Compressional and shear wave velocity and attenuation measurements were obtained in the laboratory from 50 mm diameter, cylindrical, limestone core samples over a confining pressure range of 5 – 60 MPa. Normal and tangential fracture compliance values, as a function of confining pressure, were calculated for a single fracture cut perpendicular to the long axis of the core. The ratio of the normal to tangential compliance was approximately 0.4 and was independent of the applied stress. Values of normal and tangential fracture compliance calculated were of the order 10^-14 m/Pa, and decreased with an increase in confining pressure. Both Q^-1</sup>_P and Q^-1</sup>_S1/Qs were shown to be small for these samples. A borehole test site was constructed in a Carboniferous limestone quarry, at Tytherington, situated north of Bristol, UK. This quarry was chosen because the rock type was fairly homogeneous and the fractures could be mapped in the quarry walls as well as down three, 40 m vertical boreholes drilled in-line in the quarry floor. Wireline logs were obtained in all the holes and a seismic crosshole survey was carried out between the two outermost boreholes. An estimate of in-situ normal fracture compliance, Z_N, was obtained from the log and crosshole data, in 4 different ways, using effective medium theories as well as the displacement discontinuity theory. An additional estimate of Z_N was obtained from a separate borehole test site constructed in fractured Devonian meta-sediments at Reskajeage, Cornwall, UK. These fractures were much larger in size than those observed at Tytherington quarry. From the above field and laboratory measurements, fracture compliance was shown to increase approximately linearly with the size of the fractures. In addition, a study of crosshole seismic attenuation was performed at Tytherington quarry. Q was found to be frequency dependent. This frequency dependence was interpreted as being due to scattering rather than intrinsic attenuation.

Rock masses may present remarked geostatic stress anisotropy and anisotropic material properties; thus, the tunnel alignment with the geostatic principal stress directions and with the axes of material anisotropy is unlikely. Nevertheless, tunnel design often neglects those misalignments and; yet, the misalignment effects were unknown. In this doctoral research, tunnels under complex anisotropic conditions were modelled analytically and numerically with 3D nonlinear Finite Element Method (FEM). When the tunnel misaligns with the geostatic principal stress directions, anti-symmetric axial displacements and shear stresses are induced around the tunnel. Analytical solutions for misaligned shallow and deep tunnels in isotropic elastic ground are provided. The analytical solutions were validated with 3D FEM analyses. Near the face, the anti-symmetric axial displacements are partially constrained by the tunnel face, producing asymmetric radial displacements and stresses. The asymmetric radial displacements at the face can be divided into a rigid body displacement of the tunnel cross-section and anti-symmetric radial displacements. Those asymmetries may affect the rock-support interaction and the plastic zone developed around the tunnel. In anisotropic rock masses, the tunnel misalignment with the axes of material anisotropy also produces anti-symmetric axial displacements and stresses around the tunnel. It occurs because when the tunnel is not aligned with the principal material directions, the in-plane stresses are coupled with the axial displacements (i.e. the compliance matrix is fully populated). Thus, tunnels in anisotropic rock mass not aligned with the geostatic principal stresses and with the axes of material anisotropy are substantially more complex than tunnels not aligned with the principal stress directions in isotropic rock mass. An analytical solution for misaligned tunnels in anisotropic rock mass is provided. It was observed that the relative orientation of the geostatic principal stresses with respect to the axes of material anisotropy plays an important role. The axial displacements produced by far-field axial shear stresses and by the rock mass anisotropy may compensate each other; thus, axial and radial displacements around the tunnel are reduced. On the other hand, those anti-symmetric axial displacements may be amplified; thus, the ground deformations are increased. Asymmetric radial and axial deformations, and asymmetric spalling of the tunnel walls are commonly observed on tunnels in anisotropic rock masses. The tunnel misalignment with the geostatic principal stress directions and with the axes of material anisotropy could be associated with those phenomena that, so far, are not well comprehended

<p>Crustal stress measurements play a crucial role in understanding how the subsurface deforms. As one of the most popular methods for stress characterization in deep wellbores, borehole breakout analysis examines the shape of drilling-induced compressive failures to determine stress directions and magnitudes, assuming that the rock formation is both isotropic and linearly elastic. To ensure accurate stress interpretations, the dissertation investigates the validity of underlying presumptions from two perspectives: (1) the effect of rock anisotropy (i.e., elastic anisotropy, and strength anisotropy) on wellbore failure patterns; and (2) the characterization of rock nonlinear elastic mechanical behaviors. </p> <p>The developed computer program, <em><strong>EASAfail</strong></em>, has broad applicability in calculating wellbore failure patterns for a wide range of scenarios. It takes into account factors such as elastic stiffness matrices of the rock, stress tensors in the surrounding environment, and the presence of weak planes. The program's generality allows it to handle various rock types with different degrees of symmetry in their elastic properties, as well as weak planes that are weaker than the intact rock matrix. By analyzing these factors, the program reveals that the patterns of wellbore failure in elastic and strength anisotropic rock formations are highly influenced by the sliding of weak planes. Complications from two modes of borehole failure, either in the intact rock matrix or in the weak planes, can cause the breakout azimuth to deviate from the direction of the minimum horizontal stress. </p> <p>In addition to hypothetical scenarios generated from numerical models, a case study from the field is presented to underscore the impact of foliations on the anomalous rotations of breakout azimuths. The wellbore was located in Northeastern Alberta, Canada, transecting both the sedimentary column and crystalline basement. Breakout rotations identified from caliper and image logs were highly likely caused by the slippage along foliations, supported by the close correlation between breakout azimuths and dip directions of foliations as well as polarization directions analyzed from dipole sonic logs. Stress magnitudes constrained from Monte Carlo simulations further reveal a lower stress field when rock anisotropy is taken into account, compared to what is inferred conventionally. </p> <p>The characterization of rock nonlinear elasticity involves the utilization of the third-order elastic (TOE) model. To measure the TOE moduli in a static manner, test-specific protocols were proposed based on the nonlinear stress-strain behaviors of the rock. By arranging the stress-strain responses obtained from hydrostatic, uniaxial, and triaxial compressive tests into a linear system of equations, it becomes possible to invert the equations for the TOE moduli. These analytical equations were validated through calculations from finite element models. </p> <p>By employing the established protocols, the TOE moduli were derived for four different rock types with varying pore structures when subjected to hydrostatic and uniaxial compressions. The TOE model successfully captured the nonlinear stress-strain responses exhibited by Indiana limestone, Vif-type Fontainebleau sandstone, and Snake River Plain basalt. However, it was found to be inadequate for Franc-type Fontainebleau sandstone, which displayed noticeable hysteresis and experienced significant strains. Future geomechanical applications will undoubtedly gain advantages from utilizing the inverted TOE moduli obtained through static measurements, as they allow for the examination of the impacts of nonlinear elasticity in rocks. </p>