Numerical simulation based heuristic investigation of inertia-induced phenomena and theoretical solution based verification by the damped wave equation for the dynamic deformation of saturated soil based on the u–w–p governing equation

Abstract The theoretical and numerical solutions for the one-dimensional dynamic deformation of saturated ground were obtained using the u–w–p governing equation. The numerical analysis was performed based on the finite element method, and the occurrence of superficially peculiar phenomena, i.e., S-shaped settlement–time relation, non-harmonic oscillation in the settlement/pressure–time relation in highly permeable soil, and inconsistency in the vertical load and immediate pressure was identified heuristically. The theoretical solution of the damped wave equation was derived from the original governing equation expressed as the superposition of several modes with different eigenvalues, and this solution could successfully explain the phenomena observed heuristically. It was noted that the phenomena were induced by the presence of inertia, because the static solution and u–p analysis did not exhibit such phenomena. The verification of the analysis was conducted owing to the correspondence of the theoretical solutions of the damped wave equation and the u–w–p analysis results.