inflection. As labelled by the two upward arrows, the first inflection
occurs at the stress value much lower than the previous peak stress because of 7 years
delay time, while the second inflection occurs at the stress value a little higher than 34
MPa, much lower than the peak stress value in the measuring loadings.
According to our model, one of the characteristics of the rock type that has the second
inflection is the presence of considerable creep. At the same time, the first DRA
inflection in this kind of rock would occur at much lower stress than the preloaded peak
stress even without delay time.
Holding time and preload times
According to result from section 6.6.2, the accuracy of determining the DRA inflection
increases along with the preload times and the holding time. This result is consistent
with experiments methods by many researchers.
In their review, Yamshchikov et al. [60] claimed that the clearness of the deformation
memory effect manifestation increases along with the holding time of preload. In order
to guarantee the successful deformation memory effect, Hunt et al. [26, 125] maintained
the preload with the unchanged peak stress of 18.5% [26] and 15% [125] of UCS, for 1
hour; Seto et al. [123] held the preloaded peak stress, of 17% of the UCS, for 3 hours;
Makasi and Fujii [136] kept preloaded peak stress of 30% of UCS for 1 hour. This is
School of Civil and Resource Engineering The University of Western Australia
132
consistent with result 1 from section 6.6.2. Thus our model explains the success of the
experimental method adopted by these authors.
Some researchers reported that repeated preloads are required to obtain “saturated strain
state” [86, 123, 127] and then to guarantee the successful deformation memory effect.
“Saturated strain state” means residual strain does not increase in repeated loading.
Chan [28] and Wu and Jan [86] used 500 loading cycles to initiate the previous peak
stress; Chang [25] used 1000 repeated loads to simulate the in situ stress. Park et al. [85]
performed preloads 10 times on the Hwangdung Granite. Again, this is consistent with
result 1 from section 6.6.2. Our model gives an explanation for the method they used.
Yamshchikov et al. [60] also pointed out that, if the holding time was below a certain
threshold, the deformation memory effect would pick up a lower stress value with the
decrease of the holding time. This phenomenon can be seen from Figure 6-18. When
holding time Tc is below 6 times of preload time σp/r, σdra1 becomes lower along with
decrease of the holding time. However, when holding time Tc is over 6 times of preload
time σp/r, σdra1 keeps unchanged with the change of the holding time. Actually, “a
certain threshold” by Yamshchikov et al [60] is the time period for creep completeness
according to the result of our model. If creep finishes in the rock sample, the MF will
not occur. Similarly, when the number of preload cycles is high enough for the creep to
complete, the MF does not occur either. This result can be proved by experiments in
Ref. [86], where no MF was observed up to 14 days in the experiments with 500
repeated loadings. However, compared with the case of maintaining the preload for long
time, repeated preloads method is not recommended for the purpose of the creep
completeness. It should be noted that, the “saturated strain state” mentioned above is not
equal to creep completeness.
According to Yamamoto [62, 113], the in situ stress memory is a long term memory.
This can also be explained from the point of view of creep completeness. The formation
of the in situ stress is a long term geological process (the holding time is long), which
can guarantee the creep completeness in rock masses. Therefore, no MF should be
observed for the cases when the rock memory is used to recover in situ stress.
School of Civil and Resource Engineering The University of Western Australia
133
6.8 CONCLUSIONS
It is traditionally assumed that the DRA can only recover the previous stresses that are
high enough to produce crack initiation or propagation. Our experiments show that the
DRA can also detect lower stresses, insufficient to induce any damage accumulation in
rock. We put forward a different mechanism of rock memory based on the frictional
sliding over the pre-existing cracks or interfaces.
We considered a simplified rheological model where friction is reduced to cohesion
only and a dashpot element is introduced to account for the time-dependent behaviour.
The cohesions are different in different cracks, while all other parameters are assumed
to be the same. We demonstrated that the frictional sliding mechanism does produce
inflections in the DRA curve. In multi-crack situations the main controlling parameter is
the distribution of cohesions. The detectible previous stress falls between the minimum
cohesion and two times of the maximum cohesion, all other stress values are not
detectible.
One can expect that the larger the number of cracks the wider the detectible stress
interval. However, the increase of the number of cracks, which is essentially the
increase in the sample size, leads to a smoother DRA curve and subsequently the
reduction of accuracy of the identification of the inflection points and hence the stress
reconstruction. The accuracy of the stress determination also depends upon a
combination of the rheological parameters of the rock and cracks. While it is tempting
to take the number of cracks, i.e. the sample size as another controlling parameter, in
practice there are considerable restrictions in the sample size. One reason is that at
present the samples be subcored from a core in many different directions in order to
determine the principle directions of the previous loading.
The presence of the dashpot leads to stress relaxation and creep deformation: stress
relaxation becomes greater along with the longer time elapsed between the preload and
the laboratory measuring cycles. This explains the fading phenomenon whereby the
fidelity of stress reconstruction reduces with the (usually uncontrollable) delay time
between collecting the sample from the stress environment and the DRA testing. The
accuracy of the DRA increases with the increase of the extent of creep deformation,
which is related to the preload holding time and preload times. This explains why so
School of Civil and Resource Engineering The University of Western Australia
134
many researchers adopted long holding time or repeated loading cycles to initiate the
memory in their experiments. If the creep finishes, no MF can occur, which explains
why the in situ stress memory is a long term memory and also why in some cases, no
MF is observed in the laboratory experiments.
The frictional sliding over pre-existing cracks and interfaces constitute a mechanism of
non-elastic deformation and the deformation memory effect in the low stress region
below the crack initiation threshold without crack production.
(1) The deformation memory effect and the memory fading can be modelled using a
combination of friction elements and dashpots.
(2) In our model, DRA inflections exist in the range from minimum cohesion to two
times of maximum cohesion.
(3) The accuracy of the DRA method depends on the rock type, the holding time,
repeated preload times and delay time. The accuracy increases with increase of
holding time or repeated preload times, while the memory fading occurs along
with the delay time.
(4) When the creep deformation finishes in the preload(s), no memory fading occurs,
this is the reason why in situ stress memory is a long term memory. The
artificial memory effect shares the same mechanism with the in situ stress
memory effect. The difference for them is the different length of the holding
time. Therefore, the artificial memory in the laboratory can be used to simulate
the in situ stress memory and the long holding time is preferred.
Acknowledgements.
H. J. Wang acknowledges the financial support by China Scholarship Council, the
Fundamental Research Funds for the Central Universities in China (2010B13914) and
Jiangsu 2010 College Graduate Student Research and Innovation Program Foundation
(CX10B_215Z). A. V. Dyskin acknowledges the financial support from the Australian
Research Council through the Discovery Grant DP0988449.
School of Civil and Resource Engineering The University of Western Australia
135
CHAPTER 7. THE INFLUENCE OF SAMPLE BENDING
ON THE DRA STRESS RECONSTRUCTION
7.1 INTRODUCTION
The Deformation Rate Analysis (DRA) [57] utilizes the stress-strain curves obtained
from uniaxial tests on rock samples to reconstruct the in-situ stress the rock was
subjected to. The approach is based on examining the inelastic strain between two
successive loading cycles in a uniaxial test. The loading program is shown in Figure
7-1.
Figure 7-1 Loading process of pre-stress (1st cycle), 2nd and 3rd cycles.
The pre-stress is the maximum previous stress that the specimen has been subjected. It
is the first loading in the lab experiments and the in-situ stress in the tests for stress
reconstruction. The 1st and 2nd cycles are the loading cycles applied after the pre-stress,
in order to produce the DRA graph. The difference in strain between 1st and 2nd cycles is
shown in Figure 7-2(a). This can be expressed as follows:
ijijij (3)
Figure 7-2(b) shows the strain difference Δεij(σ); the maximum gradient change in the
graph of stress vs. strain difference curve is called the inflection point. According to the
DRA the stress of the inflection point is assumed to be equal to the pre-stress.
stre
ss
time
Loading process
prestress
1st cycle
2nd cycle
School of Civil and Resource Engineering The University of Western Australia
136
Figure 7-2 Stress and strain curve. A black arrow shows a strain difference (Δεij) under same
stress. b): An inflection point which indicates PMS is marked with arrow.
It should be noted that because the DRA is based on the strain difference and
subtraction increases relative error, the strain measurements must be conducted with
high accuracy. Typically, the strain was determined as the average between the strains
measured by one or several strain gauges glued on different parts of the sample. In most
cases, the strain was measured using the average strain of two [26, 27, 32, 33, 85] or
four [31, 57-59, 63, 64, 113, 114, 137] strain gauges. Some authors [25, 28, 29, 34, 138]
used only one axial strain gauge. If the strain were uniform within the sample, the
averaging would indeed lead to a reduction of the measurement errors. In reality
however the stress/strain field is not uniform owing to a number of factors. The first
factor is of course the sample heterogeneity, which leads to the stress/strain non-
uniformity. Usually the sample heterogeneity is associated with its microstructure
(grains, foliation, etc.) and thus produces small-scale stress/strain non-uniformity. When
the strain gauges used are large enough this type of non-uniformity averages out.
The second factor is the non-parallelness of the sample ends and non-coaxiality of the
applied loading. Even if the sample is perfectly homogeneous, the second factor can
lead to the development of a bending moment and, subsequently to the sample bending
and non-uniform stress/strain distribution [139, 140]. We call this situation the bending
effect. We note that the bending effect produces the stress/strain non-uniformity at the
scale of the sample and thus cannot be averaged out, no matter how large the strain
gauges are.
stre
ss
strain
Stress-strain curve
prestress
1st cycle
2nd cycle stra
in d
iffe
renc
e
stress
DRA
School of Civil and Resource Engineering The University of Western Australia
137
The bending effect can lead to different measurements at different strain gauges. (We
note that in [61], two axial strain gauges were used and the strain difference from each
gauge was plotted separately. However, the influence of bending might not be detected
with only two strain gauges placed at opposite sides of the sample diameter if bending
happened in the direction normal to the diameter, Figure 7-3).
Figure 7-3 The strain gauges A and C would have the same strain reading if the non-parallelness is
only in the B-D direction.
The bending effect leads to a number of errors in rock testing. It can for example reduce
the measured strength of the sample, because the fracture begins at the sample part
subjected to the maximum stress. Indeed, the induced maximum stress may reach the
local strength when the average stress is lower than the induced stress. (The situation is
of course complicated by the possibility of the size effect, which can make small rock
volumes stronger.)
In the DRA, the stress non-uniformity can lead to the shift of the inflection points
obtained by the DRA from strain measurements at separate locations. This will cause a
scatter of the pre-stress values obtained by the DRA from different strain gauges and the
subsequent reduction in the accuracy of the stress reconstruction. Indeed, in the process
of loading, the pre-stress will be successively reached in different parts of the sample
owing to the stress non-uniformity. Therefore, instead of a single inflection point, a
distribution of the inflection points will be recorded. This spreading of the inflection
point can make its identification less accurate, if at all possible.
Strain gauge
A
B D
C
Sample
B A D D A C
School of Civil and Resource Engineering The University of Western Australia
138
In this paper we investigate the influence of the bending effect and the rock foliation on
the stress-strain curves obtained in the laboratory rock testing followed by the DRA.
The strain acting at a specific location of the rock sample was recorded by a glued strain
gauge. Based on the recording, the actual stress was recalculated from the average stress
based on the degree of bending (here called the bending level). We then examine the
influence of bending and anisotropy on the DRA method. We aim to distinguish the
difference in the DRA readings resulted from the rock anisotropy, and reduce the error
introduced by bending in the DRA method.
7.2 EXPERIMENTAL APPARATUS AND PARAMETERS
7.2.1 The influence of bending and rock heterogeneity on volumetric strain
We used glued double strain gauges, which ensure the simultaneous measurements of
the axial and lateral strains. By placing four cross type strain gauges at the positions
shown in Figure 7-4, the strain non-uniformity caused by the bending effect and/or
heterogeneity can be detected by comparing the stress-strain curves for each strain
gauge.
Figure 7-4 Locations of the strain gauges on a sample.
Axial strain gauges 270°
Location 0°
Location 90° Location 180°
Location 270°
Lateral strain gauges 270°
School of Civil and Resource Engineering The University of Western Australia
139
Figure 7-5 The bending effect created by: (a) unleveled bottom platform, (2) non-parallelism of the
sample ends, and/or (c) eccentric loading.
In order to analyse the influence of the bending effect, rock foliation, anisotropy and
sample heterogeneity we tested 15 porphyry samples, which do not have any visible
foliation and 16 slate samples with strong foliation. We used a servo-controlled loading
machine of 5t capacity. The loading was displacement-controlled, applied by the
movement of the upper platform, while the bottom platform was fixed, Figure 7-5. In
this particular loading frame, the centre of the bottom platform was slightly offset from
the axis of the loading bar, which caused loading eccentricity and subsequently the
bending effect in the samples. Another possible source of the bending effect was the
non-parallelism of the sample ends. According to [97], the non-parallelism is ± 0.02mm
and the planarity of each sample end is allowed to be within 0.02mm, which will create
strain of 500 micro-strain higher at the highest spot of the sample end than the lowest
spot.
We introduce the bending level as follows:
Bending level = [εmax(σ) – εave(σ)] /εave(σ) (21)
where εmax(σ) is the maximum measured axial strain, εave(σ)is the average axial strain
The samples for testing were sub-sampled in 6 orientations from few consecutive pieces
of exploration core of around 1.5 meters. The variation of the deformation modulus
between 6 orientations indicates the level of anisotropy. The test parameters are listed in
Table 8.
Upper platform
Bottom platform
Sample
Loading bar
Strain gauge
(a) (b) (c)
School of Civil and Resource Engineering The University of Western Australia
140
Table 8 The details of rock samples and test parameters. All samples were prepared in accordance
with ISRM standard for unconfined compressive strength (UCS) [97].
Lithology Aplite Porphyry Slate
Visible foliation None Strong
Elastic (static)
modulus (GPa)
Range 50-66 32 – 82
Average 58 49
Maximum/Minimum 1.3 2.6
Poisson’s ratio 0.138 – 0.22 0.163 - 0.418
Sample diameter (mm) 19.2 19.2
Sample length (mm) 38 - 45 35 - 40
Sample density (t/m3) 2.52 – 2.58 2.75 – 2.95
According to the variation of the modulus shown in Table 8, the aplite porphyry
samples show a lower level of anisotropy than the slate samples. Therefore the aplite
porphyry samples are considered to be close to isotropic, while the strong foliation in
the slate samples creates anisotropy, which resulted in considerable variations in the
deformation moduli and the Poisson’s ratio. The foliation also creates a small-scale
heterogeneity.
Figure 7-6 shows the stress-strain plot measured on an aplite porphyry sample. The
axial strain gauges at the 0° and 90° locations, Figure 7-4, were under higher stress than
the strain gauges at the 180° and 270° locations; hence the strains recorded by the strain
gauges 0° and 90° are higher than the ones recorded by the 180° and 270° gauges. The
bending level in both axial and lateral direction is 13%.
In the foliated samples the strain/stress non-uniformity is caused by both the bending
effect and the rock foliation/heterogeneity. Figure 7-7 shows the stress-strain plot of a
slate sample under the same test conditions as used in testing the aplite porphyry
samples. The axial strain gauge at 0° shows slightly higher strain indicating that that
location was under a higher stress than the location of the strain gauge at 180°. The
axial strain gauges at 90° and 270° show the same strain, which suggests that these
locations were under the same stress as the average stress. The small difference between
School of Civil and Resource Engineering The University of Western Australia
141
the axial strains measured at different locations suggests that the difference in strain
caused by the bending effect was minor as compared to the axial strain values
associated with the foliation.
Figure 7-6 The stress-strain plot of the aplite porphyry sample (H782 D2). Considerable non-
uniformity in the stress/strain distribution is seen (bending level=13%). The axial strain is positive
and lateral strain is negative.
Figure 7-7 The stress-strain plot for a slate sample (PR2 D1). The axial strain is positive and lateral
strain is negative.
The strain recorded by the lateral strain gauges is not proportional to the strain recorded
by the axial strain gauges. We note that the lateral strain gauges at 90° and 270° are
0
50
100
-500 0 500 1000 1500 2000
Str
ess
(MP
a)
Strain (microstrain)
Stress-Strain Plot
0°180°90°270°
0
5
10
15
20
25
-300 0 300 600
Str
ess
(MP
a)
Strain (microstrain)
Stress-Strain Plot
0°180°90°270°
School of Civil and Resource Engineering The University of Western Australia
142
parallel to the movement of the foliation under loading, as shown in Figure 7-8. This
non-elasticity indicates sliding over the foliation planes, which affects differently the
strain gauges differently positioned with respect to the orientation of the foliation. The
sliding obviously produces higher strains, which explains why the bending has only
minor effect.
Figure 7-8 Sketch of the sample showing the strain gauge locations and orientation with respect to
the direction of foliation.
7.2.2 Compensation of bending in the DRA stress reconstruction
As discussed above, the non-perfect test conditions can create a non-uniform
stress/strain distribution in the sample and produce different strain readings at different
locations in both the axial and lateral directions. Since the strain recorded by each strain
gauge is not directly related to the average stress due to the bending effect, the strain
difference in the DRA method will not correspond to the average stress, either.
Bending leads to a stress/strain distribution across the sample cross-sections. In
particular, normal stress z and strain z components have distributions z(x,y,z) and
z(x,y,z) respectively in the co-ordinate frame (x,y,z) with the z-axis sent along the
sample axis, Figure 7-9. In order to estimate the effect of bending on the DRA stress
reconstruction we model the sample as a Euler beam under bending. This means that the
stress/strain distribution is assumed to be linear across the sample width. Consider a
cross section running through the locations of strain gauges. Let the position of this
cross section corresponds to co-ordinate z0. The beam approximation gives the
following distributions for the normal stress and strain components in the z-direction:
Lateral strain gauge 270° Lateral strain
gauge 90°
School of Civil and Resource Engineering The University of Western Australia
143
, , , , , (22)
where z ,z are the average stress and strain respectively.
Choosing the x-axis to run through the locations of two opposite strain gauges, Figure
7-9 we obtain
(23)
where zl
z is the axial strain measured at the side of the sample, zl is the normal stress
in that location.
Figure 7-9 The sample with co-ordinate frame (x, y, z). The z-axis is directed along the axis of the
sample, the x-axis runs through the pair of opposite strain gauges.
Figure 7-10 presents the strain difference plot (the DRA plot) of the aplite porphyry
sample shown in Figure 7-6. The inflection point in the strain curve registered by strain
gauge 270° is not identifiable. The inflection points calculated from the average stress
in the strain gauges located at 0°, 90° and 180° are 42MPa, 42MPa and 57MPa,
respectively. There is a significant discrepancy between the results. The stresses in
Figure 7-10(b) were calculated using equation 23 and represent the actual stress acting
at each strain gauge (see Appendix C). Now all DRA plots show inflections at stresses
around 50MPa, which was the pre-stress in this test.
z
x
y
School of Civil and Resource Engineering The University of Western Australia
144
Figure 7-10 The DRA curves with recognisable inflection points from individual strain gauges
located at 0°, 90° and 180° of aplite porphyry sample H782 D2: (a) the original curves recorded
form the strain gauges. The inflection points are not consistent; (b) the curves corrected using
equation 8; the inflection points now indicate stresses close to the pre-stresses.
The influence of the bending effect on the inflection point is explained in Figure 7-11.
The strain gauges placed at 0° and 90° reached the pre-stress (50MPa) when the average
stress was only 42MPa. The strain gauge 180° was under less stress and it only reached
the pre-stress when the average stress was 57MPa. Therefore, the inflection points from
these three strain gauges indicate the values of 42MPa, 42MPa and 57MPa for the pre-
stress when plotting the strain difference against the average stress.
Figure 7-11 Actual stresses calculated at the measurement locations using equation 8 vs. the
average stress. The pre-stress of 50MPa shall result in the number of ‘recovered’ stresses from the
DRA of strain measurements at different strain gauges (shown by arrows).
-25
-15
-5
0 50 100
Str
ain
diff
eren
ce (
mic
rost
rain
)
Average stress (MPa)
Lateral DRA Curve Before Stress Correction
0°90°180°270°
-25
-15
-5
0 50 100
Str
ain
diff
eren
ce (
mic
rost
rain
)
Actual stress (MPa)
Lateral DRA Curve After Stress Correction
0°180°90°270°
0
50
100
0 20 40 60 80 100
Act
ual s
tres
s (M
Pa)
Average stress (MPa)
Average Stress v.s Actual Stress
0° 180°
90° 270°
School of Civil and Resource Engineering The University of Western Australia
145
DRA for another aplite porphyry sample (H782 E2) is shown in Figure 7-12 and Figure
7-13. The pre-stress of 38MPa should result in a number of recovered stresses if the
DRA is used on the strain measurements from a local strain gauge, as illustrated in
Figure 7-12.
Figure 7-13(a) shows that there are two inflection points at 30MPa and 46MPa in the
strain difference curve recorded by the gauge 180°. It should be noted that sometimes
the strain difference from the gauge under lower stress shows an early, unrelated
inflection point, so that low stress is neglected. The locations 0° and 270° reach pre-
stress when the average stress is around 30MPa. The strain difference at gauge 180°
would show an inflection point at stress of about 30MPa, and another inflection point at
stress of 46MPa. After the stress correction all inflection points become close to each
other pointing out to the stress of 38MPa, which is the pre-stress, Figure 7-13(b).
Figure 7-12 Actual stresses calculated at the measurement locations using equation 8 vs. the
average stress. The pre-stress of 38MPa shall result in the number of ‘recovered’ stresses from the
DRA of strain measurements at different strain gauges (shown by arrows).
Figure 7-14 shows the standard deviation of the inflection points picked from four
lateral strain gauges in each aplite porphyry sample. The difference between the lateral
inflection points at the different locations is reduced after the average stress was
corrected by the equation 8. It is seen that the correction introduced by equation 8
achieves a threefold reduction in the standard deviation and hence in the error of
reconstruction.
0
40
80
0 20 40 60 80
Act
ual s
tres
s (M
Pa)
Average stress (MPa)
Average Stress v.s Actual Stress
0°180°90°270°
School of Civil and Resource Engineering The University of Western Australia
146
Figure 7-13 The DRA curves of aplite porphyry sample H782 E2: (a) the original curves recorded
form the strain gauges. The inflection point in the strain curve registered by strain gauge 270° is
not identifiable. The inflection points at other curves are not consistent; (b) the curves corrected
using equation 8; the inflection points now indicate stresses close to the pre-stresses of 38MPa.
Figure 7-14 At the various bending levels, the standard deviation of the inflection points in each
aplite sample is reduced after the bending effect is eliminated by the equation 8.
The slate sample, Figure 7-7 and Figure 7-8, shows only a minor bending level (7.5%)
during loading. The axial stress can be adjusted using the equation 8 in order to correct
the bending effect in the slate sample. Figure 7-15 presents the DRA plots before and
after stress correction. With the bending effect being minor compared to the foliation-
controlled deformation, the discrepancy of the pre-stress values inferred from the
-20
-10
0
0 20 40 60 80 100
Str
ain
diff
eren
ce (
mic
rost
rain
)
Average stress (MPa)
Lateral DRA Curve Before Stress Correction
0°180°90°270°
-20
-10
0
0 20 40 60 80 100
Str
ain
diff
eren
ce (
mic
rost
rain
)Actual stress (MPa)
Lateral DRA Curve After Stress Correction
0°180°90°270°
0
5
10
0 10 20 30Sta
ndar
d de
viat
ion
(MP
a)
Bending level (%)
Before and After Stress Correction
Before
After
School of Civil and Resource Engineering The University of Western Australia
147
inflection points on the curves produced by the strain gauges placed at 0°, 90° and 270°
is smaller than 3MPa both before and after correction. The inflection point in the strain
curve registered by strain gauge 180° is not identifiable due to the very small strain
difference between two successive loading cycles.
Figure 7-15 The pre-stress values inferred from identifiable DRA inflection points: (a) before stress
correction and (b) after stress correction.
7.3 CONCLUSION
Bending of samples under uniaxial compression due to the imperfections of the loading
frame and/or sample preparation can considerably affect the in-situ stress reconstruction
based on the DRA. Laboratory testing of two types of rock samples – macroscopically
homogeneous and isotropic aplite and foliated and hence anisotropic slate using three
loading cycles (the first loading to a pre-stress to be reconstructed followed by two
‘measuring’ cycles needed for the DRA) showed the following.
In the homogeneous and isotropic aplite porphyry and slate samples the bending can
create the non-uniform stress distribution in the loading (axial) direction sufficient to
affect the DRA-based stress reconstruction. The bending effect was shown to cause
considerable scatter in the pre-stress values reconstructed from the stress-strain curves
from the individual strain gauge locations. In order to compensate for the sample
-17
-7
3
0 5 10 15 20 25
Str
ain
diff
eren
ce (
mic
rost
rain
)
Average stress (MPa)
Lateral DRA Curve Before Stress Correction
0°90°180°270°
-17
-7
3
0 5 10 15 20 25
Str
ain
diff
eren
ce (
mic
rost
rain
)
Corresponding stress (MPa)
Lateral DRA Curve After Stress Correction
0°180°90°270°
School of Civil and Resource Engineering The University of Western Australia
148
bending at least four axial strain gauges are needed glued at the sample lateral surface
opposite, each pair of strain gauges attached opposite to each other, both pairs being
perpendicular to each other. The compensation formula is based on the assumption that
the stress/strain non-uniformity cause by bending can be approximated by assuming that
the sample bends as a classical beam. It is shown that the proposed compensation model
allows one to achieve a threefold reduction in the error of stress reconstruction.
In the foliated and hence heterogeneous and anisotropic slate samples the deformation
was predominantly controlled by foliation (low shear modulus in the direction of
foliation and/or sliding). For these samples the bending effect was inessential and
correspondingly the scatter of the pre-stress values inferred from the stress-strain curves
from the individual strain gauge locations was small.
The effect of the microscopic heterogeneity of the samples was minor, below the
accuracy of the pre-stress reconstruction offered by the DRA.
School of Civil and Resource Engineering The University of Western Australia
149
CHAPTER 8. DISCUSSION: THE INFLUENCE OF
STRESS APPLIED EARLIER THAN PRE-STRESS
8.1 INTRODUCTION
The proposed mechanism of deformation rate effect in [69] demonstrated that cohesion
and frictional resistance in the pre-existing cracks/defects can create the stress memory
which is recoverable by the DRA method. However, this mechanism also has a feature
that it can only record the previous maximum stress (PMS). Hence, if there were a stress
applied on the rock core and (1) the stress is irrelevant to the in situ stress, (2) the
magnitude of the stress was higher than the in situ stress; the in situ stress would be
masked and become irrecoverable by DRA technique. The potential sources of stress
applied on the core before conducting DRA could be the drilling induced stress, shock
waves from blasting, or subsample drilling/preparation induced stress. Because these
potential sources of stress and the magnitudes of these stresses are not monitored, these
stresses might change the inflection point of DRA technique and mislead the stress
prediction without causing any attention.
Another issue we need to address relates to the fundamental laboratory testing of the
DRA and the Kaiser effect method. If rock samples are used for the lab research
involving preload to a certain stress one needs to consider a possibility that the place in
rock mass the samples were recovered from has had the in-situ stress magnitudes higher
than that of the preload. If this is the case one has to consider a possibility that the
Kaiser effect method or the DRA recover that in-situ stress rather than the preload and
hence the test will be rendered ‘unsuccessful’. However, we have not seen a case in the
literature that DRA cannot predict the pre-stress applied in laboratory. Either the
‘unsuccessful’ tests are excluded or there are other mechanisms that can record the most
recent stress, instead of PMS.
In order to clarify the issue we have conducted two preliminary tests to investigate the
potential influence of the stress path/history on DRA technique. The first step is to
clarify whether the DRA can recover a laboratory pre-stress that is smaller than the in
situ stress. Although the exact in situ stress acted on the sample is unknown, the
overburden stress estimated by the density and depth of sample can provide a possible
School of Civil and Resource Engineering The University of Western Australia
150
stress range. The stress ratio (maximum principal stress/minimum principal stress) in
Western Australia is usually less than 3. A sample from a location with 40MPa
overburden stress could have in situ stress between 13MPa and 120MPa in the
orientation of sample’s axis. Hence, a 5MPa pre-stress is likely to be less than the in situ
stress.
The second question was to determine whether the DRA technique can recover the
laboratory stress, which is smaller than the previous maximum laboratory-applied stress.
We have applied the different magnitudes of stress to the ultramafic rock, felsic
volcanics and volcanic sediment samples in different stress path sequence.
In line with the above reasoning, we have applied 5MPa laboratory pre-stress to an
ultramafic rock sample with 40MPa overburden stress, to see if the DRA method can
recover the laboratory pre-stress that is smaller than the in situ stress.
8.2 EXPERIMENTAL SETUP
We used the rock samples drilled out from rock cores between one and two weeks
before conducting the tests. The samples were 18-19mm in diameter and 40mm- 45mm
in length. The strain was measured using glued double strain gauges, which ensure
simultaneous measurements of the axial and lateral strains. By placing four cross type
strain gauges at the positions shown in Figure 8-1, the strain non-uniformity caused by
the bending effect and/or heterogeneity can be detected by comparing the stress-strain
curves for each strain gauge.
Figure 8-1 Locations of the strain gauges on a sample.
Axial strain gauges 270°
Location 0°
Location 90° Location 180°
Location 270°
Lateral strain gauges 270°
School of Civil and Resource Engineering The University of Western Australia
151
The tests sequences and details are shown in Table 9. All samples were prepared in
accordance with ISRM standard for unconfined compressive strength [97]. The samples
were loaded using a servo-controlled loading machine of 5t capacity. The load was
displacement-controlled, applied by the movement of the upper platform, while the
bottom platform was fixed. All samples were subjected to 2 loading cycles under a
constant loading/unloading rate of 7~9 MPa/min. The average strain difference between
2 cycles was calculated by taking average of readings of 4 strain gauges.
Table 9 Details and the stress path history of the tested rock samples. The cells marked in blue are
the loading cycles using for generating strain difference curve and investigating the memory of the
previous stress.
ID WA51 B4 XT F3 SF117 E3
Rock type Ultramafic
rock
Felsic
volcanics
volcanic
sediment
Tangent modulus 118 67 112
Poisson’s ratio 0.17 0.26 0.26
Estimated overburden stress (MPa) 40 21 12
Anisotropy level* 12 7 8
Applied stress (MPa) or time
gap (zero MPa) between 2 tests
1 5 65 35
2 15 65 35
3 20 3 months 16 months
4 20 10 7
5 24hours 36 20
6 15 36 30
7 5 90
8 20
9 20
10
* anisotropy level was calculated by taking the standard deviation of young’s modulus
in the 18 samples (from 6 orientations). The orientations are listed in the appendix B.
School of Civil and Resource Engineering The University of Western Australia
152
8.3 TEST RESULT
8.3.1 The laboratory pre-stress that is smaller than the in situ stress
The results of 1st to 3th loading cycles applied on the ultramafic rock sample (WA5B4)
show that the DRA technique can determine a laboratory pre-stress that is smaller than
the in situ stress. Figure 8-2 (a) shows the DRA inflection point between 2nd and 3rd
cycles is close to 5MPa, which is the laboratory pre-stress in the 1st loading cycle. As
we discussed previously, the in situ stress ratio (maximum principal stress/minimum
principal stress) is usually less than 3 in the Western Australia. The sample WA51B4
from Western Australia is likely to have the in situ stress between 13MPa and 120MPa
at the sample’s axis, because the estimated overburden stress is 40MPa. Hence 5MPa is
unlikely to be higher than the in situ stress at the orientation of sample’s axis.
8.3.2 The number of pre-stress that DRA technique can recorded
The results of 2nd to 4th loading cycles applied on the ultramafic rock sample (WA51B4)
show that the DRA technique can only determine one previous maximum stress (PMS).
The inflection point between 3rd and 4th cycles only indicates a stress at around 15MPa
(maximum stress at the 2nd cycle, see Figure 8-2(b)), and does not show any sign at the
5MPa. Hence, in the ultramafic rock, DRA technique can only recover one PMS.
Figure 8-2 (a) The average axial strain difference between 2nd and 3rd cycles from an ultramafic
rock (WA51B4) shows a memory of maximum stress applied at 1st cycle. (b) The strain difference
between 3rd and 4th cycles from the same sample only shows an inflection point at 15MPa, which is
the maximum stress at 2nd cycle. The maximum stress at 1st cycle (5MPa) did not show any sign on
the strain difference curve.
0
5
0 5 10 15
Mic
rost
rain
Stress (MPa)
Strain difference between 2nd and 3rd cycles
(a)
0
5
0 5 10 15 20
Mic
rost
rain
Stress (MPa)
Strain difference between 3rd and 4th cycles
(b)
School of Civil and Resource Engineering The University of Western Australia
153
The result of 1st to 4th cycles in the sample WA51B4 answers (1) DRA method can pick
up the laboratory stress that is smaller than the in situ stress, and (2) DRA technique
cannot predict more than one previous stress. In order to clarify that the stress DRA
technique indicates is PMS or most recent stress, we then applied stress (6th to 9th
cycles) one day after completing the previous 4 cycles. In the Table 9, the 5th cycle was
the time gap between 4th and 6th cycles and there was no stress applied on the sample.
8.3.3 The most recent stress (lower than PMS)
The maximum stress at 6th cycle is 15MPa, which is lower than the PMS was applied a
day before 6th cycle. The average axial strain difference between 8th and 9th cycles
shows there was no memory recovered by DRA technique. There could be a drop/
fluctuation in the strain difference curve around 17MPa, but the drop was smaller than 1
microstrain and difficult to distinguish from the noise. Hence we considered it is not a
inflection point (Figure 8-3 (a)).
However, we found that in the felsic volcanics sample XTF3, the DRA can recover the
stress that is not PMS. The sample was subjected to 65MPa 3 months before we applied
10MPa (4th cycle, see Table 9) on the sample. The load of 10MPa was recovered by the
strain difference between 5th and 6th cycles (Figure 8-3 (b)).
Figure 8-3 (a) The ultramafic rock sample does not show a memory of most recent stress (5MPa on
7th cycle), because the most recent stress is lower than the PMS. (b) The felsic volcanics sample
show a memory of the most recent stress (10MPa on 4th cycle), even the most recent stress is lower
than the PMS.
0
5
0 5 10 15 20
Mic
rost
rain
Stress (MPa)
Strain Difference between 8th and 9th cycles
(a)
0
5
0 10 20 30 40
Mic
rost
rain
Stress (MPa)
Strain Difference between 5th and 6th cycles
(b)
School of Civil and Resource Engineering The University of Western Australia
154
Figure 8-4 The volcanic sediment sample does not have a detectable memory of most recent stress
(7MPa at (a) and 20MPa at (b)).
Because the time gaps between PMS and the most recent stress (before conducting
DRA test) in these two samples are different, it is possible that the ultramafic rock
(WA51B4) did not have enough time to recover from the PMS; hence, it was not able to
record the most recent stress at that moment. To clarify the ability to recover the most
recent stress, which is not purely time dependent, we have conducted another test with
16 months’ time gap between PMS (35MPa) and the most recent stress in a volcanic
sediment sample (SF117E3). The result shows that the DRA technique was still not able
to recover the most recent stress after 16 months’ time gap (Figure 8-4).
There are two possibilities to explain the conflicting DRA results for samples SF117E3
and XTE3. It might be: (1) the most recent stress, which is lower than PMS, can only be
recovered by DRA in certain rock/material type, and this rock/material type has an
unknown mechanism to record the stress lower than PMS; or (2) the most recent stress,
which is lower than PMS, can be recovered by DRA in any rock/material type, but
different rock/material requires different time period after PMS to gain the ability of
recording memory. A further investigation is required to provide more
detailed/systematic tests.
0
5
0 10 20
Mic
rost
rain
Stress (MPa)
Strain Difference between 5th and 6th cycles
0
5
0 10 20 30
Mic
rost
rain
Stress (MPa)
Strain Difference between 6th and 7th cycles
School of Civil and Resource Engineering The University of Western Australia
155
8.4 DISCUSSION AND SUGGESTION
Although the tests from three samples of different lithology are not sufficient to analyse
the influence of in-situ preloads on the laboratory results on stress recovery, they
provided some information for designing future research. First, the time gap between
PMS and the following stress has a potential to influence the stress recovered by the
DRA. The time gap required to “gain back the ability of recording previous stress”
might be lithology/material dependant. Second, the DRA technique is able to predict the
most recent stress, instead of PMS. Third, although the DRA technique can predict the
most recent stress, it can only pick one historic laboratory pre-stress in our tests. We
confirm that DRA method can recover a laboratory pre-stress which is smaller than the
in situ stress, but it is not clear if it can recover one laboratory pre-stress and in situ
stress at the same time.
We have also noticed that the lithology of rock sample does not fully determine the
recoverability of the PMS. For example, sample WA51B4 in Table 9 is ultramafic and
shows a clear inflection point of PMS, but we have also found that there are several
ultramafic rock samples from different drilling location that do not show a clear
memory of PMS when tested under the same conditions. It might be that the physical
properties of the ultramafic samples are different, so their ability of recording a stress is
different.
School of Civil and Resource Engineering The University of Western Australia
156
CHAPTER 9. CONCLUSIONS
Rock memory is a phenomenon that can be used to recover the in situ stress by testing
rock cores that are usually kept at large numbers after the exploration drilling. We
investigated two commonly used methods of stress recovery from the rock memory: the
Kaiser effect method and the DRA.
Our results show that the Kaiser effect method of the in situ stress determination has
severe limitations. First, the results of stress determination are easily affected by the
noise from environment and from the sample ends (Ghost Kaiser effect). As it is
impossible to completely eliminate the acoustic pulses generated by the end effect, a
multichannel source location system is needed to separate the acoustic signal related to
the rock memory from the noise. Second, the use of the Kaiser effect is impeded by the
uncertainty about its mechanism. For instance, the hypothesis that the Kaiser effect is
caused by the generation new cracks/damage during loading cannot explain the memory
recovered by the Kaiser effect in the low stress to strength region.
Furthermore, even if the noise from the environment/sample ends is absent, the quality
of the stress reconstruction depends upon the number of cracks generated during
loading. When the pre-stress (or the in situ stress) reaches a high stress level (compared
to the sample UCS), the process of crack generation/growth can create sufficient change
in the stress path in the following loading cycle. The acoustic bursting caused by the
damage accumulation is likely to imitate the Kaiser effect and mislead the analysis. This
“false bursting” cannot be distinguished even by the source location system. This makes
the use of the Kaiser effect for stress determination very difficult and unreliable.
We proposed a rheological model as the mechanism of the deformation rate effect at
low stress to strength region. The model, that comprises cohesion, spring, and dashpot
elements, demonstrates the memory by the frictional sliding mechanism and
accommodates time-dependant behaviours of the deformation rate effect. The model
shows that the “memory” of the in situ stress in rock would not fade if the creep
deformation caused by the in situ stress has finished. However, the laboratory pre-stress
usually has very short holding time compared with the in situ stress to allow creep
deformation works. Hence the memory of laboratory pre-stress would fade with long
School of Civil and Resource Engineering The University of Western Australia
157
delay time, and the memory of in situ stress might not be affected by the delay time. In
terms of increasing the accuracy of the in situ stress reconstruction by DRA method, the
size of sample should be reduced and the loading rate should be as low as possible.
We identified the factors that affect the stress reconstruction. The bending effect was
shown to cause considerable scatter in the pre-stress values reconstructed from the
stress-strain curves from the individual strain gauge locations. A compensation formula
was developed for stress reconstruction, based on the classical beam theory. Since the
bending effect is a source of potential error in the uniaxial compression test, four
crossed type strain gauges can simply provide enough information for checking the
degrees of bending and the information for compensation formula.
In the ultramafic rock and felsic volcanics sample, the DRA technique can record the
most recent stress (applied in laboratory), whether the in situ stress/previous laboratory
applied stress is higher than the most recent stress or not. Hence we believe there is a
mechanism, which can record the stress memory of most recent stress, instead of
previous maximum stress. This mechanism can explain the fact that we have not seen a
case on the literature that DRA cannot predict the pre-stress applied in laboratory. Our
experience does not deny the potential of cohesion and friction resistance as a
mechanism of deformation rate effect. However, there should be another mechanism,
which is able to record the stress other than PMS or can gain back the ability of
recording stress within few months.
An important indicator of the onset of mechanism of rock memory based on crack
generation/growth is the onset of dilatancy. It is generally difficult to determine the start
of dilatancy only from the stress-strain curve or stress-volumetric strain curve. An
additional indicator is the variation in the rock stiffness (the tangent modulus) during
loading. The trends of tangent modulus at the 1st cycle can be classified into 3 types of
behaviour: the increasing type, the constant type, and the reducing type.
We also found that contrary to a common belief that the rock reduces its stiffness after
repeated loads, it may actually increase. The increase is controlled by the residual strain
of the first unloading. This relationship is independent of the maximum stress level a
rock had been subjected to and it seems to be similar for different rock types. The
School of Civil and Resource Engineering The University of Western Australia
158
finding provides additional information to understand the deformation behaviours of
rock.
School of Civil and Resource Engineering The University of Western Australia
159
CHAPTER 10. RECOMMENDATIONS FOR FUTURE
RESEARCH
10.1.1 The Kaiser effect
Since the Kaiser effect can only be observed on the condition that the PMS is higher
than the onset of dilatancy, it is important to find the precursor/indicator for the onset of
dilatancy.
The size of crack determines the amount of energy which is available to generate the
acoustic pulse. It is possible that certain cracks are too small to produce a detectable
acoustic pulse. Hence, the better understanding of crack size in a sample could provide
help in analysing the record of acoustic emission. A practical way to measure the
size/number of cracks in a rock sample still needs to be found. We suggest an indirect
method (i.e. change in wave velocity, or change in modulus under load) might be able to
indicate the change in the crack size/number.
10.1.2 The deformation rate analysis
It is important to develop methods of distinguishing the inelastic strain from elastic
strain, and determining the amount of inelastic strain. Without understanding the source
of inelastic strain, it is difficult to evaluate the DRA method. As the first step, it is
important to find the mechanism of increasing the tangent modulus under repeated load.
Then, the research on the relationship between the inelastic deformation/damage
mechanism and PMS could be commenced.
It is also important to conduct more experimental work on the difference between long-
term memory (in situ stress) and short-term memory (laboratory applied stress). The
result will help to improve the mathematical model proposed in Chapter 5 and Chapter
6.
A further experimental work should also be designed to investigate the possibility of
recovering PMS/most recent stress in different rock types, time gap, and stress level.
The results that show/do not show a memory of stress history can provide an indication
of the mechanism of inelastic deformation and damage accumulation in place.
School of Civil and Resource Engineering The University of Western Australia
160
School of Civil and Resource Engineering The University of Western Australia
161
CHAPTER 11. REFERENCES
[1] Stacey T, Wesseloo J. Application of indirect stress measurement techniques (non strain gauge based technology) to quantify stress environments in mines. The University of the Witwatersrand and SRK consulting; 2002. p. 68. [2] Tensi HM. The Kaiser - effect and its Scientific Background. 26th European Conference on Acoustic Emission Testing. Berlin, Germany2004. [3] Goodman RE. Subaudible Noise During compression of Rocks. Geol soc of America Bull. 1963;74:487-90. [4] Lavrov A. The Kaiser effect in rocks: principles and stress estimation techniques. Int J Rock Mech Min Sci. 2003;40:151-71. [5] Kurita K, Fujii N. Stress memory of crystalline rock in acoustic emission. Geophys res letters. 1979;6:9-12. [6] ISRM. ISRM-Suggested Method for in situ stress measurement from a rock core using the Acoustic Emission technique. 5th International Workshop on the application of Geophysics in Rock Engineering. Toronto2002. p. 61-6. [7] Holcomb DJ. General theory of the Kaiser effect. Int J Rock Mech Min Sci & Geomech. 1993;30:929-35. [8] Barr SP, Hunt DP. Anelastic strain recovery and the Kaiser effect retention span in the Carnmenellis Granite, U.K. Rock Mech Rock Eng. 1999;32:169-93. [9] Filimonov YL, Lavrov AV, Shafarenko Y, Shkuratnik VL. Memory Effects in rock Salt Under Triaxial Stress State and Their Use for Stress Measurement in a Rock Mass. Rock Mech Rock Eng. 2001;34:275-91. [10] Hazzard JF, Young RP. Simulating acoustic emissions in bonded-particle models of rock. Int J Rock Mech Min Sci. 2000;37:867-72. [11] Holcomb DJ. Observations of the Kaiser effect under multiaxial stress states: implications for its use in determining in situ stress. Geophys res letters. 1993;20:2119-22. [12] Hughson DR, Crawford AM. Kaiser effect gauging: The influence of confining stress on its response. 6th ISRM Congress. Montreal, Canada: International Society for Rock Mechanics; 1987. p. 981-5. [13] Jayaraman S. Kaiser effect studies in rocks. America: The Pennsylvania State University; 2001. [14] Kramadibrata S, Simangunsong GM, Matsui K, Shimada H. Role of acoustic emission for solving rock engineering problems in Indonesian underground mining. Rock Mech Rock Eng. 2010;44:281-9. [15] Lehtonen A, Cosgrove JW, Hudson JA, Johansson E. An examination of in situ rock stress estimation using the Kaiser effect. Eng Geol. 2012;124:24-37. [16] Li C, Nordlund E. Assessment of damage in rock using the Kaiser effect of acoustic emission. Int J Rock Mech Min Sci & Geomech. 1993;30:943-6. [17] Mori Y, Obata Y. Electromagnetic emission and AE Kaiser effect for estimating rock in-situ stress. Report of the Research Institute of Industrial Technology: Nihon University; 2008. p. 1-16. [18] Shkuratnik VL, Lavrov AV. Memory effects in rock. J Min Sci. 1995;31:20-8.
School of Civil and Resource Engineering The University of Western Australia
162
[19] Tuncay E, Obara Y. Comparison of stresses obtained from Acoustic Emission and Compact Conical-Ended Borehole Overcoring techniques and an evaluation of the Kaiser Effect level. Bull Eng Geol Environ. 2012;71:367-77. [20] Tuncay E, Ulusay R. Relation between Kaiser effect levels and pre-stresses applied in the laboratory. Int J Rock Mech Min Sci. 2008;45:524-37. [21] Villaescusa E, Li J, Windsor CR. A comparison of overcoring and AE stress profiles with depth in Western Australian Mines. In: Lu, Li, Kyorholt, Dahle, editors. Insitu Rock Stress. Trondheim, Norway: Taylor & Francis Group; 2006. [22] Villaescusa E, Li J, Windsor CR. Flying Fox Mine, Western Area, Western Australia. Stress measurements from oriented core using the Acoustic Emission method. Western Australia: Curtin University of Technology Western Australian School of Mines; 2005. p. 21. [23] Villaescusa E, Windsor CR, Machuca L. Stage 2, ZINIFEX, Rosebery Mine. Stress measurements from oriented core using the Acoustic Emission method. Western Australia: Curtin University of Technology; 2007. p. 24. [24] Yamshchikov VS, Shkuratnik VL, Lykov KG. Stress measurement in a rock bed based on emission memory effects. J Min Sci. 1990;26:122-7. [25] Chang JF. Investigating the laboratory experiments to estimate pre-stress on black schist [Master thesis]. Tainan: National Cheng Kung University; 2007. [26] Hunt SP, Meyers AG, Louchnikov V. Modelling the Kaiser effect and deformation rate analysis in sandstone using the discrete element method. Computers and Geotechnics. 2003;30:611-21. [27] Hunt SP, Meyers AG, Louchnikov V, Oliver KJ. Use of the DRA technique, porosimetry and numerical modelling for estimating the maximum in-situ stress in rock from core: South African Institute of Mining and Metallurgy; 2003. [28] Chan SC. Investigating the laboratory experiments to estimate pre-stress on Changchikeng Sandstone [Master thesis]. Tainan: National Cheng Kung University; 2008. [29] Lin HM, Wu JH, Lee DH. Evaluating the pre-stress of Mu-Shan sandstone using acoustic emission and deformation rate analysis. In: Lu, Li, Kjorholt H, Dahle, editors. In-situ Rock Stress. London: Taylor & Francis Group; 2006. p. 215-22. [30] Louchnikov V, Hunt SP, Meyers AG. Influence of confining pressure on the deformation memory effect in rocks studied by particle flow code, PFC2D. In: Lu, Li, Kjorholt H, Dahle, editors. In-situ Rock Stress. London: Taylor & Francis Group; 2006. [31] Seto M, Nag DK, Vutukuri VS. In-situ rock stress measurement from rock cores using the acoustic emission method and deformation rate analysis. Geotech Geol Eng. 1999;17:241-66. [32] Villaescusa E, Seto M, Baird G. Stress measurements from oriented core. Int J Rock Mech Min Sci. 2002;39:603-15. [33] Villaescusa E, Windsor CR, Li J, Baird G, Seto M. Stress measurements from cored rock. Minerals and Energy Research Institute of Western Australia Project M3292003. p. 14. [34] Chen M, Zhang Y, Jin Y, Li L. Experimental study of influence of loading rate on Kaiser effect of different lithological rock. Chinese J Rock Mech Eng. 2009;28:2599-604. [35] Li L, Zou Z, Zhang Q. Current situation of the study on Kaiser effect of rock acoustic emission in in-situ stress measurement. Coal Geol & Exploration. 2011;39:41-5.
School of Civil and Resource Engineering The University of Western Australia
163
[36] Shi L, Zhang X, Jin Y, Chen M. New method for measurement of in-situ stresses at great depth. Chinese J Rock Mech Eng. 2004;23:2355-8. [37] Su C, Gao B, Nan H, Li X. Experimental study on acoustic emission characteristics during deformation and failure processes of coal sample under different stress paths. Chinese J Rock Mech Eng. 2009;28:757-66. [38] Zhang G, Chen M, Zhao Z. Research on influence of Kaiser sampling deviation on stress measurements at great depth. Chinese J Rock Mech Eng. 2008;27:1682-7. [39] Zhang G, Jin Y, Chen M. Measurement of in-situ stresses by Kaiser effect under confining pressures. Chinese J Rock Mech Eng. 2002;21:360-3. [40] Zhao K, Jin J, Liu M, Wang X, He G, Zhi X. Experimental research and numerical simulation of acoustic emission of memory effect of rock stress under point load. Chinese J Rock Mech Eng. 2009;28:2695-702. [41] Zhao K, Li Y, Liu M, Zhao K. The application of rock homogeneity degree confirmation by numerical simulation of rock Kaiser effect. China Tungsten Industry. 2007;22:1-4. [42] Zhou X, Deng M, Zhang F. New method to study in-situ stress of rock mass by AE and structure analysis of rock mass. J Chongqing Jianzhu University. 2001;23:109-13. [43] Alkan H, Cinar Y, Pusch G. Rock salt dilatancy boundary from combined acoustic emission and triaxial compression tests. Int J Rock Mech Min Sci. 2007;44:108-19. [44] Eberhardt E, Stead D, Stimpson B, Read RS. Identifying crack initiation and propagation thresholds in brittle rock. Canadian Geotech J. 1998;35:222-33. [45] Eberhardt E, Stimpson B, Stead D. The influence of mineralogy on the initiation of microfractures in granite. In: Vouille G, Berest P, Balkema AA, editors. 9th International Congress on Rock Mechanics. Paris1999. p. 1007-10. [46] Eberhardt E, Stead D, Stimpson B, Read R. Changes in acoustic event properties with progressive fracture damage. Int J Rock Mech Min Sci. 1997;34:071B-663. [47] Eberhardt E, Stimpson B, Stead D. Effects of grain size on the Initiation and propagation thresholds of stress-induced brittle fractures. Rock Mech Rock Eng. 1999;32:81-99. [48] Martin CD, Chandler NA. The progressive fracture of Lac du Bonnet granite. Int J Rock Mech Min Sci & Geomech. 1994;31:643-59. [49] Brace WF, B. W. Paulding J, Scholz C. Dilatancy in the fracture of crystalline rocks. J Geophys Res. 1966;71:3939-53. [50] Bieniawski ZT. Mechanism of brittle fracture of rock, part II - experimental studies. Int J Rock Mech Min Sci. 1967;4:407-23. [51] Cai M, Kaiser PK, Tasaka Y, Maejima T, Morioka H, Minami M. Generalized crack initiation and crack damage stress thresholds of brittle rock masses near underground excavations. Int J Rock Mech Min Sci. 2004;41:833-47. [52] Katz O, Reches Z. Microfracturing, damage and failure of brittle granites. J Geophys Res. 2004;109:B01206. [53] Martin CD. The strength of massive Lac du Bonnet granite around underground openings. Manitoba, Canada: University of Manitoba; 1993. [54] Yuan SC, Harrison JP. An empirical dilatancy index for the dilatant deformation of rock. Int J Rock Mech Min Sci. 2004;41:679-86. [55] Seto M, Villaescusa E. In situ stress determination by acoustic emission techniques from McArthur River Mine cores. In: Dhamsiri VN, Randal C, editors. 8th Australia New Zealand Conference on Geomechanics: Consolidating Knowledge. Hobart, Tasmania: Australian Geomechanics Society; 1999.
School of Civil and Resource Engineering The University of Western Australia
164
[56] Boyce GM, McCabe WM, Koerner RM. Acoustic emission signatures of various rock types in unconfined compression. Acoustic Emissions in Geotechnical Engineering Practice: American Society for Testing and Materials; 1981. p. 142-54. [57] Yamamoto K, Kuwahara Y, Kato N, Hirasawa T. Deformation Rate Analysis: A new method for in situ stress estimation from inelastic deformation of rock samples under uni-axial compressions. Tohoku Geophys J. 1990;33:127-47. [58] Tamaki K, Yamamoto K, Furuta T, Yamamoto H. Experiment of in-situ stress estimation on basaltic rock core samples from hole 758A, Ninetyeast ridge, Indian Ocean. In: Weissel J, Peirce J, Taylor E, Alt J, al. e, editors. The Ocean Drilling Program, Scientific Results: College Station; 1991. p. 697-717. [59] Tamaki K, Yamamoto K. Estimating in-situ stress field from basaltic rock core samples of hole 794C, Yamato basin, Japan Sea. In: Tamaki K, Suyehiro K, Allan J, Mcwilliams J, al. e, editors. The Ocean Drilling Program, Scientific Results: College Station; 1992. p. 1047-59. [60] Yamshchikov VS, Shkuratnik VL, Lavrov AV. Memory effects in rocks (Review). J Min Sci. 1994;30:463-73. [61] Shin K, Kanagawa T. Kaiser effect of rock in acousto-elasticity, AE & DR. The 5th conference on AE/MA in Geologic structures and materials1995. p. 197-204. [62] Yamamoto K. The rock property of in-situ stress memory: Discussions on its mechanism. International workshop on Rock Stress: Measurement at Great Depth. Tokyo1995. p. 46-51. [63] Utagawa M, Seto M, Katsuyama K. Estimation of initial stress by Deformation Rate Analysis (DRA). Int J Rock Mech Min Sci. 1997;34:317. [64] Yamamoto K, Yabe Y. Stresses at sites close to the Nojima Fault measured from core samples. The island Arc. 2001;10:266-81. [65] Yamamoto K, Seto N, Yabe Y. Elastic property of damaged zone inferred from in-situ stresses and its role on the shear strength of faults. Earth Planets Space. 2002;54:1181-94. [66] Dight PM. Determination of in-situ stress from oriented core. In: Lu M, Li CC, Kjorholt H, Dahle H, editors. In-Situ Rock Stress - Measurement, Interpretation and Application2006. p. 167-75. [67] Xie Q, Qiu P, Yu X, Gama CD. Initial-stress measurements with AE and DRA combined technique. J China Coal Society. 2010;35:559-64. [68] Fujii Y, Kondo K. Influence of stress larger than preload but acted for shorter duration in tangent modulus method: A new method to measure in-situ rock stress. ISRM International Symposium 2010 and 6th Asian Rock Mechanics Symposium. New Delhi, India: Indian National Group of ISRM; 2010. p. 35. [69] Wang HJ, Dyskin AV, Hsieh A, Dight P. The mechanism of the deformation memory effect and the deformation rate analysis in layered rock in the low stress region. Computers and Geotech. 2012;44:83-92. [70] Hayashi M, Kanagawa T, Hibino S, Motozima M, Kitahara Y. Detection of anisotropic geo-stresses trying by acoustic emission and non-linear rock mechanics on large excavating caverns. 4th ISRM Congress. Montreux, Switzerland: International Society for Rock Mechanics; 1979. [71] Yoshikawa S, Mogi K. A new method for estimation of the crustal stress from cored rock samples: Laboratory study in the case of uniaxial compression. Tectonophysics. 1981;74:323-39.
School of Civil and Resource Engineering The University of Western Australia
165
[72] Momayez M, Hassuni EP. Application of Kaiser effect to measure in-situ stresses in underground mines. The 33th US Symposium on Rock Mechanics. Santa Fe, NM: American Rock Mechanics Association; 1992. p. 979-88. [73] Deng J, Wang K, Huang R. In-situ stress determination at great depth by using acoustic emission technique. Rock Mech. 1995:245-50. [74] Seto M, Utagawa M, Katsuyama K, Nag DK, Vutukuri VS. In situ stress determination by acoustic emission technique. Int J Rock Mech Min Sci. 1997;34:281. [75] Wang HT, Xian XF, Yin GZ, Xu J. A new method of determining geostresses by the acoustic emission Kaiser effect. Int J Rock Mech Min Sci. 2000;37:543-7. [76] Seto M, Utagawa M, Katsuyama K. Some fundamental studies on the AE method and its application to in-situ stress measurements in Japan. 5th International Workshop on the Application of Geophysics in Rock Engineering. Toronto, Canada2002. [77] Filimonov Y, Lavrov A, Shkuratnik V. Effect of Confining Stress on Acoustic Emission in Ductile Rock. Strain. 2005;41:33-5. [78] Lehtonen AV, Sarkka P. Evaluation of rock stress estimation by the Kaiser effect. In: Lu M, Li CC, Kjørholt H, Dahle H, editors. International Symposium on In-Situ Rock Stress. Trondheim, Norway: Taylor & Francis Group; 2006. p. 135-42. [79] Villaescusa E, Windsor CR, Machuca L. ZINIFEX, Rosebery Mine. Stress measurements from oriented core using the Acoustic Emission method. Western Australia: Curtin University of Technology; 2006. p. 34. [80] Keshavarz M, Pellet FL, Hosseini KA, Rousseau C. Comparing the results of acoustic emission monitoring in brazilian and uniaxial compresssion tests. 5th Asian Rock Mechanics Symposium, ISRM Internnational Symposium. Tehran, Iran2008. [81] Ulusay R, Tuncay E, Tano H, Watanabe H. Studies on in-situ stress measurements in Turkey. 1st Collaborative Symposium of Turk-Japan Civil Engineers. 2008. [82] Villaescusa E, Machuca L, Windsor C, Simser B, Carlisle S. Stress measurements at great depth at Craig-Onaping Mines, Sudbury Canada. In: Diederichs M, Grasselli G, editors. 3rd CANUS Rock Mechanics Symposium. Toronto2009. [83] Villaescusa E, Machuca L, Lei X, Funatsu T. In-situ stress measurements using oriented core - A comparison of uniaxial vs triaxial acoustic emission results. In: Xie, editor. Rock Stress and Earthquakes. London: Taylor & Francis Group; 2010. [84] Windsor CR, Villaescusa E, Machuca LA. A comparison of rock stresses measured by WASM AE with results from other techniques that measure the complete rock stress tensor. In: Xie, editor. Rock Stress and Earthquakes. London: Taylor & Francis Group; 2010. [85] Park P, Park N, Hong C, Jeon S, Kim Y. The influence of delay time and confining pressure on in situ stress measurement using AE and DRA. In: Elsworth D, Tinucci JP, Heasley KA, editors. 38th US symposium. U. S. A: Swets & Zeitlinger Lisse; 2001. p. 1281-4. [86] Wu JH, Jan SC. Experimental validation of core-based pre-stress evaluations in rock: a case study of Changchikeng sandstone in the Tseng-wen reservoir transbasin water tunnel. Bull Eng Geol Environ. 2010;69:549-59. [87] Li Y, Qiao L, Sui ZL. In-situ stress measurement based on acoustic emission in combination with core orientation techniques. In: Xie F, editor. Rock stress and earthquakes. London: Taylor & Francis Group; 2010. p. 892. [88] Filimonov Y, Lavrov A, Shkuratnik V. Acoustic Emission in Rock Salt: Effect of Loading Rate. Strain. 2002;38:157-9.
School of Civil and Resource Engineering The University of Western Australia
166
[89] Han J, Wu S, Tan C, Sun W, Zhang C, Ding Y, et al. Studies on geostress by comparing result of AE method with that of hydraulic fracturing technique in Dongjiangkou granite in east Qinling. Chinese J Rock Mech Eng. 2007;26:81-6. [90] Li H, Zhang B. In-situ stress measurement of Fangshan granite. Chinese J Rock Mech Eng. 2004;28:1349-52. [91] Li Y, Dong P. In-situ stress measurement of reservoir using Kaiser effect of rock. Chinese J Rock Mech Eng. 2009;28:2802-7. [92] Li M, Qin S, Ma P, Sun Q. In-situ stress measurement with Kaiser effect of rock acoustic emission. J Eng Geol. 2008;16:833-8. [93] Tang S. Application of AE - Based ground stress survey technology in metallic mines. Min R & D. 2002;22:18-20. [94] Wang X, Ge H, Song L, He T, Xin W. Experimental study of two types of rock sample acoustic emission events and Kaiser effect point recognition approach. Chinese J Rock Mech Eng. 2011;30:580-8. [95] Xu J, Tang X, Li S, Yang H, Tao Y. Experimental research on acoustic emission rules of rock under cyclic loading. Rock and Soil Mech. 2009;30:1241-6. [96] Zheng Z, Zhang J, Wang W. Measurement of in-situ stresses with acoustic emission effect in Haizi coal mine. Coal Geol & Exploration. 2008;36:68-72. [97] ISRM. Suggested Method for Determining the Uniaxial Compressive Strength and Deformability of Rock Materials. International Society of Rock Mechanics: ISRM; 1979. p. 137-40. [98] Hsieh A, Dight P, Dyskin AV. Ghost Kaiser effect at low stress: the role of the sample ends. Int J Rock Mech Min Sci. 2012;submitted. [99] Hsieh A, Dyskin AV, Dight P. The tangent modulus and relationship between residual strain and increase in bulk modulus in rock after applied stress under uniaxial compression test. Int J Rock Mech Min Sci. 2013;submitted. [100] Dyskin AV. Relation between acoustic emission and dilatancy in uniaxial compression of brittle rocks. Physics of the Solid Earth. 1989;25:473-7. [101] Lajtai EZ. Microscopic fracture processes in a Granite. Rock Mech Rock Eng. 1998;31:237-50. [102] Eberhardt E, Stead D, Stimpson B. Quantifying progressive pre-peak brittle fracture damage in rock during uniaxial compression. Int J Rock Mech Min Sci. 1999;36:361-80. [103] Hawkes I, Mellor M. Uniaxial testing in rock mechanics laboratories. Eng Geol. 1970;4:177-285. [104] Johnson TL. Measurement of elastic properties and static strength. New York: Columbia University; 1984. p. 52. [105] Santi PM, Holschen JE, Stephenson RW. Improving elastic modulus measurements for rock based on Geology. Environ & Eng Geosci. 2000;6:333-46. [106] Dyskin AV, Salganik RL. Model of dilatancy of brittle materials with cracks under compression. Mechanics of solids. 1987;22:165-73. [107] Germanovich LN, Dyskin AV, Tsyrulnikov MN. Mechanism of dilatancy and columnar failure of brittle rocks under uniaxial compression. Trans Dokl USSR Acad Sci Earth Sci Sec. 1990;313:6-10. [108] Walsh JB. The effect of cracks on the uniaxial elastic compression. J Geophys Res. 1965;70:399-411. [109] Cook NGW, Hodgson K. Some detailed stress-strain curves for rock. J Geophys Res. 1965;70:2883-8.
School of Civil and Resource Engineering The University of Western Australia
167
[110] Lama RD, Vutukuri VS. Handbook on Mechanical Properties of Rocks: Trans Tech Publications; 1978. [111] Deere DU, Miller RP. Engineering classification and index properties for intact rock. Illinois: University of Illinois; 1966. p. 327. [112] Fairhurst C. Stress estimation in rock: a brief history and review. Int J Rock Mech Min Sci. 2003;40:957-73. [113] Yamamoto K. A theory of rock core-based methods for in-situ stress measurement. Earth Planets Space. 2009;61:1143-61. [114] Kuwahara Y, Yamamoto K, Hirasawa T. An experimental and theoretical study of inelastic deformation of brittle rocks under cyclic uniaxial loading. Tohoku Geophys J. 1990;33:1-22. [115] Diederichs MS, Kaiser PK, Eberhardt E. Damage initiation and propagation in hard rock during tunnelling and the influence of near-face stress rotation. Int J Rock Mech Min Sci. 2004;41:785-812. [116] Salganik R. Mechanics of bodies with many cracks. Mechanics of solids. 1973;8:135-43. [117] Salganik R. Overall effects due to cracks and crack-like defects. In: Sih G, Zorski H, editors. 1st International Symposium on Defects and Fracture. Tuczno, Poland1982. p. 199-208. [118] Fairhurst C. Stress estimation in rock: a brief history and review. International Journal of Rock Mechanics and Mining Sciences. 2003;40:957-73. [119] Dight P. Stress states in open pits. Keynote lecture – Slope Stability in Mining and Civil Engineering. Vancouver2011. [120] Hudson JA, Harrison JP. Engineering rock mechanics: An introduction to the principles. Pergamon, Oxford: Elsevier; 2000. [121] Dight P, Dyskin AV. Accounting for the effect of rock mass anisotropy in stress measurements. Deep Mining 07 Proc 4-th International Seminar on Deep and High Stress Mining. Nedlands, Western Australia2007. p. 415-24. [122] Yamamoto K, Kuwahara Y, Kato N, Hirasawa T. Deformation Rate Analysis: A New Method for In Situ Stress Estimation from Inelastic Deformation of Rock Samples under Uni-Axial Compressions. Tohoku Geophysical Journal (Science Report of Tohoku University, Series 5, Geophysics). 1990;33:127-47. [123] Seto M, Nag DK, Vutukuri VS. In-situ rock stress measurement from rock cores using the acoustic emission method and deformation rate analysis. Geotechnical and Geological Engineering. 1999;17:241-66. [124] Kuwahara Y, Yamamoto K, Hirasawa T. An experimental and theoretical study of inelastic deformation of brittle rocks under cyclic uniaxial loading. Tohoku Geophys J (Sci Rep Tohoku Univ, Ser 5). 1990;33:1-21. [125] Hunt SP, Meyers AG, Louchnikov V, Oliver KJ. Use of the DRA technique, porosimetry and numerical modelling for estimating the maximum in-situ stress in rock from core. International Society for Rock Mechanics10th Congress Technology roadmap for Rock Mechanics South Arfican Institute of Mining and Metallurgy; 2003. [126] Seto M, Villaescusa E, Utagawa M, Katsuyama K. In situ stress evaluation from rock cores using AE method and DRA. Shigen-to-Sozai. 1998;114:845-55. [127] Lin HM, Wu JH, Lee DH. Evaluating the pre-stress of Mu-Shan sandstone using acoustic emission and deformation rate analysis. In: Lu, Li, Kjørholt, Dahle, editors. In-situ Rock Stress. London: Taylor & Francis Group; 2006. p. 215-22. [128] Holcomb DJ, Costin LS. Detecting Damage Surfaces in Brittle Materials Using Acoustic Emissions. Journal of Applied Mechanics. 1986;53:536-44.
School of Civil and Resource Engineering The University of Western Australia
168
[129] Utagawa M, Seto M, Katsuyama K. Estimation of initial stress by Deformation Rate Analysis (DRA). International Journal of Rock Mechanics and Mining Sciences. 1997;34:317.e1-.e13. [130] Yamamoto H. An experimental study on stress memory of rocks and its application to in situ stress estimation [Master thesis]: Tohoku Univ.; 1991. [131] Chang CF. Investigating the Laboratory Experiments to Estimate Pre-Stress on Black Schist [Master thesis]: National Cheng Kung University; 2007. [132] Russell AR, Wood DM. Point load tests and strength measurements for Brittle spheres. Int J Rock Mech Min Sci. 2009;46:272-80. [133] Seto M, Souma N, Aeda N, Matsui H, Villaescusa E, Katsuyama K. Methodology and Case Studies of Stress Measurement by the AE and DRA methods Using Rock Core. Shigen-to-Sozai. 2001;117:829-35. [134] Yabe Y, Omura K. In-situ stress at a site close proximity to the Gofukuji Fault, central Japan, measured using drilling cores. Island Arc. 2011;20:160-73. [135] Yabe Y, Yamamoto K, Sato N, Omura K. Comparison of stress state around the Atera fault, central Japan, estimated using boring core samples and by improved hydraulic fracture tests. Earth, Planets, and Space. 2010;62:257-68. [136] Makasi M, Fujii Y. Effects of strain rate and temperature on tangent modulus method. Korean Rock Mechanics Symposium 2008. Korea: Korean Society for Rock Mechanics; 2008. p. 279-85. [137] Yamamoto K, Yamamoto H, Kato N, Hirasawa T. Deformation Rate Analysis for In Situ Stress Estimation. 5th Conference on Acoustic Emission/Microseismic Activity in Geologic Structures and Materials. Pennsylvania: Trans Tech Publications; 1991. p. 243-55. [138] Holmes C. Deformation rate analysis and stress memory effect in rock [Final year thesis]. Perth: The University of Western Australia; 2004. [139] Gustkiewicz J. Uniaxial compression testing of brittle rock specimens with special consideration given to bending moment effects. Int J Rock Mech Min Sci & Geomech. 1975;12:13-25. [140] Hoskins JR, Horino FR. Effect of end conditions on determining compressive strength of rock samples: U.S. department of the interior, Bureau of Mines; 1968.
School of Civil and Resource Engineering The University of Western Australia
1
Appendix A. Samples of groups VR1 & VR2 rock samples VR1
Table A- 1 The basic information of VR1 samples
Weight Diameter (mm)
Length (mm)
Density (g/cm3)
Velocity (m/s)
Modulus (GPa)
Poisson’s ratio
A1 37.98 18.5 49.65 2.84 6533 89 0.28
A2 39.13 18.8 49.60 2.86 6359 86 0.29
A3 35.41 18.6 45.95 2.83 6564 85 0.27
B1 38.52 18.5 49.70 2.88 6372 92 0.28
B2 38.03 18.5 48.90 2.89 6351 91 0.28
B3 37.63 19.2 45.90 2.85 6652 90 0.28
C1 39.13 18.7 49.70 2.87 6372 85 0.29
C2 37.12 18.6 47.90 2.85 6562 87 0.28
C3 36.44 18.7 46.80 2.85 6500 86 0.28
D1 32.25 18.6 41.25 2.89 6445 93 0.28
D2 35.4 18.5 45.55 2.88 6902 97 0.29
D3 31.22 18.3 41.00 2.89 6508 89 0.29
E1 40.99 19.1 49.65 2.90 6365 88 0.28
E2 40.76 19.1 49.60 2.86 6526 87 0.26
E3 36.1 19.1 42.80 2.94 6794 96 0.30
F1 40.85 19.1 49.65 2.86 6365 87 0.27
F2 38.23 18.6 49.65 2.83 6448 79 0.28
F3 39.95 19.2 48.65 2.84 6574 82 0.29
Average 36.94 18.8 46.66 2.86 6508 82 0.28
Table A- 2 The legend of the figures from next page. The axial 0 is the axial strain gauge at the
location 0.
Stress-Stra in Plot
0
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Axial 0 Axial 180 Axial 90 Axial 270
Lateral 0 Lateral 180 Lateral 90 Lateral 270
School of Civil and Resource Engineering The University of Western Australia
2
VR1 A1 Stress-Strain Plot
0
20
40
60
80
100
-500 0 500 1000 1500
Strain (micro strain)
Str
ess
(M
Pa
)
VR1 A1 Acoustic emission rate
0
20
40
60
80
100
0 20 40 60 80 100
Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
VR1 A2 Stress-Strain Plot
0
20
40
60
80
100
-500 0 500 1000 1500
Strain (micro strain)
Str
ess
(M
Pa
)
VR1 A2 Acoustic emission rate
0
10
20
0 20 40 60 80 100
Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
VR1 A3 Stress-Strain Plot
0
20
40
60
80
100
-500 0 500 1000 1500 2000
Strain (micro strain)
Str
ess
(M
Pa
)
VR1 A3 Acoustic emission rate
0
10
20
0 20 40 60 80 100Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
VR1 B1 Stress-Strain Plot
0
20
40
60
80
100
-500 0 500 1000 1500
Strain (micro strain)
Str
ess
(M
Pa
)
VR1 B1 Acoustic emission rate
0
10
20
0 20 40 60 80 100Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
School of Civil and Resource Engineering The University of Western Australia
3
VR1 B2 Stress-Strain Plot
0
20
40
60
80
100
-500 0 500 1000 1500Strain (micro strain)
Str
ess
(M
Pa
)
VR1 B2 Acoustic emission rate
0
10
20
0 20 40 60 80 100Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
VR1 B3 Stress-Strain Plot
0
10
20
30
40
50
60
70
80
90
100
-500 0 500 1000 1500
Strain (micro strain)
Str
ess
(M
Pa
)
VR1 B3 Acoustic emission rate
0
20
40
0 20 40 60 80 100Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
VR1 C1 Stress-Strain Plot
0
20
40
60
80
100
-500 0 500 1000 1500
Strain (micro strain)
Str
ess
(M
Pa
)
VR1 C1 Acoustic emission rate
0
10
20
0 20 40 60 80 100
Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
VR1 C2 Stress-Strain Plot
0
20
40
60
80
100
-500 0 500 1000 1500
Strain (micro strain)
Str
ess
(M
Pa
)
VR1 C2 Acoustic emission rate
0
10
20
0 20 40 60 80 100
Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
School of Civil and Resource Engineering The University of Western Australia
4
VR1 C3 Stress-Strain Plot
0
20
40
60
80
100
-500 0 500 1000 1500
Strain (micro strain)
Str
ess
(M
Pa
)
VR1 C3 Acoustic emission rate
0
10
20
0 20 40 60 80 100
Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
VR1 D1 Stress-Strain Plot
0
20
40
60
80
100
-500 0 500 1000 1500
Strain (micro strain)
Str
ess
(MP
a)
VR1 D1 Acoustic emission rate
0
10
20
0 20 40 60 80 100
Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
VR1 D2 Stress-Strain Plot
0
10
20
30
40
50
60
70
80
-500 0 500 1000 1500
Strain (micro strain)
Str
ess
(M
Pa
)
VR1 D2 Acoustic emission rate
0
20
40
60
80
0 20 40 60 80
Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
VR1 D3 Stress-Strain Plot
0
20
40
60
80
100
-500 0 500 1000 1500
Strain (micro strain)
Str
ess
(MP
a)
VR1 D3 Acoustic emission rate
0
10
20
0 20 40 60 80 100
Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
School of Civil and Resource Engineering The University of Western Australia
5
VR1 E1 Stress-Strain Plot
0
10
20
30
40
50
60
70
80
90
100
-500 0 500 1000 1500
Strain (micro strain)
Str
ess
(M
Pa
)
VR1 E1 Acoustic emission rate
0
10
20
0 20 40 60 80 100
Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
VR1 E2 Stress-Strain Plot
0
10
20
30
40
50
60
70
80
90
100
-500 0 500 1000 1500
Strain (micro strain)
Str
ess
(M
Pa
)
VR1 E2 Acoustic emission rate
0
10
20
0 20 40 60 80 100
Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
VR1 E3 Stress-Strain Plot
0
20
40
60
80
100
-1000 -500 0 500 1000 1500Strain (micro strain)
Str
ess
(M
Pa
)
VR1 E3 Acoustic emission rate
0
10
20
0 20 40 60 80 100
Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
VR1 F1 Stress-Strain Plot
0
20
40
60
80
100
-500 0 500 1000 1500
Strain (micro strain)
Str
ess
(M
Pa
)
VR1 F1 Acoustic emission rate
0
10
20
0 20 40 60 80 100
Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
School of Civil and Resource Engineering The University of Western Australia
6
VR1 F2 Stress-Strain Plot
0
20
40
60
80
-500 0 500 1000 1500Strain (micro strain)
Str
ess
(MP
a)
VR1 F2 Acoustic emission rate
0
10
20
0 20 40 60 80
Stress (MPa)
Str
ain
(m
icro
str
ain)
AE hit rate cy1
AE hit rate cy2
VR1 F3 Stress-Strain Plot
0
20
40
60
80
100
-1000 0 1000 2000 3000Strain (micro strain)
Str
ess
(MP
a)
VR1 F3 Acoustic emission rate
0
10
20
0 20 40 60 80 100
Stress (MPa)
Str
ain
(m
icro
stra
in)
AE hit rate cy1
AE hit rate cy2
School of Civil and Resource Engineering The University of Western Australia
7
ROCK SAMPLES VR2
Table A- 3 The basic information of VR1 samples
Weight (g)
Diameter (mm)
Length (mm)
Density (g/cm3)
Velocity (m/s)
Modulus (GPa)
Poisson’s ratio
A1 37.63 18.23 49.65 2.91 - 98 0.27
A2 37.82 18.23 49.70 2.92 6716 97 0.26
A3 36.67 18.10 48.84 2.92 6690 93 0.29
B1 36.17 18.80 44.75 2.91 6581 92 0.29
B2 37.34 19.13 44.65 2.91 6664 94 0.27
B3 36.35 19.15 43.80 2.88 6738 94 0.28
C1 38.87 19.00 46.65 2.94 6570 94 0.28
C2 39.41 19.23 46.80 2.90 6592 96 0.26
C3 38.6 19.15 46.00 2.91 6667 94 0.28
D1 31.06 17.85 43.70 2.84 6621 93 0.26
D2 30.94 18.20 41.30 2.88 6883 96 0.28
D3 32.74 17.78 45.90 2.87 6652 93 0.27
E1 35.26 18.68 44.40 2.90 6627 101 0.26
E2 36.36 18.63 46.00 2.90 6667 96 0.28
E3 36.55 18.73 45.50 2.92 6691 100 0.27
F1 39.81 18.73 49.65 2.91 6709 96 0.27
F2 35.34 18.75 44.25 2.89 6808 97 0.27
F3 34.82 18.73 43.35 2.92 6773 96 0.27
Average 36.21 18.61 45.83 2.90 6685 96 0.27
Table A- 4 The legend of the figures from next page. The axial 0 is the axial strain gauge at the
location 0.
Stress-Stra in Plot
0
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Axial 0 Axial 180 Axial 90 Axial 270
Lateral 0 Lateral 180 Lateral 90 Lateral 270
School of Civil and Resource Engineering The University of Western Australia
8
VR2 A1 Stress-Strain Plot
0
20
40
60
80
-500 0 500 1000 1500
Strain (micro strain)
Str
ess
(MP
a)
VR2 A1 Acoustic emission rate
0
10
20
0 20 40 60
Stress (MPa)
AE
Eve
nt /
MP
a AE hit rate cy1
AE hit rate cy2
VR2 A2 Stress-Strain Plot
0
20
40
60
80
-500 0 500 1000 1500
Strain (micro strain)
Str
ess
(M
Pa)
VR2 A2 Acoustic emission rate
0
10
20
0 20 40 60
Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
VR2 A3 Stress-Strain Plot
0
20
40
60
80
-500 0 500 1000 1500
Strain (micro strain)
Str
ess
(M
Pa
)
VR2 A3 Acoustic emission rate
0
10
20
0 20 40 60
Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
School of Civil and Resource Engineering The University of Western Australia
9
VR2 B1 Stress-Strain Plot
0
20
40
60
80
-500 0 500 1000 1500
Strain (micro strain)
Str
ess
(M
Pa
)
VR2 B1 Acoustic emission rate
0
10
20
0 20 40 60
Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
VR2 B2 Axial Stress-Strain Plot
0
20
40
60
80
-500 0 500 1000 1500
Strain (micro strain)
Str
ess
(M
Pa)
VR2 B2 Acoustic emission rate
0
10
20
0 20 40 60 80
Stress (MPa)
AE
Eve
nt /
MP
a AE hit rate cy1
AE hit rate cy2
VR2 B3 Stress-Strain Plot
0
20
40
60
80
-500 0 500 1000
Strain (micro strain)
Str
ess
(M
Pa
)
VR2 B3 Acoustic emission rate
0
10
20
0 20 40 60Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
VR2 C1 Axial Stress-Strain Plot
0
10
20
30
40
50
60
70
80
-500 0 500 1000 1500
Strain (micro strain)
Str
ess
(M
Pa
)
VR2 C1 Acoustic emission rate
0
10
20
0 20 40 60
Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
School of Civil and Resource Engineering The University of Western Australia
10
VR2 C2 Axial Stress-Strain Plot
0
20
40
60
80
-500 0 500 1000 1500
Strain (micro strain)
Str
ess
(M
Pa
)
VR2 C2 Acoustic emission rate
0
10
20
0 20 40 60
Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
VR2 C3 Axial Stress-Strain Plot
0
20
40
60
80
-500 0 500 1000 1500
Strain (micro strain)
Stre
ss (
MP
a)
VR2 C3 Acoustic emission rate
0
10
20
0 20 40 60
Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
VR2 D1 Stress-Strain Plot
0
20
40
60
80
-500 0 500 1000
Strain (micro strain)
Str
ess
(M
Pa
)
VR2 D1 Acoustic emission rate
0
10
20
0 20 40 60
Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
VR2 D2 Stress-Strain Plot
0
20
40
60
80
-500 0 500 1000 1500
Strain (micro strain)
Str
ess
(MP
a)
VR2 D2 Acoustic emission rate
0
10
20
0 20 40 60
Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
School of Civil and Resource Engineering The University of Western Australia
11
VR2 D3 Stress-Strain Plot
0
20
40
60
80
-500 0 500 1000
Strain (micro strain)
Str
ess
(MP
a)
VR2 D3 Acoustic emission rate
0
10
20
0 20 40 60
Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
VR2 E1 Stress-Strain Plot
0
10
20
30
40
50
60
70
80
-500 0 500 1000
Strain (micro strain)
Str
ess
(MP
a)
VR2 E1 Acoustic emission rate
0
10
20
0 20 40 60
Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
VR2 E2 Stress-Strain Plot
0
20
40
60
80
-500 0 500 1000 1500
Strain (micro strain)
Stre
ss (
MP
a)
VR2 E2 Acoustic emission rate
0
10
20
0 20 40 60
Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
VR2 E3 Stress-Strain Plot
0
20
40
60
80
-500 0 500 1000
Strain (micro strain)
Str
ess
(M
Pa
)
VR2 E3 Acoustic emission rate
0
10
20
0 20 40 60
Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
School of Civil and Resource Engineering The University of Western Australia
12
VR2 F1 Stress-Strain Plot
0
20
40
60
80
-500 0 500 1000
Strain (micro strain)
Str
ess
(M
Pa)
VR2 F1 Acoustic emission rate
0
10
20
0 20 40 60
Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
VR2 F2 Stress-Strain Plot
0
20
40
60
80
-500 0 500 1000
Strain (micro strain)
Str
ess
(M
Pa
)
VR2 F2 Acoustic emission rate
0
10
20
0 20 40 60
Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
VR2 F3 Stress-Strain Plot
0
20
40
60
80
-500 0 500 1000 1500
Strain (micro strain)
Str
ess
(M
Pa
)
VR2 F3 Acoustic emission rate
0
10
20
0 20 40 60
Stress (MPa)
AE
Eve
nt /
MP
a
AE hit rate cy1
AE hit rate cy2
School of Civil and Resource Engineering The University of Western Australia
1
Appendix B. Sample Preparation
Drilling process and the marking procedure
The rock material is from 76mm diamond drill bit. The core diameter can have variation from 40mm to 65mm. All rock cores had been orientated and marked the depth with bottom of core mark. Most of the core was stored in core farm for more than 6 months before packing in core box and sending to us.
In order to extract 6 particular orientated samples from core, the blue lines at 90, 135, 180 and 270 are marked clockwise when bottom of core mark, which is red line, is defined as 0. The arrow on the bottom of core mark should point to the bottom of borehole. The 6 samples in the orientation which is according to core are drilled as following and marked with black arrow. The black arrow indicates drilling direction and sample orientation.
Figure B- 1. The sample orientations according to rock core and the method of marking.
The milling machine HF 50 from Hafco is employed for drilling process. The drill bit for this work is 25mm drill, which is 170mm in length, 25mm in outer diameter and 18.5mm diameter in inner diameter. The drill bit is attached to water circulation device, and then the top of water circulation is screwed into 30NT tapper of milling machine. The water circulation can reduce the heat which is produced by the drilling process. During whole process the water is controlled to be below 40 degree Celsius.
An extra power feed motor is equipped for milling machine in order to give machine a constant speed of drilling. A constant speed of drilling can offer a very smooth periphery for sample. The sample end, which is facing drill bit, is marked with identification and black arrow. The black arrow point to 0 and the 0, 90, 180 and 270 orientation is clockwise around the end. Then the red arrow is marked on sample
School of Civil and Resource Engineering The University of Western Australia
2
periphery according to the black arrow. The 2 ends are cut by a concrete cutter before end preparation.
Figure B- 2. The sample at the left with identification and indicated line on 2 ends was drilled out
and marked. The 2 ends of sample at the right was cut by concrete cutter and ready to be grinded.
End preparation
According to ISRM requirement for acoustic emission, UCS and deformation tests, 0.02 mm planarity at each end is essential. There are several ways to reach ISRM suggested planarity. Using grinding plate which is attached milling machine is most common method. However this method is not idea for small diameter sample because it’s hard to secure grinding plate to absolute vertical to sample end. Also the table of milling is not absolute solid when applying high pressure. For bigger diameter it’s possible to move sample around the plate to reach smooth face and reduce effect caused by table, but small sample is affected by table planarity and hard to be secured.
The fast way to achieve end preparation is using grinding mode. Grinding mode is made by aluminum or castle iron. Aluminum and castle iron is much harder than rock so rock will be wearing out first while grinding. The grinding mode will be grinded as well but it takes much longer time to wearing it out.
Before using grinding mode, we use dia-gauge to confirm the mode reach 0.01 mm planarity. Substandard mode can be grinded down easily by CNC lathe before using again. The diagauge which can reach 0.01 mm accuracy is also employed to measure the planarity at 2 ends. To grind the two ends flat and parallel to each other, there are few steps needed to obey. First is sample periphery. Milling machine with electric feed can drill a sample out in constant speed, and constant speed is one of the key points to offer smooth periphery. A manual feed milling machine can also offer smooth periphery if operated by experienced person.
Material property also affects sample periphery. Soft material provides smaller diameter then hard material. A sample with uniform (homogeneous) property is more likely to have smooth periphery. In the other hand, a sample with strong foliation and made up by schist and quarts would most likely to have unsmooth periphery.
School of Civil and Resource Engineering The University of Western Australia
3
Figure B- 3. Sleeve, grinding mode and grinding machine. Because 25mm diameter drill bit may
produce the diameter of sample from 17.5 to 19mm, different sleeves are applied for different
diameter samples in order to fit grinding mode.
For diameter 17.6~ 17.8 mm diameter sample, we use diameter 18 mm sleeve. For diameter 18.1~ 18.3 mm samples, 18.4 mm diameter sleeve is applied. For the sample with 19 mm diameter, 19.4 mm sleeve is in charge. The loose sleeve will attach to sample by a line and introduce unstable movement between sample and sleeves. All sleeves are 22 mm in outer diameter and be locked in 22.3 mm diameter hole in the middle of the mode.
After grinding, the sample with smooth periphery and proper sleeve will usually offer planarity within 0.01 mm at each end. However the unsmooth periphery of sample usually has 0.04 ~ 0.08 mm planarity which is not qualified. In this case we need to grind it down by sand paper. By using sand paper, 0.02 mm at each end can be achieved although it takes much longer time than others.
Figure B- 4. By using grinding mode, 0.02 mm planarity at each end is reached.
School of Civil and Resource Engineering The University of Western Australia
4
After grinding, the samples are glued with strain gauge in 0, 90, 180 and 270 positions according to the red line. There are 4 gauges on one sample.
Figure B- 5. The orientations of sample itself, gauges are glued in 0, 90, 180 and 270 surrounding
periphery.
Strain gauge
The sample now is ready to be tested. 4 strain gauges are glued on middle height of a sample. Strain gauge FCA-5-11 from TML Company is design for general purpose in mild steel, which has similar temperature compensation with hard rock. It is idea for small rock sample.
Figure B- 6. Sample storage, sample with strain gauges.
Sample height and diameter is recorded by calibrator with 0.05mm accuracy. The sample for UCS purpose will be measured 2 diameters in 90 degree at upper, middle and lower parts of sample. All samples are weighted by weight meter before attaching strain gauge.
Seismic velocity measurement
Velocity is one of most important information for our study. The frequency generator with P wave sensor can produce 20 volts and 900 Hz signal which goes across a sample. Lower frequency has better penetration. But the first arriving signal in lower frequency tends to be smoother curve then in higher frequency, therefore it increases the difficulty of judging arrival time. The time lag between two ends of sample minus time lag
School of Civil and Resource Engineering The University of Western Australia
5
between two sensors is the true time lag in sample length. Each sample is measured at least twice in an opposite order.
Figure B- 7. Frequency generator and logging system.
Strain gauge calibration
Before starting a test, a calibration factor for translating volts from gain to strain is required for Young’s modulus and Poisson’s ratio. The strain gauge comes with its own calibration factor which has 1% error. However, temperature compensation of the material, glue, test material, test procedure and wire might change little portion of the calibration factor. In order to get an exact calibration factor in our test condition, an aluminum sample is used because of its stable property.
The Young’s modulus and Poisson’s ratio are 70GPa and 0.35 in aluminum 6000 series, respectively. We have two aluminum samples, aluminum A is 19.8 mm in diameter and 500 mm in length; aluminum B is 18 mm in diameter and 450 mm in length. Periphery of both samples is polished and with two strain gauges (FCA-5-11) attached on. Two stain gauges are located in 0 and 90 positions.
Figure B- 8. Aluminium A sample with strain gauge.
School of Civil and Resource Engineering The University of Western Australia
6
To apply force on aluminium sample, axial loading machine is controlled by a computer to increase the load in constant rate. The loading controlled program allows loading machine to apply continuously at a constant displacement rate. The displacement rate is within 0.02 - 0.2 mm /min, which gives around 1 – 40 MPa /min. Because material is loaded within elastic zone, the stress rate is roughly in constant.
The loading rate we have been using is from 10 ~ 20 MPa/min depends on material. The loading machine records time and stress. For strain, we have a logging system in acoustic emission working station. There are an acquisition box, circuit board and PCI-2 Based AE system to form a logging system. Strain gauge wire on aluminium is soldered to a circuit board which connects to acquisition box. Then PCI-2 Based AE system translates volts from acquisition box to strain and acoustic emission data. The AEwin program allows us to process data out in .txt file.
Figure B- 9. Loading machine and circuit board.
School of Civil and Resource Engineering The University of Western Australia
1
Appendix C. Example of Using Compensation of Bending in the DRA Stress Reconstruction
Stress Correction Calculation
The equation 23 in section 7.2.2 corrects the non-uniformed stress distribution due to non-perfect test conditions in a sample.
(1)
where zl
z is the axial strain measured at the side of the sample, zl is the normal stress
in that location. The sample with co-ordinate frame (x, y, z). The z-axis is directed along the axis of the sample, the x-axis runs through the pair of opposite strain gauges.
The following table shows the stress recorded by load cell for sample H782 D2. It is an average stress calculated by the applied load and area of sample cross-section. The corrected stress at the location of each sensor was calculated by equation 23. The actual record interval is around every 0.066 MPa and all calculation/analysis were done using the actual records. The accuracy of strain record is sub-micron. The data in the following table was thinned down to 1MPa per record and zero decimal in strain data for displace purpose only.
Recorded stress (MPa)
Recorded Strain (2nd cycle) Corrected stress (MPa) by using
equation 23 At 0 At 180 At 90 At 270 At 0 At 180 At 90 At 270
1 51 47 63 42 1.0 0.9 1.2 0.8 2 79 59 83 59 2.3 1.7 2.4 1.7 3 103 73 102 75 3.5 2.4 3.4 2.5 4 127 89 124 92 4.7 3.3 4.6 3.4 5 150 105 144 108 5.9 4.1 5.7 4.3 6 172 121 165 125 7.0 4.9 6.8 5.1 7 196 138 187 142 8.2 5.8 7.9 6.0 8 218 154 209 159 9.4 6.7 9.0 6.8 9 239 170 231 175 10.5 7.5 10.1 7.7 10 263 188 254 192 11.7 8.4 11.3 8.5 11 285 205 276 209 12.8 9.2 12.4 9.4 12 308 222 299 225 14.0 10.1 13.6 10.3 13 330 239 321 242 15.1 11.0 14.7 11.1 14 352 256 344 258 16.3 11.8 15.9 11.9 15 373 272 366 274 17.3 12.6 17.0 12.7 16 396 290 388 292 18.5 13.6 18.2 13.6 17 417 306 410 308 19.6 14.4 19.3 14.5
School of Civil and Resource Engineering The University of Western Australia
2
18 439 323 432 324 20.8 15.3 20.4 15.4 19 461 340 454 341 21.9 16.2 21.6 16.2 20 483 357 476 358 23.1 17.0 22.7 17.1 21 504 372 496 374 24.2 17.9 23.8 17.9 22 526 389 518 391 25.3 18.7 25.0 18.8 23 547 404 539 406 26.5 19.6 26.1 19.7 24 569 422 562 424 27.6 20.5 27.3 20.6 25 590 438 582 439 28.7 21.3 28.4 21.4 26 610 454 603 455 29.9 22.2 29.5 22.3 27 632 469 624 471 31.0 23.1 30.6 23.1 28 652 485 644 488 32.2 23.9 31.8 24.0 29 674 501 666 504 33.3 24.8 32.9 24.9 30 693 517 685 519 34.4 25.6 34.0 25.7 31 714 533 706 535 35.5 26.5 35.1 26.6 32 735 549 727 551 36.7 27.4 36.3 27.5 33 754 563 745 566 37.8 28.2 37.3 28.4 34 775 580 766 583 38.9 29.1 38.5 29.3 35 794 595 786 598 40.0 30.0 39.6 30.1 36 815 611 806 615 41.2 30.9 40.7 31.1 37 834 626 825 630 42.3 31.7 41.8 31.9 38 854 642 845 646 43.5 32.7 43.0 32.9 39 874 657 864 662 44.6 33.5 44.1 33.7 40 894 671 883 677 45.7 34.3 45.2 34.6 41 912 686 902 692 46.8 35.2 46.3 35.5 42 933 702 922 709 48.0 36.1 47.4 36.4 43 952 717 941 724 49.1 37.0 48.5 37.3 44 970 732 960 739 50.2 37.8 49.6 38.2 45 990 746 979 754 51.3 38.7 50.7 39.1 46 1009 761 998 769 52.4 39.6 51.8 40.0 47 1028 776 1016 784 53.5 40.4 52.9 40.9 48 1047 791 1036 800 54.6 41.3 54.0 41.7 49 1066 806 1054 815 55.8 42.2 55.2 42.6 50 1085 820 1073 830 56.9 43.0 56.3 43.5 51 1104 836 1092 845 58.0 43.9 57.4 44.4 52 1123 850 1111 860 59.2 44.8 58.5 45.3 53 1141 865 1129 875 60.3 45.7 59.6 46.2 54 1160 880 1148 890 61.4 46.5 60.7 47.1 55 1179 895 1167 905 62.5 47.4 61.9 48.0 56 1197 909 1184 920 63.6 48.3 62.9 48.9 57 1216 923 1203 934 64.7 49.2 64.0 49.7 58 1235 939 1223 950 65.9 50.1 65.2 50.7 59 1253 953 1241 965 67.0 51.0 66.4 51.6 60 1273 968 1260 980 68.1 51.8 67.5 52.5 61 1290 982 1278 995 69.2 52.7 68.6 53.4
School of Civil and Resource Engineering The University of Western Australia
3
62 1309 997 1296 1010 70.3 53.6 69.7 54.3 63 1327 1011 1314 1024 71.4 54.4 70.8 55.1 64 1345 1026 1333 1039 72.6 55.3 71.9 56.0 65 1364 1040 1351 1054 73.7 56.2 73.0 56.9 66 1383 1056 1370 1069 74.8 57.1 74.2 57.9 67 1400 1069 1387 1083 75.9 57.9 75.2 58.7 68 1419 1084 1407 1098 77.0 58.9 76.4 59.6 69 1436 1098 1425 1113 78.1 59.7 77.5 60.5 70 1454 1112 1442 1127 79.2 60.6 78.6 61.4 71 1472 1127 1460 1141 80.3 61.5 79.7 62.3 72 1490 1141 1478 1156 81.4 62.3 80.8 63.2 73 1509 1156 1497 1171 82.6 63.3 82.0 64.1 74 1527 1170 1515 1186 83.7 64.1 83.1 65.0 75 1544 1184 1533 1200 84.7 65.0 84.2 65.9 76 1562 1199 1552 1215 85.9 65.9 85.3 66.8 77 1580 1213 1570 1229 87.0 66.8 86.4 67.7 78 1598 1227 1587 1243 88.1 67.6 87.5 68.5 79 1617 1243 1607 1259 89.2 68.6 88.7 69.5 80 1634 1256 1624 1273 90.3 69.4 89.8 70.4 81 1652 1270 1642 1287 91.4 70.3 90.9 71.2 82 1669 1284 1660 1301 92.5 71.2 92.0 72.1 83 1687 1299 1678 1316 93.6 72.0 93.1 73.0 84 1705 1314 1697 1331 94.7 73.0 94.3 73.9 85 1723 1328 1715 1345 95.8 73.9 95.4 74.8 86 1741 1342 1733 1359 96.9 74.7 96.5 75.7 87 1758 1356 1751 1373 98.0 75.6 97.6 76.5 88 1776 1371 1770 1388 99.1 76.5 98.8 77.5 89 1794 1385 1788 1402 100.2 77.4 99.9 78.3