Abstract
The effective elastic compliance of rock that contains cracks is evaluated from energy considerations, as first proposed by Eshelby [1957]. The compliance of rock depends on the compliance of the solid matrix, the directional distribution of the cracks, an ‘inhomogeneity’ interaction tensor, and the shape distribution of cracks, which are assumed to be shaped like pennies. The effective compliance is linearly elastic for small-amplitude elastic waves. Anisotropic crack distribution causes elastic anisotropy, with associated acoustic birefringence. Nonhydrostatic stress causes stress-induced anisotropy, owing to anisotropic closure of cracks. Although velocities are uniquely determined from the distribution of cracks, the distribution cannot be determined uniquely from the velocities. The theoretical results compare favorably with measured compressional velocities and crack distribution in Salisbury granite and with measured stress-induced compressional and shear velocity anisotropy in Barre granite.
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