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Wave propagation characteristics at the welded interface of double-porosity solid and double-porosity dual-permeability materials

ABSTRACT In the present study, propagation characteristics (reflection/refraction phenomena) at the welded interface of two dissimilar double-porosity media are investigated. Both the double-porosity materials behave dissipative to wave propagation due to the presence of viscosity in pore fluid. All the waves (i.e. incident, reflected and refracted) are considered as inhomogeneous (i.e. different directions of propagation and attenuation). Reflection and refraction coefficients are calculated theoretically in the form of eight inhomogeneous linear equations. Reflected and refracted waves energy shares are represented with two different energy matrix. For the incidence of and SV waves, the partition of incident energy among various reflected and refracted waves is calculated numerically for particular numerical examples. The impacts of various physical properties (like, pore-fluid viscosity, double-porosity structure, wave-induced fluid flow and permeability) of double-porosity dual-permeability materials on the partition of incident energy are depicted graphically at each angle of incidence. Numerically, the conservation of incident energy during the reflection/refraction process is obtained at each angle of incidence.