Effective properties of viscoelastic media with crack-like inclusions

Self-consistent effective field method is applied to the calculation of effective properties of a medium that consists of a viscoelastic host material (matrix) and a random set of elliptical fluid-filled cracks. Viscoelastic behavior of the matrix phase is described by a linear Boltzman model with a weak singular kernel. The conventional principle of correspondence between elastic and viscoelastic problems allows deriving explicit expressions for the effective viscoelastic parameters of an isotropic medium containing a set of parallel cracks or cracks with homogeneous distribution over the orientations. For long elastic waves, the complex wave numbers of propagating waves in the medium with cracks are obtained. The wave velocities and quality factors of some real cracked rock materials are calculated. (C) 2012 Elsevier Ltd. All rights reserved.