Wave propagation across the imperfectly bonded interface between cracked elastic solid and porous solid saturated with two immiscible viscous fluids

The present study is aimed at understanding the effect of a vertically aligned crack, present in the elastic half space on the propagation of attenuated waves. These waves are incident at a point on the interface between the porous half space and the cracked elastic half space. The analysis is based on Snell's law for reflection and refraction of an incident wave at the interface. A loose bonding at the interface between the porous half space and the cracked elastic half space has been considered and represented here as the tangential slip. The proposed model is solved for the propagation of harmonic plane waves. The final equations are in the form of Christoffel equations from which we find four reflected waves (three longitudinal body waves and one transverse body wave) and two refracted waves (one longitudinal body wave and one transverse body wave). The expression of reflection-refraction coefficients and energy share of each reflected and refracted waves for a given incident wave is obtained in closed form and computed numerically in the present study. Numerical examples are considered for the partition of the incident energy in which we have studied the effect of aspect ratio, crack density and loose bonding parameter.