Wave propagation in double-porosity dual-permeability materials: Velocity and attenuation

This study considers the propagation of harmonic plane waves in a double-porosity solid saturated by a viscous fluid. Two different porosities are supported with different permeabilities to facilitate the wave-induced fluid-flow in this composite material. The variation of the fluid content in the pores due to the wave-induced flow is expressed in terms of the dilatation of constituent particles in the porous aggregate. This fluid-flow can be considered through the constitutive relations with modified anelastic coefficients. The modified coefficients, being frequency dependent and complex, illustrate the dispersive and anelastic behaviour of double-porosity dual-permeability materials. Relevant equations of motion are solved to explain the propagation of three longitudinal waves and one transverse wave in double-porosity dual-permeability medium. A numerical example is considered to illustrate dispersion in velocity and attenuation of the four waves. Effect of wave-induced fluid-flow is analysed with changes in wave-inhomogeneity, pore-fluid viscosity and double-porosity structure.