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This study is mainly focused on the behavior change of shear waves. These waves propagate through an inhomogeneous sandwiched water-saturated porous layer in between inhomogeneous elastic layer and inhomogeneous sandy half space under the assumption of non-local theory. Different types of inhomogeneities based on the depth of the layers have been considered in terms of elastic moduli and densities of the medium. Due to the availability of fluid in the second layer, we consider loose bonding at the interfaces in between these three layers, as fluid movement through the interfaces may be possible. A complex dispersion equation has been derived with respect to the boundary conditions. Real and imaginary parts of the dispersion equation provide us with the phase velocity of shear wave and dissipation due to loose bonding at the interfaces, respectively. This dispersion equation has been solved numerically with the help of Newton Raphson method. For validation of the present problem, the numerical solution of dispersion equation has been depicted here graphically in terms of phase velocity c c 2 of shear wave vs. non-dimensional wave number k H 1 (where k is the wave number and H 1 is the thickness of the second porous layer). Also, we discuss about the impact of depth ratios, inhomogeneity of the medium, non-local parameters, loose bonding, and porosity of the sandwiched layer on the propagation of the shear wave. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]