3-D transport and acoustic properties of Fontainebleau sandstone during true-triaxial deformation experiments
Introduction
The proceedings of papers presented at the International Workshop on true-triaxial testing of rocks [1] held in Beijing on October 17, 2011 at the 12th International Congress on Rock Mechanics is the first book ever comprehensively addressing all the aspects of true-triaxial testing (TTT) of rocks. Issues such as testing techniques and procedures, strength and deformational responses, failure mechanics and failure criteria have been the focal points of research on the development of a compressional testing machine capable of controlling intermediate principal stress (σ2) and least principal stress (σ3) independent of each other [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16]. The development of an advanced true-triaxial testing system equipped with seismic and resistivity sensors combined with the option of 3-D permeability to evaluate the transport properties and fracture delineation is comparatively new [17], [18], [19], [20], [21], [22], [23], [24], [25]. True-triaxial testing machines have been categorized into three types based on the loading methods and boundary conditions: (1) rigid loading in all directions; (2) flexible loading in all directions; and (3) mixed loading by Takahashi [25] each with their own advantages and disadvantages. Numerical modeling of a Mogi-type TTT system [26] has shown that deformation of a rigid platen, loading eccentricity, loading a blank corner and end friction still remain the essential problems, dictating the formation of failure surfaces between the loading faces of σ1 and σ3 axes. The study concludes that usage of rigid platens in a Mogi-type apparatus causes a complex end friction effect leading to stress concentration and suggests that the friction coefficient must be less than 0.03. Shi et al. [26] on testing a modeling specimen, without the corner effect, showed that the failure zones emerge at the specimen vertex, confirming the fact that the stress concentration is caused by the friction effect (a value of 0.05 was used); however, the consequent propagation of the failure zones is completely different.
Mogi׳s outstanding contribution to the field of TTT phenomena shows us how magnitudes of σ2 and σ3 affect the shape of stress–strain curves and failure modes of rocks. The tetrahedron shear failure criterion proposed by Mogi has explicitly shown that Mohr׳s theory neglects the influence of σ2 which assumes that failure of rocks is solely a function of normal stress acting perpendicular to the plane of shearing. Mogi showed that shear faulting happens parallel to the plane containing σ2, and the fracture angle with respect to σ1 plane decreases with an increase in magnitude of σ2, especially under prevailing lower σ3. In addition, anisotropic dilatancy is encouraged when the ratio between σ2 and σ3 increases due to opening of the cracks normal to the σ3 direction. Hamison and his research team on using a Mogi-type testing set up [27], [28] confirmed Mogi׳s, Takashi׳s [29] and Koide׳s [30] conclusions on the effect of σ2 on the strength of various rocks and the onset of dilatancy. The full review of the results of TTT experimental research and conventional true-triaxial apparatus developments carried out by various investigators are presented in detail in [31], [32].
The research conducted by Spetzler et al. [17] marks the beginning of more advanced types of geophysical TTT systems in which P and S seismic wave velocities were incorporated within polyaxial loading machines. Sayers et al. [18] measured elastic wave velocities along three principal stress directions in a 50 mm cube under hydrostatic and deferential stresses concluding that P and S velocities can be compared with the velocities obtained from the calculation of a medium containing a crack density characterized by anisotropic orientation. 3-D permeability and nine components of elastic wave velocities under polyaxial stresses with varying horizontal independent principal stresses were measured by King et al. [20]. A 5 mm thick magnesium metal plate with matching elastic properties of rock (sandstone) was used at the interface in order to reduce the frictional effects at the rock-loading platen. This study showed that VP and VS measured along the σ1 direction increased monotonically during the fracturing process, whereas VP and VS along σ3 first increases and then decreases when σ1 becomes greater than 80–100 MPa, confirming the fact that the induced fractures propagated in the direction normal to the σ3 direction and parallel to the plane containing σ1–σ2 directions. King et al. [21] modified their TTT system by one of the authors (Young) to include four small diameter ultrasonic transducers (pinducers) characterized with a frequency range up to 2 MHz and each loading platen was covered with compliance compatible metal face plates to reduce frictional effects at specimen boundaries. This modification facilitated capturing of acoustic emission events to be processed for fracture initiation/delineation purposes and processing of AE data for understanding the evolution of a focal mechanism. Such an addition caused elimination of the 3-D permeability measurements due to the incorporation of the face plates in combination with AE sensors. The earlier acoustic emission event locations in the study carried out by King et al. [21] clearly confirm the effect of boundary conditions in the experiment. With further deferential loading increments AE location maps a couple of conjugate fracturing networks including the formation of failure surfaces between the loading faces of maximum and minimum principal stresses as modeled in [26] in spite of using compliance matched face plates between the specimen and loading platens.
To increase our understanding of how three-dimensional compressive stress regimes’ effects induce seismicity, change elastic properties and transport fluids under true-triaxial stress regimes, a state-of-the-art true-triaxial geophysical imaging cell is used at the Rock Fracture Dynamic Facility (RFDF) at the University of Toronto. Reporting on the analysis of the evolution of 3-D stress–strain behavior, 3-D permeabilities and its anisotropy and failure pattern using seismic wave velocity measurements combined with acoustic emission techniques is the research objective of the current study.
Section snippets
True-triaxial geophysical imaging cell (TTGIC)
The detailed design and development of RFDF׳s true-triaxial rock testing system is given in [22], and only some of the important features of this system are explained here. The TTGIC has a couple of unique features and components including the following: (1) precision cubic inner alignment box; (2) cubic metal skeleton pressure vessel; (3) cubic skeleton rubber seal (CSRS); (4) inflatable flexible membrane; (5) fully instrumented loading platens; and (6) 3-D resistivity measurements (Fig. 1,
Experimental set up and testing procedure
Two experiments were carried out using a true-triaxial ultrasonic imaging cell within a custom-made polyaxial loading frame. In the first experiment, a Fontainebleau specimen was tested at hydrostatic stresses of 5 and 10 MPa and at stress ratios ranging from σ2/σ3=5 to failure under unequal triaxial compressive stresses. In this experiment, σ3 and σ2 were kept at a constant stress of 10 and 50 MPa respectively under load control mode on two paired horizontal actuators (along the X= σ3 and Y=σ2
3-D stress–strain–elastic wave velocity relationship for FTB3 and FTB4
FTB3 specimen fails at 540 MPa of axial stress whereas FTB4 fails at 490 MPa (Fig. 3). It is worth mentioning that the failure in FTB3 has taken place in a controlled way by decreasing σ3 = 5 MPa at post-peak stress to facilitate controlled failure. This was done to avoid sudden failure of the specimen and minimize possible damage within the true-triaxial geophysical imaging cell. Fig. 4 shows the variation of volumetric strain as a function of mean stress for both specimens and indicates that the
3-D X-ray CT scanning, thin section preparation and analysis of fault systems
Specimens FTB3 and FTB4 were recovered undisturbed from TTIGC after the test. FTB3 specimen was placed into open plastic bags, de-gassed under vacuum, and then immersed in a low viscosity epoxy mixed with a fluorescent dye. After immersion, specimen FTB3 was returned to atmospheric pressure, and the plastic bags sealed. Next, the bagged specimen was placed in a pressure vessel in which the hydrostatic stress of 10 MPa was applied overnight while the epoxy solidified. The process ensures that
Conclusion
Two experiments were carried out using a unique true-triaxial geophysical imaging cell within a custom-made polyaxial loading frame. Comparison of the evolution of VP, VS1 and VS2 as a function of mean stress between the two experiments confirms the fact that specimen FTB3 is characterized by the higher values of ultrasonic wave velocities beyond hydrostatic stress due to the higher compaction of pore space and micro-cracks. 3-D closure of pore spaces and intergranular cracks affects the shear
Acknowledgment
Mehdi Tabari Ghofrani and Hamed Ghaffari helped with experimental work and their efforts are highly appreciated. Karl Peterson is sincerely acknowledged for his contribution with thin section preparation. Dylan Roberts’ technical support is also greatly appreciated. Discussion with Zeev Reches is truly appreciated. Applied Seismology Consultant׳s Ltd. is acknowledged for providing the InSite software package for processing of induced seismicity data and the Itasca Education Partnership is
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