Elastic and acoustic properties of anisotropic materials with multiple cracks

Anisotropic elastic materials containing multiple elliptical cracks of different orientation distributions are considered using the (self-consistent) effective field method. The method allows, in particular, accounting for mutual positions of cracks. The derived effective elastic stiffness tensor applies to a broad range of the crack density. Group velocity surfaces (wave surfaces) of cracked materials are constructed. It is shown that, for the isotropic materials with parallel penny shaped cracks, the wave surfaces are close to ellipsoidal. A method of solution of the inverse problem and determination of fracture parameters from acoustical data (group velocities of quasi-longitudinal and quasi-transverse waves of various directions in damaged rock materials) is proposed. Examples of application of the method are presented, and its accuracy is assessed. The results can be used for determination of crack density in rock materials by acoustical methods.