3-D transport and acoustic properties of Fontainebleau sandstone during true-triaxial deformation experiments

Highlights

• We investigate the effect of 3-D stress on deformation, transport and ultrasonic properties of sandstone rocks.

• 3-D independent permeability values measured along the three axes are sensitive to initial values of applied σ₃ and σ₂.

• AE hypocenter locations show the timely development of polymodal fault system under 3-D state of stress.

• Source mechanism inferred from AE events validates the formation of such fault systems.

Abstract

Fontainebleau sandstone specimens have been tested in a true-triaxial geophysical imaging cell under hydrostatic (σ₁=σ₂=σ₃), traditional triaxial (σ₁=σ₂>σ₃) and true-triaxial (σ₁> σ₂>σ₃) stress regimes. The research objectives are to recognize the effect of various stress ratios σ₂/σ₃ under varying magnitudes of σ₂ and σ₃ on 3-D stress–strain responses, 3-D transport, 3-D ultrasonic wave velocities, and acoustic emission properties. Comparison of the variation of 3-D directional permeability between the specimens shows that higher magnitude of σ₃ and σ₂ disrupts the 3-D interconnectivity of the pore spaces and intergranular cracks, irrespective of the magnitude of applied stress ratio σ₂/σ₃. The observed permeability anisotropy between the two specimens is a function of inherent oriented pores and cracks, stress ratio σ₂/σ₃ and the magnitude of applied σ₃ and σ₂ stresses. Temporal and spatial evolution of the AE hypocenter locations combined with the examination of micro-CT and thin section images shows the timely development of polymodal fault systems during peak to post-peak stresses and validates the development of the source mechanism inferred from the acoustic emission events.

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 V_P and V_S measured along the σ₁ direction increased monotonically during the fracturing process, whereas V_P and V_S 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.