Modelling Anisotropy Pattern of Dry Rocks as a Function of Applied Stress

We propose an analytical model for seismic anisotropy caused by application of an anisotropic stress to an isotropic dry rock. We first consider an isotropic linearly elastic medium (porous or non-porous) permeated by a distribution of discontinuities with random (isotropic) orientation (such as randomly oriented compliant grain contacts or cracks). Geometry of individual discontinuities is not specified. Instead, their behaviour is defined by a ratio of the normal to tangential excess compliances. When this isotropic rock is subjected to a small compressive stress (isotropic or anisotropic), the specific surface area of cracks aligned parallel to a particular plane is reduced in proportion to the normal stress traction acting on that plane. This effect is modelled using the Sayers-Kachanov non-interactive approximation. The integral over the orientation distribution is evaluated using Taylor expansion of the stress dependency of the specific surface area of cracks. Comparison of the model predictions with the results of laboratory measurements shows a reasonable agreement for moderate magnitudes of uniaxial stress (up to 30 MPa). The results suggest that the relations between anisotropy parameters do not change with increasing stress.