Body waves propagation in a fluid-saturated transversely isotropic poroelastic solid with a potential method

This study is focused on the propagation of plane harmonic body waves in a transversely isotropic linear poroelastic fluid-saturated medium in the framework of the simplified u-p formulation. A set of two scalar potential functions is employed to decouple the coupled fluid continuity equation and equations of motion, such a way that the governing equations for the potential functions are resulted in the form of either scaled wave motion or a combination of repeated wave motion and transport equation. The velocities and corresponding attenuation coefficients of both longitudinal and transverse waves are extracted from the acoustic equations for the body waves. To show the validity of the analytical solution developed in this paper, the degeneration to the case of a singlephase transversely isotropic, and consequently isotropic solid is presented. The motivation behind this was to provide the possibility of comparing the results of this study and the developed solution with those reported in the literature. Besides, the effects of mechanical and hydraulic parameters of materials on the velocity of propagation and attenuation coefficient of the waves are investigated in more detail. To this end, various synthetic poroelastic transversely isotropic materials are denfied, and the dependency of wave motion to these parameters is illustrated by plotting the graphs.