Effective properties of randomly distributed poroelastic cylinders in a poroelastic matrix

Many media (such as geological formations or osseous tissues) are composites made up of at least two basic materials which can themselves obey complex constitutive laws. Such composites exhibit a wide range of mechanical properties that are essential to estimate using relatively simplified formulas. Here, wave propagation in a random heterogeneous medium (the composite) consisting of a distribution of parallel poroelastic cylinders in a poroelastic matrix is considered. The cylinders and the matrix are Biot’s porous media saturated with fluid. Expressions for the three effective wavenumbers (fast, slow and shear) are provided in the low frequency range using the Conoir and Norris multiple scattering formula accounting for wave conversions, up to the order of $n_0^2$ ($n_0$ is the number of cylinders per unit area). Basing upon this effective wavenumbers, quantities such as mass densities, bulk and shear poroelastic moduli, and diffusion coefficient are estimated at the static limit.