Effect of local fluid flow on reflection of plane elastic waves at the boundary of a double-porosity medium

Abstract

This study solves a mathematical model for the propagation of harmonic plane waves in a double-porosity solid saturated by a viscous fluid. An eigen-system of order four implies the existence of three longitudinal waves and a transverse wave in the composite porous medium. Eigenvalues of this system define the four complex velocities, which are resolved further to define the phase velocities of four attenuated waves in the medium. Variation of the fluid content in pores due to the wave-induced flow is expressed in terms of dilatations of the constituents in porous aggregate. Reflection of plane waves is studied at the stress-free plane surface of the medium. A numerical example is solved to calculate the partition of the incident energy among the four reflected waves. Conservation of the incident energy flux at the boundary is obtained through the presence of an interaction energy share, even when the poroelastic solid is saturated with a non-viscid fluid. This interaction energy disappears in the absence of the wave-induced flow in non-dissipative porous medium. Else, this interaction energy represents the net dissipation effect of the wave-induced flow as well as the pore-fluid viscosity on the partition of the incident energy at the free surface.