Effective elastic properties and wave surfaces of rock materials containing multiple cavities and cracks (effective field approach)

Abstract

The paper is devoted to simulation of the effective elastic properties of rock materials containing two substantially different types of defects simultaneously: random sets of ellipsoidal pores (cavities) and elliptical cracks. For solution of the homogenization problem and calculation of the effective elastic properties of such materials, the self-consistent effective field method is used. For composites with one type of heterogeneities, the method coincides with the Mori–Tanaka method. The method allows deriving analytical expressions for the effective elastic stiffness tensors of the materials containing pores and cracks of various scales. These tensors have correct symmetry with respect to tensor indices and provide physically reasonable values of the effective elastic constants in wide regions of porosity and crack density. The materials with pores and cracks of substantially different sizes and of close sizes are considered. The method predicts substantially different effective elastic constants of the materials with these microstructures. Comparison of the components of the effective elastic stiffness tensors for the materials with various values of porosity and crack density are presented. Wave surfaces of acoustical waves in the materials containing pores and cracks are constructed. It is shown that for materials with spherical pores and circular cracks, the shapes of these surfaces are close to ellipsoidal. The results of the paper can be used for determination of fracture level in damaged rock materials by acoustical methods.