An Experimental Investigation of the Mechanical ...

An Experimental Investigation of the Mechanical Behaviour of Sandstones With Reference to Borehole Stability

A thesis submitted to the University of Manchester for the degree of Doctor of Philosophy in the Faculty of Science and Engineering

Submitted December 1998

Robert J. Cuss

Rock Deformation Laboratory Department of Earth Sciences University of Manchester Oxford Road Manchester M13 9PL

2

Contents List of Figures and Tables

7

Abstract

12

Declaration

13

Copyright and Intellectual Property Rights

13

Preface

14

Dedication

15

Acknowledgements

16

List of Symbols and Units Used

17

1. Introduction 1.1 Nature of the problem 1.2 Aims and objectives 1.3 Thesis structure

19 19 20 21

2. The Deformation of Sandstone 2.1 Basic mechanical behaviour 2.1.1 Elastic behaviour 2.1.2 Inelastic behaviour 2.1.3 Models of rock deformation 2.1.4 Rock strength parameters 2.2 Basic fracture mechanics 2.2.1 Modes of brittle fracture 2.2.2 Fracture initiation and growth 2.2.3 Fluid influences on fracturing 2.2.4 Fracture classification 2.3 Brittle modes of geomaterial deformation 2.3.1 Dilatant shear-localisation and brittle faulting 2.3.2 Frictional grain boundary sliding 2.3.3 Shear-enhanced compaction and cataclastic flow 2.3.4 Ductile deformation mechanisms: higher temperature phenomena 2.4 Uniaxial brittle deformation 2.5 Hydrostatic sediment deformation 2.6 Triaxial sediment deformation 2.6.1 Pore-pressure effect: Law of effective stress and poroelastic effect 2.6.2 The role of effective stress 2.6.3 Strength changes with effective stress: Failure criteria 2.6.4 Yield strength changes with effective stress: yield envelopes 2.6.5 Critical state theory of soil mechanics 2.6.6 Critical state theory and real sediments 2.6.7 Plastic potential surface 2.7 Other influences on rock deformation 2.7.1 Moisture influence 2.7.2 Rock texture influence and pre-existing planes of weakness 2.7.3 Experimental influences

24 24 24 25 26 27 27 27 28 30 30 31 32 34 35 36 37 38 40 41 43 44 47 49 52 53 54 54 56 57

3

2.8 Summary of Chapter 2

59

3 The Failure of Boreholes 3.1 Outline of the borehole problem 3.2 Elastic analysis of the borehole problem: the Kirsch solution 3.2.1 Stress trajectories determined by the modified Kirsch solution 3.2.2 Linear-elastic theory prediction of bore failure 3.2.3 Borehole failure with transversely isotropic far-field stresses 3.2.4 Borehole failure with anisotropic far-field stresses 3.3 Extended models of borehole breakout 3.3.1 Elastoplasticity models 3.4 Micromechanical observations of breakout formation 3.4.1 Time-dependent borehole deformation 3.5 Additional complexities of the ‘real’ borehole environment 3.5.1 Bore geometry considerations 3.5.2 Lithological controls on bore failure 3.5.3 The influence of drilling-fluids and fluid-flow on borehole stability 3.6 Typical down-hole conditions 3.6.1 Vertical stress component 3.6.2 Horizontal loading stress 3.6.3 Pore pressure and temperature 3.6.4 Chemical environment 3.7 Summary of Chapter 3

60 60 61 63 66 66 70 72 76 78 81 82 82 84 85 88 88 88 92 92 93

4. Experimental procedures and starting materials 4.1 Uniaxial compression tests 4.2 Uniaxial compression apparatus 4.2.1 Calibration of the uniaxial apparatus 4.2.2 Data logging and test procedure 4.2.3 Data reduction and calculation of the fundamental elastic constants 4.3 Brazilian test apparatus 4.4 Triaxial compression tests 4.5 Heard-type triaxial apparatus 4.5.1 System of measurement 4.5.2 Data logging system 4.5.3 Machine limitations on the data 4.5.3.1 Axial loading system 4.5.3.2 Apparatus stiffness 4.5.3.3 Piston deflection during hitpoint experiments 4.5.4 Design of Heard III triaxial tests 4.6 Large specimen apparatus: BigRig 4.6.1 Modification 1: Axial loading system 4.6.2 Modification 2: Pore fluid system 4.6.3 System of measurement 4.6.4 Data logging 4.6.5 Machine limitations on the data 4.6.6 Design of the BigRig triaxial tests 4.6.6.1 Hydrostatic pore volume expulsion tests 4.6.6.2 Hydrostatic borehole closure tests 4.7 Data processing for triaxial compression tests

94 94 94 96 97 97 98 99 99 102 105 105 107 108 108 109 110 112 112 113 114 114 116 116 117 118

4

4.8 Petrographic and petrophysical characteristics of the starting material 4.8.1 Penrith sandstone 4.8.2 Darley Dale sandstone 4.8.3 Tennessee sandstone 4.9 Sample preparation 4.10 Sample recovery and thin section fabrication 5. The experimental deformation of intact sandstone 5.1 Uniaxial compression experiments 5.1.1 Unconfined axial compression experiment 5.1.1.1 General form of the uniaxial stress-strain curves 5.1.1.2 Observations of the failed samples 5.1.1.3 Calculation of the uniaxial elastic moduli 5.1.1.4 Uniaxial compression elastic anisotropy 5.1.1.5 Moisture effect on uniaxial strength 5.1.2 Diametral compression test; Brazilian test 5.1.2.1 General form of the Brazilian stress-strain curves 5.1.2.2 Moisture effect on tensile strength 5.1.2.3 Tensile strength anisotropy 5.1.2.4 Observations of the failed samples 5.2 Constant displacement-rate experiments 5.2.1 General form of the stress-strain curves 5.2.1a Penrith sandstone 5.2.1b Darley Dale sandstone 5.2.1c Tennessee sandstone 5.2.2 General appearance of the deformed samples 5.2.3 Calculation of strength parameters 5.2.4 Compactive yield envelope 5.3 Hydrostatic deformation experiments 5.3.1 Comparisons between the experimental methods 5.3.2 Form of the hydrostat 5.3.3 The effect of reloading 5.3.4 Hydrostatic deformation determined by the hitpoint method 5.3.5 Hydrostatic deformation determined by the CPV method 5.3.6 Determining the grain crushing pressure P* 5.3.7 Pore fluid chemistry effect 5.3.8 Normalised yield envelope 5.4 Microstructures and deformation mechanisms from triaxial experiments 5.5 Microstructural evolution of sandstone with strain at 100MPa pressure 5.5.1 Tennessee sandstone 5.5.2 Darley Dale sandstone 5.5.3 Penrith sandstone 5.6 Microstructural evolution of sandstone with effective pressure 5.6.1 Tennessee sandstone 5.6.2 Darley Dale sandstone 5.6.3 Penrith sandstone 5.7 Microstructures and deformation mechanisms from hydrostatc experiments 5.7.1 Tennessee sandstone 5.7.2 Darley Dale sandstone

119 120 121 122 123 125 126 126 126 126 130 131 132 135 135 136 136 137 138 138 141 141 141 142 142 145 147 149 150 152 155 156 157 157 158 160 163 163 164 167 169 171 171 173 175 177 177 178

5

5.7.3 Penrith sandstone 5.8 Summary of Chapter 5

179 181

6 The Experimental Deformation of Bored Sandstone 6.1 Methods for studying borehole failure 6.1.1 Direct bore failure studies 6.1.2 Large specimen tests: Hollow cylinder tests 6.1.3 The use of acoustic emissions 6.1.4 Other methods 6.2 Methodology adopted for the study of borehole failure 6.2.1 The bored constant pore-pressure volumometry test 6.2.2 The bladder closure method 6.2.3 Direct observation tests 6.3 Mechanical results of the experimental study 6.3.1 Results of the bored constant pore-pressure volumometry (BCPV) 6.3.1.1 The deflected hydrostat method of determining borehole failure 6.3.1.2 Observed time-dependent deformation 6.3.1.3 The effect of bore diameter on stability 6.3.2 Results of the bladder closure method 6.3.3 Results of the direct visualisation tests 6.3.4 Comparisons of the mechanical techniques 6.4 Microstructural analysis 6.4.1 Microstructural observations of bore failure in Tennessee sandstone 6.4.1.1 Microstructural observation using the bladder closure method 6.4.1.2 The micromechanics of borehole breakout in Tennessee sst. 6.4.1.3 Is breakout randomly orientated? 6.4.2 Microstructural observations of bore failure in Darley Dale sandstone 6.4.2.1 The effect of bore diameter 6.4.2.2 Observations of the bladder closure samples 6.4.2.3 The micromechanics of bore deformation in Darley Dale sst. 6.4.3 Observations of bore failure in Penrith sandstone 6.4.3.1 Observations of the bladder closure samples 6.4.3.2 The micromechanics of borehole deformation in Penrith sst. 6.5 Comparisons between all experimental data 6.6 Summary of Chapter 6

182 182 182 183 184 184 185 185 186 186 186 187 187 190 190 194 196 197 198 199 207 208 210 213 218 218 220 221 225 225 226 227

7. General Discussion and Synthesis Discussion 1: Intact rock deformation 7.1 Uniaxial sandstone deformation 7.2 Hydrostatic compaction behaviour of sandstone 7.2.1 The Hertzian model of predicting P* 7.3 Triaxial sandstone deformation 7.3.1 Localised brittle deformation regime (P/P*0.5) 7.3.3 The brittle-ductile transition (P/P*=0.4-0.5) 7.3.4 Influence of experimental geometry 7.3.5 Soil mechanics approach Discussion 2: Bore failure 7.4 Borehole failure mechanisms 7.4.1 Early breakout features

229 229 229 230 232 233 234 235 236 237 237 238 238 238

6

7.4.2 Bore failure mode 7.4.3 Breakout models 7.5 Breakout alignment in hydrostatic stress states 7.5.1 The case of non-hydrostatic, strength anisotropic conditions 7.6 Influence of bore diameter on strength 7.7 Validation of borehole experimentation Discussion 3: Common features 7.8 Water weakening 7.8.1 Mechanisms of water weakening 7.9 Time-dependent deformation 7.9.1 Time-dependent deformation of initially intact rock 7.9.2 Time-dependent deformation of bored rock 7.10 Inferences of bore failure from intact sandstone deformation

239 241 244 245 248 249 251 251 252 253 253 254 255

8 Conclusions and Implications

257

9 Recommendations for further work

261

10 References

263

Appendix A: BigRig axial control system A.1 System of measurement A.2 Data logging and servo-control system A.3 Computer programs Archimedes master logging computer BBC servo-controller computer

276 276 276 278 279 281

7

List of Figures and Tables Figure 2.1 Mechanical behaviour of materials and basic models of rock deformation

26

Figure 2.2 Schematic representation of the three fundamental modes of crack displacement

28

Figure 2.3

Classification of microcracks and fractures

31

Figure 2.4

Brittle deformation modes

33

Figure 2.5 Complex volume changes seen during shear-localisation deformation of Tennessee sandstone at 20MPa effective pressure

34

Figure 2.6

Mechanical behaviour of geomaterials in uniaxial compression

37

Figure 2.7

Hydrostatic deformation and grain crushing

39

Figure 2.8

The effect of pore pressure and poroelasticity

41

Figure 2.9

The effect of confining pressure on mechanical behaviour

43

Figure 2.10 Yield envelopes for porous materials

48

Figure 2.11 The critical state theory of soil mechanics in the Q-P-v space

50

Figure 2.12 Plastic potential surfaces

53

Figure 2.13 Change in mechanical response of sandstone with moisture content and the dependence of strength with grain contact area

55

Figure 2.14 The effect of changing sample size and shape on the mechanical stress-strain response of materials

58

Figure 3.1 The four most common geometries of borehole measured using the dipmeter calliper logging tool

61

Figure 3.2

63

Model used in the calculation of the modified Kirsch solution

Figure 3.3 The graphical representation of the stress intensity created around hydrostatically and non-hydrostatically loaded boreholes predicted from the modified Kirsch solution

64

Figure 3.4 Failure of a borehole under hydrostatic stress conditions as predicted from elasticity theory and Mohr-Coulomb failure criterion

67

Figure 3.5

Borehole failure modes under laterally isotropic far-field stresses

68

Figure 3.6

Borehole failure prediction from elasticity theory

71

Figure 3.7 model

Borehole failure prediction using the pressure-dependent elastic

Figure 3.8

Elastoplastic models of borehole failure

75 77

Figure 3.9 Representation of the progressive deformation processes in the formation of breakout of the Mine-by test tunnel

80

Figure 3.10 The time-dependent development of the Mine-by test tunnel

82

8

Figure 3.11 Pore-pressure anisotropy created around a well-bore

87

Figure 3.12 Typical stress and temperature conditions within a sedimentary basin

89

Figure 3.13 Variation of stress with depth

91

Figure 4.1

The uniaxial compression rig

95

Figure 4.2

Detailed drawing of the Heard III type apparatus

100

Figure 4.3

Detailed drawing of the force gauge system on Heard III

103

Figure 4.4 Modifications made to the Heard III apparatus to measure the movement of the axial loading piston during the hitpoint experiment

104

Figure 4.5

106

Calibration of Heard III

Figure 4.6 The axial distortion and piston deflection of Heard III determined by performing a hitpoint test using a stiff tungsten-carbide dummy sample

109

Figure 4.7

Diagram of the BigRig apparatus

111

Figure 4.8

Schematic representation of the pore-pressure system of BigRig

113

Figure 4.9

Calibration of the pore pressure system of BigRig

115

Figure 4.10 The variation in pore pressure, and resultant volume change, observed in the pore fluid system over a five day period

116

Figure 4.11 Apparatus modification to measure porosity reduction with increasing hydrostatic confining pressure

117

Table 4.1

119

Porosity and average grain sizes for three sandstone types studied

Figure 4.12 Photomicrograph of intact Penrith sandstone

120

Table 4.2

121

Mineral constituents of the three sandstone types studies

Figure 4.13 Photomicrograph of intact Darley Dale sandstone

122

Figure 4.14 Photomicrograph of intact Tennessee sandstone

123

Table 4.3

Dimensions of the test samples

124

Table 5.1

Results of the unconfined uniaxial compression tests

127

Figure 5.1 Stress-strain relationship of the unconfined uniaxial compression of three sandstones

128

Figure 5.2 Anomalous result of uniaxial test RJCA12 and what this might indicate

129

Figure 5.3

130

Representation of the failed uniaxial sample

Figure 5.4 Calculation of the elastic constants for Tennessee sandstone using unconfined uniaxial compression stress-strain data

132

Table 5.2 The fundamental elastic constants calculated from uniaxial compression data (oven dry)

132

9

Table 5.3 Elastic constants for three sandstones determined from uniaxial unconfined tests

133

Figure 5.5 Results of uniaxial deformation of Tennessee sandstone in orthogonal directions and with different pore fluids

134

Figure 5.6

137

Results of the tensile Brazilian test

Table 5.4 Table of test results for stress/strain curves generated during constant displacement tests

139

Figure 5.7

140

Triaxial stress-strain behaviour of three sandstones

Figure 5.8 Visual condition of the jacketed samples tested using Heard III for constant displacement tests

143

Figure 5.9

144

The determination of yield

Table 5.5 Table of results for peak, residual, and yield strengths determined from constant displacement-rate tests

146

Figure 5.10 Strength parameters sandstones

147

versus

confining pressure for three

Figure 5.11 Yield envelope of three sandstones plotted in the differential versus effective mean stress space

148

Table 5.6 Summary of the volumetric strain versus confining pressure for the hitpoint tests

149

Table 5.7 Summary of the pore strain versus effective pressure for the constant pore pressure volumometry tests

150

Figure 5.12 Hydrostatic compaction of three sandstones

151

Figure 5.13 Comparisons between the three methods used for measuring the hydrostatic compaction of sandstone

152

Figure 5.14 Hydrostatic compaction of Penrith sandstones to pressures in excess of the grain crushing pressure

153

Figure 5.15 Repeat hydrostatic loading of Penrith sandstone to pressures in excess of the grain crushing pressure

156

Figure 5.16 Hydrostatic compaction variation of sandstone with different pore fluids

159

Figure 5.17 Critical effective pressure for the onset of grain crushing under hydrostatic loading as a function of the product of initial porosity and grain radius

160

Figure 5.18 Yield envelope for sandstone in the normalised differential versus effective mean stress space

161

Figure 5.19 Yield surface for sandstone in the Q-P-φR space

163

Figure 5.20 Microstructural evolution of Tennessee sandstone at 100MPa confining pressure

165

10

Figure 5.21 Microstructural evolution of Darley Dale sandstone at 100MPa confining pressure

168

Figure 5.22 Microstructural evolution of Penrith sandstone at 90MPa confining pressure

170

Figure 5.23 Microstructural evolution of Tennessee sandstone with increasing confining pressure

172

Figure 5.24 Microstructural evolution of Darley Dale sandstone with increasing confining pressure

174

Figure 5.25 Microstructural evolution of Penrith sandstone with increasing confining pressure

176

Figure 5.26 Effect of 500MPa hydrostatic loading on Darley Dale and Tennessee sandstones

178

Figure 5.27 Microstructural evolution of Penrith sandstone during hydrostatic loading to pressures in excess of the grain crushing pressure

180

Table 6.1 Summary of results for borehole failure using the bored constant pore volumometry method

187

Figure 6.1 Determining the onset of borehole failure by changes in the hydrostat

188

Figure 6.2

Hydrostatic deflection of Tennessee sandstone in more detail

189

Figure 6.3

Creep of Penrith sandstone pre- and post-failure of bore

191

Figure 6.4 Reduction in the onset of grain crushing (breakout formation pressure) for three sandstones with increasing bore diameter

193

Table 6.2 failure

194

Results from the bladder closure method of detecting borehole

Figure 6.5 Comparisons of determining the onset of borehole failure by the two adopted methods

195

Table 6.3 Results from the microstructural tests conducted by the direct visualisation method on 5mm bored samples

197

Figure 6.6

Pre-breakout damage in Tennessee sandstone

199

Figure 6.7

Progressive development of breakout in Tennessee sandstone

201

Figure 6.8 The main features of borehole breakout in Tennessee sandstone in more detail

202

Figure 6.9 The damage noted along the length of a broken-out borehole in Tennessee sandstone and the nature of spalled material

203

Figure 6.10 Multiple breakout feature seen in test RJC T06h

205

Figure 6.11 Breakout development at pressures much greater than the breakout formation pressure for Tennessee sandstone

206

11

Figure 6.12 Photomicrograph of 5mm bore within Tennessee sandstone tested by the bladder closure method to an effective pressure of 300MPa

208

Figure 6.13 Model of breakout development in Tennessee sandstone

209

Figure 6.14 Determining a reference direction in Tennessee sandstone

211

Figure 6.15 The formation orientation of breakout in Tennessee sandstone

212

Table 6.4

212

Direction of borehole breakout compared to reference direction

Figure 6.16 Formed breakout features in Darley Dale sandstone

214

Figure 6.17 The main features of breakout in Darley Dale sandstone

215

Figure 6.18 Breakout development at elevated pressures in Darley Dale sandstone

217

Figure 6.19 Features of the bladder closure method for Darley Dale sandstone

219

Figure 6.20 Model of breakout development in Darley Dale sandstone

221

Figure 6.21 Pre-breakout features of Penrith sandstone

222

Figure 6.22 Early breakout feature in Penrith sandstone

223

Figure 6.23 Features of breakout at elevated effective pressures for Penrith sandstone

224

Figure 6.24 Features observed around the bore tested using the bladder closure method in Penrith sandstone

225

Figure 7.1 Predictions of bore failure using the elastic model of Zoback et al. (1985) and measured elastic properties

242

Figure 7.2 Variation in breakout geometry with strength anisotropy in the borehole model of Zoback et al. (1985)

246

Figure 7.3 The predicted reduction in yield envelope for Penrith sandstone as bore diameter increases

256

Figure A.1 Schematic representation of the data acquisition, logging, and servocontrol system of BigRig

277

12

Abstract The drilling of boreholes into reservoir rocks at depth leads to a localized stress concentration around the bore periphery, which can result in failure. The aim of this thesis is to further the understanding of the failure of sandstones around boreholes. To investigate the stress-strain behaviour of initially intact rock, unconfined uniaxial compression, constant displacement triaxial, and hydrostatic experiments were conducted. To investigate the mechanical behaviour of boreholes, experimental tests were conducted on bores of diameter between 2 and 5mm, using pore-fluid volumometry and a new technique employing a pressurized bladder placed within the bore. Three sandstones were used in experiments; Tennessee sst (φ=0.07), Darley Dale sst (φ =0.12), Penrith sst (φ =0.25). Uniaxial compression experiments yielded the fundamental elastic constants. Triaxial experimentation showed peak strength has a non-linear dependence of confining pressure for all three sandstones, which was not sufficiently well described by linear Mohr-Coulomb theory. Yield data in the differential stress versus effective mean stress (Q-P) space produced approximately circular envelopes that decreased in size with increasing φ. Yield envelope normalisation with respect to the grain crushing pressure (P*) resulted in a singular yield envelope for sandstone. Microstructural analysis showed that dilatant shear localisation was restricted to the low pressure portion of the Q-P diagram (P/P*0.5. Hydrostatic deformation experiments showed four distinct regions of deformation. 1) non-linear compaction, 2) linear (elastic) compaction, 3) hydrostat deflection at P*, which microstructurally signifies the onset of impingement fractures formed at critically-stressed grain contacts (only seen in Penrith sandstone). 4) a secondary linear-hydrostatic response. A Hertzian contact model gave a good approximation of P* given φ and R. The methodologies adopted for determining the deformation of boreholes sufficiently described the stages of borehole breakout development. However, the utilisation of a pressurized bladder within the bore produced unclear results and altered failure mode. Two modes of breakout development were observed. In Darley Dale and Penrith sandstones, a shear mode of intergranular fracture produced broad and shallow features with breakout width unaltered during growth. In Tennessee sandstone an extensional mode of intragranular fracture was observed. Initially a process zone formed on the bore periphery producing a narrow but deep breakout feature. This appears to stabilize resulting in the detachment of large clasts on the breakout flank to create an elliptical form. Breakout features in Tennessee sandstone consistently align with respect to a rock reference frame under hydrostatic load. This alignment is thought to be produced by strength anisotropy (determined from uniaxial compression experimentation), or by ‘frozenin’ stresses. Existing breakout models predict alignment should occur in the direction of the minimum far-field stress (Sh). Further modelling in this study showed that up to ±20° variation in alignment with respect to Sh can result due to the strength anisotropy observed. Time-dependent pore-fluid expulsion illustrated that brittle creep is initiated during grain crushing. This is due to sub-critical crack growth, presence of clays, or rock permeability. During bore deformation, creep is initiated during the closure of porosity around the bore periphery and the formation of a plastic zone. Enhanced creep initiates during breakout growth. All rocks showed that extrapolated bore failure pressure is approximately 0.2P*. This does not correspond to uniaxial compressive strength, indicating that a lateral confinement effect is created by the circular bore. Penrith sandstone showed pronounced bore strength sensitivity with diameter. This was not associated with experimental artefacts.

13

Declaration No portion of the work referred to in this thesis has been submitted in support of an application for another degree or qualification of this or any other university or other institute of learning.

Copyright and Intellectual Property Rights (1) Copyright in text of this thesis rests with the Author. Copies (by any process) either in full, or of extracts, may be made only in accordance with instructions given by the Author and lodged in the John Rylands University Library of Manchester. Details may be obtained from the librarian. This page must form part of any such copies made. Further copies (by any process) of copies made in accordance with such instructions may not be made without the permission (in writing) of the Author. (2) The ownership of any intellectual property rights which may be described in this thesis is vested in the University of Manchester, subject to any prior agreement to the contrary, and may not be made available for use by third parties without the written permission of the University, which will prescribe the terms and conditions of any such agreement.

Further information on the conditions under which disclosure and exploitation may take place is available from the Head of Department of Earth Sciences.

14

Preface The Author obtained a B.Sc. (Hons) in Geophysics (Geology), Class I from the University of Liverpool in July 1995. Undergraduate project titled “Micro-gravity survey of the Williamson tunnels, Edge Hill, Liverpool” has been present by the author at the following conference: (1) “The application of microgravity to industrial archaeology in a 'brown-field' site.” Cuss, R.J. & Styles, P. Poster presentation at Geosciences ’98, Keele, April 1998. (2) “The application of microgravity in industrial archaeology: An example from the Williamson tunnels, Edge Hill, Liverpool” Cuss, R.J. & Styles, P. Paper in; Geological Society Special Publication, In press.

In September 1995, the author commenced his Ph.D. studies upon which the work reported within this thesis is based. Some of the work reported here has been presented by the author at the following conferences: (1) " Porosity reduction up to the onset of grain crushing and shear enhanced compaction for three porous sandstones in response to hydrostatic loading. " Cuss, R.J. & Rutter, E.H. Oral presentation at the Tectonic Studies Group (Geological Society of London) Annual Meeting, Durham, December, 1997. (2) “Porosity Reduction and the Onset of Grain Crushing for Three Porous Sandstones in Response to Hydrostatic Loading.” Cuss, R.J. & Rutter, E.H. Poster presentation at the Tectonic Studies Group (Geological Society of London) Annual Meeting, Durham, December, 1997. (3) "An Experimental Study of the Fracturing Around the Periphery of Boreholes in Sandstones." Cuss, R.J. & Rutter, E.H. Poster presentation at Geosciences ’98, Keele, April 1998.

15

For My Family

16

Acknowledgements Time for all those thank yous to all those people who have helped and inspired during the past three and a bit years. Firstly I must thank my supervisor, Ernie. I’ve learnt a lot during this study, mostly thanks to Ernie. I appreciate that he showed faith in me, I knew very little about rock deformation and structural geology before starting this study, he’s taught me a lot. The freedom to make my own mistakes and guidance to get me back on track has been invaluable and really appreciated. The sponsors (BG plc) deserve a huge thanks. Thanks to Brian Bellwood, Karl Bird, and Sue Khela. I also owe a huge debt of gratitude to Ernie’s partner in crime, Rob Holloway. He taught me a lot about rigs and general mechanics (and warped my views on life, love, and women). Without Rob none of this would have been possible. Richard Mason played a vital role in constructing the servo-control system of the (unfinished) BigRig. He was also brilliant at helping out with problems I had with BBC Basic! Robert Alcock (Department of Physics) also tried to help in solving a specific BBC related problem. Much appreciated thanks to both of them. Then there’s the lab members all of which helped, distracted, and taught me a lot. In no particular order, thanks to Tony, Dan, Jalal, Christine, Peter, Iona, Bobby, Joolz, Betty, and Hossein. Then there were the visitors, Luigi, Luis, Carla, Gabriel, Anka, and Ela. Many thanks to other department members, particularly Harri Williams for teaching me how to make thin-sections, Carolyn Holloway, Pam Collins, Richard Hartley for helping me make my poster, and Dr. Giles Droop for allowing me to use his microscope. From my previous life in Liverpool, I must thank my old lecturers. In particular Pete Styles for inspiring me when I really wanted to throw in the towel, and Mike Cheadle, mainly for being Cheadle, and for encouraging me to do this research (ta!). My mum and dad have been their usual supportive selves and that has been more than appreciated. My brother Phil and Andy have inspired me all through my life, and I hope I’ve done them proud. Special thanks to Andy for lending me his printer to produce this thesis. Cheers to Jen’s family too. I leave the largest praise until last, a massive thanks to Jen, my long suffering partner. Only we will know how much of this is down to you.

17

List of Symbols and Notation Used Notation Maximum value Minimum value min For Darley Dale sandstone DyDSS For Penrith sandstone PenSS For Tennessee sandstone TenSS Initial value 0 ′ Effective value  Mean value ∂ Differential value 2 ∇ Laplacian operator Cartesian reference frame xyz Polar reference frame r θ rθ Principal reference frame 123 Intact material i Bored material b N- P- R-dir Reference directions in Tennessee sandstone max

Abbreviations BCM = bladder closure method BCPV = Bored CPV CPV = constant pore-pressure volumometry method CSL = critical state line Common symbols α = Biot’s poroelastic term αcr = ratio of c to R ασ = stress trajectory δij = Kronecker delta ε = normal strain • ε = strain rate · ε p = plastic strain-rate vector ε pp = plastic volumetric strain ε pq = plastic shear strain ε1 ε2 ε3 = principal strains εx εy εz = Cartesian normal strains εa εd = axial/diametral strain εh = horizontal lateral strain εp = Pore strain εv = volumetric strain φ = porosity φf = angle of internal friction

γ = shear strain η = viscosity µ = coefficient of internal friction ν = Poisson' s ratio θ = fault angle σ or σN = normal stress (MPa) · σ = stress rate vector σ1 σ2 σ3 = principal stresses σh σH σv = horizontal and vertical stress σx σy σz = Cartesian normal stresses σa = axial stress σd = differential stress Dσ = deviatoric stress σij = applied far-field stress σθ = cirumferential/hoop stress σr = radial stress σt = tensile stress τ = shear stress τo = cohesive strength τrθ = polar shear stress τxy = Cartesian shear stress B = Skempton’s coefficient b = ultimate strength c = crack length C = rock strength C* = onset of cataclastic flow C′ = onset of shear localisation E = Young’s modulus E(σr) = pressure dependent elastic modulus G = rigidity modulus Gc = crack extension force K = bulk modulus of compressibility Ke = measured bulk modulus ethanol saturated KI = stress intensity factor = fracture toughness KIc = critical stress intensity factor Kw = measured bulk modulus water saturated M = mass P = effective mean stress P* = grain crushing pressure P*2 = second grain crushing event

18

P*bx = borehole breakdown pressure where; x = bore diameter Pbdt = brittle-ductile transition pressure Pc or σc = confining pressure Pcr = critical hydrostatic pressure for Hertzian fracture formation Pi = hydrostatic inflection pressure Pp or σp = pore pressure Ps = sand producing pressure Pw = internal borehole pressure Q = differential stress qu = uniaxial compressive strength R = grain radius r = bore radius S = hydrostatic far-field stress SH Sh Sv = far-field stresses T = temperature t = time T0 = tensile strength v = void ratio Y = yield strength Y1 Y2 Y3 Y4 = mechanically derived yield strengths Chapter 2 Kb Kd Ks Ku = K; b drained, d dry rock, s solid part of rock, u undrained m s = degree of particle interlocking /fracturing (Hoek-Brown relationship) vc = critical specific volume vs = specific volume Chapter 3 θ = angular position around the borehole wall a = internal radius of plastic zone

b = external plastic radius B Mp β = constants in plastic model K1 K2 K4 B = constants in pressure dependent model ∆P = differential borehole pressure pb = far-field pore pressure pR = pore pressure variable at the elastoplastic interface R = distance from centre of bore Ra = outer radius of active plastic zone Rp = outer radius of passive plastic zone Chapter 4 φcs = cross-sectional area Carea = corrected cross-sectional area CDispl = corrected displacement D = displacement FGZ = force gauge zero FkN = force (kN) FmV = force (mV) k = strain gauge factor L = load l = sample length MD = machine stiffness MDispl = machine displacement MF = force gauge stiffness P = diametral load r = sample radius Vin = strain gauge supply voltage Vout = Wheatstone bridge output Vsp = calibration supply voltage Chapter 7 φT = angle between SH and T0max

Introduction: Chapter 1 19

1. Introduction 1.1 Nature of the problem Geophysical borehole studies have shown that bores drilled for the extraction of hydrocarbons tend to alter geometry with time. As a borehole is drilled, and material removed, the rock surrounding the hole has to accommodate and support the stresses that were within the removed material. This leads to a modification of the stress around the hole (stress concentration), which if greater than the strength of the rock, leads to failure. Plumb & Hickman (1985) highlighted that four common failure geometries were observed as measured using the dip-meter calliper log. Well-bore breakout is the most common geometry of failure in hydrocarbon reservoir rocks, and represents the modification of the circular bore to an elliptical form. The borehole example is essentially the problem of a hole in a loaded infinite plate. In rock stressed below its elastic-limit with widely spaced and tightly precompressed or healed joints, it is often acceptable to consider any opening, including isolated fractures, as long holes of constant cross-section in an infinite volume (Goodman 1989). Thus, the problem of void response to stress regimes is one of the most fundamental problems of rock mechanics. Considerable effort has been afforded to this problem since the 1980’s as breakout failure affects hydrocarbon recovery. As bores begin to fail, loose sand material detaches from the wall-rocks (sand production). As breakout occurs, larger clasts of material detach as breakout growth occurs. This material causes two problems: a). Loose material progressively fills the bore, damaging equipment or affecting hydrocarbon recovery, or b). loose material is brought to the surface as hydrocarbons are extracted. The latter problem raises issues of sand disposal, which can become expensive and politically sensitive. As breakout features continue to grow they can become highly unstable, and may result in catastrophic bore collapse. This can considerably raise pressures within the bore and is potentially dangerous to drilling engineers. Thus a thorough knowledge of the mechanics of bore failure is required in order to minimize the potential of bore failure and production loss, and to understand the processes that


cause sand production and borehole breakout (and thus to be able to recommend remedial measures). From an academic point of view, borehole breakout represents a simple means of estimating far-field tectonic stress regimes. A more detailed knowledge of breakout formation mechanisms, and an awareness of all material influences on bore response (i.e. the influence of material anisotropy), will help refine existing models, yielding more accurate predictions. Elasticity analysis has been traditionally applied to predict the stress concentration around the bore using the modified Kirsch solution (Zoback et al. 1985, Zheng et al. 1989). Two modes of borehole failure have been identified. The work of Bell and Gough (Bell & Gough 1979, Gough & Bell 1982), and Zoback et al. (1985) suggest that bore geometry modification occurs through the formation of shear-surfaces, which progressively deepen the breakout feature in the direction of the minimum far-field stress. Zheng et al. (1989) introduced an alternative extensional mode of breakout formation. Many models of breakout growth have been devised. These model the borehole system in terms of linear-elasticity, non-linear elasticity, pressure dependent elasticity, or elastoplasticity. Each model can explain certain observed features very closely, but are usually contradicted by other fundamental observations. No single borehole model can accurately predict the failure mode of breakout growth observed in all common geomaterials. Thus, direct observation of bore failure may enable models to be refined and to discern which failure mode is more likely.

1.2 Aims and objectives The main aim of this study was to further the knowledge and understanding of the mechanical processes that cause borehole failure. Few detailed microstructural studies exist on the micromechanics of bore failure (e.g. Haimson & Song 1993, Lee & Haimson 1993). Those that have been reported, generally consider rock types that are less applicable to those encountered in hydrocarbon reservoirs (e.g. pure carbonates and granite). Field evidence of breakout growth is substantial, as boreholes are commonly drilled for the extraction of hydrocarbons, and many other circular openings behave in a


similar manner (e.g. tunnels and shafts). However, field studies can only observe endmember deformations and do not have the ability to isolate individual environmental parameters or to study the progression of failure. A first objective of this study was therefore to observe the deformation of sandstones around small-scale bores within the laboratory environment. This allows individual environmental parameters to be isolated to observe the effect of each parameter. This aim required the design and construction of experimental apparatus capable of observing bore deformation. To describe fully the deformation of sandstone around a bore, it was necessary to characterize intact-rock behaviour in terms of mechanical stress-strain response and the resultant microstructural deformation. Then comparisons could be made with the deformation observed around boreholes. A second objective of this study was to observe the progressive deformation occurring during breakout development using microstructural analysis. This evidence could then be compared with the predictions made from borehole models to evaluate which models more or less accurately describe bore deformation. This study did not aim to construct a new mathematical model of breakout growth, but attempted to compare the new experimental findings with previously published models. Both objectives were realized by experiments on three sandstone types which are similar in mineralogy, but vary in porosity, grain size, and proportions of mineral constituents. From a full characterisation of the material in the intact and bored states it is possible to make predictions of the behaviour of other porous sandstones with different petrographic characteristics.

1.3 Thesis structure Proceeding this introduction, chapter two introduces the previous work carried out on the mechanical deformation of intact sandstone. Initially, the concepts of rock and fracture mechanics are introduced and defined with reference to the modes of brittle deformation observed in sandstones. This is followed by a detailed introduction to uniaxial, hydrostatic, and triaxial rock deformation performed in laboratory experiments. This chapter introduces all the parametric influences that may act upon sandstones.


The borehole problem is introduced in chapter three from a theoretical, experimental and field perspective. Initially the problem is outlined from the original field observations. This is followed by introducing the Kirsch solution to evaluate the stress concentration around a bore in a homogeneous linear elastic material, and the subsequent borehole models formulated using elasticity, poroelasticity, pressuredependent elasticity, and elastoplasticity. These predictions are then compared with field and experimental observations and the modes of borehole failure are introduced. The second half of chapter three introduces the additional complexities that are encountered in the ‘real’ borehole environment. These are documented to illustrate the complex nature of the ‘real’ environment in comparison with the experimental and theoretical frameworks. The introduction of typical down-hole environmental parameters ensures the design of realistic experiments. Chapter four outlines the experimental programme, giving detailed descriptions of the utilized experimental apparatus including the uniaxial compression, Heard-type, and large specimen (BigRig) testing apparatus. Detailed accounts are made of the modifications made to these apparatus, with mechanical and digital logging systems described. Data processing techniques are introduced and discussed. Finally the intact material is described and sample preparation and recovery techniques are defined. The results from the intact portion of this study are presented in chapter five. Unconfined uniaxial and triaxial test results are introduced, the fundamental elastic constants are calculated and yield envelopes described for each material. The detailed hydrostatic deformation experiments are introduced which describe the failure of Penrith sandstone by pore collapse. The hydrostatic results are used to normalize the yield envelopes of each sandstone to create a unified yield envelope. The effects of pore fluid chemistry are also introduced. Finally the microstructural analysis describes the deformation modes of the triaxial and hydrostatic experiments. Chapter six introduces the experimental results obtained for bored samples of sandstone. Initially the methods for detecting bore failure are discussed to validate the experimental methodology utilized. Mechanical results are introduced and discussed with reference to bore failure modes, with comparisons made between the different experimental methodologies. The microstructural analysis of all available data is then


introduced and failure mechanisms are proposed. Finally all bored sample results are compared. Chapter seven is a general discussion and synthesis and argues the key points made during the investigation. The initially intact specimen results are discussed with reference to previous work to identify failure mechanisms and explain pore-fluid chemistry effects. The bored sample problem is then thoroughly scrutinized. The validity of the proposed models of breakout formation is argued with reference to field and experimental observations. The validity of the experimental study is also discussed. Key features identified during the experimental breakout of sandstone are discussed and the hypothesized mechanism of breakout formation argued. Finally, intact and bored results are compared to ascertain what each study predicts about the others. Chapter eight reiterates the primary conclusions found during this investigation and discusses the various implications the findings have on the borehole problem. Finally, chapter nine briefly explores areas of further research potential.

Sandstone Deformation: Chapter 2 24

2. The Deformation of Sandstone This chapter introduces and defines the terms and concepts of rock mechanics that will be used later to describe and interpret the results of the experimental investigation of the mechanical behaviour of sandstone. Deformation properties for many sandstone-types have been published over a wide range of environmental conditions. Generally, only low-temperature work relevant to a hydrocarbon recovery scenario will be introduced.

2.1 Basic mechanical behaviour In situ, rocks are subjected to a heterogeneous stress-field, created in a vertical sense by the weight of overlying rock, which is partially transmitted into the horizontal sense (Poisson effect Ch.3.6.2). Additional horizontal stresses are created by erosion (Goodman 1989), tectonic activity created by lithospheric resistance to plate motion, rock anisotropy, and geological discontinuities. A complex stress-field results, which is described locally by an orthogonal set of axes corresponding to the maximum (σ1), intermediate (σ2), and minimum (σ3) principal stress components. Commonly, σ1, σ2, and σ3 are parallel with either vertical (σv) or horizontal (σh and σH) stress components. These forces act on geomaterials, which in response deform to maintain equilibrium and support the load. Materials show a combination of elastic, plastic, brittle, and/or ductile behaviour, dependent on possible deformation mechanisms. 2.1.1 Elastic behaviour Elastic material behaviour (figure 2.1), by definition, is fully recoverable once applied load is removed, and is described by the following: E=

σ ε

ν=−

ε1 ε3

K=

∂Pc E = ∂ε v 3(1 − 2ν )

G=

E ∂τ = ∂γ 2(1 + ν )

Eq.2.1

where; E is Young’s Modulus, ν is Poisson’s ratio, K is bulk modulus, G is shear modulus, σ is normal stress, ε is normal strain, εv is volumetric strain, Pc is hydrostatic confining pressure, τ is shear stress, and γ is shear strain. Young’s modulus (E) describes material stiffness and is equal to the amount of stress required to achieve unit length-parallel extensional elastic strain. It derives from Hooke’s law, which states “the power of any spring is in the same proportion with the tension thereof”. A linear relationship exists between stress and strain describing E. For

Sandstone Deformation: Chapter 2 25

real elastic deformation, as the applied stress is released the strain tends to follow a dissimilar hysteresis loop (see figure 2.1a). Poisson’s ratio (ν) describes the translation of vertical stresses into additional horizontal strains. For an isovolumetric deformation ν=0.5, with axial strain translated symmetrically into the two radial dimensions. Rocks generally have ν≈0.25, thus axial loading results in elastic volume decrease. The bulk modulus of compressibility (K) describes the resistance to dimensional alteration described by ν. The shear modulus (G) describes the resistance to shear. In homogeneous isotropic elastic solids, the elastic constants are equal in the three orthogonal directions. In geomaterials, elastic anisotropy is common, with the elastic constants dissimilar in the orthogonal directions. All rocks exhibit elasticity at small strains, but in highly compressible materials, such as unlithified sediments, wholly elastic behaviour is extremely limited in extent (Burland 1989). Thus, weak sedimentary rocks normally exhibit strongly non-linear stress-strain relationships with hysteresis (Vaughan 1985). 2.1.2 Inelastic behaviour Elastic deformation is observed until the elastic limit, where yield signifies the onset of large, permanent non-recoverable (inelastic) deformation. After yield, either plastic, ductile, or brittle behaviour is observed. Perfect-plastic behaviour initiates at a critical threshold of yield stress, with permanent strain continuing rapidly and indefinitely with stress magnitude maintenance (figure 2.1a). Granular media are among the best examples of phenomenologically plastic materials (Vardoulakis & Sulem 1995). Generally, geomaterials are not perfectplastic media, with strain-hardening or strain-softening observed. Strain-hardening results from granular inter-locking or porosity collapse, requiring increasing amounts of stress to continue strain. Strain-softening results from granular fragmentation and bondage severance, less stress is required to continue strain at higher deformations. Brittle behaviour represents a near-instantaneous stress reduction (figure 2.1b) involving some combination of fracture and frictional sliding, and is common in geomaterials at low pressures. Stable frictional sliding along fractures requires less energy than fracture initiation (dynamic µ Sv

S v (the o retic al; fro m o v e rb u rd en )

Figure 3.13: Variation of stress with depth. a). Collated world-wide in situ stress data showing average horizontal stress becomes increasing hydrostatic with respect to vertical stress with depth. The shaded area is predicted from elastic theory. (From Hoek & Brown 1980). b). Horizontal stress components with depth for the Illinois Deep Hole experiment. Sh approximates Sv, with SH predicted from fracture strength for µ=0.6 with fluid at hydrostatic pressure. (From Haimson & Doe 1983).

Borehole Failure: Chapter 3 92

Introduced studies suggest stress regimes become both increasingly and decreasingly hydrostatic with depth. The observed decrease in ratio of horizontal stress to vertical stress with depth is paradoxical with other aspects of the brittle behaviour of the upper crust. Pop-ups, stress-relief buckles, and late-forming faults are possible sources to explain the conflict of opinion (Engelder 1992). The paradox of observations makes it difficult to predict the stress regime for the North Sea. The extensional tectonic nature of the area suggests that at least one horizontal stress component will be less than the vertical stress component. The author could not find stress magnitude data for the North Sea. Case studies show horizontal stresses range from σH=σh to σH>2σh. 3.6.3 Pore pressure and temperature As highlighted in chapter 2, the existence of pore-pressure (Pp) in rocks strongly influences mechanical behaviour and can cause extension fracturing even under purely compressive stress conditions. High Pp can develop simply from compaction of impermeable sediments as their volume decreases. Variations between the coefficient of thermal expansion for water and sediments results in Pp build-up with temperature. Figure 3.12 shows a general hydrostatic pore-pressure gradient assuming a saturated water porefluid. Localized variations occur creating over-pressure lithologies, resulting in a fluid potential and fluid pressure gradients. Complex Pp profiles exist with depth which is a contributory factor to the complex σv profile. Generally Pp=50MPa within wells, thus pressure reduction may be induced to enhance hydrocarbon removal. In general, temperature increases 15-30°C per kilometre depth, the thermal gradient of the North Sea is approximately that of figure 3.12. Natural gas is temperature sensitive and destroyed at approximately 180°C (~6km depth), this imposes an upper temperature (and stress) limit on the hydrocarbon borehole problem. 3.6.4 Chemical environment As reviewed in Ch.2.7.1, pore-fluid chemistry has a profound effect on the mechanical response of rocks. North Sea natural gas contains small amounts of ethane, butane, and propane, but is essentially a non-toxic methane gas. Thus, gas and oil saturated reservoirs will tend to be stable.

Borehole Failure: Chapter 3 93

3.7 Summary of Chapter 3 • The borehole system is extremely complex and dynamic in nature. • Four common borehole geometries are identified in the field, one is erroneous; wellbore breakout is the most common geometry. • The drilling of bores locally concentrates stress around the bore. The modified Kirsch and Lamé solutions describe the stress concentration in elastic media as shown by photoelasticity. Models of bore failure combine the Kirsch solution and a failure criterion. • Using elasticity, Bell and Gough predict a deep and narrow breakout, Zoback et al. predict a broad and shallow breakout. Mastin (1984) and Cheatham (1993) extend elasticity to describe stability. Elastic models closely describe initial breakout form. • Extended models use poroelasticity, non-linear elasticity, pressure-dependent elasticity, elastoplasticity, and non-associated plasticity. Extended models predict stress is dissipated locally around the bore periphery, failure initiation would thus migrate from the bore-wall into the wall-rock • Several models and field/experimental evidence shows shear failure, other evidence shows extensional failure. Differences in modes may be rock controlled. • The Mine-by showed considerable time-dependent deformation. • The real bore environment is exceptionally complex: • Bore geometry considerations include drilling damage, radius, ellipticity, and inclination • Lithological controls include anisotropy and fracturing • Drilling fluids and fluid flow profoundly influence bore stability • Porosity and permeability evolution further complicates stress • Hydrocarbon basins are complex systems with variable stress regimes, chemical, and environmental conditions which stabilize or enhance deformation

Experimental Procedures: Chapter 4 94

4. Experimental procedures and starting materials The mechanical behaviour of sandstone can be determined using uniaxial deformation rigs to measure rock properties at atmospheric conditions, and triaxial rigs to simulate deformation at burial depth and temperature. The use of the term “triaxial” is here used in its traditional sense (Paterson 1978), with two of the three principal stresses equal, and should not be confused with “polyaxial” tests (Jaeger & Cook 1979) where all three principal stresses are different. These will be termed “true triaxial”. In the course of this experimental investigation three different deformation apparatuses were utilized. For atmospheric conditions, the uniaxial compression rig was used, with the Heard-type and large specimen rigs used for triaxial deformation. The ability to test larger samples gave the scope to observe directly deformation around scaled boreholes.

4.1 Uniaxial compression tests Uniaxial compression tests are widely used in engineering practice (Hudson & Harrison 1997), they are simple and require minimal equipment sophistication. The deformation of rocks at room pressure and temperature allow the calculation of the fundamental elastic constants that describe material elasticity. 4.2 Uniaxial compression apparatus The uniaxial compression rig (figure 4.1a) was constructed by R.F. Holloway in 1988 to test rocks under unconfined conditions. It is relatively simple, comprising two horizontal stiff beams that are held in place by two stiff vertical columns. The assembly is rigidly held together, such that the application of load places all welds into compression, thereby minimising weaknesses and non-linear stiffness response in the apparatus. Strain-gauged cylindrical samples were loaded in uniaxial compression between two steel platens by a hand operated 23ton hydraulic EnerpacTM ram. Later tests were conducted on a similar rig which created load through a motor, gearbox, and screw-jack arrangement similar to the Heard style apparatus (§4.5, figure 4.2). The lower platen consists of a 10ton load-cell. The platen set-up incorporates a spherical seat so that the force applied is directed down the centre of the specimen so as not to place any lateral forces on it which would result in inaccuracies. A calibrated Bourdon tube pressure gauge in the hydraulic system gave estimates of force applied in tonsforce. The hand-pump

Experimental Procedure: Chapter 4 95

EnerpacTM 23 tonne hydraulic ram

Bourdon tube pressure gauge

Stiff upper body

Upper platen Strain gauged sample

Stiff vertical columns

10ton load cell

Elastic bands to hold load cell in position if failure violent

Lower platen

Stiff lower body

0

50

100

150

200

mm

a.

Hydraulic hand pump

Valve

Valve used to isolate pump from ram

+ Vin Active strain gauge from deforming sample

Passive strain gauge from dummy granite sample.

Vout

b.

Passive strain gauge from dummy granite sample.

Active strain gauge from deforming sample

0

Figure 4.1: The uniaxial compression rig. a). The arrangement of the experimental apparatus. b). The Wheatstone bridge configuration. The passive and active strain gauges are wired into the bridge to remove the effect of temperature from the strain results. The output from the system is measured by a digital voltmeter. Two Wheatstone bridges are used, one for axial strain-gauges and one for circumferential strain-gauges.


system allows force to be raised in 2.2kN intervals (0.25tonf), with the resultant axial and circumferential strains noted. Cored samples were prepared with TMLTM 20x3mm PFL-20-11 strain-gauges to measure sample deformation. These consist of foil conductors mounted on a 31x7mm polyester base, with a normal resistance of 120±0.3Ω which changes linearly with lengthdeformation. Two pairs of strain-gauges were cemented parallel to the sample axis and circumference using P-2 polyester adhesive. The glue allows a maximum of 3% strain at room temperature, irrespective of humidity, and is compatible with all rock types. The axial and circumferential oriented strain-gauges yield the axial strain (εa) and diametral strain (εd) respectively of the sample. The circumferentially orientated gauges directly measure circumferential strain (εc) which is equal to diametral strain. Each pair of active strain-gauges were wired into two Wheatstone bridge configurations (figure 4.1b) together with a similar arrangement of passive gauges mounted on an adjacent unstressed dummy sample of granite. This renders the out-of-balance signal from the bridges independent of temperature variation. The Wheatstone bridge is energized by a stabilized power supply, with the out-ofbalance voltage from the bridge, as measured by a digital voltmeter (DVM), varying as the resistance of the active gauges changes with strain. Two DVMs were used to display the bridge output of the axial and circumferential strain-gauge systems, with a third DVM measuring the output from the axial load-cell. 4.2.1 Calibration of the uniaxial apparatus Axial and circumferential strain measurements are taken directly from the temperature compensated Wheatstone bridge, with the strain-gauge calibration supplied by the manufacturer (represented by the gauge factor, k). Stress is determined by a 10tonf strain-gauge load-cell which was accurately calibrated by Stretton (1996) against a 10tonf proving ring and an InstronTM 10tonf loadcell. The proving ring and load-cell were placed in series in a hydraulic press and loaded and unloaded full range three times. Data collected at 0.5tonf (4982N) increments, was linearly regressed producing a relationship with a root mean square error of 0.03 (300N). Supply voltage during calibration was noted, this is compared with the supply voltage during any testing, differences between these voltages will proportionately affect load-cell output.


4.2.2 Data logging and test procedure The 23 tonne hydraulic EnerpacTM ram is manually operated by one person, with logging conducted manually by three others. The output voltages representing the three variables (axial strain, circumferential strain, and load) were noted from digital volt meters (DVM) as load was increased in quarter tonsforce intervals until sample failure. A few seconds were allowed after load application to allow the system to equilibrate. Strain gauge voltage and load cell supply voltage were recorded using a DVM. Later tests using constant displacement rates applied by a motor and gearbox arrangement were logged using an identical logging system as used on the Heard-type apparatus (see section 4.5.2). 4.2.3 Data reduction and calculation of the fundamental elastic constants Data were transferred into a spreadsheet where stress (σ) axial strain (εa) diametral strain (εd) and volumetric strain (εv) could be calculated. These results were used to calculate Young's modulus (E), Poisson's ratio (ν), bulk modulus of compressibility (K), and uniaxial compressive strength (qu). The recorded experimental values of load (mV) were converted to stress (MPa) as stress is the applied force per unit area:

σ=

L φcs

Eq.4.1

L Vin Vsp φcs

= Load(kN) =(21.02+(4.72×F(mV))) ×(Vin/Vsp) = Experimental supply voltage = Calibration supply voltage =12.302V = Cross-sectional area (m2)

TMLTM publishes the calibration of its strain gauges with reference to a gauge factor (k) this constant is calculated for batches of strain gauges. Strain (ε) is thus: Vout = Strain gauge supply voltage Vin Eq.4.2 Vout = Voltage output of Wheatstone bridge. 0.5Vin k Axial strain (εa) and diametral strain (εd) were calculated from the above relationship.

ε=

Volumetric strain (εv) was calculated as the sum of the strains in all three dimensions ensuring the correct sign of the strains. Axial strain should result in a shortening, whilst diametral strain should be expanding. therefore:

ε v = ε a + 2ε d

from:

ε v = ε1 + ε2 + ε3

Eq.4.3

Young's modulus (E) is calculated as the ratio of stress to strain in the elastic domain obeying Hooke's law. As shown in chapter 2 (§2.4), uniaxial stress-strain curves are non-


linear. E is best described by the steepest portion of these curves as this region is not affected by non-linear stiffness created by the closure of pre-existing damage. Thus: E=

δσi δεi

δσi /δεi = Change in stress/strain in the i direction = Direction of load i

Eq.4.4

Poisson's ratio (ν) is the relationship of extension normal to an applied stress to the extension parallel to it. This is equal to the rate of change of diametral strain with axial strain in the elastic region: ν=

εx εy

Eq.4.5

εx /εy = Strain in the x/y direction = Direction of application of load y

Bulk modulus (K) describes the amount of volumetric strain caused by an applied stress. Bulk modulus is related to Young’s modulus (E) and Poisson’s ratio (ν); note: K=∂V/∂P is not used as applied pressure is not hydrostatic: K=

E 3(1 − 2ν )

Eq.4.6

Uniaxial compressive strength (qu) defines the strength of a material when stressed under uniaxial compression. It is the value of stress required to cause failure in an unconfined sample of material, it is therefore the maximum stress observed prior to ultimate failure. 4.3 Brazilian test apparatus The measurement of direct tensile strength of rocks is difficult because stress concentrations at the specimen grips can induce premature failure, unless the specimen is pre-machined with a reduced cross-sectional area to concentrate the load, which raises costs. A number of simpler, and thus cheaper, methods have been devised to measure the tensile properties by means of tensile stress induced in compressional loading. The Brazilian test loads a sample diametrically to measure the tensile strength. The diametral loading of cylindrical samples creates a stress concentration which, when sufficient, creates a mode I, or tensile, fracture as σx≠0, σy≠0, σz≠0, and τxy=0. The same apparatus is used for Brazilian tests as for uniaxial compression tests, with constant displacement rate of the upper platen created by a motor and gearbox arrangement. 25mm diameter cores are loaded diametrally between the loading platen and the static lower platen. A 10tonf load-cell is placed in series with the loading system and measures loading force (the same load-cell as used in the uniaxial compression rig). The output from the load-cell is logged every second, with the maximum stress level at failure being the measurement of interest.


Reproducibility of the results for the Brazilian test tends to be poor due to the assumption that the stress distribution prior to fracture corresponds to that of the purely elastic state (Paterson 1978), and results can vary with specimen preparation, test procedure, and equipment used (Mellor & Hawkes 1971). The original design of the apparatus requires curved loading platens which apply load to a specific area of the cylindrical samples, this requires exact machining. Instead, cardboard strips are placed at the interface between the flat loading platen and sample to distribute the load evenly over the top edge of the sample. This reduces the risk of creating a stress concentration at the interface which would result in premature failure and is the recommended procedure. The theoretically derived stress distribution for a cylinder loaded in diametrical compression shows maximum tensile stress (kPa) normal to the compression direction will be given by: To = −

P Eq.4.7 πlr

P r l

= Diametral load (kN) = Sample radius (m) = Sample length (m)

Tensile strength is equated to the tensile stress at failure and tends to be approximately one tenth of uniaxial compressional strength (qu).

4.4 Triaxial compression tests Triaxial conditions can be imposed upon samples by the application first of a hydrostatic confining pressure created by a fluid medium within a high pressure vessel. Deviatoric stress is imposed by a driven pair of pistons axially loading the sample. Rocks can thus be tested at simulated depth at a range of confining pressure, pore pressure, temperature, and strain rate. Hydrostatic compression tests can also be conducted to describe how the rock behaves under the influence of confining pressure alone. 4.5 Heard-type triaxial apparatus The Heard-type triaxial rig (Heard 1963), which will hereafter be referred to as Heard III, was designed as a means of testing rock samples at confining pressures up to 400MPa, pore fluid pressures up to 200MPa, temperatures up to 400°C, differential loads up to 1GPa, with strain rates in the range 10-3s-1-10-8s-1. Detailed accounts of the apparatus are given by Rutter (1970, 1972), Zhang (1988), Walker (1991), Covey-Crump (1992), Stretton (1996), and Wanten (1996). Each of these experimental studies involved

Experimetnal Procedure: Chapter 4 100

Drive motor

Displacement dial gauge

Displacement LVDT Drive gear train

Main drive gears

Thermal cut-out switch Thrust sleeve Control thermocouple

Ball screw Water cooling coils

Thrust block Packing sleeve

Anti-rotation pins Upper piston

Moving piston seal Specimen assembly

Specimen thermocouple Furnace

Pressure vessel

Lower piston

Confining pressure inlet pipe Force gauge

Packing nut

Force gauge pressure seal

Water cooling coils

Support frame

Force gauge LVDT 0

50

100 150 200 mm

Figure 4.2: Detailed drawing of the Heard III type apparatus showing all component parts (after Covey-Crump 1992).


modifications to the machine according to the desired task. This description is relatively brief, and accounts for only the basics of the set-up and the modifications made to the apparatus for this study. For this investigation Heard III was used for two types of test; triaxial compression tests, and hydrostatic compression tests. Figure 4.2 shows a detailed drawing of the Heard apparatus. Heard III has a thick walled pressure vessel fabricated from Jessop-Saville H50 pressure die-casting steel, into which the piston and specimen assembly is sealed. The specimen is jacketed using annealed, thin-walled copper tubing, which allows tests to be conducted with a different confining pressure outside the jacket compared to the pore pressure within the sample. Before assembly, the copper tube is heated to approximately 700°C by means of a butane flame, and quenched under running water. Copper oxide forms on the surface and is removed by soaking for a few seconds in 50% nitric acid. The jacket is thoroughly cleaned in water and dried in an oven for a few minutes, before the sample is placed inside. Once annealed, the 0.25mm thick tubing is weak compared to the test material, supporting a force equivalent to about 2MPa on the sample, and therefore does not significantly affect results. Annealing takes place immediately before testing so that the material is still weak and ductile, avoiding the effects of age-hardening. The jacket - sample assembly is attached to the upper and lower pistons using internally tapered steel swaging rings, which are forced over the outside of the jacket and tapered piston ends forming a pressure seal between jacket and piston. Hydrostatic confining pressure is generated by compression of a low-viscosity silicone oil (Dow Corning 200 dimethyl siloxane polymer, η=5×10-6m2.s-1), entering the ®

vessel through a cross bore. Prior to this investigation water and oil were used as confining fluids. Water led to problems of corrosion, while oil prolonged the life of the apparatus at a cost of limiting operational temperature to 400°C. Stretton (1996) showed that higher viscosity oil than used in this study displayed transient polymerisation problems at room temperatures and confining pressures greater than 227MPa; resulting in blockage, transiently non-uniform pressure in the pipe-work, and a high possibility of damage to the pump. This necessitates the use of low-viscosity oils at elevated pressures. The internal volume of the system does not remain constant as the upper piston advances into the vessel. The change in volume increases the confining pressure (up to 10MPa), especially when the oil is at its least compressible (low temperatures and high confining pressures). An identical second reservoir pressure vessel in parallel with the


primary pressure vessel can therefore be used to maintain constant pressure (±2MPa) when the pistons of the two vessels are driven in opposing directions, maintaining a constant fluid volume. However, the system is not perfect due to slight variations in motor running speeds and differences in bore size. In practice, if both motors were running in opposing directions the pressure slowly reduced. This problem was overcome by manually operating the regulating vessel between limits. Confining pressure is contained in the vessel at the top of the apparatus by means of a moving piston seal, and at the bottom of the apparatus by means of a static pressure seal. The upper seal consists of a dynamic o-ring and a maintenance-free fixed seal arrangement. The sample and piston assembly rests directly on the elastic element of the internal force gauge. The hollow upper piston had a 2mm bore which allowed pore fluid pressures to be applied to the test sample. However, pore pressure tests were not conducted and the vented hollow piston ensured sample pore pressure remained at atmospheric pressure. All tests were conducted at room temperature, although the apparatus is capable of operation up to 420°C. Axial displacement of the loading piston was created by a drive motor and gear train system, with horizontal rotation translated into axial movement of the loading piston by means of a ballscrew. When engaged, each gear within the drive train allowed axial displacement to be changed by an order of magnitude, with a total of five orders of magnitude change in velocity available. Different motors can be used to give different displacement rates within these order of magnitude steps. All axial loading tests were conducted with the lowest gear ratio, as sandstones tend to be insensitive to strain rate, so that a specimen might be loaded to 10% shortening in about ten minutes. An identical drive system was used on the reservoir rig. 4.5.1 System of measurement During triaxial compression tests there are four variables which are measured; confining pressure, temperature, axial load, and cross-head displacement. An Intersonde HP28 strain-gauge pressure transducer measured confining pressure in the range 0-500MPa. The transducer was connected into the confining pressure piping system outside the vessel enclosure along with a Bourdon tube pressure gauge used for direct visualization of pressure. Specimen temperature is measured by a chromel-alumel thermocouple which is placed in a 3.175mm diameter bore in the pressure vessel wall opposite the specimen


position. The output obtained is given with respect to a temperature regulated reference junction which is held at a constant 30±0.5°C. The temperature control of the laboratory meant only small changes in temperature were observed, the exact measurement of temperature is not vital in room temperature experiments. D iffere ntial lo ad

P re ssu re ve sse l A c tiv e ga u g e len g th

U n stressed ro d F o rce g a u ge c o lu m n F o rce g a u ge se al a sse m b ly

A p p rox im a te ly ze ro strain in th is sec tio n

W a te r co o lin g c o ils LV D T 0

1 00

50

1 50

LV D T co re

mm

LV D T h ou sin g

Figure 4.3: Detailed drawing of the force gauge system on Heard III, showing the active deforming portion and the static body of the force gauge.

An internal force gauge (Figure 4.3) was used to measure the axial load on the specimen. The force gauge column is fixed rigidly to the vessel at its lower end in series with the sample; the lower piston rests directly on top of the column. As the system is loaded the column shortens elastically. The column is hollow and contains a rod, fixed to the bore at the upper end, that is not subjected to any stress, and therefore does not change its dimensions. This rod connects the top of the column with the core of a DC-linear variable differential transformer (LVDT), the body of which is housed within a water cooled block attached to the lower end of the column. Application of load to the column therefore displaces the LVDT core relative to its body by an amount proportional to applied load. The LVDT produces an output which can be calibrated against the differential load applied. The active length of deforming force gauge lies within the


pressure seals, therefore no correction is needed for seal friction, but the force gauge does register output change linearly proportional to change in confining pressure.

0

100 150 200

50

mm

Magnetic clamping block

Lengthened anti-rotation pins and supports

0.001´´ division dial gauge

Figure 4.4: Modifications made to the Heard III apparatus to measure the movement of the axial loading piston during the hitpoint experiment. Two additional dial gauges were added to measure the movement of the thrust block, thus giving piston movement. Two gauges removed the effect of thrust block rotation during loading.

TM

Crosshead displacement was measured using a Schaevitz

DC type LVDT, the

body of which was attached to the apparatus frame, and the core to the top of the ballscrew column. The placement of this transducer outside of the dynamic system can lead to error created by the distribution of strain in the ballscrew. As the upper piston is driven the main drive gear will move until all 'slack' has been taken up from the system before the piston moves. The upper section of the core was connected to a 0.001inch (0.0254mm) divided dial gauge which acts as a springload on the core and gives a direct reading of displacement should any electrical errors occur with the logging system. Displacement of the upper piston was more directly measured for the hitpoint tests using the adapted apparatus as shown in figure 4.4. Two 0.001inch divided dial gauges were attached to the apparatus frame by magnetic clamping blocks and connected to the piston system via


adapted anti-rotation pins of the thrust block. Two gauges were used and measurements averaged to eliminate any rotational movement of the thrust block at lower pressures. The pressure, displacement and force gauge transducers were all served with the same regulated 24 volt power supply. 4.5.2 Data logging system Data were logged using the HeardLog3 software running on an Archimedes microcomputer which is a development of the RockDef software (Neumann 1994). The outputs from the confining pressure, displacement, force gauge and temperature transducers were relayed sequentially to the computer via a switch array and digital volt meter (DVM). The switch array consisted of 15 double pole changeover relays which have a low resistance and a very short operating time allowing a logging cycle of 6 seconds. Switching was controlled by the logging program with communication to the switch array via the 8 bit parallel user port. Data from the switch array were read by a Thurlby 4½ digit DVM with a resolution of 0.01mV. A digital RS232 serial connection transferred data from the DVM to the microcomputer. Raw data is saved as a data file which consists of a sequence of records each of six fields of 10 digits. Data is stored in the memory of the computer and periodically saved to an internal RAM filing system to improve data security. 4.5.3 Machine limitations on the data Extensive calibrations were undertaken on Heard III during November, December, and May 1995/1996. The experimental apparatus can be seen as a system consisting of two springs in series, one spring representing the apparatus and the other representing the test sample. Calibrations allow the mechanical behaviour of the spring representing the apparatus to be fully characterized; thus thorough calibration allows the apparatus distortion to be removed from the results, allowing sample deformation to be studied. The output from the pressure transducer was calibrated against a HeiseTM Bourdon tube gauge at intervals of about 7MPa over the range 0-280MPa. Linear regression was applied to the data as shown in Figure 4.5a giving a root mean square error of 1MPa. The calibration data for the thermal characteristics of Heard III were those calculated by Stretton (1996), using the manufacturer's calibration data for the chromel-alumel thermocouples.


Confining pressure (MPa)

300 250 y = 2.943647x - 1.162045 R2 = 0.9999837

200 150 100 50 0 1

0

a.

5

4

3

2

7

6

8

9

10

Pressure transducer output (mV)

30

y = -0.2159742x + 1.434669 R2 = 0.9998238

Displacement (mm)

25 20 15 10 5 0 -50

-40

-20

-30

b.

0

-10

10

70

30

50

40

4.6

50 4.55 40 4.5 30 4.45 y = 4.3747x + 27.48

Load (kN)

20 10 0 0

R2 = 0.992

@300MPa

4.4

Force gauge stiffness; MF (kN/mV)

4.65

60

c.

20

Transducer output (mV)

y = -1.04413´10-3 + 4.66648 R2 = 0.978891

dMFdP=slope/intercept

4.35 1

2

3

4

5

Force (mV)

6

7

8

d.

50

100

150

200

Confining pressure (MPa)

Figure 4.5: Calibration of Heard III. a). Calibration of the Intersonde HP28 pressure transducer of the hydrostatic confining pressure system. b). Calibration of the SchaevitzTM DC type LVDT attached to the cross-head system. The non-linearity at above ô30mVô imposes operational limits upon the apparatus. c). Calibration of force gauge stiffness (MF) at 30kPSI. d). Plotting MF at different confining pressures yields the calibration constant dMFdP.


4.5.3.1 Axial loading system Measurement of the displacement of the upper piston is required to calculate the strain within a sample, and the strain rate for the test. The output of the displacement transducer was calibrated against the 0.001inch (0.0254mm) divided dial gauge by raising the main drive gear about 1mm and taking readings of the dial gauge and LVDT. Figure 4.5b shows the LVDT gave a linear output between ±30mV (±12mm). As load is applied to a sample the force gauge column is subjected to a number of forces. Of interest is the axial force transmitted through the sample. However, the confining medium acts upon both sample and column, causing the column elastically to distort, by an amount dependent on its stiffness and the confining pressure. The output of the force gauge will thus not only indicate transmitted axial load, it will have a component dependent on force gauge column pressure and temperature. To correct for these, tests were run with no axial load to determine how the force gauge zero output varied with pressure and temperature. Force gauge zero calibration (dFGZ) compensates the zero load point for any changes in pressure (dFGZdP) and/or temperature (dFGZdT). The variation of force gauge output with confining pressure was investigated by pressurizing the vessel to 320MPa and allowing it slowly to leak. Readings of force-gauge output and pressure were logged for several runs until zero pressure had been achieved. The application of linear regression to these data found the calibration constant dFGZdP. As all tests were conduced at room temperature it was not necessary to investigate dFGZdT; values obtained by Stretton (1996) were sufficient. Force gauge stiffness was determined by conducting loading tests at pressures of 50, 140, and 200MPa and comparing the output from the force gauge with the output from a precisely calibrated load-cell which was placed in series with the loading system in place of the thrust block. Linear regression was applied to the load-cell versus force gauge readings at each pressure (MF - figure 4.5c) and plotted against confining pressure to give the change in force-gauge stiffness with confining pressure (dMFdP), figure 4.5d. Values for dMFdT used were those measured by Stretton (1996) and with very small changes in temperature this effect is negligible. Given these calibrations, the differential load can be determined at any point during the experiment by noting initial force gauge zero, temperature and pressure immediately prior to loading of the specimen.


4.5.3.2 Apparatus stiffness As confining pressure is applied to the apparatus it undergoes elastic distortion dependent on confining pressure and temperature. Axial distortion of both sample and vessel will be detected by the displacement transducer, therefore the apparatus distortion must be removed to calculate the strain of the sample. The stiffness of an elastic material is defined as the applied force per unit change in length. Therefore, apparatus stiffness is equal to the applied axial force divided by the resultant axial displacement. A tungsten carbide (WC) dummy specimen of dimensions 9.5mm diameter and 21.3mm length was assembled within the vessel, repeat tests were made to relate the true force gauge reading with displacement. The slope of the force gauge versus displacement is equal to the stiffness of the apparatus at that pressure. A sample correction is virtually unnecessary as WC has a stiffness of 1.78x109N.mm-1, compared to the calculated machine stiffness of 5.5x107N.mm-1. The sample is approximately 33 times stiffer than the vessel, resulting in a 1% error in calculation of machine stiffness if the presence of the dummy sample were ignored. The variation in apparatus distortion with pressure (dMDdP) is equal to the slope of machine compliance (the inverse of stiffness) with pressure. Increasing confining pressure leads to a reduction in compliance of the pressure vessel, therefore increasing stiffness. Axial displacement correction errors at room temperature will thus be most evident at lower pressures. The effect of apparatus distortion with temperature used was that calculated by Stretton (1996). 4.5.3.3 Piston deflection during hitpoint experiments The hitpoint experiment measures changes in axial sample length at different confining pressures by driving the upper piston and probing the sample for the onset of axial load transmission. This yields length and determines sample volume at different hydrostatic confining pressures. This method is designed to observe small variations in sample length with pressure change, these variations are masked by vessel expansion and piston contraction with increased confining pressure. To describe fully the apparatus distortion, a hitpoint test was run using a dummy tungsten carbide (WC) sample, measured at 40MPa intervals in the range 0-350MPa. Two dial gauges (as shown in figure 4.4) were used to measure piston movement, and a chart recorder and dedicated DVM were added to the system to monitor force gauge output, allowing hit to be more accurately determined.


A correction was made for the distortion of the dummy sample. A value for bulk modulus of compressibility (K) for WC was not available, but by using the Young’s modulus for WC and assuming that the ratio of K to E is the same as for steel, it was possible to estimate KWC. The bulk modulus allowed sample distortion to be calculated as;

δl =

Pc l Eq.4.8 3K

l = Sample length Pc = Confining pressure

Therefore, at 300MPa the WC sample will account for 3.77µm shortening within the observed 1.198mm change in length of the system. Thus, the dummy sample only accounts for 0.3% of the observed distortion, whereas Tennessee sandstone, the stiffest material tested in this investigation, accounts for one third of the total axial distortion. Figure 4.6 shows the resultant piston deflection versus confining pressure data for several test runs and the relationship found by multiple regression. 1 .4

C orrected ax ial d isto rtion (m m )

1 .2 1 S c a tte r to o g re a t

0 .8

S c a tte r d e c re ase s w ith in c re a se d p ressure

0 .6 0 .4

y = 8 .4 7 0 9 ×1 0 x - 1.8 1 6 5 ×1 0 x - 1 .3 9 1 5 ×1 0 x + -3 -3 7 .5 0 5 5 ×1 0 x + 6 .5 6 93 ×1 0 -11

0 .2

4

-8

3

-5

2

2

R = 0 .9 3 0 4 0

-0 .2

50

100

150

200

250

300

C on fin in g p ressu re (M P a)

Figure 4.6: The axial distortion and piston deflection of Heard III determined by performing a hitpoint test using a stiff tungsten-carbide dummy sample.

4.5.4 Design of Heard III triaxial tests Two types of triaxial tests were conducted using Heard III; constant displacement rate and hydrostatic volumetric strain (hitpoint) tests. The constant displacement rate test, which is analogous to the constant strain test, was conducted with the drive motor advancing the upper piston at a constant rate. The resultant environmental parameters were recorded along with the force transmitted through the sample. Stress and strain were calculated for the constant confining pressure tests,


which were all conducted at the highest strain rate. A suite of tests were conducted over a range of confining pressures to describe the mechanical behaviour of the material. Secondary tests were conducted to different strains to describe microstructural features of the deformation at one pressure. The hydrostatic volumetric strain test (hitpoint test) describes the volumetric variation of samples with increased confining pressure by measuring changes in sample length by the hitpoint method. Once the stationary loading piston contacts the sample, stress is transmitted to the force gauge. This hitpoint indicates the length of the sample once corrections are made for piston and vessel deflection. Hitpoints were measured from 0-250MPa at 7MPa intervals in both up and down-pressure cycles. As pressure is reduced special care is needed as the sample tends to recover elastically and the vessel shrinks in length. If the piston is not satisfactorily retracted load can be placed upon the sample as the pressure is lowered, which in extreme cases could result in sample failure. 4.6 Large specimen apparatus: BigRig The large specimen rig, which will hereafter be referred to as BigRig, has been used as a triaxial seismic testing apparatus, measuring the velocity of seismic wave propagation through lower-crustal rocks (Khazanehdari 1996). The modification of the seismic rig to the triaxial BigRig required substantial modifications by R.F. Holloway. Figure 4.7 shows a detailed drawing and photo of the BigRig apparatus. BigRig can test materials at confining pressures of 500MPa, pore fluid pressures of 200MPa, axial loads of 300kN, and variable strain rates in the range 10-3-10-8s-1 at room temperature. The hardened steel pressure vessel has a large 50mm diameter ×250mm length bore and was supplied by Pressure Products of Glossop, UK, with a rating of 500MPa at 300°C. Hydrostatic confining pressure is created by compressing Reolube DOS low viscosity oil (η=30-35mm2.s-1) using an air pump and a 10× intensifier system. The oil is only suitable for low temperatures, and necessitated the use of Viton o-rings, as the oil reacts with Nitrile rubber (T. James, University of Manchester, pers. com, 1997). 25mm diameter cylindrical samples were jacketed using 3mm thick PVC tubing, sealed onto the piston ends by means of an o-ring. Confining pressure acting on the outside of the jacket seals the material onto the o-ring, allowing a different pore pressure within the sample compared to the confining pressure outside. The jacketing material


Printed MotorsTM DC motor

Support collar

a.

Primary gear box 50mm travel RSTM LVDT

Oilite bearings

Anti-rotation worm-and-wheel gear arrangement

Plan view

Main drive gear Secondary gearbox Pivot arm Recirculating ball-screw

0

50 100 150 200 mm

Closure nut

Upper block

Wood insulation Double walled steel shield

Sample Upper piston Lower piston Gearbox

Pressure vessel

Servo-controller computer display Signal 1 generator

Water cooling coils

Switchbox Display DVM’s Pressure display 1 Oscilloscope

Bottom block Pressure inlet

Servo-controller computer Pore-pressure generator

Printed MotorsTM amplifier

b.

Pore-pressure regulator

Pressure generator

Figure 4.7: Diagram of the BigRig apparatus. a). Detailed cross-section of the apparatus showing the added servo-controlled gearbox. b). Photo of the experimental rig showing all parts required to operate and log the apparatus. Note: 1 Used for seismic wave velocity calculation - not used in this study.


does not leak, unless pore pressure exceeds confining pressure. PVC is weak compared with the test material. Confining pressure is maintained within the pressure vessel by means of statically sealed closure blocks held in place by large nuts. The lower block has the confining pressure inlet pipe sealed within it, and supports the force gauge. The upper block houses the driving piston which is sealed using a moving seal similar to that used on the Heard-type apparatus. A 2mm bore within the upper piston allowed pore-pressure to be transmitted to the test sample. 4.6.1 Modification 1: Axial loading system BigRig was modified to perform axial loading tests on the pre-existing seismic rig by adding an axial loading system, consisting of a servo-motor and gearbox, and force gauge system. Due to time restraints, this system was not fully completed or implemented. For future reference the axial loading system is described in appendix A. 4.6.2 Modification 2: Pore fluid system Pore pressure (Pp) is generated within the test sample by the pore-pressure system (figure 4.8). A brief description follows of the system, which was more extensively described by Wanten (1996). The system comprises three distinct parts; the first generates the desired test pressure, the second consists of the sample assembly, the third maintains the pressure during the test. Test pressure was created by the compression of the pore fluid, either water or ethanol, by means of a 5cc capacity Nova SwissTM hand pump rated at 400MPa. Once a nominal 3.5MPa pressure is produced within the system the hand pump is isolated by means of a valve. As a sample compacts, its pore space reduces, thus reducing the total volume of the pore pressure system and raising Pp. Pressure was maintained by a second, servo-driven Nova SwissTM pore pressure regulator controlled by a Newport InfinityTM C Processmeter (ICP), that monitored the pressure measured by a 10MPa range RSTM pressure transducer. When pressure exceeds the limits set within the ICP (3.5±0.033MPa) the pore pressure regulator piston is driven in the corresponding direction to maintain constant pressure. The low volume of the pore system resulted in high pressure changes with small volume changes, resulting in an oscillating pore pressure as the pressure regulator attempted to maintain constant pressure (hunting). The volume of the system was therefore increased by introducing a 150ml external reservoir so that the corresponding


pressure change with volume change was suitably damped. The external reservoir desensitizes the response which gives more uniform results, and reduces the risk of accidentally overloading the 10MPa rated pressure transducer. In case of catastrophic failure of test samples, which would result in rapid pressure rises, a copper rupture disc was added to protect the pressure transducer. Pre-loaded thin copper disks are sealed over a 1mm bore, these hold pressure and were determined to fail at approximately 7MPa. The failure of the disks was found to be consistent to within 0.5MPa, and no deleterious effects were seen with work hardening or geometrical softening of the disk assembly over time. The arrangement of the valves within the pore pressure system allows parts of the system to be isolated during sample assembly, reducing the risk of air entering the system.

Copper ru p tu re d isc

V2

V3

To sam ple assem b ly

F lu id in le t rese rv o ir V 1

P re ssu re tran sd u c er

TM

N o v a S w iss h a nd p u m p

in o ut

S e rv o -c o n tro lle d TM N o v a S w iss p u m p

8 8 :8 8

D riv in g m o to r a n d g e a rb o x

P o ten tio m eter

R e serv o ir p ressu re v e ssel TM

N ew to n p an e l m e ter a n d co n tro lle r

Figure 4.8: Schematic representation showing the pore-pressure system of BigRig. Initial pressure is created by the hand-pump, which is isolated by V1 once operational pressure is achieved. Pressure changes created by the compacting sample raises pore-pressure, which results in the panel meter operating the servo-controlled pump to return pressure to operating levels. The copper rupture disc protects the pressure transducer in case of high pressure rises created by jacket failure.

4.6.3 System of measurement During hydrostatic compression tests there are three variables which are measured; confining pressure, pore pressure, and pore volume.


Confining pressure was measured outside of the pressure vessel by an Intersonde HP28 pressure transducer with a range 0-700MPa. The transducer was connected to a calibrated EurothermTM digital indicator, supplying the pressure transducer with 12V DC and giving a visual indication of pressure. A Bourdon tube pressure gauge connected into the pressure line also indicated pressure. A temperature compensated RSTM strain gauge pressure transducer measured pore pressure in the range 0-10MPa with an accuracy of 1%. The gauge was energized by a stabilized 10V DC supply, with the 0-100mV output displayed on a calibrated NewportTM Digital Panel Meter (DPM). Pore volume changes were measured by a potentiometer attached to the piston of the pore pressure regulator, energized by a stable 12V power supply. 4.6.4 Data logging The full servo-control system constructed to control the operation of BigRig is described in appendix A as the system was not utilized in this study. The experimental rig consisted of four transducers which measure force, confining pressure, pore pressure, and pore volume change. Data were relayed sequentially to a 5½ digit Thurlby ThandarTM computing multimeter (DVM) with a resolution of 0.001mV via a Time ElectronicsTM programmable switch. The switch array consisted of 15 double pole changeover relays which have a low resistance and a short operating time. Switching is implemented by the Archimedes 440 logging computer via an IEEE-488 connection, and data were transferred from the DVM in digital form to the logging computer via an IEEE connection. A secondary DVM logged any channel which required higher logging rates and was connected to the computer via the IEEE bus. Calibrated digital panel meters provide visual indication of the environmental parameters. Data were logged using the BigRigLog software running on an Archimedes 440 microcomputer. This program is similar to HeardLog3 (§4.5.2) and RockDef (Neumann 1994). 4.6.5 Machine limitations on the data Extensive calibrations were undertaken on the BigRig apparatus between September and November 1997. The pressure transducer connected to the confining pressure line was calibrated against a Bourdon tube Heise gauge by Khazanehdari (1996). This calibration was seen to be sufficient for this experimental study.


3

P ore p ressu re (M P a)

2.5 2 1.5 y = 0.0 83 35 - 0 .1 32 09

1

R 2 = 0 .9 97 58 0.5 0

a.

5

0

10 25 15 20 P ore p ressu re tra n sdu cer ou tp u t (m V )

35

30

P ore reg u la to r v olu m e (m l)

3 2 .5 2 1 .5 1

-5

2

-7

R 2 = 0 .9 9 9 93

0 .5 0

b.

y = 2 .5 4 8 4 1 ×1 0 x + 0.0 1 9 0 8 x + 4 .2 1 6 4 x 1 0

0

20

40

60

80

100

120

140

P oten tiom eter read ing (m V )

Figure 4.9: Calibration of the pore pressure system of BigRig. a). Calibration of the RSTM 10MPa pore pressure transducer. b). Calibration of the pore pressure regulator potentiometer.

The low pressure transducer attached to the pore pressure system was calibrated against a low pressure Bourdon tube gauge, in the pressure range 0-9MPa. Figure 4.9a shows the linear response found and the calibration constant for the pore-pressure transducer. The potential divider attached to the pore pressure volumometer system was calibrated by comparing the volume of fluid expelled using a manometer with the DC output from the potential divider (Figure 4.9b). During initial testing, anomalous results were noted, with oscillating pore pressures with day-long periods (Figure 4.10). Despite the laboratory being temperature regulated, the small-volume pore pressure system was unacceptably temperature sensitive. The nature of the pressure response was not easily described by temperature readings, making


calibration of the phenomenon extremely difficult. To overcome and minimize the effect, the pore pressure apparatus was lagged using a combination of polystyrene sheeting and bubble-wrap. The external reservoir was also placed within the double-skinned outer casing of the testing apparatus. Surface area exposure was dramatically reduced with the temperature sensitivity becoming much reduced. Observed variations were insignificant compared to the variations created during experimentation (e.g. adiabatic temperature change).

0 0:00

0.7

0 0:00

D ay 4

D ay 5 5 /11/97 - 05 :4 0

D ay 3

3 .7

3 .6

0.5

0

4/11 /9 7 - 10 :0 0

4 /11 /9 7 - 0 0:00

3 /11/97 - 1 5:00

2/11 /9 7 - 1 6 :10

3 /11 /97 - 0 5:00

S tart; 1/11 /9 7 - 1 6 :00

3 .4

2/11 /9 7 - 0 8:20

2/11 /9 7 - 01 :4 5

0.4

3 .5

3 .3

0.6

0.3 0.2 0.1

50

100

150 200 3 T im e (10 second s)

250

300

R esulta nt ob served volu m e ch an ge (m l)

P ore flu id pressu re (M P a)

1 2:00

D ay 2

D ay 1

E n d ; 5/11 /9 7 - 10 :2 0

3 .8

0

Figure 4.10: The variation in pore pressure, and resultant volume change, observed in the pore fluid system over a five day period before thermal insulation applied.

4.6.6 Design of the BigRig triaxial tests Two test types were conducted on the BigRig apparatus; hydrostatic pore volume expulsion tests, and hydrostatic borehole closure tests. 4.6.6.1 Hydrostatic pore volume expulsion tests Hydrostatic volumetric strain was investigated by monitoring the expulsion of pore fluids from the compacting samples. Saturated samples were assembled as shown in Figure 4.11a, and confining pressure of 5MPa applied to the samples within the pressure vessel. Pore pressure was raised to the operating 3MPa and the pore generator was isolated from the system. A few minutes were allowed for the entire system to equilibrate. Confining pressure was steadily increased, during which time the sample would compact and expel fluid. Pore pressure was kept constant by the pore pressure volumometer, which also measured the volume of expelled fluid. If fluid expulsion


exceeded the 5ml of the volumometer, the hand-operated pore pressure generator was used to 'back-off' the volumometer system. Tests were conducted with increasing confining pressure up to 500MPa limit of the experimental apparatus.

Fluid expelled to volumometer

Pore pressure inlet pipe

Fluid expelled to volumometer

Holding nut Seal

Top block

Spacer reducing risk of spalling material entering pore regulator system

Upper psiton

Pore pressure within sample vents to air around the outside of the pore pressure inlet pipe and through this hole

Upper bladder seal Bladder

Bored sandstone sample PVC jacketing material

PH2O bladder Brass end plug seal

0

10

20

30

mm

PH2O sample Seals

Lower piston

a.

b. Hydrostatic confining pressure acting on sample

Figure 4.11: Apparatus modification to measure porosity reduction with increasing hydrostatic confining pressure. a). The simple apparatus arrangement to monitor whole sample deformation. b). The bladder used to monitor bore closure, and the arrangement of seals to allow the sample to vent to air.

4.6.6.2 Hydrostatic borehole closure tests To investigate the deformation around the periphery of the bore, the borehole closure test was designed using the apparatus as shown in Figure 4.11b. As pressure increases, the response of the bore was monitored by measuring the volume of expelled fluid from a pressurized bladder within the hole. The bladder, which is made of silicon rubber with outer diameters of 3 or 5mm (according to hole size), was placed within the bore and sealed at the bore bottom using a brass plug, and at the piston end within the pore pressure inlet pipe. The nature of these seals necessitated a lower operating pore pressure of 1.5MPa. With compaction, the pore pressure within the sample is unknown,


so the sample was vented to air, with pore-fluid escaping around the edge of the pore pressure inlet pipe. Tests were conducted similarly to those of pore volume expulsion test, with pressure gradually increased to a maximum of 500MPa.

4.7 Data processing for triaxial compression tests The processing procedure aims to correct the dataset for the effects of the elastic distortions of the apparatus. Raw observed values (mV) are converted into Système International d'Unités (SI units), allowing the stress and strain experienced by the sample to be calculated. Data were processed in a spreadsheet using the following relationships. For more detailed explanation of data processing see Zhang (1988). The parameters of temperature (T), confining pressure (P), and displacement (D), and their corresponding initial values at the point of onset of load (To, Po, and Do), are computed from their simple calibration constants. The stress transmitted through the sample was calculated from the force gauge reading, which is corrected for the change in force gauge zero with pressure and temperature, and force gauge stiffness. Stress is defined as force per unit area i.e. the force applied across the cross-sectional area of the sample. With deformation, axial strain will be translated into radial strain (Poisson relationship), thereby changing cross-sectional area (Carea). Stress is:

σ=

FkN × 1000 Carea Eq.4.9

=Corrected cross-sectional area = Area0×(1 + ε) = (MF×FmV)×(1+(P×dMFdP)-(TM×dMFdT)) = Force gauge stiffness = [FGZ0+(((P-P0)×dFGZdP)+((TM-TM0)×dFGZdT))]-FGZ = Force gauge stiffness dFGZdP/dFGZdT = Force gauge change with pressure/temp dMFdP/dMFdT = MF change with pressure/temperature Carea FkN (kN) MF FmV

Strain is simply defined as the ratio of change in length to original length, with strain rate defined as the strain per unit time. Displacement of the system is corrected for the distortion of the pressure vessel due to pressure and temperature (MDispl), to generate a corrected displacement (CDispl) which corresponds to the displacement of the sample. Thus strain is:

ε=

δl CDispl = l length Eq.4.10

CDispl (mm) = Displ - [FkN x (MD x (1 - (P x dMDdP) + (T x dMDdT))] MD = Machine stiffness dMDdP/dMDdT = MD change with pressure/temperature


Mechanical constants and data analysis were calculated within a spreadsheet.

4.8 Petrographic and petrophysical characteristics of the starting material Three rock types, Tennessee, Darley Dale, and Penrith sandstones were chosen, due to their similar fabrics and homogeneous nature. These have approximate porosities of 7, 12, and 25% respectively, and average grain diameters of 75, 200, and 150µm respectively. Initial porosity (φ) was measured using three methods; (a) comparing dry and saturated densities (giving effective φ), (b) comparing volume of intact sample with the volume of crushed material determined using a density bottle (giving total φ), and (c) determining void proportion using scanning electron microscopy (giving total φ). Sample volume of cylindrical cores was measured using a micrometer giving accurate volume readings (±0.1%). Sample mass was determined using a balance with an accuracy of 0.01g (±0.01%). Pore-saturation was achieved by placing samples in a bath of ethanol or water within a vacuum for at least 20 minutes. The calculated values (table 4.1) are consistent with published results.

Sandstone type Penrith Darley Dale Tennessee

Porosity (method a) 28.2 13.8 7.65

Porosity (method b) 28.5 14 7.8

Porosity (method c) 25.2 11.3 6.8

Porosity (%) 28 13.5 7.5

Average grain diameter (µm) 129.6 171.4 74.66

Table 4.1: Porosity and average grain sizes for three sandstone types studied. Porosity method a compares dry and saturated densities, method b compares intact and crushed volumes, method c is determined using scanning electron microscopy.

Total porosity (φ), determined using the density bottle (method b) and scanning electron microscopy (SEM - method c) methods, should be greater than effective porosity (φ′) determined using the saturated volume method (method a). As shown in table 4.1, φ determined by method c is consistently lower than φ′ measured by method a. Underwood (1970) showed that porosity determined from a two-dimensional thinsection will correspond to porosity within the three-dimensional sample. Thus, this can not explain the discrepancy. It is probable that the SEM method is not observing all the pores present within the sample, variations of ±5% porosity were measured using this


technique. Thus, the SEM method is underestimating total porosity. Total porosity determined using method b is consistent with φ′ measured using method a. Average grain diameter (R) was determined using optical microscopy. R is approximated by dividing the total number of grains cutting the horizontal cross-hair by the width of the full-scale view (determined using a calibrated scale to an accuracy of 5µm). 80 measurements were taken at 40 localities within two slides of each rock type at two optical magnifications (×4 and ×10). The calculated average is displayed in table 4.1 with an accuracy of ±2.1µm, these values are consistent with published results. 4.8.1 Penrith sandstone

Figure 4.12: Photomicrograph of intact Penrith sandstone.

0

mm

0 .5

In hand specimen, Penrith sandstone is a friable rock with red coloration and no obvious sedimentary features. In thin section (figure 4.12), grain size is on average 130µm, although larger grains up to 300µm were observed. Granular sorting is moderate to high with subrounded to angular grains with low to moderate sphericity. Rock fabric is grain point and side contact supported, creating angular and low to high sphericity pores. Red staining (hematite) was observed around grain peripheries. Pre-existing


damage is slight, with some clusters of microfractures associated with grain contacts. Only one healed microcrack per 3-4 grains was typically observed. Mineralogically (table 4.2), the rock consists of 70% quartz, 15% feldspar, 5% clay, 3% hematite, and traces of chlorite and calcite. Both detrital and authigenic quartz was observed with quartz overgrowths common. Cement material consists of authigenic quartz, calcite, and other clay minerals. These observations are consistent with those of Hawkins & McConnell (1992).

Sandstone type Penrith

Quartz (%) 70

Feldspar Clay (%) (%) 15 5

Mica (%)

Darley Dale

70

20

6

3

Tennessee

75

10

8

3

Haematite Trace (%) mineral 3 Chl, Cal Kln, Cal, Chl

Cement Qtz, Cal, other clay Qtz, mica Lm, Qtz, mica

Table 4.2: Mineralogical constituents of sandstone types studied. Cal = calcite, Chl = chlorite, Kln = kaolinite , Lm = limonite, Qtz = quartz.

4.8.2 Darley Dale sandstone In hand specimen, Darley Dale sandstone has a yellow appearance with no clear sedimentary features. It is strong and non-friable. In thin section (figure 4.13), grains are on average 170µm, although larger grains up to 600µm were observed. Granular sorting is poor, with subrounded to subangular grains of low to high sphericity. Rock fabric is grain supported, creating sutured and indented point and side contacts. Angular pores of 13% volume are difficult to observe under the microscope. Grains show pre-existing damage, including fracturing seen on the rock surface, healed microcracks, red staining around pores, subgrains, and quartz dissolution. Localized clusters of intragranular fractures were observed, with some grains highly fractured, possibly before diagenesis. Indented grain contacts show undulose extinction within quartz similar to stress patterns observed in glass beads using photoelasticity (Gallagher et al. 1974). This implies stress formation of these features at grain impingements. Other grain contacts show impingement fractures indicative of local stress concentrations. Mineralogically (table 4.2), the rock consists of 70% quartz, 20% feldspar, 3% detrital mica and 6% clay, small amounts of kaolinite, calcite and chlorite were detected. Both monocrystalline and polycrystalline, detrital and authigenic quartz were observed. Crystalline quartz formed as


a fibrous phase in pore spaces with quartz overgrowths developing around existing minerals. The fine grained cement material consists of quartz. These observations are consistent with those of Wong et al. (1997).

Figure 4.13: Photomicrograph of intact Darley Dale sandstone.

0

mm

0 .5

4.8.3 Tennessee sandstone In hand specimen, Tennessee sandstone has an orange/red coloration with clear cross-bedding features. The fine grained rock is strong and non-friable. In thin section (figure 4.14), grains are on average 75µm in diameter, with larger grains up to 150µm observed. Granular sorting is moderate with subrounded to angular grains of low to moderate sphericity. Rock fabric is grain supported, creating angular and low sphericity pores which are difficult to observe under the microscope. Grains are mostly intact, although some display intragranular fractures associated with grain contacts. Other preexisting damage was noted, including healed microcracks, intergranular fracturing, dissolution and mineral alteration. Mineralogically (table 4.2), the rock consists of 75% quartz, 10% clay, and 3% detrital mica. Both monocrystalline and polycrystalline, detrital and authigenic quartz were observed, with small amounts of quartz overgrowth. The veryfine grained cement material consists of limonite, quartz, and possibly mica. These


observations are consistent with observations by Keaney et al. (1998) and Rutter & Hadizadeh (1991).

Figure 4.14: Photomicrograph of intact Tennessee sandstone.

0

mm

0 .5

4.9 Sample preparation All tests were conducted on cylindrical samples of material with differing diameters for the different testing apparatus. The aspect ratio of the core (length:diameter) has a significant effect on the stress and subsequent strain distribution within the sample, Jaeger & Cook (1979) summarize this problem. Poirier (1985) states that a 3:1 ratio produces the optimum balance between sample buckling and bulging. However, samples used during the hitpoint method were prepared with a 4:1 aspect ratio as no axial loading would be made on the sample. This was calculated as the maximum length possible, giving machine limitations. The additional length increased the change in length with volumetric strain, thus amplifying the sensitivity of the test. Table 4.3 summarizes the sample dimensions used during the different tests. Samples for both tests conducted on Heard III and BigRig have dimensional restrictions imposed by the testing apparatus and jacketing material. The uniaxial unconfined tests were not jacketed and samples were prepared with cross-sectional areas as large as


possible to maximize the accuracy of load measurement and minimize effects of sample heterogeneities.

Testing apparatus Heard III BigRig Uniaxial I Uniaxial II Brazilian tests

Test type/material Triaxial Hitpoint All PenSS TenSS/DyDSS All All

Diameter (mm) 9.5 9.5 25 50 36 25 25

Length (mm) 22-25 30-35 60-65 100-110 70-80 60-65 10

Table 4.3: Dimensions of the test samples.

Cylindrical cores were cut perpendicular to bedding from the test material using a high speed diamond-tipped, water-lubricated coring tool. The large cores used for unconfined uniaxial tests were found to be too rough, with circumferential weaknesses created by the coring process. The samples were further ground using a Universal cylinder grinder with a diamond wheel. This greatly improved the sample surface. This machine uses a oil based lubricant, so samples were cleaned in alcohol and water to remove any absorbed oil. Samples were cut to length using a fine saw blade. Core ends were squared off and planed using a V-block and ‘wet or dry’ paper or a diamond wheeled AbwoodTM horizontal grinder. Six readings of length and four readings of diameter at each end and in the middle of the sample were recorded using a MitutoyoTM digital micrometer with an accuracy of 0.01mm. More dimensional readings were taken for the larger samples. Results were averaged and standard deviations calculated for the diameter and length of each sample. Strain gauges were cemented to the sides of the unconfined uniaxial test cores shortly before use. During the final preparation stage of the 9.5mm cores, Penrith sandstone was found to be very weak and friable with material plucking from the corners of sample. Under confining pressure, the copper jacketing material was also forced into the gap created between the corner of the sample and the sharp piston corner, resulting in jacket failure. Therefore it was necessary to reinforce the sample corners with strain gauge P-2 resin. Once dry, the samples could be finished off with sharp corners.


Axially symmetric bores were drilled in 25mm diameter cores using masonry drills. The core was clamped into a lathe and drilled to ensure the bore was centred within the sample. Robertson (1955) showed that an outer to inner sample diameter should be 4:1. Bores were therefore drilled to a maximum of 6mm diameter to maintain a low bore to diameter ratio, ensuring deformation did not propagate immediately to the outer diameter of the core, thereby affecting the test. Samples must act as if the bore was within an infinite plate with no local boundary conditions. Bores were drilled 0.6 of sample length, to observe bore-bottom effects and to have intact rock to compare with the material around the periphery of the bore. All cores were stored in an oven until immediately prior to use to ensure that no atmospheric moisture entered the sample. BigRig, uniaxial, and Brazilian samples were vacuum saturated for 20 minutes with pore fluid immediately before testing to ensure full saturation of the material. Excess fluid was dried from the outside of saturated uniaxial tests to ensure that no short-circuiting of the strain-gauge connection occurred. 4.10 Sample recovery and thin section fabrication The copper jacketed samples were cut from the piston assembly using a handsaw. Care was taken not to damage the pistons and to ensure full recovery of the unbroken sample. PVC jacketed samples were carefully removed from the pistons. End length measurements were taken using a digital calliper, and samples were visually examined to ascertain whether pressure fluid leakage had occurred and the condition of the sample. Samples were vacuum impregnated with resin prior to the making of the thinsection. Heard test samples were vacuum impregnated in a bath of Araldite resin, while BigRig samples used LR White resin. Keystone blue A die was added to the Araldite. Bores samples were cut radially using a water lubricated fine diamond-edged saw, with axial cuts perpendicular to features of interest being made on other samples. All jacketing material was removed prior to the fabrication of thin sections. The cut surface was initially ground on a CutrockTM diamond grinding mill, and ground flat to a 1000 grade finish using silicon carbide powder. This ground surface was glued to a 400 grade polished standard thin section slide using DevconTM epoxy resin. Samples were finished to a 30µm thickness using 4F, 1000, and 1200 grade Al2O3 polishing powder by hand on glass plates. Samples were finished using a Buehler Ecomet IIITM polishing mill, and carbon coated for examination in the scanning electron microscope (SEM) as required.

Intact Results: Chapter 5 126

5. The experimental deformation of intact sandstone To describe the mechanical deformation of the intact sandstone, three types of tests were performed. These tests were (a) uniaxial compression, (b) constant displacementrate, and (c) hydrostatic compression. Results from these tests, and inferences derived from other studies, are sufficient to describe the mechanical behaviour of the intact material. Results of deformation experiments on intact material are presented below. Each experimental study is presented separately, with comparisons made between each method.

5.1 Uniaxial compression experiments Two types of unconfined uniaxial deformation experiments were conducted. The uniaxial compression test describes the elastic properties of materials in a compressional sense, while the diametral compression test, hereafter referred to as the Brazilian test, describes the tensile properties of materials. Both sets of experiments are run until ultimate failure occurs. 5.1.1 Unconfined axial compression experiment To describe the unconfined uniaxial deformation of the test material a total of 17 tests were conducted, the results are summarized in table 5.1. Two tests were made on oven-dry samples, with singular tests made both water and alcohol saturated to investigate pore chemistry effects. To test for elastic anisotropy in oven-dry Tennessee sandstone two tests were conducted in each of three orthogonal directions. Of the 17 uniaxial tests, three experiments failed due to logging problems with the force gauge. Experimental results showed high degrees of reproducibility. 5.1.1.1 General form of the uniaxial stress-strain curves Figure 5.1 shows a summary of the results obtained for the three sandstones under oven-dry conditions, and the interpretation of the stress strain curve for Tennessee sandstone. Figure 5.1a shows the uniaxial stress-strain relationship for the three sandstones, showing high levels of reproducibility. The materials display similar stressstrain responses with variations in overall strength, which decreases with increased porosity. Tennessee sandstone is approximately three times stronger than Penrith sandstone, and twice as strong as Darley Dale sandstone. With only three rock types, it is difficult to ascertain the relationship between strength and physical material


characteristics. However, these sandstones show a tentative relationship between strength and amount of grain contact as shown by Dyke & Dobereiner (1991) and Zhang et al. (1990). Lower porosity rocks generally have higher degrees of grain contact, which can be estimated by the product of grain radius and porosity, and will thus be stronger.

Rock type

Test No.

Direction

Pore fluid

Uniaxial Young’s Poisson’s Bulk strength modulus E modulus ratio ν (MPa) (GPa) K (GPa) RJC A12u Oven dry 28.3 6.05 0.173 3.09 Penrith RJC A16u Oven dry 28.4 5.89 / / RJC A36u Water 9.37 / / / RJC A37u Ethanol 9.09 / / / RJC B14u Oven dry 48.1 10.5 0.092 4.29 Darley RJC B15u Oven dry 47.9 11.4 0.098 4.71 Dale RJC B28u Water 37.6 7.07 0.128 3.17 RJC B29u Ethanol 38.7 / / / RJC C17u N-dir Oven dry 89.9 6.66 0.078 2.63 Tennessee RJC C18u N-dir Oven dry 88.4 6.49 0.091 2.64 RJC C40u N-dir Oven dry 91.2 7.73 0.053 2.89 RJC C41u P-dir Oven dry 106 9.94 0.059 3.76 RJC C42u P-dir Oven dry 107 9.69 0.046 3.56 RJC C44u P-dir Oven dry 98.6 11.5 0.07 4.46 RJC C43u R-dir Oven dry 86 11.9 0.085 4.79 RJC C46u N-dir Water 69.4 6.06 0.083 2.43 RJC C45u N-dir Ethanol 83.9 6.88 0.039 2.49 Table 5.1: Results of the unconfined uniaxial compression tests. Direction for Tennessee sandstone is defined in 5.1.1.4 (pp.133).

The basic geometry of the stress-strain curves (figure 5.1b) is consistent with the observations of Dobereiner et al. (1990), and Dyke & Dobereiner (1991) for sandstone, and Rutter (1993) for granite. Initially there is a significant difference between axial and diametral strains as axial load is translated into the closure of pre-existing microcracks and simple pore-elastic compaction, as opposed to being translated into diametral extensional strain. The translation of axial load to diametral strain as expected for perfectly elastic materials does not initiate until pre-existing microcracks and some porespace closes. With closure, stress concentrates within the grain framework, resulting in elastic deformation, as observed by the linear elastic region of the curve. Existence of this region is not strongly evident, and is rapidly superseded with the formation of new fractures which initiate at applied stresses below about one third of the uniaxial strength. New fractures signify the onset of dilatancy, with permanent damage progressively accumulating in the sample. Initially damage accumulation is slow, with axial cracks forming. At stresses approximately half uniaxial strength, the density of dilatant microcracks results in sample volume increase.


Failure of Tennessee sandstone

90

Diametral strain ed

Stress s (MPa)

80 70 60

Volumetric strain ev

50

Axial strain ea

Failure of Darley Dale sandstone

40 Failure of Penrith sandstone

30 20 10

a. -0.008

Penrith sandstone Darley Dale sandstone Tennessee sandstone

0

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.008

0.01

0.012

Strain e

90 Diametral 80 strain

Axial strain

Volumetric strain

70

High degree of reproducibility

Slow propagation of microcracks

Stress s (MPa)

Fast propagation of microcracks

60

Irrecoverable deformation

Onset of volume increase

50 40

Onset of dilatancy

30 20

Elastic region

10

b. -0.0075

Failure

Uniaxial compressive strength qu

Closure of microcracks

-0.005

-0.0025

0

0.0025 Strain e

0.005

0.0075

0.01

0.0125

Figure 5.1: Stress-strain relationship of the unconfined uniaxial compression of three sandstones. a). Stress-strain results showing high levels of reproducibility and similar responses for all three rock types with variations in overall strength. b). Interpretation of stress-strain curves for Tennessee sandstone using observations of the deformed sample, anomalous response of Penrith sandstone (figure 5.2), and observations of Dyke & Dobereiner (1991).


At approximately two-thirds uniaxial strength, deformation accelerates. Diametral strain increases as void closure allows axial stress to be translated into diametral strain. Void closure increases grain contact, and thus stress concentration, resulting in the formation of new tensile microfractures. Damage accumulated per strain increment increases, and these propagate at a higher velocity. Fractures continue to interact until macroscopic failure occurs, relieving sample stress. 30

S tress σ (M P a )

P re m a tu re failure

C o nsta n t v o lu m e d efo rm a tio n

25 D ila tio n II 20

D ila tio n I

15 A n o m a lo u s resu lts

Vo lu m e tric strain εv

D iam etral strain εd

A x ial strain εa

O n se t o f loc alised de fo rm a tio n

10

5

P e n rith sa nd sto n e te st R JC A 1 2 P e n rith sa nd sto n e te st R JC A 1 6

0 -0 .0 3 5

-0 .0 3

-0 .0 2 5

-0 .0 2

-0 .0 1 5

-0 .0 1

-0 .0 0 5

0

0 .0 0 5

0 .0 1

S tr a in ε Figure 5.2: Anomalous result of uniaxial test RJCA12. One strain gauge is indicating a localized feature which highlights the onset of localized deformation, and two dilatation events.

Figure 5.2 shows the results obtained for Penrith sandstone. One test shows anomalous features which help to explain the form of the stress-strain curve in relation to the observations of Dyke & Dobereiner (1991). At the onset of dilatancy there is significant deformation recorded in the diametral plane, at higher stresses the two test results differ with respect to circumferential strain but are comparable with respect to axial strain. This indicates a circumferential strain gauge was positioned over a localized deformation event, such as a fracture, and thus the data indicate localized diametral strain. Therefore, the identified onset of localized deformation signifies the onset of dilatancy with the formation of a microfracture under the strain gauge. This fracture opens, until at a stress level approximately half uniaxial strength, the fracture apparently closes. A secondary opening is observed, followed by closure. Finally


catastrophic opening causes macroscopic failure. Dilatation event I occurs during the slow propagation of microcracks, with dilatation II highlighting the onset of fast microcrack propagation as implied by the enhanced dilatation rate. Between the two dilatation events approximately constant volume deformation occurs. P lan view o f rad ially c ra ck e d se g m en t

Tw o co n ica l fea tu res cre ated

S m all ax ial c ra ck s

T h in a xia l c ra ck s

θ

C rac k s o rie n ta te d a t θ, th e fau lt an g le

A p p are nt fra ctu re o rie n ta tio n

S p a lled seg m e n t

A p p are nt fra ctu re su rfa ce c o nn e cts o p p osite co rn ers o f th e c y lin drica l sa m p le Figure 5.3: Representation of the failed sample. The sample has failed by the creation of two orientations of cracks; at an angle equal to the fault angle, in the axial direction. These orientated fractures communicate creating a pair of conical shaped blocks. The apparent fracture orientation of the conical body simply traverses from the corners of the sample. Triangular segments also form.

5.1.1.2 Observations of the failed samples Examination of fracture orientation within deformed samples allows deformation mechanism to be inferred. Figure 5.3 shows a summary of the geometry of the failed samples, which were not significantly different between the three rock types. Millimetre scale fractures within the sample were oriented in three directions; axially, circumferentially, and approximately at the fault angle (≈30° to axial load). Communication of the three oriented fractures divided the sample into a number of geometric bodies. Conical shaped blocks formed at either end of the sample, with the rest of the cylindrical body breaking into pieces as shown in figure 5.3. The cone is made up of a series of fault-angle oriented fractures which communicated with axial fractures to create the stepped-conical shape. The conical surface interconnected the opposing corners


of the cylindrical sample. This observation is consistent with Peng & Johnson (1972), who attributed the cone-crack formation to frictional effects created at the sample-platen interface. Stress concentrations at the sample corners, and non-uniform stress distribution within the sample, results in a cone-in-cone feature. Peng & Johnson showed different deformation modes with different frictional components. Therefore, the observed features are possibly a result more of experimental conditions than of deformational characteristics. Thus the triaxial experiments may describe deformation mode more accurately. The sandstones were seen to deform by the creation of axial and fault angle oriented microcracks which communicated to create macroscopic failure. No significant differences were observed between rock types, indicating similar deformation mechanism in brittle unconfined conditions. Slight differences were observed between materials associated with the ‘cleanness’ of fracture, which showed stronger materials fractured with planar cracks and less granulation, with the weak Penrith sandstone generating significant amounts of loose sand at failure. 5.1.1.3 Calculation of the uniaxial elastic moduli The fundamental elastic constants (Young' s modulusE, Poisson' s ratioν, and bulk modulus of compressibility K) were calculated using the method described in Ch.4.2.3. Figure 5.4 summarizes graphically the calculation of the elastic moduli for the elastic region of uniaxial deformation of Tennessee sandstone. Young’s modulus is the slope of axial stress versus axial strain, Poisson' s ratio is the ratio of axial to diametral strain, bulk modulus is related to E and ν. Values are taken where the slope of E is at a maximum, to account for initial non-linearity. Figure 5.4 shows a non-constant apparent ν, implying that the amount of diametral strain created by axial stress is changing during the test, and a good fit for E. For a nonporous elastic medium, Poisson’s ratio should be constant as axial strain is translated into diametral strain. The product of two effects creates the non-constant ν. 1). Void space tends progressively to close resulting in axial stress not being fully translated into diametral strain so that apparent ν is anomalously low. 2). Friction created between the sample ends and loading platens restricts the movement of the sample ends, resulting in ‘barrelling’ instead of the assumed perfectly homogeneous deformation in axial crosssection. The circumference of the sample will thus not be constant along its length, being


greatest at its centre (where the strain gauges are cemented), and least at its ends where friction acts. Therefore progressive barrelling will create an increasing apparent ν initially

0 .2

26 24

E lastic reg io n

E lu s du ’s ng

18

od lk m u b e of S lo p

12

0

10 0

10

20

30

A xia l S tress σ (M P a )

0 .0 0 3

40

y= 6 57 0.8 x-7 .22 72 R 2 = 0.99 61

ou

16 14

0 .0 5

A x ial strain εa

mo

20

fY

0 .1

22

eo

P o int o f m a x im u m slo p e

op

0 .1 5

Sl

L in e arly in crea sin g P o isso n ’s ratio

S tress σ (M P a)

A p p a ren t P oisso n ’s ratio ν ( εd / εa )

in the elastic regime and progressing into the inelastic regime.

u lu s

0 .0 0 4

K

0 .0 0 5

S tra in ε

Figure 5.4: Calculation of the elastic constants for Tennessee sandstone using unconfined uniaxial compression stress-strain data. Poisson’s ratio (ν) is taken where the slope of axial strain with stress is maximum. Bulk modulus K is calculated from values for Young’s modulus (E) and ν.

Table 5.2 shows the calculated elastic constants for oven-dry samples in uniaxial compression. Recorded results are comparable with published data for Bunter (Yates 1992) and Penrith (Dyke & Dobereiner 1991) Sandstones.

Units

Penrith sandst.1 5.971 3.086 0.173 28.35

Darley Dale sandst.1 10.95 4.501 0.095 47.99

Tennessee sandst.1 6.959 2.719 0.074 89.86

Bunter sandst.2 10

Penrith sandst.3

E GPa Young’s modulus K GPa Bulk modulus Poisson’s ratio ν qu MPa 65-87 38.5 Uniaxial compressive strength Table 5.2: The fundamental elastic constants calculated from uniaxial compression data (oven dry). 1this study. 2Yates (1992). 3Dyke & Dobereiner (1991). Note: Tennessee sandstone is expected to show significant elastic anisotropy and measurements are quoted perpendicular to bedding. Anisotropy will be less apparent in Darley Dale and Penrith sandstones.

5.1.1.4 Uniaxial compression elastic anisotropy Tennessee sandstone has a slight bedding feature which allows a reference plane to be determined. No such feature is seen in Darley Dale and Penrith sandstones. Elastic anisotropy was investigated for Tennessee sandstone with respect to the reference direction. Penrith sandstone cores from different source blocks were not always cut in


the same direction, but the reproducibility of the uniaxial results for Penrith sandstone suggests that this material is mechanically isotropic. Figure 5.5a shows the results for Tennessee sandstone obtained in the three orthogonal directions. The calculated elastic properties are shown in table 5.1 and 5.3. Three tests were conducted in the ‘normal’ direction (N-direction), which was the orientation of all other test cores. Two tests were conducted in the reference (bedding) plane (R-direction) parallel to the dip direction. Two tests were conducted on cores parallel to bedding but perpendicular to the R-direction (P-direction), representing strike of the bedding (see figure 6.14).

Rock type

Directn

Pore fluid

Uniaxial Young’s Poisson’s Bulk Tensile strength modulus E modulus strength ratio ν (MPa) (GPa) K (GPa) (MPa) N Oven-dry 89.9 6.67 0.074 2.72 4.34 Tennessee R Oven-dry 92.3 11.7 0.085 4.79 3.98 P Oven-dry 106 9.81 0.058 3.92 3.78 N Water 69.4 6.08 0.083 2.43 1.62 R Water / / / / 1.49 P Water / / / / 1.09 N Ethanol 83.9 6.88 0.039 2.49 2.71 R Ethanol / / / / 2.78 P Ethanol / / / / 2.07 Oven-dry 47.9 10.8 0.095 4.5 2.47 Darley Water 37.7 7.07 0.128 3.17 0.53 Dale Ethanol / / / / 1.52 Oven-dry 28.4 5.96 0.173 3.09 0.61 Penrith Water / / / / 0.03 Ethanol / / / / 0.08 Table 5.3: Elastic constants for three sandstones determined from uniaxial unconfined tests.

Variations in stress-strain response in the different directions are observed (figure 5.5a) showing significant elastic anisotropy. N-direction tests gave similar results showing the high degree of reproducibility. Deformation in the P-direction is similar to the N-direction, with the samples showing slightly different axial strains, but overall this direction is significantly stronger and stiffer than the N-direction. Results for the Rdirection show significant spread, as deformation in the diametral sense occurs at a lower stress level for one of the samples. Overall the R-direction is intermediate in uniaxial strength between the N and P-directions, but is the stiffest of the three directions. The failed samples show no significant differences in deformation mode, thus the spread of results is created by slight differences in degree of cementation. The


120 Spread of results

High reproducibility Diametral strain

Axial load (MPa)

100

Good reproducibility

80 n

N-dir - RJC C17u

60

n

N-dir - RJC C18u c

Axial strain

Vol 40 strain

P-dirn - RJC C41u n

P-dir - RJC C42u n

R-dir - RJC C43u

20

n

R-dir - RJC C44u

a.

0

-0.005

-0.01

0.01

0.005

0

0.015

Strain

100

Enhanced failure rate

90

Diametral strain

b.

70

Onset of premature failure

60 50 Volumetric strain

40

Axial strain

30

Oven-dry - RJC C17u

20

Ethanol saturated - RJC C45u

10

Water saturated - RJC C46u

0

-0.005

-0.01

Axial load (MPa)

80

0

0.015

0.01

0.005

Strain

R-dirn

35

P-dirn

N-dirn

Water

Ethanol

E x

yE

x 83

6

Dry N-dirn - RJC C40u

=

=


68

5 07

Dry P-dirn RJC C41u

yE

= yE

x

.1

66 67 .8

8.9 81 =9

20

yE

=1 174

6x

x


25

yE

Axial stress (MPa)

30

15

n

10 5

K

Dry R-dirn RJC C43u n

N-dir Ethanol Water

o

km

Bul

us dul

Dry P-dir RJC C42u

R-dirn P-dirn

0

0

0.001

0.002

0.003 0.004

Ethanol satd - RJC C45u Water satd - RJC C46u

(Transposed along abscissa)

c.

Dry R-dirn RJC C44u

0.005

0.006

0.007

0.008

0.009

Axial strain/Volumetric strain Figure 5.5: Results of uniaxial deformation of Tennessee sandstone in orthogonal directions with different pore fluids. a). Differences in stress-strain results in orthogonal directions showing elastic anisotropy. b). Differences in stress-strain result with pore fluid content. c). Calculation of the elastic constants for Tennessee sandstone in orthogonal directions with different pore fluids.


reference direction was determined from a slightly dipping band within a core that is otherwise mostly horizontally bedded within the N-direction cores. The R-direction cores could have been taken in such a way that one core is through the dipping layer seen in the N-direction, while the other was taken through the horizontal layers. Figure 5.5c shows there are significant variations in the elastic constants in the different directions. The R-direction shows the stiffest characteristics and is approximately 1.7 times stiffer than in the N-direction, with P-direction being intermediate. These results, and those of figure 5.5a, demonstrate significant elastic anisotropy in Tennessee sandstone. 5.1.1.5 Moisture effect on uniaxial strength The effect of pore fluid on the elastic properties was investigated on all three rocks. However, three tests failed on Penrith sandstone and Darley Dale sandstone, resulting in a full data-set only for Tennessee sandstone. Figure 5.5b shows that the stress-strain response is different using the three pore fluids. Water saturation promotes both axial and diametral strain, resulting in failure at a much lower stress. Volumetric strain is enhanced at stress levels greater than 45MPa compared with oven-dry. This indicates that water accelerates failure once fracturing and microcracking begins. This acceleration of volumetric strain was also noted, and was more pronounced, for ethanol saturated tests. However, ethanol shows generally stronger characteristics than oven-dry up to a stress of 70MPa, where upon accelerated deformation begins. Figure 5.5c shows that, although overall strength is affected by pore fluid, the elastic characteristics remain unaltered. Both bulk and elastic moduli are not significantly altered, indicating that pore fluid content only becomes significant once new fractures begin to form.

5.1.2 Diametral compression test; Brazilian test To describe the tensile mode I behaviour of the samples in unconfined conditions 30 Brazilian tests were conducted on 25mm diameter cores. Mode I tensile fractures form when σx≠0, σy≠0, σz≠0, and τxy=0. For all three rocks two tests were conducted each oven-dry, water and ethanol saturated. For Tennessee sandstone two tests were conducted in orthogonal directions with all pore fluids. All tests were successful.


5.1.2.1 General form of the Brazilian stress-strain curves Figure 5.6a shows the response of the sandstones to axial load. Initially there is a non-linear response as the specimen end and experimental apparatus ‘bed in’ and porosity and pre-existing damage closes. The experimental artefact highlighted for Penrith sandstone (figure 5.6a) is evident in all rock types and tungsten carbide at the same stress level. When sample stress equals gravity force produced by the weight of the main loading gear, the slack within the ballscrew is taken up, resulting in a stress drop. With the removal of slack load increases. This feature is purely a machine artefact, and should not affect the stress level at which the sample fails. 5.1.2.2 Moisture effect on tensile strength Figure 5.6b shows the tensile strength results for the three rocks using three pore fluids. The spread of results for oven-dry conditions is generally more significant than when the samples are saturated with pore fluids. Paterson (1978) concluded that the reproducibility of Brazilian test results is often poor due to the assumption that the stress distribution prior to fracture corresponds to that of the purely elastic state. Mellor & Hawkes (1971) showed that results can vary with specimen preparation, test procedure, and equipment used. Thus, reproducibility may have been affected by contamination of the samples prior to the start of the tests and subtle variations in experimental set-up. Atmospheric moisture will be absorbed by the samples with time, as will body moisture as the samples are handled during dimensional measurement. The amount of time and handling prior to testing may not be constant, and so some samples might be contaminated more than others. These observations of spread for results also appear in figure 5.6c for the orthogonal directions within Tennessee sandstone. Saturation with pore fluid will minimize the effect of contamination. Differences in experimental set-up may affect stress distribution within the samples, and samples oriented differently may fail at different stress levels. In general, ethanol saturated samples showed 60% of the tensile strength of ovendry for Tennessee and Darley Dale sandstones, with water saturation showing approximately 35%, and 20% respectively. Penrith sandstone showed the most pronounced weakening, with ethanol and water saturated samples showing 15% and 4% of dry strength respectively. Therefore, water promotes tensile fracture most for Penrith sandstone, followed by Darley Dale and Tennessee sandstones. Ethanol also affected Penrith sandstone more than the other rock types.


Tens ile stren g th T (M P a )

0 .8

6

2 .5

0 .9

D arley D ale sa n dsto n e

P enrith sa n d ston e

Ten nesse e san d sto ne 5

2

0 .7 0 .6

4 1 .5

0 .5 3 0 .4 1 0 .3 0 .2

2

E x pe rim en tal artefac t

0 .5

1

0 .1

a.

0

0

0

T im e

sec s

0

30

Ten nesse e san d sto ne

W a te r sa tu ra te d

sig n ifican t sp read

E th an ol sa tu ra te d

O ven d ry

D arley D ale san d sto ne

P enrith san d sto ne

b.

0

1

2

3

4

5

6

4

5

6

Ten sile stren gth T (M P a )

R e feren ce d irec tio n

Pd irec tio n

N o rm al d irec tio n W a ter saturated

c.

0

1

E th a n ol satu ra te d 2

O v e n dry

3

Ten sile stren gth T (M P a )

Figure 5.6: Results of the tensile Brazilian test. a). Form of tensile strength versus strain results for three sandstones. The highlighted experimental artefact is created by the loading system of the apparatus. b). Results of Tensile strength for three sandstones. Pore fluid has a significant affect on tensile strength. c). Tensile strength of Tennessee sandstone in the orthogonal directions.

5.1.2.3 Tensile strength anisotropy Figure 5.6c shows the results obtained in the three orthogonal directions for Tennessee sandstone. Although not conclusive, generally the R and N-directions are similar, with the P-direction being weaker. This suggests initiated fractures are likely to


form in the P-direction. Results for all three directions oven-dry are similar, suggesting fluid weakening is more significant in the P-direction. 5.1.2.4 Observations of the failed samples All samples failed through the creation of a single mode I fracture running directly from the point of contact between the loading piston and sample edge traversing through the centre of the sample. Both Tennessee and Darley Dale sandstones failed cleanly, while Penrith sandstone tended to produce large quantities of sand at failure. Some Tennessee sandstone samples in the P and R-directions showed smaller fractures created in the direction of the bedding features, particularly along the darker-red bands. This suggests the red banding feature is weaker than the bulk-rock, and failure tends to initiate from this source.

5.2 Constant displacement-rate experiments The constant displacement-rate experiment, which is comparable to a constant strain-rate test, allowed the sandstones to be studied for the effect of confining pressure and axial load. The effects of temperature and strain-rate were not investigated in this study as brittle deformation tends to be relatively insensitive to these parameters (Paterson 1978). Constant displacement-rate tests were conducted at room temperature with strain rates of 3×10-4s-1 at constant confining pressures of 25-300MPa. Tests were conducted without pore pressure, with samples vented so as not to create an unpredictable pore pressure within the sample. In total 39 constant displacement-rate tests were conducted on the three sandstones, in addition 15 tests were conducted to progressively increasing strains to study development of microstructural features. Of the 20 tests conducted on Penrith sandstone, one test failed due to a split jacket that had been punctured during the assembly process. Of the 18 tests conducted on Tennessee sandstone, one test failed due to jacket failure, and one test gave anomalous results. Of the 16 tests conducted on Darley Dale sandstone, only one anomalously low failure stress result was recorded. The results of these tests were converted into true stress/conventional strain values (using method of Ch.4.7) and are summarized (table 5.4) and represented graphically in figure 5.7.


Sandstone type Penrith

Test Confining Stress at strain of number pressure 2% 5% 10% 20% 30% RJC A08 23.4 70 78 75 75 86 RJC A21 41.5 78 84 94 112 123 RJC A04 41.6 41 49 58 73 92 RJC A20 71.1 71 89 112 156 181 RJC A07 84.8 92 103 125 171 215 RJC A27m 89.9 69 RJC A25m 90.4 63 81 117 RJC A24m 90.2 66 85 125 183 RJC A06 104.1 100 125 156 218 283 RJC A03 108 91 118 154 202 238 RJC A19 109.4 49 71 116 183 215 RJC A02 141.5 61 97 140 232 RJC A18 142.3 62 102 171 274 317 RJC A17 172.7 52 104 187 323 365 RJC A01 192 68 114 RJC A10 212.5 63 119 222 372 418 RJC A22 240.7 82 155 267 420 442 RJC A09 280.3 89 167 276 464 485 Darley Dale RJC B11 38.9 171 155 155 RJC B04 78.5 166 236 227 RJC B18m 100.4 235 RJC B19m 100.4 284 RJC B20m 100.5 223 293 280 RJC B21m 100.4 250 282 273 RJC B06 104.5 76 137 167 185 RJC B10 108.1 225 282 288 278 RJC B05 140.5 252 320 347 352 RJC B09 172.3 223 340 377 390 RJC B12 202.4 261 388 436 401 RJC B08 233 265 391 466 487 RJC B07 254.6 222 359 459 477 RJC B13 276.1 261 397 503 515 Tennessee RJC C14 44.5 178 185 RJC C03 69.9 291 215 205 RJC C04 73.6 230 221 212 RJC C15 75.8 246 297 RJC C21m 100 312 RJC C20m 100.2 386 RJC C19m 100.6 357 327 RJC C13 106.7 338 447 RJC C05 132.6 385 505 422 RJC C10 173.2 470 450 RJC C06 213.7 595 585 RJC C09 240 520 682 RJC C08 260.8 514 731 630 RJC C07 275.7 530 477 Table 5.4: Table of test results for stress/strain curves generated during constant displacement-rate tests. Test numbers including suffix ‘m’ are microstructural experiments that have been conducted to different strains at given confining pressures (note: these tests are not taken to ultimate failure).

0

100

200

300

400

RJC A08

@28MPa

RJC A20

@71MPa

RJC A19

@109MPa

RJC A18

@142MPa

0.4

0

100

200

300

400

500

600

0

0.05

RJC B10

@106MPa

RJC B05

0.15

Strain e

0.1

0.2

0.25

Darley Dale Sandstone

RJC B11

@39MPa

RJC B04

@79MPa

RJC B09

@141MPa

@173MPa

RJC B12

RJC B08

@203MPa

@233MPa

RJC B13

@276MPa

Stress s (MPa)

Stress s (MPa)

Figure 5.7: Stress-strain behaviour of three sandstones.

0.5

Penrith Sandstone

RJC A21

RJC A17

@173MPa

RJC A10

@213MPa

RJC A22

@241MPa

RJC A09

@281MPa

@41MPa

0 0.2 0.1 0.3 Cross-over of results -dilatation to compaction Strain e

Stress s (MPa)

500

0

100

200

300

400

500

600

700

800

0

0.02

Yield strength

RJC C14

@44MPa

RJC C03

@70MPa

RJC C15

@76MPa

RJC C13

@107MPa

RJC C10

@173MPa

RJC C09

@240MPa

RJC C06

@214MPa

RJC C08

@261MPa

Residual strength

Strain e

0.06

0.08

0.1

Tennessee Sandstone 0.04

Peak strength



5.2.1 General form of the stress-strain curves Several characteristics can be noted about the form of the stress-strain curves, including; stress level and strain at failure, and mode of failure as reflected by the form of the curve. The three rocks show a marked difference in the amount of strain prior to failure by faulting. Penrith sandstone is weakest, with tests being conducted up to 50% strain. At such a high strain in triaxial compression there will be significant effects created by the experimental apparatus, such as jacketing and piston-end effects, and heterogeneous strain to a degree that renders stress data meaningless. Therefore, there is a limit to the amount of strain that tests can usefully be taken to. Tennessee sandstone shows the greatest strength, with peak stress and failure by faulting occurring at less than 5% strain. Darley Dale sandstone is intermediate in strength and strain before faulting. All three rocks display a linear portion of the stress-strain curve which represents elastic deformation in accordance with Hooke’s law, followed by permanent inelastic deformation. 5.2.1a Penrith sandstone Penrith sandstone (Figure 5.7a) clearly shows a mechanical change within the range of tests conducted. At the lowest pressure (28MPa) the mechanical behaviour is elastic-strain softening-strain hardening (Note: mechanical behaviours, which hereafter will appear italicized, as defined in Ch.2.1). This response progresses to elastic-strain hardening with additional plastic behaviour observed above 70MPa. At confining pressures above 213MPa, elastic-strain hardening-strain softening-plastic response is observed. Each mechanical change represents a subtle change in deformation mode, but generally ductile deformation behaviour is observed. The yield point (i.e. the point at which permanent deformation begins) is not obvious in all tests. A marked change in curve form occurs between 100 and 140MPa implying a significant change in mechanical deformation mode. 5.2.1b Darley Dale sandstone Darley Dale sandstone displays a change in mechanical behaviour (Figure 5.7b). At pressures less than 80MPa elastic-brittle-plastic deformation behaviour is observed, with faulting obvious in the macroscopic samples (figure 5.8c). This progresses to elastic-plastic up to pressures of 175MPa, with no faulting seen in the macroscopic sample, suggesting pervasive cataclastic deformation. At pressures above 200MPa


elastic-strain hardening-strain softening behaviour is observed. The mechanical change between 173 and 203MPa suggests a marked deformation mode change. Darley Dale sandstone thus shows characteristics of a transition from brittle to ductile deformation. 5.2.1c Tennessee sandstone Tennessee sandstone (Figure 5.7c) only displays elastic-brittle-plastic mechanical behaviour, with the formation of brittle faults with frictional sliding along the fault. The macroscopic samples (Figure 5.8e- f) all show the formation of brittle faults at an angle of approximately 30° to the axial load. Tennessee sandstone data highlights a feature that is apparent in the other materials. The slope of the initial loading part of the stress strain curve systematically increases with confining pressure. At low pressures there is a non-linear component prior to elastic deformation. This can be explained in two possible ways. It is; 1) an experimental artefact corresponding to the progressive bedding-in of the apparatus, 2) due to volumetric strain in the sample created by pore reduction and the closure of preexisting microcracks, with these features closing due to the confining pressure alone at elevated pressures prior to the addition of axial load. If the feature is an experimental artefact, then it should only affect apparent strains, and stress is more important in this study. If it is created by pore reduction, then it is a real feature of the specimen behaviour, and of importance. This feature was apparent during testing of a tungsten carbide dummy sample, but was less pronounced than in the rock materials. This suggests that the feature is a product of both possible explanations. 5.2.2 General appearance of the deformed samples Some features of the deformed samples have already been introduced. There are a number of limitations to the interpretation of the mechanical data which may be clarified by features observed in the deformed samples. Figure 5.8 shows a summary of these features. When examined, most samples show the features of figure 5.8b, with the jacketing material compressed onto the sample. Figure 5.8a shows a Penrith sandstone sample that has been tested to a large strain. Material can be seen to have ‘flowed’ around the edges of the loading piston as the sample barrelled. This highlights one limitation of mechanical testing under confining pressure. Friction is created between the sample and piston, which limits the sample deformation at the ends, creating a conical area at the sample end where little deformation has occurred. This causes barrelling as the frictional component hinders the translation of axial strain into

Experimental results: Chapter 5 143

diametral strain. These features are an exacerbated form of the same problem experienced in unconfined uniaxial tests (§5.1.1.2). If strains are low these effects tend to be negligible, but may affect results if data accuracy is at a premium. In this investigation, where yield is being studied, this effect can be neglected. Singular fault

Singular fault

a.

RJC A21 e: 0.458 s: 41.5MPa

RJC C11

RJC B21

c.

e: 0.135 s: 100MPa

e.

Multiple faulting

Buckle

RJC A26

b.

e: 0.1 s: 89.9MPa

d.

Penrith sandstone 0

RJC B07 e: 0.205 s: 255MPa

Darley Dale sandstone 30 10 mm 20

e: 0.061 s: 109MPa

f.

e: 0.153 s: 69.8MPa

RJC C03

Tennessee sandstone

Figure 5.8: Visual condition of the jacketed samples tested using constant displacement tests.

During compression, some samples buckled (figure 5.8d), which may significantly affect mechanical data. Buckling is usually produced by a sample noncentred within the apparatus. Stress is effectively relieved from the sample giving a lower apparent strength. Few samples were seen to buckle, and these anomalous results were rejected. Figure 5.8c, e, and f all represent tests that showed the formation of a brittle fault within the sample, with 5.8f showing a fault system created at lower pressures. The majority of all observed faults initiated from the corners of the sample. Peng (1971) concluded that theoretical solutions for stresses within cylindrical elastic bodies indicate that stress within a specimen is markedly non-uniform. At failure, stresses are not simply axial and equal to the axial load divided by the cross-sectional area, as assumed in data processing. Hawkes & Mellor (1970) showed that stress distribution varies within samples, with low axial stress at the sample ends due to friction, and high stress concentrations at the sample corners and at regions within the sample approximately one radius from the sample end. Fractures will initiate at these stress


stress concentrations at the sample corners and at regions within the sample approximately one radius from the sample end. Fractures will initiate at these stress concentrations, at applied stress levels less than if the stress distribution was uniform throughout the sample. However, Brady (1971) showed that stress within triaxial compression tests tends to be much more uniform. Thus, although stress concentrations will be created at the specimen ends, these concentrations are not significantly greater than the uniform stress, therefore influencing where failure initiates, but not significantly affecting the stress level at which failure occurs.

D arle y D a le sa nd ston e

Te n ne ssee sa nd ston e

R JC B 11

S tre ss σ

R JC C 1 4

P en rith sa nd ston e R JC A 20

a.

S tr a in ε

In te rc ep t of line a r fits o f th e ela stic a nd stra in h ard e nin g re g ion s

ti c b e h av io u r E la s

Y1

rd in h a

v io u

r

Y3 O bse rve d re su lt h a s re turn ed to lin e ar in strain h ard e nin g re g io n

Y4

S tre ss σ

b.

S tra

ha g be e n in

Y 2 O bse rve d re su lt h a s v a rie d fro m th e lin e ar b y a se t a m o u n t.

If w e ll d e fin e d th e e n d o f e la stic b e ha v iou r ca n be id en tifie d . S tr a in ε

Figure 5.9: Determination of yield. a). Difficulties in identifying yield in experimental results. For Penrith and Darley Dale sandstones, a curved result is observed with no clear elastic region. For Tennessee sandstone, the elastic region displays non-linearity. b).Yield identification criterion. Yield strength is determined by observing four simply defined values. If Y1 is not observable, Y2 is used, with Y3 and Y4 used in extreme cases.


5.2.3 Calculation of strength parameters Peak strength (figure 5.7c, 2.9a) can be simply determined as the greatest stress observed during the test. Residual strength only occurs during brittle deformation, and is defined as the lowest stress observed after peak strength. Both of these parameters are simply extracted using a spreadsheet. Figure 5.9a shows the difficulties in determining yield as not all materials behave as perfect elastic bodies. Yield in Tennessee sandstone can easily be determined as all samples show initially linear elastic deformation, with a clearly defined yield point. On the other hand, for some samples of Darley Dale and Penrith sandstones the progression from linear elastic to inelastic strain hardening or plastic behaviour is gradual, with no clear cut-off of where yield occurs. To determine yield consistently for all tests, the criterion of figure 5.9b was adopted. Y1 is the elastic limit, Y2 determines yield as the stress-strain curve deviates from the linear by a set amount. For samples which show linear strain hardening, Y3 is more pronounced. Although this is not yield, it represents a maximum with yield occurring at lower stress levels. For strain hardening and plastic tests Y4 represents a good approximation of yield, representing the intersection of the linear elastic and strain hardening/plastic regions. In brittle tests peak strength can also be used as an approximation for yield strength. Values for the stress and strain at all of these points (if applicable), and for peak and residual strength, were calculated for all tests (table 5.5). Figure 5.10a shows peak, residual, and yield strengths plotted for Tennessee sandstone, with Figure 5.10b showing the peak stress for all three sandstones. The resultant best-fit slopes (figure 5.10a), found by linear regression, for peak, residual, and yield stresses, are all approximately equal with differing intercepts as expected. Slope of residual strength has the largest spread of results, suggesting frictional characteristics of material may be influenced by experimental conditions, i.e. the gouge or the fault angle created in the faulted sample is not always consistent. However, all three parameters do approximate to linear relations closely. Figure 5.10b shows the slope of ultimate strength for all three sandstones. The relationship of strength with confining pressure has traditionally been assumed to be linear, the Mohr-Coulomb relationship. However, many studies, including Byerlee (1967, 1975), have shown a non-linear relationship. The fit of the data using linear regression is good, although a non-linear relationship approximates the observed results


for Tennessee sandstone more closely. Observed uniaxial compressive strength do not correspond to the intercept of the slope of ultimate strength, except in the case of Penrith sandstone. This implies non-linearity, but may only exist at low pressures. The data is inadequate to discriminate between the linear and non-linear fits.

Sandstone type

Test number

Confining Peak Residual Yield strength (MPa) pressure strength strength Y1/Y2 Y3 Y4 (MPa) (MPa) (MPa) Penrith RJC A08 27.9 78.8 / 54.6 78.6 78.6 RJC A21 41.5 83.5 / 59.3 83.8 83.8 RJCA20 71.1 184 / 25.9 79.5 67.7 RJC A19 109.4 217 / 13.2 54.1 37.7 RJC A18 142.3 319 / 24.3 66.6 40 RJC A17 172.7 371 / 10.4 41.2 23.9 RJC A10 212.7 418 / 33.9 54.3 44.4 RJC A22 240.7 445 / 21.2 92.3 48.7 RJC A09 281 495 / 6.7 14.1 10.8 Darley RJC B11 38.9 180 / 146 / / RJC B04 78.5 239 / 201 238 239 RJC B10 108.1 288 / 180 287 287 RJC B05 140.5 353 / 190 352 352 RJC B09 172.3 393 / 185 / / RJC B12 202.4 440 / 197 / / RJC B08 233 498 / 150 / / RJC B13 276.1 538 / 167 / / Tennessee RJC C14 44.5 317 185 250 / / RJC C15 75.8 426 297 279 / / RJC C13 106.7 551 437 409 533 500 RJC C05 132.6 514 417 359 512 500 RJC C10 173.2 606 434 389 600 600 RJC C06 213.7 711 574 565 705 700 RJC C09 239.9 707 563 546 700 700 RJC C08 260.8 751 625 523 737 740 Table 5.5: Table of results for peak, residual, and yield strengths determined from constant displacement-rate tests using the criterion described in text.

Assuming a linear Coulomb fit of ultimate strength, there are differences between the three sandstones. All three slopes are similar, ranging from 1.5-2, with different intercepts, that approximate to the uniaxial compressive strength. The strongest rock, Tennessee sandstone, has the greatest slope, but the weakest material, Penrith sandstone, does not have the lowest slope. This implies that the slope of ultimate strength is not dependent on porosity. This suggests that grain dimension may be more important, as there is a tentative relationship between slope of ultimate strength and average grain dimension, with larger grain sized material having lower slopes.


90 0 80 0

h y = 2 .03 72 x + 2 40.94 ngt 2 s tre R = 0 .97 23 e t im a

U ltim a te stren g th (M P a )

70 0 60 0

pe S lo

lt

50 0

S lo

40 0

fr pe o

es

ls id u a

tre n

g th

y = 2 .00 45 x + 1 09.22 R 2 = 0 .96 25

30 0 20 0

n s tre ie ld

10 0

a.

of u

S lo

g th

P ea k stren g th R e sid u al stre n gth Yie ld stren g th

fy 76 x + 7 2.8 41 p e o y = 1 .95 2 R = 0 .99 18

0 0

50

10 0

15 0

20 0

25 0

30 0

C o n fin in g pressu re (M P a ) 90 0

L in ea r fit

80 0 70 0

.9 =0 :R

U ltim ate strength (M P a)

2

60 0

2 .0 y=

50 0

372

2 x+

40 0

1 .5 5 y=

96 x

4 4 0 .9

+ 12

N o n -lin ea r fit

723

2 0 .9 9 R = : 7 2 .2

y = -5 .9 9 ×10 x + 3.9 9x + 10 1 2 R = 0.9 91 8 -3

2

48

4 975 2 = 0. R 01 : 4 2 .3 x+ 4 6 1 .7 1 y= P en rith sa nd sto n e

30 0 20 0

D a rle y D ale san d sto ne Te n ne sse e san d sto ne

10 0 0

b.

0

50

10 0

15 0

20 0

25 0

30 0

C o n fin in g pressu re (M P a )

Figure 5.10: Strength parameters versus confining pressure for three sandstones. a). Slope of ultimate, residual, and yield strength for Tennessee sandstone. b). Slope of ultimate strength for all three sandstones. Closed symbols denote triaxial compression tests; open symbols denote unconfined uniaxial compression tests. The unconfined uniaxial compression tests suggest nonlinearity at low confining pressures.

5.2.4 Compactive yield envelope As introduced in chapter 2.6.4, the representation of yield within the differential [P=(σ1-σ3)/2] versus mean effective [Q=(σ1+σ3)/2] stress space describes the yield surface (Atkinson & Bransby 1978) for porous materials. The QP diagram represents a means to predict failure mode for given stress-states, as brittle faulting and cataclastic flow are restricted to specific regions of the diagram assuming strain vector normality for associated plasticity (yield surface = plastic potential surface) (Wong et al. 1997).


Normalizing the yield envelopes with respect to their grain crushing pressure P*, which represents the onset of yield under purely hydrostatic conditions, gives a singular yield envelope for porous sandstones (Wong et al. 1997). Figure 5.11 shows the yield data for all three sandstones in the QP stress space. For each rock type, a polynomial envelope is plotted as the least-squares best fit of the yield data, which approximates the yield surface. These envelopes are similar for the three rocks, increasing in size with decreasing porosity/increasing strength. Only Penrith sandstone has a fully described yield envelope, with Darley Dale sandstone almost complete, and Tennessee sandstone represented by only half of the envelope. The normalization of the yield envelopes in the QP space with respect to P* will result in a singular envelope for sandstone. The determination of P* can be conducted by testing the hydrostatic compaction of sandstone under hydrostatic conditions. The results for the normalized QP yield surface will be presented after the determination of P* is described. 700

D ifferen tia l stress Q (M P a )

600 500 400 300

P en rith san d sto n e D arley D ale san d sto n e Ten n e sse e san d sto n e Yield en v elo p e

200 100 0 0

100

200

300

400

500

600

E ffectiv e m ea n stress P (M P a ) Figure 5.11: Yield envelope of three sandstones plotted in the differential versus effective mean stress space.


5.3 Hydrostatic deformation experiments To describe the hydrostatic deformation of the test material, two types of experiment were conducted on the three sandstones (see Ch.4.5.4 and 4.6.6 for methods). Using Heard III, hitpoint experiments were conducted to pressures of 250MPa. Using BigRig, constant pore pressure volumometry (CPV) experiments were conducted to pressures of 500MPa. The hitpoint experiment determined overall sample volumetric strain by measuring the change of length of samples as pressure was incremented. CPV experiments measured the volume of expelled saturated pore fluids whilst maintaining constant pore pressure. Pore volume strain is equal to granular strain, but fluid volume expelled is not equal to the total volume change. CPV experiments were conducted with water and ethanol pore fluids, with hitpoint experiments conducted under oven dry conditions. In total 12 hitpoint experiments were conducted on the three sandstones, with 18 conducted using the CPV method. Extensive calibrations and appraisal of the test methods were made to ascertain the suitability of each method to detect volumetric strain. No test failures occurred once experimental design had been developed. Table 5.6 shows a summary of the hitpoint experimental data, with table 5.7 showing a summary for the CPV experiments. Figure 5.12 summarizes the hitpoint (figure 5.12a) and CPV (figure 5.12b) experimental results.

Test Test P* K εv @ (MPa) o N. 50 100 150 200 250 MPa GPa RJC A01 I 0.01 0.013 0.022 0.044 0.054 / / Penrith RJC A13 I 0.02 0.022 0.027 0.074 0.095 146-181 / RJC A14 II 0.05 0.1 0.129 0.2 0.27 147-176 1.14 RJC A15* II 0.027 0.041 0.1 0.129 0.157 106-140 3.59 RJC B01 I 0.028 0.059 0.076 0.097 0.121 / 2.44 Darley Dale RJC B02 I 0.03 0.06 0.089 0.102 0.116 / 2.44 RJC B03* II 0.024 0.029 0.034 0.036 0.041 / 11.8 RJC B16 II Failed - anomalous result / / RJC B17 II 0.021 0.027 0.029 0.031 0.033 / / RJC C01 I 0.05 0.065 0.079 0.097 0.125 / 2.31 Tennessee RJC C02 I 0.041 0.068 0.091 0.101 0.125 / 2.36 RJC C16* II 0.016 0.025 0.029 0.031 0.035 / 11.9 Table 5.6: Summary of volumetric strain v. confining pressure for the hitpoint tests. Test method II is an improved technique (compared with test method I) which includes a chart recorder to more accurately define each hitpoint. Different calibration constants have been used for each test method. * most relyable results. Sandstone type


Test P* K Pore Runs εv @ (MPa) o N. 100 200 300 400 500 MPa GPa fluid RJC P01 0.027 133 6.64 Ethanol 2 Penrith RJC P04 0.022 0.034 165 7.65 Ethanol 4 RJC P05 0.041 0.058 170 7.86 Ethanol 5 RJC P07 0.024 121 5.39 Water 1 RJC P08 0.020 0.043 175 6.99 Ethanol 1 RJC P09 0.019 0.039 136 7.05 Ethanol 1 RJC P10 Logging error / / Ethanol 1 RJC P11 0.028 0.077 167 7.76 Ethanol 4 RJC P16 0.034 0.094 0.119 0.129 0.137 138.6 7.19 Ethanol 4 RJC D01 0.007 0.013 0.015 0.017 / 48.6 Ethanol 1 Darley RJC D02 Logging error / / Ethanol 1 Dale RJC D03 0.015 0.019 0.024 0.028 0.033 / 21.9 Ethanol 4 RJC D04 0.017 0.022 0.026 0.031 0.036 / 21.7 Ethanol 4 RJC D15 0.015 0.02 0.025 0.03 0.036 (443) 19.5 Water 1 / 58 Ethanol 4 Tennessee RJC T01 0.036 0.038 0.039 RJC T10 0.02 0.026 0.028 0.03 0.031 / / Ethanol 1 RJC T11 0.014 0.017 / 32.2 Water 1 Table 5.7: Summary of pore strain v. effective pressure for constant pore pressure volumometry tests. Note: P* for test RJC D15 is inferred mechanically and not microstructurally. Rock type

5.3.1 Comparisons between the experimental methods As shown by figures 5.12 and 5.13, there are significant differences between the results of hydrostatic volume changes between the two experimental procedures. Figure 5.13 shows that the high sampling rate of the CPV method gives the most reliable results. The manometer method, which measures pore fluid expulsion at atmospheric pressures, gives comparable results. However, air bubble expulsion from the compacting samples gave anomalous time-dependent results as bubbles expand once outside of the sample-piston assembly. The raising of the pore fluid pressure compresses any air bubbles within the sample, yet these are also suppressed from expanding when outside of the sample assembly. The CPV method also allows time dependent effects to be studied. As shown in figure 5.13, at pressures above 160MPa Penrith sandstone shows a time dependent deformation behaviour seen in the CPV results, this is not apparent in the manometer method test results. The slope of the linear compaction region, at pressures of 75-170MPa, is consistent for the CPV and manometer methods. However, this slope is different for the hitpoint method. The CPV/manometer and hitpoint methods measure different physical properties. The hitpoint method observes overall sample compaction, which includes the compaction of the pore matrix and the granular constituents of the sample. The pore-fluid expulsion methods only observe the pore matrix compaction, and thus show significantly different volumetric compaction rates.


Ty pe III h y drosta tic c om pac tion

18

D o w n -p re ssu re re la xa tio n

14 U p -p ressu re co m p a ctio n

12 P e rm an ent d e fo rm a tio n

Volu m etric stra in εv (% )

16

10 8 6

4

B u lk m o d u lu s fro m u n ia xial c o m p re ssio n test

E n ha n ce d c o m p ac tion

-3

O n se t o f e n h an c ed c om pa c tio n P * P en S

L in e ar c o m p ac tion

2

S; y

=3

6 -4 + 9 .7 10 x × 5 .2

×1 0

2 -2 : R = 0 .9 9 5 -5 x + 2 .0 6 ×1 0 0 1 × 6 .4 8 = y D y D SS : 2 -2 -5 1 0 : R = 0 .9 6 3 ×10 x + 1 .5 2 × Ten S S : y = 8 .4 4

C lo su re o f m ic ro c ra c ks, sim p le c om pa c tio n a n d e xp e rim ental a rtifac ts

0

50

0

150

100

250

200

300

C o n fin in g p ressu re σc (M P a)

a. 5 4 .5

2

P o re red u ction (% )

4 -2

3 .5 3 P

2 .5

S en

S:

y=

1 .3

0 ×1 34

x

.4 +1

27

:R

.9 =0

97

3 + 1 .2 7 ×1 0 x 5 6 .5 4

2 9 .9 8 3 :R =

-3

D yD S

S: y =

2 -3 4 7 : R = 0 .9 9 2 2 4 ×1 0 x + 1 .1 Te n SS : y = 1 .7

2 1 .5

P enrith sandstone test R JC P 11 P enrith sandstone test R JC P 16 D arley D ale sandstone test R JC D 03 D arley D ale sandstone test R JC D 04 Tennessee sandstone test R JC T 01 Tennessee sandstone test R JC T 10

1 0 .5

0

b.

0

50

100

150

200

250

300

350

400

450

500

E ffectiv e p ressu re σc - σp (M P a)

Figure 5.12: Hydrostatic compaction of three sandstones. a). Hydrostats determined using the hitpoint method, showing linear compaction rates with Penrith sandstone having enhanced compaction at 125MPa. b). Hydrostats determined using the constant pore pressure volumometry method. Results represent pore space compaction as a function of overall sample volume. The linear region relates to the bulk modulus of the pore space.

At low pressures significant amounts of compaction occur, which can be approximated as being equal to the intercept of the linear compaction region. The CPV method gives a lower intercept than the manometer and hitpoint method. This is due to the CPV tests not observing the initial 2-3MPa of the test due to the necessity of having higher confining pressure than pore pressure.

Vo lu m etric stra in : P o ro sity red u ctio n (% )


8 7 H itp o int m eth o d σp = 0M P a

6 5

M a no m eter m e th o d σp = 0M P a

O ffse t o n Y -ax is as first 5 M P a o f testin g is o m itte d

4 3 2

A b ility to o b se rv e tim e d ep e n de n t b eh av io u r P o re v o lu m o m etry m e th o d σp = 3M P a In cre asin g sa m p le ra te ∴ inc rea se d ac cu ra cy

1

P en rith sa n d sto n e

0 0

50

100

150

200

250

C o n fin in g p ressu re σc (M P a ) Figure 5.13: Comparisons between the three methods used for measuring the hydrostatic compaction of sandstone.

Superseding the linear compaction region is an increased compaction rate at 160MPa for the CPV and manometer methods, and 130MPa for the hitpoint method. Although significant differences exist between the hitpoint and CPV methods, both yield useful data which can be used to describe the hydrostatic compaction of the sandstones. The increased sample rate of the CPV method has resulted in this method being used quantitatively to describe the compaction behaviour. 5.3.2 Form of the hydrostat Figure 5.14 summarizes the features observed within the hydrostat for Penrith sandstone, which is similar to the other test materials. Figure 5.14a shows a singular run to a pressure exceeding P*, with figure 5.14b showing a complete hydrostat to a pressure of 500MPa. All observed features are consistent with hydrostats obtained by other workers (Fabre & Gustkiewicz 1997, Wong et al. 1997). At low effective pressures (0 resulting in stability and strain hardening, creating compactive cataclastic flow (Hobbs et al. 1990). The yield envelope of sandstone can be described by equations 2.12 and 2.13, given the value of P* which, as shown (§5.3.8), can be predicted from the parameters of porosity (φ) and grain radius (R). These parameters can be determined microstructurally. Extending the yield envelopes in the Q-P-φR space gives the singular yieldsurface for porous materials (figure 5.19). The third axis is chosen as φR, instead of R or void ratio (v), as strength is seen to scale with this product. This surface shows the regions of brittle and ductile deformation, separated by the brittle-ductile transition. This line corresponds to the critical state line of deformation. Wong et al. (1997) show that in the vicinity of the transitional zone, experimental inelastic compaction is consistently greater than the theoretical prediction. This suggests that the associated flow rule and strain vector normality condition are not applicable in the transitional regime. Thus, non-associated flow exists in the brittle-ductile transition zone. The critical state unified model (figure 5.19) can predict the complex deformation history of a sediment (as introduced in Ch.2.6.5).


Differential stress Q (MPa)

Ductile deformation; shear-enhanced compaction and cataclastic flow Brittle-ductile transition Critical state Brittle deformation; line 1400 shear localisation 1300 1200

1000 900 800 700 600 500 400 300 200 100 0

1100 1000 900

)

800 700 600 400 300

em

tiv

c ffe

200

ss

tre

s ean

500

Pa

M P(

Normal consolidation line

E

100 0 5

10

Pr od

uc

to

15

fp

oro

sit

Penrith sandstone Darley Dale sandstone Tennessee sandstone Critical state line Yield surface Yield envelope

20

ya

nd

av

25

era

ge

gra

in

30

rad

ius

fR (

35

mm )

40

Figure 5.19: Yield surface for sandstone in the Q-P-fR space as determined from the yield envelopes of three sandstones.

5.4 Microstructures and deformation mechanisms from triaxial experiments 45 thin-sections were made from the Heard-type constant displacement-rate triaxial experiment samples. These can be split into two groups; 1) microstructural variations seen at one given confining pressure as strain increases, 2) microstructural variations seen in deformed samples with increasing confining pressure. By fully describing the microstructure and inferring deformation mechanism it is possible to establish mode of failure and how these relate to mechanical property variations seen in the stress-strain results. 5.5 Microstructural evolution of sandstone with strain at 100MPa pressure A series of tests were conducted on the three sandstones at approximately 100MPa effective pressure to different strains to investigate the microstructural evolution of deformation with strain. At this pressure, the microstructural evolution of Tennessee sandstone represents the brittle regime of deformation. Penrith sandstone represents the ductile regime, with Darley Dale sandstone representing the brittle-ductile transition.


5.5.1 Tennessee sandstone A suite of five tests were conducted to increasing strains in the range 0-0.08 to observe the microstructural variations during the fracturing process at a confining pressure of approximately 100MPa. This effective pressure represents the brittle regime of deformation. In it’s pre-testing intact state, Tennessee sandstone has a porosity of approximately 7%, and shows little evidence of pre-existing damage. After the application of a hydrostatic confining pressure of 100MPa, there was some permanent damage, in the form of slight porosity closure and new microfracturing. Fractures formed as a result of porosity closure around pores and in corners of grains near to high concentrations of cement. Some pre-existing fractures have closed, while some of the healed microcracks appear more prominent, suggesting that they have re-activated. No shear movements were apparent along any fractures. Some permanent deformation was observed within the mechanically elastic region (ε=0.027). In thin-section, a 200-300µm wide band of concentrated damage was

observed. Damage within the bulk-sample was observed as a lowering of porosity, and the resultant stress-concentrations create axially-oriented impingement fractures. Also, axially oriented healed microfractures are beginning to re-activate. Small fragments from comminuted grains are beginning to collect in the available remaining pore-space. Microfractures are randomly oriented within the zone of concentrated damage where porosity closure is more advanced. Shear movements have occurred along the concentrated damage zone with a fine-grained gouge material, made up of broken grains and cement, beginning to form and collect along the zone. By peak-stress (ε=0.035), damage has clearly formed into a shear zone inclined

approximately 30° to the axial load, as shown in figure 5.20a, with other smaller-scale shear-zones visible. Along the 150-200µm wide zone, a very fine gouge material has developed with larger grains approximately 0.5Ri (where Ri = average grain radius of starting material) floating within the matrix. These show shear movements are occurring, with the detached grains apparently ‘rolling’ within the ‘flowing’ gouge. The shear zone is not homogeneous, and broadens in places. These broadened areas are created by the coalescence of smaller off-set shear-zones. This indicates that more than one formed before the larger scale zone was created. Other smaller shear-zones formed within other parts of the sample, suggesting that many areas of localized damage


Shear fault

600

400

Stress (MPa)

Limit of damage

200

0 0

Localised damage

a.

Strain 0.04

0.08

e=0.035 sd=520MPa

Formation of band of localized shear deformation

RJC C20m 0

mm

1 Limit of damage

In

ten

se

da

ma

ge

Wider shear zone

Axial fracturing

400

RJC C13m

Stress (MPa)

600

Finer gouge

200

0 0

Strain 0.04

0.08

b, c. e=0.08 s =435MPa

Fine grained gouge

d

Axial cracking

Development of shear localization band

She

ar m

ove

me

nt

RJC C13m 0 PPL

mm

0.5 Axial direction

Figure 5.20: The microstructural evolution of Tennessee sandstone at 100MPa confining pressure. The photomicrograhs (plane polarized light) show the damage accumulated by the constant displacement-rate test at strains of (a) 3.5%, (b) and (c) 8%. Damage is created by closing porosity creating axial contact fracturing, which with increased strain localizes into a shear band where a fine grained gouge is made of the damaged periphery material. The over-all damaged zone does not alter with strain, with the shear zone widening.


formed before one larger preferred zone formed. The main feature observed originates from the corner of the sample, which will inevitably be an area of concentrated strain. Thus, the non-uniform stress concentration within the sample created by the constrains of the experimental configuration is influencing the resultant failure. Axially oriented impingement microfractures formed within ±2.5mm of the zone, with the most intense damage created within ±1mm. Away from the damaged zone, deformation is minimal. During the stress-drop stage of failure (ε=0.05), observed damage broadened

within the shear-zone and became more developed. The shear zone widened to approximately 300µm width, although the damage zone around the shear was still the same width. Therefore, no new damage was being accumulated by the continued compression of the sample, because the strain was being absorbed by the movement along the shear-zone. The gouge became finer, and the ‘floating’ grains are reduced in size to about 0.1Ri at the centre of the shear zone, with more grains being consumed at the margins of the zone. Within the damaged zone outside the shear-zone, intragranular fracturing intensified, reducing grain size to approximately 0.1-0.3Ri. Fragments of comminuted grains were plucked and consumed into the gouge as movement occurred. No further changes were observed in the intact zone away from the shear-zone. With further increased strain (ε=0.08), the stress level within the sample becomes

constant. In thin-section (figure 5.20b-c) the shear-zone had widened to 200-500µm with the damaged zone beyond not altering perceptibly. The gouge became even finer (grain-size indistinguishable) with small (0.1Ri) floating clasts. Many anastomosing veins of gouge formed within the 3mm wide damaged zone, absorbing considerable strain. In summary, as confining pressure is applied to the sample, porosity reduces and some new microfractures are formed in random orientations. With axial load within the elastic region porosity closes preferentially in the axial direction, resulting in the formation of axial impingement fractures between point contacts. Damage concentrates within a 200-300µm wide band angled 30° to the axial load, with continued fall of porosity as fracture density increases within this shear band. By peak-stress, axial microfractures formed within a 5mm band with the formation of a 150-200µm shearzone. Within the zone, a very fine grained gouge is formed with some clasts of size 0.5Ri. With increased strain the damage zone does not broaden and the intact regions


remain roughly constant in volume. The central shear zone broadens and the gouge material becomes finer grained, with the floating clasts reducing in size. The shear zone becomes 200-500µm wide, with anastomosing ‘veins’ of gouge. Damage within 1mm of the shear bands is intense, with grains splitting up to 10 times. These become plucked into the gouge with increased strain. Therefore Tennessee sandstone fails through shear-localization deformation at 100MPa. 5.5.2 Darley Dale sandstone A suite of seven tests was conducted to strains in the range 0-0.24, at a confining pressure of approximately 100MPa, to observe the microstructural variations during the brittle-ductile transition. In it’s pre-testing intact state, Darley Dale sandstone has a porosity of approximately 14% with poorly sorted subrounded to subangular grains. Few grains are fractured and many show healed microcracks. Simple pressurization to 100MPa produced little change. During the near-elastic region (ε=0.01), some

permanent porosity reduction occurred accompanied by fracturing, although the bulk of the material remained unaltered. Some pre-existing, axially-oriented fractures opened, with axially-oriented healed microcracks more prominent. At the yield point (ε=0.025)

some permanent porosity reduction (