Reflection/Refraction of a Dilatational Wave at a Plane Interface Between Uniform Elastic and Swelling Porous Half-Spaces

The present work deals with the reflection and refraction phenomena of a plane dilatational wave striking obliquely at a plane interface between a uniform elastic half-space and a swelling porous elastic half-space. The swelling porous half-space consists of solid, liquid (viscous) and gas (inviscid) constituents. Two problems have been considered: (1) when the inhomogeneous dilatational wave is made incident at the interface after propagating through the porous half-space (2) when the homogeneous dilatational wave is made incident at the interface after propagating through the uniform elastic solid half-space. The equations giving the amplitude ratios and the expressions for the partition of incident energy among various reflected/refracted waves have been presented. Numerical computations have been performed for a specific model consisting of sandstone, water (viscous) and carbon dioxide as solid, liquid and gas phases, respectively, of the porous medium and granite stone as a uniform elastic medium. The variations of amplitude ratios and corresponding energy ratios against the angle of incidence and frequency have been illustrated graphically. It has been verified that during reflection/refraction phenomena, the sum of energy ratios is equal to unity at each angle of incidence.