Wave-induced flow of pore fluid in a cracked porous solid containing penny-shaped inclusions

Abstract

An aim of current study is to analyze the contribution of reflected longitudinal waves to wave-induced fluid flow (WIFF) in the cracked porous solid. Initially, we investigate the time harmonic plane waves in cracked porous solid by employing the mathematical model proposed by Zhang et al. (2019). The solution is obtained in form of the Christoffel equations. The solution of the Christoffel equations indicates that there exist four (three dilatational and one shear) waves. These waves are attenuated in nature due to their complex and frequency-dependent velocities. The reflection coefficients are calculated at the sealed pore stress-free surface of cracked porous solid for the incidence of P 1 and S V waves. It is found that three longitudinal waves contribute to WIFF and the contribution of these waves to the induced fluid in the cracked porous solid is analyzed using the reflection coefficients of these longitudinal waves. We analytically show that the fluid flow induced by these longitudinal waves is linked directly to their respective reflection coefficients. Finally, a specific numerical example is considered to discuss and to depict the impact of various parameters on the characteristics of propagation like phase velocity/attenuation, reflection coefficients and WIFF of longitudinal waves.