Scattering of Harmonic Waves by a Circular Cavity in a Porous Medium: Complex Functions Theory Approach

Abstract

An analytical solution for the evaluation of scattering of waves by a circular cavity in infinite isotropic elastic porous media is presented. Two groups of complex functions for solid skeleton and pore fluid in a two-dimensional complex plane are introduced in order to solve the Biot equations. Stress, displacement, and pore pressure fields induced by incident and scattered waves in the medium and especially in the vicinity of the cavity are evaluated in this complex plane. The validation of the proposed solution is shown by various numerical examples. A parametric study including the effects of fluid compressibility changes, shear modulus, and permeability variations, several wave numbers, and wave types (fast, slow, and shear waves) is performed.