Wave-induced dynamic response of saturated multi-layer porous media: Analytical solutions and validity regions of various formulations in non-dimensional parametric space

In this paper, dynamic response of saturated-layered porous media under harmonic waves is evaluated through a semi-analytical solution. The coupled differential equations governing the dynamics of saturated or nearly saturated porous media such as soils containing all the inertial terms of solid and fluid phases are presented for a multi-layer system. Possible simplifications of the equations which are called formulations are introduced based upon the presence of inertial terms associated with the phases. The semi-analytical solutions to the response of multiple layers for all the formulations are presented in terms of pore water pressure and stress variations considering a set of non-dimensional parameters and their respective ratios. Validity of the formulations is presented in a non-dimensional parametric space. The maximum discrepancies in the pore pressure response of the formulations leading to validity regions are illustrated for typical dynamic problems. Subsequently, the effects of layering and drainage conditions on these regions are also presented. The proposed semi-analytical solution may be served as a benchmark one for validating the coupled numerical solutions, which can be used to deal with real scientific and geo-engineering problems in the emerging field of computational geomechanics.