Applicability of simplified formulations based on Biot’s theory

Based on the Biot’s theory, three simplified formulations are proposed. The simplifications mainly include neglecting the relative acceleration terms in the dynamic mixture equilibrium equation and the generalized Darcy’s law, neglecting the relative acceleration terms in the dynamic mixture equilibrium equation and all the inertial terms in the generalized Darcy’s law, and neglecting all the inertial terms in the equations. The applicability of the simplifications are discussed with the help of analytical solutions for one-dimensional finite fully saturated poroelastic column. Two non-dimensional parameters are introduced to discuss the effects of permeability, excitation frequency and porosity.