Dilatational Spherical Wave Propagations of Multiple Energy Sources in Viscous Fluid-Saturated Elastic Porous Media

Biot developed a representative model for the propagation of stress waves in a porous elastic solid containing a compressible viscous fluid, which is the fundamental theory about wave propagation in porous media. The solution proposed in that work has the same form under the model with or without fluid viscosity, though it is conflicted with the energy dissipation when the viscosity of flow is involved. In this study, the solution under the viscosity model has been modified with the exponential time dissipation term introduced to different forms under light and heavy viscosity, which complies with Biot’s oscillation form when there is no damping caused by fluid viscosity, and makes more sense as less oscillatory when the viscosity becomes large, as the energy will be dissipated in that case.