Stress-induced ultrasonic wave velocity anisotropy in fractured rock

Abstract

The closure of cracks in rock under an applied compressive stress can significantly affect the permeability of the rock. Crack closure may be monitored using ultrasonic wave velocities, since these are significantly reduced in the presence of open cracks. When a non-hydrostatic compressive stress is applied to a rock, an initially isotropic distribution of cracks will become anisotropic and the rock will display an elastic anisotropy determined by the orientation distribution of those cracks remaining open. The crack orientation distribution function gives the probability of a crack having a given orientation with respect to a set of axes fixed in the rock. The coefficients W Imn of a series expansion of this function in generalized Legendre functions can be obtained to order I = 4 from the angular variation of the elastic wave velocity. This allows construction of microfracture pole figures, which specify the orientation distribution of open cracks. The theory is applied to the measurements of Nur and Simmons, who applied a uniaxial compressive stress to a sample of Barre granite. Cracks with normals aligned along the stress direction are closed preferentially in agreement with the theory of Walsh. However, for crack normals perpendicular to the applied stress there is some evidence of crack opening that is not predicted by the theory. This is also observed in the electron microscope study of Batzle et al. and a possible mechanism is discussed.