Abstract
The behavior of saturated, porous media under dynamic or quasi-static loads was firstly formulated by Biot. Based on Biot’s theory, various possible simplifications have been proposed such as neglecting the second time derivative of the relative displacement. In addition, an even more simplified version has been proposed where the inertial terms in the generalized Darcy’s law are neglected as well. This paper aims to explore the advantages and limitations of that simplified formulation with the help of a linear one-dimensional (1D) poroelastic column subjected to periodic dynamic loading. Two non-dimensional parameters which are related to the permeability, excitation frequency, and material properties are introduced, and the analytical solutions are obtained and depicted graphically in cases of varied permeability and frequencies. Subsequently, a schematic diagram is developed to serve as guideline to determine whether the simplification is tenable, or the only meaningful solution is available by complete Biot’s theory.
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