Comparison of calculated and observed crack densities and seismic velocities in westerly granite

Crack lengths and widths in virgin and previously stressed Westerly granite have been measured by using the scanning electron microscope (SEM). Seismic velocities computed from the observed crack aspect ratios and porosities in virgin rock are compared with previously measured values both in the unconfined state and as a function of hydrostatic pressure. These comparisons suggest that even with careful SEM observation one may fail to see a substantial number of the cavities present; these are almost exclusively in the high aspect ratio fraction. Agreement between the results of noninteractive and self-consistent velocity calculations is poor at low confining pressures but excellent at pressures in excess of a few hundred bars. The inability of present theoretical treatments to predict seismic velocities in rocks as a function of differential stress lies not with velocity calculations but with the lack of a quantitative model for the development of cracks in dilatant rocks. However, in its present form O'Connell and Budiansky's self-consistent, isotropic theory can provide information about crack densities in stressed rock from seismic velocity data if measurement paths are carefully chosen. By combining computed crack densities with measurements of dilatant volumetric strain, it is found that the average aspect ratio of stress-induced cracks increases with stress, reaching a maximum of 2–3 parts in 103 at 80% of the fracture strength.