In situ stress reconstruction using rock memory · eng. 2013;submitted (Chapter 6, the contribution of the student is the model and discussion of results, 20%) 6. Hsieh A, Dyskin

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

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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


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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.


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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.


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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%)


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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


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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


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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


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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



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


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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


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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



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


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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


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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


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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


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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


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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


(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


(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


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.


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.


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.


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


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


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.


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


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]).


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)


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


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


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


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


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


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


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.


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


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


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.


20

Table 3 The main claims and problems in the literatures.


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.


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


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


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.


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


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.


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


28


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].


30



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


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.


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.


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


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


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


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)


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


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)


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


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


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


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)


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


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.


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


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.



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


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


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.


49


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.



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


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


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)


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).


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)


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


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)


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).


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


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.


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


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


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.


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


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].



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


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


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


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)


Volumetric strain


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.


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)


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


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

∆


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.


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


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


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


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


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


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


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


WA51 residual strain vs E increase

r = 0.12


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


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


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


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


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


FL residual strain vs E increase

r = 0.10


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)


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.


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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


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],


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[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].


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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


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.


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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.


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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.


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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


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.


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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.


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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.


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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:


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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


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.


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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).


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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


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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)


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).


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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


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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.


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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.


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.


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.


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.


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


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.


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.


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


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.


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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


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


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).


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


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.


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.


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


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)


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)


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.


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.


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


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


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.


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


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).


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.


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


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


120

6.6 A MODEL OF ROCK WITH MULTIPLE INTERFACES


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).


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

)


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


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

)


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


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

)


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


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


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.


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]).


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


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


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.


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


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.


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


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


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


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.


7.2.1 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°


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)


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


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)


Stress-Strain Plot

0°180°90°270°

0

5

10

15

20

25

-300 0 300 600

Str

ess

(MP

a)


Stress-Strain Plot

0°180°90°270°


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°


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


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 v.s Actual Stress

0° 180°

90° 270°


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 v.s Actual Stress

0°180°90°270°


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

)



0°180°90°270°

-20

-10

0

0 20 40 60 80 100

Str

ain

diff

eren

ce (

mic

rost

rain

)Actual stress (MPa)


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


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

)



0°90°180°270°

-17

-7

3

0 5 10 15 20 25

Str

ain

diff

eren

ce (

mic

rost

rain

)

Corresponding stress (MPa)


0°180°90°270°


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.


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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


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°


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.


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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)


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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)


(b)


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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)


0

5

0 10 20 30

Mic

rost

rain

Stress (MPa)



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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.


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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


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


158

finding provides additional information to understand the deformation behaviours of

rock.


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.


160


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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


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


0

20

40

60

80

100

-500 0 500 1000 1500


Str

ess

(M

Pa

)


0

10

20

0 20 40 60 80 100

Stress (MPa)

AE

Eve

nt /

MP

a

AE hit rate cy1

AE hit rate cy2


0

20

40

60

80

100

-500 0 500 1000 1500 2000


Str

ess

(M

Pa

)


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


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


3


0

20

40

60

80

100

-500 0 500 1000 1500Strain (micro strain)

Str

ess

(M

Pa

)


0

10

20

0 20 40 60 80 100Stress (MPa)

AE

Eve

nt /

MP

a

AE hit rate cy1

AE hit rate cy2


0

10

20

30

40

50

60

70

80

90

100

-500 0 500 1000 1500


Str

ess

(M

Pa

)


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


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


0

20

40

60

80

100

-500 0 500 1000 1500


Str

ess

(M

Pa

)


0

10

20

0 20 40 60 80 100

Stress (MPa)

AE

Eve

nt /

MP

a

AE hit rate cy1

AE hit rate cy2


4


0

20

40

60

80

100

-500 0 500 1000 1500


Str

ess

(M

Pa

)


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


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


0

10

20

30

40

50

60

70

80

-500 0 500 1000 1500


Str

ess

(M

Pa

)


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


0

20

40

60

80

100

-500 0 500 1000 1500


Str

ess

(MP

a)


0

10

20

0 20 40 60 80 100

Stress (MPa)

AE

Eve

nt /

MP

a

AE hit rate cy1

AE hit rate cy2


5

VR1 E1 Stress-Strain Plot

0

10

20

30

40

50

60

70

80

90

100

-500 0 500 1000 1500


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


0

10

20

30

40

50

60

70

80

90

100

-500 0 500 1000 1500


Str

ess

(M

Pa

)


0

10

20

0 20 40 60 80 100

Stress (MPa)

AE

Eve

nt /

MP

a

AE hit rate cy1

AE hit rate cy2


0

20

40

60

80

100

-1000 -500 0 500 1000 1500Strain (micro strain)

Str

ess

(M

Pa

)


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


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


6


0

20

40

60

80


Str

ess

(MP

a)


0

10

20

0 20 40 60 80

Stress (MPa)

Str

ain

(m

icro

str

ain)

AE hit rate cy1

AE hit rate cy2


0

20

40

60

80

100


Str

ess

(MP

a)


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


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


8


0

20

40

60

80

-500 0 500 1000 1500


Str

ess

(MP

a)


0

10

20

0 20 40 60

Stress (MPa)

AE

Eve

nt /

MP

a AE hit rate cy1

AE hit rate cy2


0

20

40

60

80

-500 0 500 1000 1500


Str

ess

(M

Pa)


0

10

20

0 20 40 60

Stress (MPa)

AE

Eve

nt /

MP

a

AE hit rate cy1

AE hit rate cy2


0

20

40

60

80

-500 0 500 1000 1500


Str

ess

(M

Pa

)


0

10

20

0 20 40 60

Stress (MPa)

AE

Eve

nt /

MP

a

AE hit rate cy1

AE hit rate cy2


9


0

20

40

60

80

-500 0 500 1000 1500


Str

ess

(M

Pa

)


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


Str

ess

(M

Pa)


0

10

20

0 20 40 60 80

Stress (MPa)

AE

Eve

nt /

MP

a AE hit rate cy1

AE hit rate cy2


0

20

40

60

80

-500 0 500 1000


Str

ess

(M

Pa

)


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


Str

ess

(M

Pa

)


0

10

20

0 20 40 60

Stress (MPa)

AE

Eve

nt /

MP

a

AE hit rate cy1

AE hit rate cy2


10


0

20

40

60

80

-500 0 500 1000 1500


Str

ess

(M

Pa

)


0

10

20

0 20 40 60

Stress (MPa)

AE

Eve

nt /

MP

a

AE hit rate cy1

AE hit rate cy2


0

20

40

60

80

-500 0 500 1000 1500


Stre

ss (

MP

a)


0

10

20

0 20 40 60

Stress (MPa)

AE

Eve

nt /

MP

a

AE hit rate cy1

AE hit rate cy2


0

20

40

60

80

-500 0 500 1000


Str

ess

(M

Pa

)


0

10

20

0 20 40 60

Stress (MPa)

AE

Eve

nt /

MP

a

AE hit rate cy1

AE hit rate cy2


0

20

40

60

80

-500 0 500 1000 1500


Str

ess

(MP

a)


0

10

20

0 20 40 60

Stress (MPa)

AE

Eve

nt /

MP

a

AE hit rate cy1

AE hit rate cy2


11


0

20

40

60

80

-500 0 500 1000


Str

ess

(MP

a)


0

10

20

0 20 40 60

Stress (MPa)

AE

Eve

nt /

MP

a

AE hit rate cy1

AE hit rate cy2


0

10

20

30

40

50

60

70

80

-500 0 500 1000


Str

ess

(MP

a)


0

10

20

0 20 40 60

Stress (MPa)

AE

Eve

nt /

MP

a

AE hit rate cy1

AE hit rate cy2


0

20

40

60

80

-500 0 500 1000 1500


Stre

ss (

MP

a)


0

10

20

0 20 40 60

Stress (MPa)

AE

Eve

nt /

MP

a

AE hit rate cy1

AE hit rate cy2


0

20

40

60

80

-500 0 500 1000


Str

ess

(M

Pa

)


0

10

20

0 20 40 60

Stress (MPa)

AE

Eve

nt /

MP

a

AE hit rate cy1

AE hit rate cy2


12


0

20

40

60

80

-500 0 500 1000


Str

ess

(M

Pa)


0

10

20

0 20 40 60

Stress (MPa)

AE

Eve

nt /

MP

a

AE hit rate cy1

AE hit rate cy2


0

20

40

60

80

-500 0 500 1000


Str

ess

(M

Pa

)


0

10

20

0 20 40 60

Stress (MPa)

AE

Eve

nt /

MP

a

AE hit rate cy1

AE hit rate cy2


0

20

40

60

80

-500 0 500 1000 1500


Str

ess

(M

Pa

)


0

10

20

0 20 40 60

Stress (MPa)

AE

Eve

nt /

MP

a

AE hit rate cy1

AE hit rate cy2


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


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.


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.


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


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.


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.


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


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


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

Documents

In situ stress reconstruction using rock memory · eng. 2013;submitted (Chapter 6, the contribution of the student is the model and discussion of results, 20%) 6. Hsieh A, Dyskin