Effective longitudinal wave through a random distribution of poroelastic spheres in a poroelastic matrix

TL;DR

This paper derives analytical expressions for the effective longitudinal wave propagation in a poroelastic medium with randomly distributed poroelastic spheres, extending classical models to account for poroelastic effects.

Contribution

It generalizes the Linton-Martin formula to poroelastic media and provides analytical expressions for effective wavenumbers and material properties in the low frequency limit.

Findings

Effective wavenumbers for fast and slow waves are derived.

Analytical expressions for effective mass density and bulk modulus are obtained.

The model extends classical scattering theories to poroelastic composites.

Abstract

A random distribution of poroelastic spheres in a poroelastic medium obeying Biot's theory is considered. The scattering coefficients of the fast and the slow waves are computed in the low frequency limit using the sealed pore boundary conditions. Analytical expressions of the effective wavenumbers of the coherent longitudinal waves (fast and slow) are deduced the Rayleigh limit using a generalization of the Linton-Martin (LM) formula to poroelastic medium up to the order two in concentration. Some effective quantities (mass density, bulk modulus) of the heterogeneous media are estimated.