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The present mathematical model is solved for the study of the effect of vertically aligned cracks present in the elastic half space on the propagation of elastic waves through the interface between double porosity solid and cracked elastic solid. Local fluid flow (LFF) between the inclusions (second fluid) and the host medium (first fluid) has been considered in double porosity solid which is possible due to wave propagation. This study follows Snell's law for reflection and refraction of an incident wave at the interface. Due to the presence of cracks in elastic half space, a loose bonding at the interface between these two media has been considered which is represented here as tangential slip. Final equation is framed in the form of Christoffel equation, which is solved analytically and found 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 phase velocities and attenuation coefficients are calculated for each inhomogeneous wave. The expression of reflection and refraction coefficients, and energy shares of each of the reflected and refracted waves for a given incident waves is found in closed form. Numerical examples have been considered to discuss the effect of crack density, aspect ratio, local fluid flow, shear consolidation parameter and loose bonding parameter, etc. on energy shares by reflected and refracted waves.

Effect of local fluid flow and loose boundary on wave propagation through interface between double porosity solid and cracked elastic solid