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An experimental investigation of textural controls on the brittle deformation of dolomite Austin, Nicholas J. 2003

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An Experimental Investigation of Textural Controls on the Brittle Deformation of Dolomite by Nicholas J. Austin B.Sc, The University of British Columbia, 2001 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTERS OF SCIENCE in THE FACULTY OF GRADUATE STUDIES GEOLOGICAL SCIENCES DIVISION DEPARTMENT OF EARTH AND OCEAN SCIENCES We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA July, 2003 © Nicholas J. Austin, 2003  In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department  or  by  his  or  her  representatives.  It is  understood  that  copying  or  publication of this thesis for financial gain shall not be allowed without my written permission.  Department The University of British Columbia Vancouver, Canada  DE-6  (2/88)  Abstract Abstract The brittle deformation of dolomite, which is a common lithology in numerous thrust systems and hydrocarbon reservoirs around the world, is strongly related to its textural features. Generally for the purpose of characterizing rock deformation these diverse features are shoehorned under the headings of porosity and grain size, based on the assumption that the concentration and length of the initial flaws vary proportionally with either one or both of these properties. In dolomite there is often substantial textural variation that influences the nature of the initial flaws, yet does not relate to grain size and/or porosity. In order to investigate the role of texture on the brittle deformation of dolomite, a series of 23 triaxial deformation experiments were performed at confining pressures of 25, 50, and 100 MPa, dry, at room temperature, on dolomite from three texturally distinct sample suites: the Badshot Formation, the Niagara Formation, and the Rock Creek quarry. The variations in the mechanical response of these mineralogically and chemically similar dolomites, and the ensuing microstructures, indicate that differences in texture can promote the transition from brittle faulting to cataclastic flow, and can vary the peak strength. Grain boundary textures promote or inhibit the ability of grains to shear and rotate with respect to one another, whereas the presence of intragranular flaws, such as cleavage, that act as weaknesses, promote intragranular deformation.  Both grain and grain boundary textures  strongly influence the mechanics of deformation, including the peak strength, due to their influence on the length and concentration of the initial flaws. An empirical failure criterion for the peak strength of dolomite is formulated that includes only the effective Young's modulus, the confining pressure, and the empirically ii  Abstract defined uniaxial compressive strength; when a grain size term is added, the quality of fit to the experimental data is significantly reduced. Porosity and the concentration and length of the initial flaws are embedded in the effective Young's modulus, which is measured from the differential stress-axial strain curve for each deformation experiment.  in  Abstract Table of Contents  Abstract  ii  List of Tables  vi  List of Figures  vii  Preface  ix  Acknowledgements  x  I. Introduction  1  II. Textural Controls on the Brittle Deformation of Dolomite: the Transition from Brittle Faulting to Cataclastic Flow 4 2.1 Introduction 5 2.2 Methodology 2.2.1 Apparatus Description 6 2.2.2 Experiments 17 2.2.3 Starting Material 17 2.3 Results 2.3.1 Mechanical 25 2.3.2 Macro and Micro Structures 28 2.4 The Transition from Trans to Intragranular Deformation 2.4.1 The Onset of Grain Crushing in Low Porosity Dolomite 34 2.4.2 The Influence of Grain and Grain Boundary Texture 38 2.4.3 The Influence of Porosity 39 2.5 Conclusion 41 III. Textural Controls on the Brittle Deformation of Dolomite: Variations in Peak Strength 3.1 Introduction 3.2 Experiments 3.2.1 Methodology 3.2.2 Experimental Results 3.3 Controls on the Peak Strength of Dolomite 3.3.1 A Modified Empirical Failure Criterion 3.4 The Relationship Between Effective Young's Modulus and Rock Texture 3.5 The Relationship Between Flaws and Grain Size 3.6 Summary  iv  43 44 45 49 51 54 61 64 72  ^  Abstract  IV. Conclusion  73  References  76  Appendix I: Data Reduction  85  Appendix II: Geochemical Data  90  v  Abstract List of Tables Chapter II Table 2.1: The stiffness of the LSR  16  Table 2.2: The sample properties, experimental conditions, and experimental results for the experiments performed as part of this study 21 Table 2.3: A list of the symbols used in chapter II  23  Chapter III Table 3.1: The sample properties, experimental conditions, and experimental results for all samples examined in this study 46 Table 3.2: A description of the symbols used in chapter III  47  Table 3.3: Correlation coefficients between sample properties, experimental conditions, and experimental results for all samples examined in this study 52 Table 3.4: Predicted flaw densities and the corresponding number of flaws per grain for each of my samples 52 Appendix I Table A l . l : A sample of raw and reduced data from an experiment on the Large Sample Rig 88 Appendix II Table A2.1: Geochemcal data for Badshot, Rock Creek, and Niagara dolomite  93  Table A2.2: Mineralogical data from Rietveld refinements  94  Table A2.3: Isotopic data  95  vi  Abstract List of Figures Chapter II Figure 2.1: The Large Sample R i g  7  Figure 2.2: The furnace and temperature gradient  11  Figure 2.3: The Large Sample R i g represented as springs  15  Figure 2.4: The bulk chemistry of Badshot, Rock Creek, and Niagara dolomite  18  Figure 2.5: Optical micrographs of undeformed dolomite  19  Figure 2.6: Grain size histograms  22  Figure 2.7: Differential stress-axial strain curves  26  Figure 2.8: A plot of peak differential stress vs. confining pressure  27  Figure 2.9: A plot of fracture orientation vs. confining pressure  29  Figure 2.10: Optical micrographs and S E M images of deformed dolomite  30  Figure 2.11: A plot of peak differential stress vs. mean stress  35  Figure 2.12: A plot of the peak mean stress vs. §*d  37  m  Chapter III Figure 3.1: Optical micrographs o f undeformed dolomite  48  Figure 3.2: Differential stress-axial strain curves  50  Figure 3.3: Correlation coefficients between sample and experimental properties and peak strength 53 Figure 3.4: The relationship between mean grain size and peak strength  55  Figure 3.5: The ability of equations 3.5 and 3.6 to explain the peak strength of dolomite 56  vii  Abstract Figure 3.6: The ability of equations 3.8 and 3.9.to explain the peak strength of dolomite 58 Figure 3.7: The range of b and c values that result in an R value of >0.89, using equation 3.9, for varying a values 60 2  Figure 3.8: The relationship between effective Young's modulus and peak strength , 62 Figure 3.9: Plots showing the relationship between the half flaw length (a) and the flaw density (Na), contoured for the measured peak strength 66 Figure 3.10: Optical micrographs and SEM images of the deformed dolomite  69  Appendix I Figure A l l : A sample load-position curve for the raw data from an experiment on the LSR 89  vni  Preface Preface  This thesis is composed of two papers in preparation for submission to The Geological Society of London Special Volume for the 2003 Deformation, Rheology, and Tectonics meeting held in April, 2003 in St. Malo, France. The first paper (chapter II) is entitled "Textural Controls on the Brittle Deformation of Dolomite: the Transition from Brittle Faulting to Cataclastic Flow," and the second paper (chapter 111) is entitled "Textural Controls on the Brittle Deformation of Dolomite: Variations in Peak Strength." Dr. Lori Kennedy is second author on both papers, while Dr. J.M. Logan and Mr. Ray Rodway are also co-authors on the first paper. I performed all data collection, processing, and analysis for both papers, as well as providing design input for, and performing a significant portion of the technical work on, the development of the Large Sample Rig (described in chapter II). Dr. Lori Kennedy supervised and financed the project, in addition to providing text revisions. Dr. J.M. Logan designed the Large Sample Rig, which is presented for the first time in chapter II, and Mr. Ray Rodway was heavily involved in many aspects of the design, construction, and testing of the Large Sample Rig.  ix  Abstract Acknowledgements This project was financially supported by a University Graduate Fellowship from the University of British Columbia for September 2001-September 2002, an NSERC PGS-A graduate scholarship (N.J. Austin) for September 2002-September 2003, an NSERC research grant (L.A. Kennedy), and a B.P. research grant. I must thank Ray Rodway for his unending help and support in the design and implementation of many aspects of the Large Sample Rig. Thanks also go to David Jones, who was instrumental in getting many of the electrical systems up and running. I am grateful to Kelly Russell and Greg Dipple, both of whom endured frequent visits regarding my many analytical and mathematical questions, as well as to Mati Raudsepp and Elisabetta Pani who provided me with guidance on many analytical techniques, including SEM and XRD.  Lastly, I must thank Lori Kennedy who has now  provided me with insightful guidance through both my undergraduate and master's projects.  x  Chapter I  Chapter I: Introduction  l  Chapter I Introduction The mechanics of brittle deformation in rocks, along with the peak strength, are strongly linked to textural properties.  Theories of fracture mechanics are predominantly  derived from Griffith's (1921, 1924) theories, which invoke the presence of initial flaws. In rocks, the presence and distribution of flaws are dictated by texture. Typically, the broad array of textural features are grouped into the domains of porosity and grain size, which is not necessarily valid in mineralogically homogeneous, texturally diverse rocks. Assumptions regarding the controls of grain size and porosity on the mechanics of deformation, including the peak strength, may, therefore, have variable applicability. The brittle deformation of dolomite (CaMg(C03)2) is of particular interest due to dolomite's common occurrence in orogenic belts, and frequent association with hydrocarbon reservoirs.  To date, there is a dearth of data pertaining to dolomite, in contrast to the  extensive database regarding the deformation of calcite.  In addition to the frequent  occurrence of dolomite in fold and thrust belts and hydrocarbon reservoirs, it is also an ideal rock type for the study of textural controls on brittle deformation. Unlike calcite, dolomite does not deform by crystal plastic processes at room temperature (Turner et al., 1954), and thus the variables related to the onset of crystal plasticity do not need to be considered. This research explores the role of texture on the mechanics of brittle deformation in dolomite, including its peak strength, in the form of two papers in preparation for submission for publication. Chapter II is an examination of the textural controls on the transition from brittle faulting to cataclastic flow in dolomite. Three sample suites are characterized in terms of textural properties, mineralogy, and chemistry.  2  A series of 23 triaxial deformation  , experiments,  Chapter I  performed using the Large Sample Rig,, enable  microstructural responses to be examined.  the mechanical and  These results are then compared to fracture  theory, and to experimental results on quartz and calcite, and the differences are explained based on textural and microstructural differences. Chapter III is an analysis of the textural controls on the peak strength of dolomite based on the same 23 experiments as chapter II. A new empirical failure criterion is derived, and is fit to both experimental data that I collected, as well as to that obtained from the literature.  The parameters involved in this failure criterion are examined based on  compressional fracture theory and elasticity to understand their relationship with the peak strength. Lastly, theories of compressional fracture mechanics are applied to the data set, and compared to textural observations in order to improve our understanding of textural controls on the peak strength. This thesis is also the first compilation of work performed on the newly established Large Sample Rig (LSR) triaxial rock press, which has been developed in the department of Earth and Ocean Sciences at the University of British Columbia. The first part of chapter II presents a description of the design and calibration of the LSR, while the method of data reduction is outlined in appendix 1.  3  Chapter II  Chapter II: Textural Controls on the Brittle Deformation of Dolomite: The Transition from Brittle Faulting to Cataclastic Flow  4  Chapter II 2.1 Introduction Rocks are inherently heterogeneous, and thus assumptions must be made to understand which properties are significant in controlling the mechanical and microstructural response to a differential stress. Generally, the two textural properties that are considered are porosity (Brace, 1978, Hatzor et al., 1997, Baud et al., 2000) and grain size (Olsson, 1974, Hugman and Friedman, 1979, Fredrich et al., 1990). The roles of intragrain flaws and grain boundary textures are seldom examined, despite the highly variable nature of both of these properties, and their effect on assumptions regarding the relationship between grain size and the concentration and length of initial flaws. The concentration and length of the initial flaws are the principal parameters in fracture theory (Griffith, 1921, Nemat Nasser and Horii, 1982, Horii and Nemat Nasser, 1985, Ashby and Sammis, 1990), and must, therefore, be accounted for in understanding the brittle deformation of rocks. The transition from deformation by brittle faulting to cataclastic flow is of particular interest, as this transition is known to strongly affect the permeability and transport properties of rocks (Zhu & Wong, 1997). While this transition has been extensively addressed with relation to sandstones (Rutter & Hadizadeh, 1991, Menendez et al., 1996, Zhu & Wong, 1996, Wong et al, 1997, Zhu & Wong, 1997) and limestones, (Fredrich et al., 1990 Baud et al., 2000) there has been very little work done on dolomite.  Dolomite is commonly  associated with limestones, and thus to better understand how these materials will behave as multiphase rocks, the mechanical responses of the homogeneous end members must be understood. Dolomite is also a common hydrocarbon reservoir rock, because it commonly  5  Chapter II contains vuggy porosity, and is frequently extensively fractured (Antonellini & Mollema, 2000). In order to investigate the brittle deformation of dolomite, a triaxial rock press previously described by Handin et al. (1972), Shimamoto (1977), and Handin et al. (1986), has been modified. Using this modified apparatus, I have performed a series of triaxial rock deformation experiments on texturally diverse dolomites covering a wide range of porosities, grain sizes, and grain and grain boundary textures. I focus my analysis predominantly on the microstructural response of these rocks to a differential stress, and interpret observed differences based on their mechanical responses, combined with the theories of fracture mechanics and what is known about the brittle response of other rock types. I compare my results primarily to the extensive experimental data for quartz and calcite to highlight the importance of mineral and textural properties on the mechanical and microstructural response of rocks to deformation.  2.2 Methodology 2.2.1 Apparatus Description The triaxial rock press used for this research (Figure 2.1) is a significantly modified version of one previously used at Texas A & M University (Handin et al, 1972, Shimamoto, 1977, and Handin et al., 1986). The vertically mounted frame has a yolked assembly, the purpose of which is to: 1) ensure the volume in the pressure vessel remains approximately constant through the use of a lower compensating piston, and 2) prevent the load generated  6  Chapter II  Lucalox A) The triaxial rock press used for this study, accompanied by a photograph of the large sample assembly. B) A schematic of the triaxial rock press used in this study, highlighting the locations of the external load cell and displacement transducer (DCDT). In succession to the right are close-up views of the pressure vessel, and the samples assemblies for both the large and small samples sizes. Figure 2.1:  7  Chapter II by the confining pressure, which may approach 80000 kg, from affecting the 100000 kg Saginaw ball-bearing screw (Griggs, 1936). Drive Train Displacements of up to 10.16 cm are generated by a 0.75 hp, 1725 rpm electric motor, controlled by a Leeson® Speedmaster motor controller, enabling the revolutions to be adjusted between 0 and 100% in forward or reverse.  The electric motor drives a gear  assembly, the drive gear of which may be adjusted to provide displacement rates of 1.8xl0" , 2  1.8xl0" , and 1.8x10"* cm s"'at full rpm. Displacement generated by the electric motor is 4  transferred to the 100000 kg Saginaw ball-bearing screw mounted between the upper fixed and moving plates (Figure 2.1) via a thrust bearing, which prevents the large loads borne by the Saginaw screw from being transmitted to the gear train and motor assembly. The use of a Saginaw ball-bearing screw ensures that the friction generated during revolution of the screw under high loads is minimized. During a compression test, the pressure and compensating vessels are drawn upwards against the upper piston. Confining Pressure System The pressure vessel, made of HI 3 steel with a Rockwell hardness of 50-52, has an ID of 8.89 cm, an OD of 25.40 cm, and a wall thickness of 8.26 cm. The upper end of the vessel is sealed with a nut and gland assembly, whereas at the base there is a compensating pressure vessel and a lower compensating piston. Confining pressure is generated with a Haskel® A G T 62/152 model gas booster, capable of producing a confining pressure of 138 MPa using high purity argon gas as a confining medium.  8  Chapter II Sample Assembly The LSR can accommodate right cylinder samples of two sizes at temperatures up to 873 K: 1) 4.76 cm x 9.53 cm, with ends parallel to better than 0.254 mm, or 2) 2.22 cm x 5.08 cm, with ends parallel to better than 0.0127 mm. Small samples are used when o~i is expected to exceed the 500 MPa load cell limit for the large sample size. The low temperature assemblies consist of one hardened HI 3 steel spacer placed between the sample and each of the upper and lower pistons. A 1.588 mm diameter hole down their center and a groove pattern on each end (Figure 2.1) facilitates the even application of fluid pressure across the ends of the sample. The high temperature sample assembly includes a thermally conductive carbide spacer placed at the ends of the sample and an insulating lucalox spacer placed between the carbide spacers and the upper and lower pistons, both of which have the same hole and groove pattern for the application of fluid pressure as the HI3 spacers. For temperatures below 373 K, the sample assembly is jacketed in two wraps of polyolefin heat shrink tubing, sealed onto the ends of the sample assembly with twisted steel wire. While argon has been observed to diffuse through polyolefin, this has not been an issue at the timescale of the experiments.  For temperatures greater than 373 K the sample  assembly is jacketed with 0.0254 cm wall thickness, annealed pure copper tubing, with an internal diameter of 4.7625 cm, which is sealed onto the upper and lower pistons with silicon O-rings.  9  .  Chapter II  Pore Fluid System A flow-through pore fluid system enables permeability to be measured using the constant flow rate, the transient pulse (Brace et al., 1968), or the sinusoidal oscillation technique (Hsieh et al., 1981, Neuzil et al., 1981). Fluid pressure is generated using a Sprague® S216JN300 air drive fluid pump, allowing a maximum fluid pressure of 230 MPa. Furnace Temperature is generated with an internal resistance furnace (Figure 2.2), consisting of helically wound coils of 0.635 mm diameter Omega® NI80 nickel-chromium wire, with a resistance of 3.33 ohms per meter, wound at a pitch of 4.5 windings per cm onto 99.8% AI2O3 mufflers with an ID of 5.715 cm, an OD of 6.35 cm, and a length of 34.29 cm, and secured with Sauerison® cement. This configuration yields a total resistance of 17 Q. for each set of coils; 15 Q. of this resistance is within the coils themselves, while 2 Q is accounted for in the lead wires. An AC voltage of 110 volts generates a current of 6.5 A in each set of coils, which results in a total power of 633 Watts for each set of coils, corresponding to a power density of 6.25 watts per cm . These conditions meet the heat generation requirements without sacrificing the longevity of the furnace. The leads, which are insulated from the cemented coils using Cotronics® rescor blanket insulation, are attached to the lower piston using 1.27 mm set screws, insulated from the piston by pyrophyllite cones. Corrosion, resulting from the condensation of water vapour at the lower piston, necessitates the replacement of the lower 2-3 cm of lead every 1-2 experiments.  10  Chapter II  Temperature (K) 273  373  573  473  673  773  873  Lucalox Upper Coils Carbide  Sample  Carbide Lower Coils Lucalox Muffler Set Temperature:  398 K  773 K  523 K  Figure 2.2: Schematics of the furnace developed for the triaxial rock press at UBC, showing its position in relation to the sample assembly. These are overlaid on the measured temperature gradients for target temperatures of 398, 523, and 773 K.  11  Chapter II The temperature gradient along the sample is minimized using two independently controlled sets of coils, situated at the upper and lower end of the sample, leaving the middle 7 cm of the sample free from direct heat (Figure 2.2) (Tullis and Tullis, 1986). Convection heating of the upper end of the sample has not caused a problem, even for temperatures up to 773 K, and thus the upper and lower heaters are run at equal voltage and power. The pistons are insulated by wrapping the upper and lower portions of the sample assembly, from the contacts between the lucalox and the carbide to the pistons in Cotronics® rescor blanket insulation, completely filling the space between the inner wall of the furnace muffler and the sample assembly. The pressure vessel is insulated from the furnace by two 0.625 cm wraps of Cotronics® rescor blanket insulation, covered by two wraps of aluminum foil, all held together by twisted steel wire. A K-type thermocouple, wired through the lower piston in the same manner as the lead wires, is placed on the outside of the foil to monitor the temperature on the inside of the vessel wall. Upon heating a sample to 873 K, the vessel has reached 464 K, however, the vessel temperature drops off by up to 75 K once the desired sample temperature is reached. As the H13 pressure vessel can safely operate to temperatures up to 623 K, an external cooling system has not yet been developed. Temperature gradients along the sample were measured by inserting a K-type thermocouple into a sample of Badshot dolomite with a center hole and, once the desired temperature had equilibrated, the temperature was measured at 1.27 cm increments along the sample at 1 hour intervals.  The absolute magnitude of the temperature gradient is  consistently less than 10% of the set temperature, with the greatest variation at the ends of  12  Chapter II the sample; the middle 5.08 cm of the sample only shows -2% temperature variation (Figure 2.2). Monitoring Digital monitoring of data is performed using a computer with a Microsoft® Windows 2000 operating system and Labview® software. Millivolt signals from all of the independent components of the system are output as a text file, after having been converted to the appropriate units based on the full scale of the measuring device. Load is measured using an external load cell, placed above the upper piston, and inside the yolk assembly (Figure 2.1).  In order to obtain a satisfactory resolution of load  measurement, an Omega ® LC411-200K load cell with an output of 3 mWV run at an excitation of 10 V over a range of 0-90718 kg is used. Displacement is measured using a Trans Tek 0246-0000 dcdt with a workable range of \ 76.2 mm and a maximum usable range of *82.5 mm, mounted between the upper fixed plate and the lower mobile plate (Figure 2.1), thus measuring the external displacement of the top of the upper piston. Confining pressure is monitored with a B L H STD 50K pressure transducer with a pressure range of 0-345 MPa, located between the two shutoff valves. It has been calibrated against a calibrated analog Maxisafe® pressure gauge with a range of 0 to 345 MPa, and is recalibrated before each experiment. Pore fluid pressure is measured both upstream and downstream of the sample using two independent Precise Sensors Inc. 555030000 pressure transducers with an output of 3 mWV, run at 10 V excitation over a pressure range of 0-207 MPa. 13  Chapter II Temperature is monitored and controlled independently using a K-type thermocouple connected to an Omega ® CN8500 controller. The controlling thermocouple is positioned at the upper end of the sample, from where both heater plates are simultaneously controlled. The IA, 120 V output of the controller is fed into two relays, and subsequently into the two sets of furnace coils. This configuration allows for different voltages to be applied to the two sets of coils, while still controlling the furnace with one thermocouple and one controller. The voltage of the load side is varied using two variable auto transformers, while 120 V is permanently applied to the control side. Calibration The stiffness of the LSR was measured based on the spring analogy of Shimamoto (1977) (Figure 2.3), which assumes that any extension of the tie rods is insignificant. Measurements were made by deforming right cylinders of HI3 steel (E=206.84 GPa) and 6061-T6 aluminum (E=9.73 GPa) in each of the sample assemblies (Table 2.1). These metals were chosen due to their significantly different elastic properties, allowing the stiffness of the LSR to be explored at both low and high loads. The variance in stiffness is greater at low loads and the stiffness measured using the aluminum is consistently lower than that measured using the steel (Table 2.1). These trends quantify the variability in observed stiffness associated with loading and the alignment of Orings, and thus explain the observed non-linearity at the onset of experimentally derived stress strain curves. The increase in stiffness with increasing confining pressure for the small sample assembly is a result of the increased pressure on the tapered spacers (Figure 2.1).  14  Chapter II Moving Plate  H 3  Saginaw Screw, Thrust Bearing, and Gear Assembly Fixed Plate  Load Cell Tie Rods  Steel Spacer Upper Piston Upper Piston Cup Lucalox Spacer Carbide Spacer  Moving Plate  Sample Carbide Spacer Lucalox Spacer  Pressure Vessel  Lower Piston Lower Compensating Pistons  Compensating Vessel  Fixed Base A schematic of the triaxial rock press with all of the components represented as springs as was done by Shimamoto (1977), illustrating the importance of understanding the stiffness prior to obtaining mechanical data on the behavior of rocks.  F i g u r e 2.3:  15  Chapter II  o  (SO  s  "S  E  o o  S3  J  a  «  60  0s  > rt CO  ©  o  , l-g 81  9  M  I  55  s  C/3  e  rt  a  "5  o  •e  o  rt  ON  oo  s — o o  ca  &o *g is ca « J3 CD  -3  £  1  -3  C5  oo  Pi  O  £ °  a E  |3>  Q £ Cfl  i  I  CO  >  E a>  H  o  o H I  1/3  u  o  id  .2  D  H I  :  t  3  on 15  2  o E  0  E  _Q  GO  16  co  Chapter II 2.2.2 Experiments A total of 23 experiments were performed on dolomite from the Imasco Minerals® quarry in the Badshot Formation of southeastern British Columbia, the Graymont® Dolime quarry in the Niagara Formation in Ohio, and the Mighty White Dolomite® quarry near Rock Creek, British Columbia, at confining pressures of 25, 50, and 100 MPa, at 296 K, at a strain rate of-lxlO" (Table 2.2). 5  2.2.3 Startine Material Chemistry and Mineralogy Bulk chemical composition was analyzed for each of the three sample suites using Xray fluorescence (data in Appendix II).  Chemical analyses were obtained from four  independent blocks of each of Badshot dolomite and Rock Creek dolomite, and from three independent blocks of Niagara dolomite. All sample crushing was performed at UBC using the procedure outlined in appendix II. CaO and MgO contents are consistent with nearly stoichiometric dolomite for all samples (Figure 2.4). stoichiometric.  The CO2 content was estimated from LOI and is also nearly  The Badshot and Niagara samples have no significant concentrations of  oxides other than CaO and MgO; the Rock Creek samples contain 7.28 moles per kg of Si02 as opposed to 56.1 and 48.2 moles per kg of CaO and MgO respectively. The mineralogy of each of the three sample suites was determined from optical thin section observation (Figure 2.5), X-ray diffraction, and Rietveld refinements (Raudsepp et al., 1999) (data in Appendix II). Badshot samples are composed of >97 vol% dolomite with accessory quartz, calcite, tremolite, and muscovite; Niagara samples are composed of >95  17  Chapter II  120 100 H  o Rock Creek  ^4 80  n  Niagara  A Badshot  CD  60 i 40 20 H 0  - B — i — B — $ B~ BaO  CaO  Cr203 Fe203 K20  -B—B—B—S—BMnO Na20  P205  Si02  SnO  Ti02  Oxide  Figure 2.4: The bulk chemistry of the three sample suites used in this study in moles per kg, presented as mean values for replicate measurements. The 2a error bars highlight the variability within each sample suite.  18  Figure 2.5: Optical micrographs of dolomite samples from each of the three Formations examined in this study. A) Badshot dolomite consisting of coarse grains with lobate grain boundaries (L) and finer polygonal grains (P). Note the presence of cleavage and twinning in almost all grains. B) Rock Creek sample RC4 with rhombohedral grains and straight grain boundaries (S), and flaws within the grains (F). C) Rock Creek sample RC5 illustrating the irregular grain boundaries that result from pressure solution (PS), and reduced concentration of flaws within the grains. D) Niagara dolomite, with inclusion filled grains, giving a "dirty" appearance, straight grain boundaries (S), and moderately developed cleavage within the grains.  19  Chapter II vol% dolomite; and Rock Creek samples are composed of >85 vol% dolomite, with accessory calcite and quartz, located predominantly in veins, and talc.  Textural Analysis Grain Size Grain size was measured using the equivalent circular diameter technique.  Grain  boundary maps, obtained by manually tracing thin section images, were imported into Scion Image® and the grain areas were measured, along with the major and minor axis ratios to ensure grains were equi-dimensional. Hand sample scale variations were accounted for by calculating mean grain size values for each block (Table 2.2, Figure 2.6). Maximum grain sizes were obtained by averaging the 10 largest grains measured in each block. Porosity Porosity was determined by independently measuring the bulk and matrix density for each core.  The matrix density was measured with a Micromeritics® multivolume  pycnometer 1305 with a precision of 6.9xl0" MPa (0.01 PSI) and a Mettler® H20 scale 5  with a precision of 0.01 mg using the technique outlined by Rust (1998). Measurements were performed on three independent blocks of Badshot dolomite, and on each of the blocks of Niagara and Rock Creek dolomite that were used for experiments. The bulk density was measured for each core individually. Volume was obtained by measuring the diameter of the core at three points along its length, and the length at two different orientations using calipers with a precision of 0.001 cm, and the mass was measured using a Mettler® PI200 scale with a precision of 0.01 g. The relationship  20  Chapter II  a a •c  3  CD  u  w  w  > < -  <8 -4->  d  a >-, u ft X! CD  T3  o TJ C  o o  O.  a CD CD  x CD  &  CO  o  ^ a 3  21  Chapter II  0  200  400  600  800  1000 1200 1400 1600 1800 2000 2200 2400 2600  0  Grain Size (fim)  20  40  60  80  100  120  140  160  180  200  220  240  260  Grain Size (um)  Figure 2.6: Grain size histograms for A) Badshot dolomite block CBB1, B) Rock Creek block RC4, C) Rock Creek block RC5, and D) Niagara block OH4, which is representative of all Niagara blocks.  22  Chapter II  major principle stress 0-3  minor principle stress  CJp  peak differential stress  a  differential stress at yield  Y  mean stress porosity coefficient of friction dm  mean grain size  dx  max grain sizes (taken from average of 10 largest grains in each thin section)  w  Weight dry  d  W  s  Weight submerged  M  Mass  Pfl  Density of the fluid  Pm  Matrix denstiy  Pb  Bulk Density  c  Cohesion  Co  Uniaxial Compressive strength Mohr Coulomb friction parameter in o> o~ space 3  P*  Grain crushing pressure (mean stress)  E ff E  Effective Young's modulus  e  True Young's modulus  T a b l e 2.3:  A list of the symbols used in chapter II.  23  Chapter II (pm-pb)/p m=<t>  (2.1)  was used to obtain porosity (Table 2.2) (see Table 2.3 for a list of symbols). Hand Sample and Grain Scale Textures Badshot dolomite has been metamorphosed to amphibolite facies and subsequently annealed (Colpron et al., 1996). At the hand sample scale, the rock is isotropic, except for minor, randomly oriented tremolite porphyroblasts, and weakly aligned muscovite. At the thin section scale, coarser grains have lobate grain boundaries, exhibit minor to no undulose extinction and few deformation twins, although well developed subgrains are present (Figure 2.5a). Growth twins are common, as is the presence of well developed {1011} cleavage (Figure 2.5a). Finer grains are inferred to be the product of dynamic recrystallization. They are predominantly polygonal, with no undulose extinction, very rare twinning, and poorly developed cleavage (Figure 2.5a). Dolomite from the Rock Creek quarry is non-foliated, with variably oriented quartz and calcite veining along with sealed cracks visible in hand sample. In thin section, grains are predominantly subhedral and equigranular (Figure 2.5b,c), although sample RC4 generally has more rhombohedral grains and straighter grain boundaries (Figure 2.5b) than RC5, which has undergone pressure solution (Figure 2.5c). Twinning and {1011} cleavage are very rare within grains, as are intra and transgranular microcracks (Figure 2.5b,c). There are intragrain flaws, although these are more prevalent in the coarser RC4 block than in the RC5 block (Figure 2.5b,c). Niagara dolomite is also non-foliated, but has extensive porosity, visible as variably sized vugs in hand sample. In thin section, the anhedral to subhedral grains, which often 24  Chapter II have straight grain boundaries, contain opaque inclusions, giving them a "dirty" appearance (Figure 2.5d), and making individual grains difficult to distinguish.  {1011} cleavage is  common (although less so than in the Badshot samples), but twinning is rare (Figure 2.5d). Pores are generally the size of the grains, and are surrounded by cleavage surfaces, resulting in sharp "tips" around pores.  2.3 Results 2.3.1 Mechanical The peak and yield stresses of all 23 experiments are presented in table 2.2, along with the experimental conditions and sample properties. Effective Young's modulus was obtained by isolating the linear elastic region of the differential stress-axial strain plot, fitting this with the best fit line, and measuring the slope. The yield stress was obtained by picking the point where the measured differential stress-axial strain curve deviated from the linear fit used to obtain the effective Young's modulus, while the peak stress was obtained from the maximum stress on the differential stress-axial strain curve. Cohesion and the coefficient of friction were obtained for each sample suite using Coulomb's failure criterion. All sample suites have a progressive increase in strength with increasing confining pressure (Figures 2.7 and 2.8). Badshot dolomite is ductile at all confining pressures (Figure 2.7a); at confining pressures of 50 and 100 MPa, it also has a stick-slip response, with the wavelength between events decreasing with increasing confining pressure.  One sample  deformed at 100 MPa has reached an apparent steady state,, showing no strain hardening or softening between ~4 and 5.5% strain.  Within the Rock Creek samples, RC4 samples  25  Chapter II  Figure 2.7: Differential stress-axial strain curves for all 23 experiments. A) Badshot dolomite, B) Rock Creek, block RC4, C) Rock Creek, block RC5, and D) Niagara Dolomite.  26  Chapter II  x x  o 6  X  • A A O Badshot •  Niagara  A Rock Creek (RC4) X Rock Creek (RC5)  20  40  60  80  100  120  Confining Pressure ( M P a )  Figure 2.8: The influence of confining pressure on the peak differential stress for dolomite from each of the three Formations studied.  27  Chapter II (Figure 2.7b) are consistently weaker than RC5 (Figure 2.7c), however this difference decreases with increasing confining pressure. All Rock Creek samples have an elastic-brittle response and exhibit very little ductility. Mechanically, the Niagara samples are the most variable (Figure 2.7d). At 25 MPa, both samples (with porosities of 12-13%) exhibit significant ductility followed by strain softening. At 50 MPa, the two samples respond very differently; sample OH1-1 (<|)=6.6%) exhibits an elastic-brittle stress-strain response very similar to the Rock Creek samples, whereas sample OH5-3 ((|)=12.8%) exhibits rapid yielding followed by gradual strain softening. At 100 MPa, OH5-1 ($=9.4%) exhibits significant ductility and strain softening, with a minor stick-slip response.  2.3.2 Macro and Micro Structures The relationship between confining pressure, sample suite, and fracture orientation is illustrated in figure 2.9.  For both the Badshot and Rock Creek samples the mean angle  between major fractures and G\ decreases as confining pressure increases from 25 to 100 MPa, whereas in the Niagara samples, major fractures are rare, and have varied orientation. All Badshot samples contain one major fault at the hand sample scale, accompanied by crumbling at the sample ends, as a result of friction between the sample and the spacers. There is generally a limited amount of comminuted material within the fault zones. The exception to this is sample ebb 1-7, deformed at 50 MPa, which has damaged ends, but contains no major faults or cracks. In thin section, Badshot samples deformed at 25 MPa contain faults and comminuted material within the fault zone (Figure 2.10a,b). 28  Transgranualar microcracks, which cut  Chapter II  O Badshot •  Niagara  •  A Rock Creek (RC4) X Rock Creek (RC5)  4 x  X  20  40  60  80  100  Confining Pressure (MPa)  A graphical depiction of the variation in fracture orientation with varying confining pressure for each of the sample suites. Figure 2.9:  29  120  Chapter II  Chapter II Figure 2.10: Images of the deformed samples. A and B) are optical micrographs of Badshot dolomite sample CBB1-9 deformed at Pc=100 MPa. Intragranular deformation along cleavage planes (I), coupled with the absence of major transgranular fractures, is visible in A), whereas in B) a large scale fault is present (F), as are transgranular microcracks (T) which run sub parallel to the fault and cut across grains. C) and D) are SEM images from Rock Creek sample RC5-1, also deformed at Pc=100 MPa. The rotation of grains relative to one another has lead to dilation along grain boundaries (D). Comminution of grains (C) is visible along the fault boundary. Away from faults, transgranular microcracks are present along grain boundaries (T), and the grains themselves are generally undeformed (D). E) and F) are SEM images from Niagara samples OH4-2 and OH5-1, deformed at Pc=25 and 100 MPa respectively. In E) intragrain deformation (I) and comminution are observed in the vicinity of the pores (P), while transgranular cracks are present along grain boundaries (T). In F), Transgranular cracks running subparallel to oT are observed in the vicinity of faults (T), which link with a large pore just out of the image. There is also extensive intragranular deformation (I).  31  Chapter II across grains and make use of grain boundaries, generally occur in a subvertical orientation, although they are also observed subparallel to the faults (Figure 2.10b). Intragranular microcracking occurs in the vicinity of faults, along cleavage planes within the grains (Figure 2.10a,b). While faults and transgranular microcracks tend to cut across grains, intragranular microcracks are present along crystallographic weaknesses, and thus change orientation at grain boundaries due to variations in grain orientation (Figure 2.10a,b). At Pc=50 MPa the same characteristics are observed, however, the degree of intragranular deformation is greater.  At 100 MPa, samples contain extensive intragranular deformation such that the  original geometry of many grains can no longer be distinguished (Figure 2.10a,b). Faults occur with similar geometries as at lower confining pressures.  All Badshot samples,  regardless of the confining pressure, are in the transitional zone between brittle faulting and cataclastic flow. Rock Creek samples all have similar characteristics at the hand sample scale, regardless of the conditions of deformation. Samples contain diagonal to subvertical faults, the orientations of which are shown in figure 2.9. In most cases, faults are accompanied by extensive damage at the ends of the samples, again related to friction between the spacers and the samples. In thin section, Rock Creek samples deformed at 25, 50, and 100 MPa all exhibit similar microstructures consisting of transgranular microcracks along grain boundaries and faults (Figure 2.10c,d). Intragranular deformation is observed within 1-2 grains of the faults, and extensive comminution of grains has occurred within the faults (Figure 2.10c,d). Distal to the faults, dolomite grains are undeformed, however, at intermediate distances to the  32  Chapter II faults, there is dilation along grain boundaries as a result of grain rotation and shear (Figure 2.10c,d). Coarse grained calcite in veins exhibits intragranular deformation. All Rock Creek samples have deformed in the brittle faulting regime. Niagara samples exhibit only very minor deformation at the hand sample scale. In both samples deformed at 25 MPa this deformation is localized at the ends, again likely due to friction between the spacer and the sample. At Pc=50 MPa (OH5-3), a single, diagonal fracture is observed, but no other significant deformation can be seen in hand sample. At 100 MPa (OH5-1) there is extensive damage in the middle of the sample, and one diagonal fault. Intragranular deformation is observed to various extents throughout all Niagara samples, consistent with the lack of hand sample scale faults (Figure 2.10e,f). Grains that surround pores form damage zones, consisting of intense intragranular deformation, with microcracks making use of cleavage planes, resulting in comminution of grains. Away from pores, intragranular deformation is suppressed resulting in textures reminiscent of the undeformed samples.  Transgranular microcracks are common, generally controlled by  porosity, and often linking pores. Between pores, microcracks are present both along grain boundaries and across grains (Figure 2.10e,f).  Where pores are favorably oriented,  microcracks parallel to a step across pores, resulting in an en-echelon geometry (Figure t  2.10e,f).  There is no variation in microstructures with varying confining pressure in the  Niagara samples.  Sample OH1-1 deformed in the brittle faulting regime, based on its  mechanical response, whereas the rest of the Niagara samples are in the cataclastic flow regime.  33  Chapter II  2.4 The Transition from Trans to Intragranular Deformation  2.4.1 The Onset of Grain Crushing in Low Porosity Dolomite The transition in the deformed microstructures between low porosity Rock Creek and Badshot dolomites is a function of some combination of grain size, grain boundary texture, and intragranular texture.  In the Rock Creek and Badshot samples, with porosities below  1.5%, deformed at confining pressures at or below 100 M P a , the transition from brittle faulting to cataclastic flow is relatively insensitive to variations in mean stress (Figure 2.11). Both the Rock Creek and Badshot samples show a continuous increase in peak differential stress with increasing mean stress, indicating that deformation is accommodated by brittle failure and/or dilatant flow (Wong et al., 1997, Baud et al., 2000).  Furthermore, with the  exception of a slight increase in the degree of intragranular deformation in Badshot samples deformed at 100 M P a , there is very little variation in microstructure as confining pressure, and thus mean stress, is varied. The importance of the size and textural properties of grains on this transition has been previously recognized. deformed  anhedral  Hugman and Friedman (1979) observed that  crystalline  Hasmark dolomite  contained  experimentally  extensive intragranular  microfractures whereas micritic, euhedral Blair dolomite contained very few microfractures. The role of grain size on the onset of hydrostatic grain crushing, which corresponds to the onset of intragranular deformation under a hydrostatic stress, was analyzed by Zhang et al. (1990) based on Hertzian fracture mechanics, which describes the stresses related to the elastic deformation of packed spherical grains. The proportionality  P*a(<K)"  (2-2)  34  Chapter II  600  O Badshot 500  et  a-  •  Niagara  A Rock Creek (RC4) X Rock Creek (RC5)  400  rf  vi a> |  et  300  G 200  100  50  100  150  200  250  300  M e a n Stress ( M P a )  Figure 2.11: The relationship between the peak differential stress and the mean stress for each experiment.  35  350  Chapter II with n= -3/2 was theoretically obtained (Zhang et al., 1990) (see Table 2.3 for a list of symbols), and was found to be in good agreement with data for consolidated sandstone, unconsolidated sand, and glass spheres, as well as for both naturally and experimentally deformed sandstones and quartzites (Wong et al., 1997). In using this relationship to analyze the data, mean stress was used as was done by Zhang et al. (1990) for the data of Hirth and Tullis (1989).  Consequently, the critical pressure for grain crushing is lower due to the  tangential contact forces generated by the differential stress (Zhang et al., 1990, Papamichos et al, 1993, Menendez et al., 1996). The Rock Creek and Badshot samples plot in distinct regions of ((>*d -mean stress m  space (Figure 2.12). Rock Creek samples, which deformed almost exclusively by brittle faulting and transgranular microcracking, inhabit a region of much lower <J>*d values than m  the Badshot samples, which deformed by a combination of brittle faulting and intragranular microcracking, consistent with Hertzian fracture theory (Zhang et al., 1990). Based on the transition in microstructures associated with varying grain size, at approximately constant porosity, equation 2.2 was used to obtain an estimate of the critical mean stress required for the transition from brittle faulting and transgranular microcracking, to cataclastic flow accommodated by intragranular deformation in dolomite (Figure 2.12). The predicted pressures required for grain crushing are much lower than predicted by Zhang et al. (1990) for quartz-rich rocks. The onset of grain crushing occurs at a lower axial stress during non-hydrostatic loading than required in hydrostatic loading (Papamichos et al., 1993). Just as important, however, is the presence of {1 OX 1} cleavage in dolomite, which microstructures indicate promotes the onset of intragranular deformation and cataclastic flow  36  Chapter II  lOOOOOOi  Porosity x Mean Grain Size (urn)  F i g u r e 2.12: An examination of the grain crushing theory of Zhang et al. (1990) based on a plot of <j)*dm vs. mean stress for all of the experiments. The upper and lower envelopes have slopes of-3/2 and require constants of 5000 and 100 respectively.  37  Chapter II (Figure 2.10a,b).  This is consistent with the observations of Tullis and Yund (1987) on  feldspar, where the ease of cracking along cleavage planes promoted cataclastic flow.  2.4.2 The Influence of Grain and Grain Boundary Textures Under a triaxial stress state, the transition from trans to intragranular deformation is also a function of the ability of grains to rotate and shear past each other, which is commonly assumed to be controlled by the mean stress (Menendez et al., 1996). In these experiments, this transition is promoted as a function of texture rather than mean stress. Badshot dolomite, with lobate grain boundaries, is not capable of readily deforming by grain rearrangement, however, due to the presence of {1011} cleavage, it can readily accommodate intragranular microcracking. In contrast, Rock Creek samples have rhomobhedral grains, that can readily deform by shearing along grain boundaries, leading to grain rotation, transgranular cracking, and deformation by brittle faulting, yet have very few intragranular flaws, inhibiting intragranular deformation. 1/2  The Hall-Petch relationship between grain size and fracture strength (o a d " ), p  m  which has been discussed extensively in the rock mechanics literature for calcite and quartz sandstones (Fredrich et al., 1990, Olsson, 1974, Hatzor and Palchik, 1998, Wong et al., 1997, Hugman and Friedman, 1979) may, therefore, not be applicable for dolomite-rich rocks (see next chapter). Texturally, dolomite is very different than either quartz or calcite. Quartz does not contain cleavage planes, which can significantly alter the relationship between grain size and the initial Griffith flaw length and/or the concentration of flaws. In calcite, which like dolomite contains perfect {1011} cleavage, fractures are strongly cleavage controlled at hydrostatic stresses above that required for grain crushing (Zhang et al., 1990). Calcite, 38  Chapter II however, is much more susceptible to crystal plastic deformation than dolomite (Turner et al., 1954, Fredrich et al., 1990, Baud et al., 2000).  The plastic yield stress in calcite is  strongly related to grain size, as grain boundaries act as barriers to both dislocation glide and twin propagation (Fredrich et al., 1990), thereby enhancing the relationship between grain size and strength which is not necessarily the case in dolomite. The transition from deformation by transgranular microcracking and faulting to intragranular deformation and cataclastic flow is strongly influenced by grain and grain boundary textures. Rock Creek samples, which deform by transgranular microcracking and faulting, have little to no cleavage or twinning within the grains and straight grain boundaries. The principal weaknesses within the rock are grain boundaries, which allow grains to shift relative to one another, leading to the formation of transgranular grain boundary microcracks and faults. Conversely, grain boundaries in the Badshot samples are lobate, and grains contain numerous cleavage and twin planes. The principal weaknesses are the cleavage planes within the grains, and thus intragranular deformation predominates, resulting in cataclastic flow.  2.4.3 The Influence of Porosity Niagara samples with porosities greater than 7% are substantially more ductile than that with a porosity of 6.6% (OH1-1) (Figure 2.7d). The samples with porosities greater than 7% plot higher in <))*d space than any of the Badshot samples (Figure 2.12), which indicates m  that they are more likely to exhibit intragranular deformation, whereas that with a porosity of 6.6% plots amongst the Badshot samples.  The intragranular deformation predicted from  figure 2.12 for samples with <))>7% occurs preferentially in damage zones, in the vicinity of  39  Chapter II pores.  In vuggy rocks deformed under a differential stress, pores act as stress risers,  promoting deformation in neighboring grains. This is enhanced by the presence of cleavage, which causes irregularities in the surfaces of pores from where cracks can initiate and propagate. The lower porosity Niagara sample (OH1-1) plots amongst the Badshot samples in figure 2.12, despite its significantly more elastic-brittle mechanical behaviour, a difference attributed to its finer grain size than the Badshot samples, coupled with straight grain boundaries that act as weaknesses, promoting transgranular deformation. The varying response of the Niagara samples is interpreted to be the result of pore collapse (Brace, 1978, Gowd and Rummel, 1980, Logan, 1987, Rutter and Hadizadeh, 1991, Baud et al., 2000). In Solnhoffen limestone, however, Baud et al. (2000) observed the onset of pore collapse in samples with porosities as low as 3% whereas this mechanism is not observed in Niagara samples until porosities greater than ~7%. The difference between my experiments on dolomite and those of Baud et al. (2000) on Solnhofen limestone may, as discussed in relation to grain size, be related to the ability of calcite to deform by crystal plastic processes at room temperature, a distinction they noted in comparing their experimental results to previous work on silicate rocks (Tullis and Yund, 1992, Hirth and Tullis, 1994). The stress intensification around pores can readily reach the critical resolved shear stress for twinning or slip in calcite, whereas this is not possible for dolomite at room temperature (Turner et al., 1954). The onset of crystal plasticity leads to crack tip blunting (Hertzberg, 1996), which inhibits crack propagation and coalescence, and prevents brittle faulting.  Further, twinning produces intragrain weaknesses, which promote intragrain  deformation and cataclastic flow (Baud et al. 2000).  40  In calcite, this results in a ductile  Chapter II response (Baud et al., 2000), whereas in dolomite crystal plastic process are not operative at low temperatures, and the rock continues to deform by brittle faulting to higher porosities than in calcite, promoting shear localization and inhibiting the onset of cataclastic flow. The role of porosity on the onset of intragranular deformation is highly texturally dependant. Dolomite deforms in the brittle faulting regime at much higher porosities than calcite, where crystal plastic processes inhibit crack growth and propagation. Further, pore size and geometry, dictate the degree to which stresses are intensified in the vicinity of the pore, and the concentration of pores dictates whether these localized regions of deformation can interact.  The ability of the damaged zones around pores to interact will dictate the  overall mechanical and microstructural response of the rock to deformation.  2.5 C o n c l u s i o n  The transition from brittle faulting to cataclastic flow in dolomite is a complex process that is intricately related to the textural properties of the rock. In dolomite with porosities below ~7%, this transition is strongly linked to the ability of grains to rotate in relation to one another, an ability that is influenced either by grain boundary texture or confining pressure. The presence of intragrain flaws, of which cleavage is the most notable in dolomite, can also strongly influence the scaling between grain size and the length and concentration of the initial flaws, thereby influencing the transition from brittle faulting and transgranular microcracking to extensive intragranular deformation and cataclastic flow. This lack of scaling between grain and flaw size and concentration is strongly related to the  41  Chapter II textural and mechanical properties of the grains or mineral, including the presence of cleavage, which may provide a plane more conducive to failure than a grain boundary. In dolomite with porosities greater than -7%, inelastic pore collapse controls the transition from brittle faulting to cataclastic flow. At relatively low strains, this deformation manifests itself as local intragrain deformation and comminution of grains in the vicinity of pores coupled with microcracking that connects and steps across pores.  This transition  occurs at porosities of - 7 % in dolomite, inconsistent with calcite in which it has been observed in rocks with porosities as low as 3%, a difference that is strongly related to the textural properties of the rocks, as well as to the mechanical properties of the mineral. While porosity and grain size are important textural properties in controlling the transition from brittle faulting to cataclastic flow, so are grain boundary textures and the presence of flaws or inclusions within the grains. All of these must be considered in an examination of the controls of the mechanics of deformation in dolomite if the spectrum of naturally occurring textures is to be investigated.  42  Chapter III  Chapter III: Textural Controls on the Brittle Deformation of Dolomite: Variations in Peak Strength  43  Chapter III 3.1 Introduction The textural properties of dolomite can vary substantially within mineralogically similar formations, and it is these variations in porosity, grain size, grain boundary texture, and intragrain texture that result in very different peak strengths. Quantification of porosity and grain size is relatively straightforward, whereas intragranular and grain boundary textures are very difficult to quantify. The role of texture on crack initiation and propagation in compressive regimes is poorly understood, despite the fact that the importance of flaws and heterogeneities in the brittle failure of materials has been recognized since Griffith's classic papers (Griffith, 1921, Griffith, 1924). These flaws are commonly related to the textural properties of the rock. Griffith's theory satisfactorily explains the initiation of cracks, but it cannot account for crack propagation and coalescence (Hoek and Bieniawski, 1966), which dictate the peak strength of rocks (Horii and Nemat-Nasser, 1985, Ashby and Sammis, 1990, Sagong and Bobet, 2002). The wing crack model proposes the nucleation and growth of a "wing crack" when the shear stress along a crack exceeds the frictional resistance, providing an explanation for crack nucleation, propagation, and coalescence (Brace and Bombolakis, 1963, Brace et al., 1966, Fredrich etal., 1990). Using experimental rock deformation data from triaxial experiments performed on texturally diverse, nearly stoichiometric dolomite, current empirical relationships are improved upon with the aim of advancing our understanding of the role of the textural properties of dolomite on its peak strength.  The theories of compressional fracture  mechanics (for a review, see Fredrich et al., 1990 and Evans et al., 1990) are compared with 44  Chapter III experimental observations to show that very few rock properties are required to empirically predict the peak strength of dolomite. This is attributed to the roles of flaws and voids on properties other than the peak strength. Grain size does not necessarily correlate well with the peak strength, a discrepancy that can be explained by the grain boundary and intragranular textures.  3.2 E x p e r i m e n t s  3.2.1 Methodology To examine the role of rock texture on the peak and yield strengths of dolomite, a series of 23 deformation experiments (Table 3.1) were performed on texturally diverse dolomite-rich rocks from the Imasco Minerals® quarry in the Badshot Formation of southeastern British Columbia, the Graymont Dolime® quarry in the Niagara Formation of Ohio, and the Mighty White Dolomite® quarry in Rock Creek, British Columbia using the LSR triaxial rock press (described in Chapter II). Experiments were performed on oven-dried right cylinders (baked at 358 K for 24 hours) with diameters of 2.22 cm and length to diameter ratios of-2:1, at confining pressures of 25, 50, and 100 MPa, at 296 K, at a strain rate of~lxl0" s (Table 3.1). 5  ]  Dolomite from each of these formations has been described in detail in the previous chapter, a summary of which is provided in table 3.1a. Badshot dolomite is a marble with lobate grain boundaries, dynamically recrystallized grains, extensive intragranular cleavage, and well developed subgrain boundaries (Figure 3.1a); Rock Creek dolomite consists of subhedral, equigranular grains with very rare cleavage or twinning (Figure 3.1b,c); and 45  Chapter III  CO  IS  c  0)  H  46  CO  Chapter III  Principle compressive stress 0-3  Least compressive stress  °"p  Peak differential stress  °Y  Yield stress  M-  Coefficient of friction  4>  Porosity Mean grain size Maximum grain size (calculated as the mean of the 10 largest grains in each block) Cohesion Unconfined compressive strength  dm  d c  x  Co  Coulomb friction parameter in G\ o space 3  Eeff  Effective Young's modulus  E  True Young's modulus  p  True compressibility  Peff  Effective compressibility Total volume Volume per crack Average crack length  V  y_ £  K, a N  a  c  Critical stress stress intensity factor Initial half flaw length Flaw density  1  Length of the wing cracks  y  The angle between the initial flaw and 0"!  Table 3.2: A description of the symbols used in chapter III.  47  Chapter III  Figure 3.1: Optical micrographs of undeformed samples from A) Badshot dolomite, highlighting lobate grain boundaries (L) and intragranular cleavage; B) Rock Creek block RC4 highlighting straight grain boundaries (S); C) Rock Creek block RC5 highlighting the irregular grain boundaries that result from pressure solution (PS) and a lower concentration of intragranular flaws than in RC4; and D) Niagara dolomite, highlighting the prevalence of intragranular flaws, giving the grains a "dirty" appearance, along with straight grain boundaries (S).  48  Chapter III Niagara dolomite consists of anhedral to subhedral grains, vuggy porosity on the size scale of grains, and extensive intragranular cleavage, although twinning is rare (Figure 3.Id).  3.2.2 Experimental Results Summarized results for each of the experiments are presented in Figure 3.2 and Table 3.1, and a detailed description is presented in the previous chapter.  C , C, and pwere 0  calculated based on Coulomb's failure criterion ai=C +tan\|/o 0  (3.1)  3  where C and \|/ are converted to C and p using the relationships 0  sinp=(tani|/-l)/(tan\|/+l)  (3.2)  C=C (l-sinp)/2cosp  (3.3)  and 0  (Sofianos and Halakatevakis, 2002) (see Table 3.2 for a description of the symbols used). Effective Young's modulus and yield stress values were obtained by isolating the elastic portion of the differential stress-axial strain curve, obtaining the slope of the best fit line to this region, and picking the stress at which the differential stress-axial strain curve deviated from this linear trend, respectively. The experimental data are supplemented with the data of Hatzor et al. (1997) performed on dolomite from the Amindav Formation in central Israel. Experiments from their data set were excluded where: 1) the data set was incomplete with respect to porosity, grain size, effective Young's modulus, or peak stress, or 2) the modal mineralogy consisted of less than 80% dolomite. C , C, and p were calculated for the data set of Hatzor et al. 0  (1997) using the method described previously. 49  Chapter III  0  2  4  6  0  Strain (%)  2  4  6  Strain (%)  Figure 3.2: Differential stress-axial strain curves for: A) Badshot dolomite, B) Rock Creek (RC4), C) Rock Creek (RC5), and D) Niagara dolomite.  50  Chapter III 3.3 Controls on the Peak Strength of Dolomite Numerous parameters, including textural properties of the rock as well as the extrinsic conditions of deformation, affect the peak and yield strengths of dolomite, and it is essential to understand the relative importance of these in order to elucidate the importance of texture.  Correlation coefficients  between the sample properties, the controlled  experimental conditions, and the experimental results quantify these relationships (Table 3.3, Figure 3.3). There is a moderate negative correlation (-0.3790) between porosity and peak strength.  The strongest correlations are between effective Young's modulus (0.4961),  cohesion (0.5477), unconfined compressive strength (0.6060), and confining pressure (0.7890) and peak stress.  Porosity is more strongly correlated to the yield stress (R=-  0.5022), as is the effective Young's modulus (R=0.5872), while cohesion, unconfined compressive strength, and confining pressure have a decreased correlation (R=0.4708, 0.5521, and 0.6544 respectively) with yield stress. Significantly, there exists only a very weak correlation between either mean or maximum grain size and peak or yield stress, despite the large range of grain sizes being studied. Combining this data with that of Hatzor et al. (1997) results in an adjustment of the correlation coefficients, although their relative importance remains consistent (Figure 3.3). The correlation between peak stress and confining pressure (0.8586) is intensified, as is that with cohesion (0.6871), unconfined compressive strength (0.7154), and effective Young's modulus (0.5693). Notably, the correlation with porosity is now significant (-0.5743), yet the correlation between peak stress and grain size remains poor (d : 0.2947, d : 0.2439). m  51  x  Chapter III A) d>  dm  dx  Eeff  C  Co  U  Pc  e rate  OP  oy  1.000  -0.113  -0.057  -0.655  -0.180  -0.240  -0.359  -0.116  0.707  -0.379  -0.502  n  -0.359  -0.829  -0.847  0.372  -0.694  -0.551  1.000  -0.095  -0.350  -0.130  0.020  dx  -0.057  0.989  1.000  -0.225  0.649  0.495  -0.847  0.032  0.092  0.089  -0.029 0.002  dm  -0.113  1.000  0.989  -0.234  0.648  0.494  -0.829  0.080  0.111  0.114  Eeff  -0.655  -0.234  -0.225  1.000  0.221  0.344  0.372  0.058  -0.794  0.496  0.587  C  -0.180  0.648  0.649  0.221  1.000  0.980  -0.694  0.178  -0.143  0.548  0.471  Co  -0.240  0.494  0.495  0.344  0.980  1.000  -0.551  0.182  -0.231  0.606  0.552  Pc  -0.116  0.080  0.032  0.058  0.178  0.182  -0.095  1.000  0.117  0.789  0.654  e rate  0.707  0.111  0.092  -0.794  -0.143  -0.231  -0.350  0.117  1.000  -0.273  -0.439  op  -0.379  0.114  0.089  0.496  0.548  0.606  -0.130  0.789  -0.273  1.000  0.941  ay  -0.502  0.002  -0.029  0.587  0.471  0.552  0.020  0.654  -0.439  0.941  1.000  <b 1.000  dm  dx  Eeff  C  Co  U  Pc  e rate  op  *  -0.242  -0.200  -0.745  -0.411  -0.454  0.171  -0.373  -0.341  -0.574  B)  n  0.171  -0.521  -0.445  -0.086  -0.705  -0.542  1.000  -0.431  -0.545  -0.438  dx  -0.200  0.976  1.000  0.010  0.625  0.516  -0.445  0.215  0.273  0.244  dm  -0.242  1.000  0.976  0.047  0.668  0.549  -0.521  0.285  0.359  0.295  Eeff  -0.745  0.047  0.010  1.000  0.372  0.468  -0.086  0.320  0.450  0.569  C  -0.411  0.668  0.625  0.372  1.000  0.971  -0.705  0.448  0.443  0.687  Co  -0.454  0.549  0.516  0.468  0.971  1.000  -0.542  0.417  0.378  0.715  Pc  -0.373  0.285  0.215  0.320  0.448  0.417  -0.431  1.000  0.611  0.859  e rate  -0.341  0.359  0.273  0.450  0.443  0.378  -0.545  0.611  1.000  0.545  op  -0.574  0.295  0.244  0.569  0.687  0.715  -0.438  0.859  0.545  1.000  Table 3.3: A) Correlation coefficients between sample properties, experimental conditions, and experimental results for my experiments. B) The same as A) except the datafromHatzor et al. (1997) is included.  ohl oh4 oh5 cb rc4 rc5  Na (flaws per mm Kic=2.47 52 44 48 2 94 370  2  ) Flaws per grain Kic=2.47 0.28 0.60 0.51 0.36 0.07 0.10  Table 3.4: Predicted flaw densities and the corresponding number of flaws per grain for each of my sample suites based on equation 3.17, using a Kic value of 2.47 MPa m and an initial flaw length (2a) equivalent to the mean grain size. 1 / 2  52  Chapter III  o This Data Set a This + Hatzor et al. (1997)  • o • o  • o  • o  • o  • o I  "dx"  dm  Eeff  Co  Pc  • • Property-  Figure 3.3: The trends in correlation coefficients with peak strength for my data set and my data set plus the data of Hatzor et al. (1997).  53  Chapter III  3.3.1 A Modified Empirical Failure Criterion It is generally assumed that a Hall-Petch relationship: o a d p  (3.4)  1 / 2 m  exists between mean grain size and the peak strength of rocks (Olsson, 1974, Hugman and Friedman, 1979, Fredrich et al., 1990), however, the poor correlation between peak stress and either mean grain size or the square root of the mean grain size for this experimental data indicates that this relationship does not hold for texturally diverse dolomites (Figure 3.4). This discrepancy is highlighted by fitting the empirical relationship proposed by Hatzor and Palchik(1998) 0 =a(Eeffa ) /<t) d b  p  c  3  (3-5)  1/2  m  to the data obtained from the present experiments and from Hatzor et al. (1997) (Figure 3.5), and comparing it to one of the same form and the same number of fit parameters, without the grain size term c=a(EeffO-3)/<t) b  (3.6)  c  p  (Figure 3.5).  Hatzor and Palchik (1998) specified that equation 3.5 is valid over 20000  MPa<E <65000 MPa; 15pm<d <50pm; 0.02<(|)<0.21; 1 MPa<o <25 MPa. The poor fit of efr  m  3  equation 3.5, especially to the coarse grained Badshot samples indicates that other textural parameters must overshadow the role of grain size in texturally diverse rocks. In equation 3.6, the value of c approaches zero, indicating that porosity is not required to fit this data set, resulting in a relationship of the form a =a(E o ) p  eff  (3.7)  b  3  54  Chapter III A)  O 25 MPa A  • 50 MPa A 100 MPa  A  cct PL, A A  CJ  • O o  a a o o  •a u  PH  Mean Grain Size (urn) B)  O 25 MPa • 50 MPa A 100 MPa  ca  PH  •  <L>  is  o  a  • •  o  Q OJ PH  -1/2  Figure 3.4: The relationship between A) mean grain size and B) the inverse square root of mean grain size and peak differential stress for my data set.  55  Chapter III  0  100  200  300  400  500  600  700  Measured Peak Differential Stress (MPa)  Measured Peak Differential Stress (MPa) Figure 3.5: A) The ability of equation 3.5 to explain the peak strength of dolomite with a=2.4587, b=0.4845, and c=-0.1372, resulting in an R of 0.4168. Note that this relationship cannot explain the unconfined samples or the Badshot samples. B) Equation 3.6 fit to the data set with a=1.3687, b=0.3624, and c=0.0301, producing an R of 0.7937. Equation 3.6 can explain the coarse grained Badshot samples (highlighted), however, unconfined samples are still not explained. 56 2  2  Chapter III This relationship dictates that, as confining pressure goes to zero, the predicted strength of the rock also goes to zero. In figure 3.5, based on equations 3.5 and 3.6, the strength of samples deformed at atmospheric pressure is significantly underestimated.  Hatzor and  Palchik (1998) solved this problem by removing the confining pressure term from the equation for unconfined samples. It is, however, desirable to obtain a continuous relationship across all confining pressures. Based on Coulomb's failure criterion (equation 3.1), under zero confining pressure, the strength of the rock is defined as the uniaxial compressive strength. Equation 3.7, therefore, becomes (3.8)  0p=a(E ffO3) +Co b  e  which results in an R of 0.92 (Figure 3.6). 2  There is a unit imbalance in this relationship that can be solved by fitting  E ff e  and  03  with different fit parameters, and correlating these so that they sum to 1 (Figures 3.6 and 3.7). This results in an equation with the form: (3.9)  Op=aE ff a +Co b  e  c  3  There is a range of fit parameters (a,b,c) that produce a unit balance without diminishing the ability of equation 3.9 to explain the experimental data (Figure 3.7).  When c=l and b=0,  equation 9 reduces to the form of Coulombs relationship, however, b may be up to 0.65 without reducing the R below 0.89 (which contains fewer significant figures than the 2  optimized R of 0.8918 to account for sample variability). Confining pressure and effective 2  Young's modulus are poorly correlated (0.058 and 0.320 for this data set and this data set combined with Hatzor et al.'s (1997)), and thus effective Young's modulus must influence the peak strength of dolomite. 57  Chapter III  Chapter III F i g u r e 3.6: A ) E q u a t i o n 3.8 fit to the data set with a=0.0003 and b=0.8796, resulting in an R  2  o f 0.9200. B ) Equation 3.9 fit to the data set with a=4.6896E-10, b=2.1138, and  c=0.8231, resulting in an R o f 0.9374. C ) Equation 3.9, optimized for a unit balance, with 2  a=0.5617, b=0.2227, and c=0.7773, resulting in an R o f 0.8918. 2  59  Chapter III  Figure 3.7: The range of b and c values that result in an R value of >0.89, using equation 3.9, for varying a values, highlighting the range of a, b, and c values that can be used without reducing the ability of equation 3.9 to explain the data set. 2  60  Chapter III If b>0, then c^l, and equation 3.9 is non-linear with respect toCT3and scales with the material property E ff. By specifying the intercept as the uniaxial compressive strength, there e  is an element of similarity to Coulomb's failure criterion. The failure criterion of Hatzor and Palchik (1998) has been modified, generating one that is intermediate between theirs and Coulomb's failure criterion. It is necessarily more simplistic than that of Hatzor and Palchik (1998), yet it provides greater insight into the role of the textural properties of dolomite than Coulomb's criterion.  3.4 T h e R e l a t i o n s h i p B e t w e e n Effective Y o u n g ' s M o d u l u s a n d R o c k T e x t u r e  Equation 3.9 indicates that the peak strength is highly dependent on the effective Young's modulus in dolomite, which is consistent with correlation coefficients (Figures 3.3 and 3.8, Table 3.3), yet no other material properties are required for a good fit. The peak strength is, however, theoretically strongly related to the porosity (Sammis and Ashby, 1986, Zhang et al, 1990), as well as to the length and concentration of the initial flaws (Horii and Nemat-Nasser, 1985, Ashby and Sammis, 1990), all of which are texturally controlled (see previous chapter). The experimental data from this work demonstrates that the effective Young's modulus of dolomite is strongly negatively correlated to porosity in dolomite (R=-0.6547 for this data set or R—0.7446 when the data of Hatzor et al. (1997) is included).  This  relationship has been theoretically analyzed by Walsh (1965a), based on calculations regarding the role of spherical voids on the compressibility of rocks under a hydrostatic  61  Chapter III  Figure 3.8: The relationship between effective Young's modulus and peak strength for my experiments, at confining pressures of 25, 50, and 100 MPa.  62  Chapter III stress.  If effective compressibility is converted to effective Young's modulus using the  relationship p =3(l-v)/E eff  (3.10)  eff  (Walsh, 1965a) then the relationship between effective Young's modulus and porosity is E r=[2E(2v-1 )(<!>-1 )]/[2+<J)-4v+v(|)]  (3-11)  ef  which produces an inverse relationship between effective Young's modulus and porosity. The length and concentration of the initial flaws does not necessarily correlate with grain size based on the poor correlation between grain size and peak strength.  Walsh  (1965b,c) derived a theoretical relationship between these flaw properties and the effective Young's modulus for both open and closed cracks: 1) for open cracks in plane stress E fr=-3Ev/(-3v+47tc )  (3.12)  3  e  2) for open cracks in plane strain Eefr=-3Ev/(-3v-47tc +47tcV)  (3.13)  3  3) for closed cracks in plane stress E fr-E/[l+(47rc /15y){(2+3p. +2p. )/(l+ P- ) -2ii} ] 3  2  4  2  3/2  e  (3.14)  4) for closed cracks in plane strain E f=E/[l+(4TO (l-v )/15v){(2+3|i +2p. )/(l+ 3  2  2  4  ef  u, ) -2u)] 2  3/2  (3.15)  In all cases, these relationships show that increasing flaw length or flaw density decreases the effective Young's modulus (Walsh, 1965c). Therefore, a decrease in effective Young's modulus should be a strong indicator of a decrease in the peak strength of the material, which is observed based on correlation coefficients. 63  Chapter III From a practical standpoint, the effective Young's modulus of a material is a powerful parameter for use in an empirical relationship as it is readily obtained from the differential stress-axial  strain curve of compression experiments.  Furthermore, no  assumptions need to be made regarding the location or nature of the initial flaws, or regarding the mechanism of deformation.  3.5 T h e R e l a t i o n s h i p B e t w e e n F l a w s a n d G r a i n S i z e  As the Hall-Petch relationship is not valid for this experimental data set, it is apparent that the textural controls on the peak strength are more complex than can be approximated by grain size, or by grain size and porosity.  From figure 3.4 it is clear that there is not a  monotonic decrease in strength with increasing grain size; the coarse grained Badshot samples are consistently as strong or stronger than the Rock Creek (RC4) samples. The theory of wing crack initiation and coalescence is used to explain the discrepancies between the Hall-Petch relationship and the current data set.  The stress  required for the initiation of wing cracks is defined as:  aHaiVy'VMaV) ' ^^ 1 2  (3.i6)  (Horri and Nemat-Nasser, 1985, Ashby and Sammis, 1990).  The only parameters that  influence the onset of wing crack propagation are Kic and p, and the half length of the initial flaw, a. Therefore, at constant confining pressure, and for constant material properties, K j and p, the stress required for the initiation of wing crack growth is governed solely by the magnitude of a.  64  C  Chapter III The peak strength, which is associated with the onset of shear failure, is governed by the coalescence of wing cracks which, in turn, is sensitive to both the initial flaw length and the concentration of these flaws. The peak stress is approximated using the 2D, plane strain equation of Ashby and Sammis (1990): o ={C +(C4((D/Do) -l)/(l+(7iD ) ((D/D ) -l)/(l-D ))}a + ,/2  1  ,/2  1  1/2  0  (3.17)  ,/2  0  3  {((D/D ) -l+0.1/cosy) /(l+(7^ 1/2  1/2  o  where  C,=((l+p ) +lty((lV) -^)  (3.18)  C =30 cosY/((l+p ) -u)  (3.19)  D=7t(l+acosY) N  (3.20)  2  ,/2  ,/2  1/2  2  ,/2  4  2  a  Do= 7i(acosY) N  (3.21)  2  a  The onset of strain softening occurs when l/a~0.75 for an optimal orientation of the initial flaws (y), with respect to 0"i, of 0.24K (Horii and Nemat-Nasser, 1985). Assuming that the material properties Kic and p remain constant, and for the optimal 1/a ratio and initial orientation of wing cracks, the peak strength of the material is sensitive to both the initial flaw length and initial flaw density (Horii and Nemat-Nasser, 1985, Sammis and Ashby, 1990). Using equations 3.17-3.20, the variation in peak 0\ for a spectrum of N and a values a  was calculated, and the measured peak strength for each experiment was plotted (Figure 3.9) in N -a space, using the p values obtained from Coulomb's relationship (equation 3.1, Table a  3.1). Plots are generated for a high Kic value of 2.47 MPa m  65  1/2  (Gunsallus and Kulhawy,  Chapter III  Chapter III F i g u r e 3.9: Plots showing the relationship between the h a l f flaw length (a), the flaw density (Na), and the measured peak strength for each experiment. A ) , B ) , and C ) are for Badshot dolomite at confining pressures o f 25, 50, and 100 M P a respectively; D ) , E ) , and F ) are for Niagara dolomite at confining pressures o f 25, 50, and 100 M P a respectively; G ) , H ) , and I) are for R o c k C r e e k ( R C 4 ) dolomite at confining pressures o f 25, 50, and 100 M P a respectively; and J), K ) , and L ) are for R o c k Creek ( R C 5 ) dolomite at confining pressures o f 25, 50, and 100 M P a respectively. In all cases the peak strength contours are made for K i c values o f 2.47 and 0.1 M P a  m  1 / 2  .  67  Chapter III 1984) and for an- exceptionally low value of 0.1 MPa m  1/2  to highlight the consequence of  varying Kic, which results for different flaw types (Fredrich et al., 1990). In figure 3.9, if either N or a are prescribed, the other is fixed for a known peak a  strength and a constant Kic value. Starting with the common assumption that grain size is a proxy for the initial flaw length (Fredrich et al., 1990, Baud et al., 2000), a range of flaw densities per unit area are predicted using the curves for Ki =2.47 MPa m C  1/2  (Table 3.4).  Flaw density in reference to unit area is difficult to analyze microstructurally, so these are converted to the number of flaws per grain area based on the measured grain sizes. This relationship predicts that Niagara blocks OH4 and OH5 contain the highest flaw densities per grain (0.60 and 0.51), followed by the Badshot samples (0.36), and Niagara block OH1 (0.28). The Rock Creek samples RC4 and RC5 have the lowest number of flaws per grain (0.07 and 0.10). Microstructural observations made in the previous chapter are not consistent with these predictions (Figures 3.1 and 3.10). The Badshot samples contain numerous cleavage planes within the grains, which are interpreted to act as initial flaws on a scale much smaller than the grain size, but with a very high density. In the deformed Badshot samples (Figure 3.10a,b) there are numerous intragranular microcracks that are present along cleavage planes. The presence of smaller, more concentrated flaws are consistent with figure 3.9; a decrease in flaw size necessitates an increase in flaw density. In both Rock Creek suites, it appears that flaw size scales with grain size, as deformation is predominantly accommodated along grain boundaries (Figure 3.10b,c), and there are few flaws in the undeformed grains (Figure 3.1b,c). The low flaw density is possibly a consequence of grain boundary orientation: there 68  Chapter III  Chapter III Figure 3.10: Images of the deformed samples. A) and B) are optical micrographs of Badshot dolomite, highlighting deformation along intragranular flaws predominantly related to cleavage planes (I), although transgranular microcracks are present (T); C) and D) are SEM images of Rock Creek dolomite highlighting microcracks present along grain boundaries (T), and comminution of grains (I) in the vicinity of faults; and E) and F) are SEM images of Niagara dolomite, highlighting transgranular microcracks which are commonly present along grain boundaries (T) and intragranular flaws (I), and the strong link of both types of deformation to the presence of pores (P).  70  Chapter III are not optimally oriented grain boundaries for wing crack initiation and propagation on every grain. In the Niagara samples, initial flaws are inferred to be a combination of pores, grain boundaries, and intragranular cleavage planes, which vary in size from the scale of grains to substantially smaller (see previous chapter) (Figure 3.Id).  Microcracks and  fractures make use of all of these features (Figure 3.10e,f). Niagara dolomite has a more heterogeneous distribution of initial flaws than either the Badshot or Rock Creek samples, and thus it is difficult to predict which flaws act as the principal initial flaws for brittle deformation. The variability in strength as a function of texture is enhanced by variations in K J C . As Kic is decreased, the required flaw density for a given flaw size is also decreased, and correspondingly, for a given flaw density, the required flaw size is decreased (Figure 3.9). Since Kic varies with flaw type in rocks (Fredrich et al., 1990), the nature of the flaws is also an important parameter in dictating the peak strength. Due to the plethora of flaws in rocks, it will be a combination of flaw length, flaw density, and the Kic values of the given flaw types that will dictate which flaws are significant for failure, and thus which flaws dictate the peak strength. The theory of wing crack coalescence and shear failure dictates that the initial concentration of flaws plays as important a role on the peak strength of rocks as the initial flaw length. Both of these variables are strongly dependant on the texture of dolomite, and assumptions cannot be made about one without considering the affect on the other. Microstructural observations support the notion that, irrespective of grain size other textural properties of the rock, including intragrain and grain boundary textures can dictate both the 71  Chapter III flaw density and the flaw length, thus varying the peak strength of the rock. Grain size cannot be assumed to be directly related to peak strength without taking textural variations into account, resulting from the strong interplay between initial flaw size and flaw density on the onset of shear failure, and thus the peak strength of dolomite.  3.6 Summary My data set is inconsistent with the Hall-Petch relationship. I, therefore propose that an understanding of the textural properties of rocks is essential in order to predict their peak strength. In developing an empirical failure criterion, I have shown that it is possible to fit my data and Hatzor et al.'s (1997) data using a relationship that is non-linear with respect to confining pressure, and that takes into account only the effective Young's modulus and the empirically defined uniaxial compressive strength. I have shown that the effective Young's modulus can be a powerful tool for use in empirical relationships due to its sensitivity to the textural properties of rocks, including porosity, flaw length, and flaw density.  Unfortunately, it does not explicitly provide  information regarding the nature of these properties. The nature of the initial flaws must be garnered from microstructural observations, and analyzed by adopting a failure theory. I have adopted the wing crack model, which necessitates that both flaw length and flaw density be considered in analyzing the peak strength of rocks in compression. Over a range of texturally diverse rocks, flaw length and density do not vary consistently with any specific textural properties, including grain size, which results in the failure of my data set to obey the Hall-Petch relationship. 72  Chapter IV  Chapter IV: Conclusion  73  Chapter IV Conclusion The brittle deformation of dolomite is strongly controlled by its textural properties, which can vary substantially between mineralogically similar Formations. These properties greatly impact both the transition from brittle faulting to cataclastic flow, as well as the peak strength. In the Rock Creek samples, the fine grains with straight grain boundaries deform predominantly by transgranular cracking and brittle faulting. The coarse grained Badshot samples, on the other hand, exhibit a much greater proportion of intragranular deformation and cataclastic flow, as a consequence of their well developed intragranular cleavage, and lobate grain boundaries. In the Rock Creek samples, therefore, the flaws most suited for crack propagation are the grain boundaries, whereas in the Badshot samples, they are the {1 Oil} cleavage planes. In the porous Niagara samples, pore collapse is the principal mode of deformation for porosities greater than ~7%, whereas below this value, samples exhibited an elastic brittle mechanical response. This distinction arises due to the stress intensification around pores, although the onset of pore collapse occurs at a much higher porosity than in calcite, where it occurs at -3% (Baud et al., 2000). The high critical resolved shear stresses required for all crystal plastic processes in dolomite at room temperature prevent crystal plastic processes from operating, whereas it is these processes that promote the onset of pore collapse in calcite. In dolomite, pore collapse is a purely brittle process, accommodated by cataclastic flow that initiates in damage zones around pores, and progressively encompasses increasingly large portions of the sample.  74  Chapter IV Just as texture plays an essential role in the transition from brittle faulting to cataclastic flow, it also strongly controls the peak strength of dolomite.  It is possible to  produce an empirical failure criterion that takes into account only the effective Young's modulus, the confining pressure, and the experimentally derived uniaxial compressive strength. Theory shows that porosity, and the concentration and length of the initial flaws are accounted for by the effective Young's modulus. The theories of wing crack initiation, propagation, and coalescence were adopted, and used to demonstrate that both the length and concentration of the initial flaws must be considered to predict the peak strength.  It is variations in either the flaw length or the  concentration of the initial flaws due to intragranular and grain boundary textures that leads to discrepancies with the Hall-Petch relationship.  This is especially true for texturally  diverse dolomites, where numerous textural properties can vary between samples, including the degree of cleavage development and the degree to which grain boundaries are straight or lobate. Variations in Kic values between different flaw types will further influence the nature of the flaws most favorable for crack propagation. The textural properties of dolomite are complex, and it is often desirable to group these diverse properties under the headings of easily measurable properties such as porosity and grain size. While examples in the literature have shown that this approach is valid over limited textural ranges, in more diverse suites of rocks is not always the case. A careful examination of the texture and microstructures in the undeformed and deformed samples is necessary in order to define the controls on the mechanics of brittle deformation, including the peak strength, of dolomite. 75  References  References  76  References References  Antonellini, M . & Mollena, P.N. 2000. A natural analog for a fractured and faulted reservoir in dolomite: Triassic Sella Group, northern Italy. AAPG Bulletin, 84;3, 314-344.  Ashby, M.F. & Sammis, C.G. 1990. The damage mechanics of brittle solids in compression. Pure Appl.Geoph, 133;3, 489-521.  Baud, P., Schubnel, A., & Wong, T.F. 2000. Dilatancy, compaction, and failure mode in Solnhofen limestone. Journal of Geophysical Research, 105;B8, 19289-19303.  Brace. W.F. & Bombolakis E.G. 1963. A note on brittle crack growth in compression. 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The transition from brittle faulting to cataclastic flow: Permeability evolution. Journal of Geophysical Research, 102;B2, 3027-3041.  84  Appendix I  Appendix I: Data Reduction  85  Appendix I Data Reduction Data reduction is performed using a spreadsheet program such as Microsoft® Excel. A sample experimental output is presented in table A 1.1 a, and the corresponding reduced data is presented in table A l . l b . The first step in reducing the data is to isolate to portion of data corresponding to the actual experiment. This is done by plotting position (column 2) against load (column 4) and picking the points at the onset of triaxial compression, and at the termination of application of a displacement (Figure A l . l ) .  This portion of the data set is  then isolated, and only this region is used for data analysis. The first column of the output data is time in seconds from a constant base date, using Greenwich Mean Time.  This is converted to the time duration of the experiment by  subtracting the initial time from each value. The third column is the position of the DCDT, in mm, based on its full range. This is converted to displacement by subtracting the position from the initial value. In order to convert displacement to strain, the stiffness of the LSR must be accounted for (see chapter II).  The stiffnesses of the low temperature sample  assemblies are listed in table 1.1. To account for these, however, load, which is output in pounds, must be converted to kilograms, using the relationship load (kg) = load (lbs) * 0.4535924  (Al)  The initial load must also be set to zero by subtracting the load at each time step by the initial load. The strain at each time increment is then calculated using the relationship e={[displacement (mm)/10-l/(stiffness (kg/cm))*load (kg)]/initial length}*100% (A2) Stress in kg/cm is calculated using the relationship 2  86  Appendix I o = (load (kg)/[(l+e/100)*cross sectional area]  (A3)  which is converted to MPa using the relationship c (MPa) = a (kg/cm )*0.0980665  (A4)  2  Confining pressure, which is output in PSI, needs to be recalibrated each experiment. This is done using an analog guage. At the onset of the experiment, the confining pressure is read off the analog guage. The digital output is then calibrated using the equation Pc (calib) = Pc (digital) - {initial Pc (digital) - initial Pc (analog)}  (A5)  which is converted to MPa using the relatinship Pc (MPa) = Pc (PSI) * 0.006894757  (A6)  The average and standard deviation of the confining pressure are calculated based on the digital data. The effective Young's modulus is obtained by isolating the linear elastic portion on the differential stress - axial strain curve, and measuring the slope, and the yield stress is obtained by picking the point at which the differential stress - axial strain curve deviates from this linear fit.  The peak stress is obtained by finding the maximum value of the  differential stress.  87  Appendix I  so CN 00 m in t— o m in OS in r~ o m m o in CN CN 00 OS CN r~ CN Tf t-~ t~ o r ^ r ^ m t~ oo rn o 00 rn T 00 CN int OS SO sq OS m sq rn rn rn rn Tf o O rn CN rn rn o r n rna> rn o o o o o o o o o Os so CN CN CN so 00 in in OS Tf cn r~ t~ CN o m Tf CN t^ SO SO 00 CN 00 00 r~; o sq sq  SO  so in  in CN SO O m o m p so CN CN  m  CN CN CN  Tf  in in in CN Tf in oo m00 <s~. OO OS p r- oo r~so oo t~~ OS in OS 00 CN CN 00 V) H Tf' OS Q . SO Tt Tt Tt so o . 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 rn  Tt  OS rn in in in in in in SO r~ r- r~r- r~ r-~  SO SO so so SO SO SO SO SO SO SO SO SO SO SO CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN  S O  m  m  88  m  m  m  m  m  m  m  m  m  m  m  m  rn m  Appendix I  70000  Position (mm)  A sample load-position curve for the raw data from an experiment on the LSR. The arrows highlight the start and end of the experiment. The plot is reversed from the differential stress-axial strain curves (Figures 2.7 and 3.2) because position decreases during compression. Figure A l . l :  89  Appendix II  Appendix II: Geochemical Data  90  Appendix II Bulk Chemistry Bulk chemistry, in wt. %, for each of the three sample suites was analyzed by ALS Chemex®, using X-ray fluorescence (Table A2.1). Chemical analyses were obtained from four independent blocks of each of Badshot dolomite and Rock Creek dolomite, and from three independent blocks of Niagara dolomite. In the case of Badshot dolomite, each block was split into three fractions prior to crushing, with each fraction being prepared independently, and each fraction was split into duplicate after crushing and prior to analysis, yielding 24 chemical analyses. In the cases of the Rock Creek and Niagara dolomite, only one fraction of each of the blocks was submitted for chemical analysis. The crushing procedure involved splitting each block in a hydraulic splitter until pieces less than ~8 cm in diameter were obtained. These fragments were fed through a steel jaw crusher and, where necessary, a steel disc mill. Prior to each suite of samples being run through the jaw crusher and disc mill, a blank sample from that suite was run to eliminate carry over contamination from the previous suite. The resulting gravel, which consisted of less than 1 cm fragments, was pulverized in a carbide ring mill for ~2 minutes. Between each sample, or fraction, the ring mill was scrubbed and air dried. The powders were then stored and transported in Nalgene® containers. Along with being used for bulk chemical analyses, these powders were also used for Rietveld analyses (Raudsepp et al., 1999) (Table A2.2), and for isotope analyses (Table A2.3).  Stable isotope analyses were performed at the Pacific Centre for Isotope and  Geochemical Research at UBC on a Finnigan Delta plus X L isotope ratio mass spectrometer  91  Appendix II utilizing a Gas Bench carbonate mineral phosphoric acid digestion system operating in continuous flow mode. Digestions were run at 345 K. Four analyses of National Bureau of Standards calcite reference standard NBS-18 gave an average dl3C (VPDB) value of -5.14 (0.08 1 standard deviation) and average dl80 (VSMOW) of 7.22 (0.22). Five analysis of NBS-19 gave values of 1.73 (0.07) VPDB and 28.36 (0.27) VSMOW. Fractionation of 180 between phosphoric acid and dolomite was corrected using the 298 K fractionation factor of Sharma and Clayton (1965) as corrected by Friedman and O'Neil (1977) and extrapolated to 345 K assuming the same temperature dependence as for phosphoric acid - calcite fractionation.  92  Appendix II  r„ U  <  co  O  "  60  S  O 60  s _° =3 fl  9 * :  u•&  id g  1  OJ  CO  o  OJ CD li  £  * O  ts * «3 fl  ^ .2  U ° -3 o o rt o a •£  +-> O M4  .rt  19 x '  co  rt  > cjI -t_* @ £ort *~rt S co S cu •° s m  cS  8 2 |Z :  OJ  |  H CO  .22 a  a  u  I*  •n a  rt  o  1  S rt  o o: ;  13 rt rt  a rt  l o g ;  to rt OJ  60  ^ .2  "rt ^ 5  3 §  rt  0  C M  T3  CO  T3  £ OJ  rt X)  -£  8*  OJ  co X U  A  § -2 •  co  •i  -P  y rt u «cort .2rt  1  o  o  pfi  <u  cs H  to 00  93  O  IM  £^ rt rt  -M  •° 'a =s OJ  'c " «  ^ u  2 2  -T3  OJ  ? ^ rt rt cj o o  o CD  rt  co  CJ  rt 9 .rt CL  o rt rt  A M; oj C  rt  r => o H rt  A p p e n d i x II  Rock Creek Rock Creek Badshot Badshot Dolomite 86.87 85.73 99.66 97.14 Quartz 0.21 7.74 0.34 0.38 Calcite 10.77 4.79 0.00 0.08 Talc 2.15 1.11 0.00 0.00 0.62 Clinochlore 0.00 0.00 0.00 Tremolite 0.00 0.00 0.00 2.40  T a b l e A 2 . 2 : V o l u m e percent mineralogy o f R o c k Creek and Badshot dolomite, based on R i e t v e l d refinements (performent b y D r . M . Raudsepp and Dr. E. Pani at U B C ) .  94  Appendix II SAMPLE  d 13C(VPDB)  d 180(VSMOW)  180 corr.  CBI D CBI E  0.51 0.70  16.55 16.72  15.72  CBI F  0.23  16.27  CBI E  0.60  CBI F CBI (avg.)  0.20 0.45  16.65 16.21 15.65  CB3 D CB3 E CB3 F  1.34 1.22 1.29 1.23  18.24 18.15 18.18 18.07  1.27  17.33  OH1 D  1.21  24.97  OH1 E OH1 F  1.18 1.16  24.96 24.86  OH1 D  1.20  24.68  OH1 E OH1 (avg.)  1.17 1.19  24.71 24.01  OH4D  1.39  24.19  OH4E  1.36  24.15  OH4F  1.31  OH4D OH4E OH4F  1.33 1.34  24.25 23.88 23.94  1.29 1.34  23.90 23.22  23.07  1.25 1.44 1.34  23.26 23.55 23.38 23.14  CB3 D CB3 (avg.)  OH4 (avg.) OH5D  180 stdev  0.22  0.23  0.06  0.07  0.02  0.14  0.03  0.16  0.07  0.16  0.03  0.14  0.04  0.15  15.89 15.44 15.82 15.38  17.41 17.32 17.35 17.24  24.14 24.13 24.03 23.85 23.88  23.36 23.32 23.42 23.05 23.11  1.31  24.09 24.38 24.21 24.26  OH5 F OH5 (avg.)  1.29  23.97  1.33  23.35  RC4D  1.49  21.84  21.01  RC4E  1.53  21.63  20.80  RC4F  1.45  21.58  20.75  RC4D  21.54  RC4E  1.46 1.48  20.71 20.62  RC4 (avg.)  1.48  20.78  RD5 D  1.38  RC5 E  1.30  20.89 20.64  20.06 19.81  OH5 E OH5 F OH5 E  13C stdev  23.43  21.45  RC5 F  1.41  21.01  20.18  RD5 D  1.37  RC5 F RC5 (avg.)  1.35 1.36  20.67 20.77  19.84 19.94  19.97  Table A2.3: 813C and 5180 isotopic data for Badshot (CB), Niagara (OH) and Rock Creek (RC) dolomites, analyzed at the Pacific Centre for Isotope and Geochemical Research at UBC.  95  

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