Finite Difference Model for Assessing Sandy Seabed Response

Abstract

In this study, a numerical model is developed using the Finite Difference Method to determine the response of sandy seabed under different loading conditions. The quasi- dynamic (u-w-p) model is presented detailed in this paper. In u-w-p model, acceleration, velocity, and displacement terms are considered different for both solid and fluid phases. u- w-p model has considered sophisticated and general condition of seabed motion. The governing equations of the model are deduced from constitutive law and conservation law under certain assumptions. In the model, numerical solutions are developed by using the finite difference method (FDM) both in 1-D with finite seabed depth and 2-D with infinite seabed depth. Three major factors (pore water pressure, effective stress and shear stress) are assessed from the proposed models. The results show that both the effective stress and the pore water pressure vary according to the depth. When the excess pore pressures are increasing, the surface settlement of seabed can be observed. Hydraulic flow is downward at the crest o and upward below the trough of the sea wave. Thus, liquefaction depths below the crest are obviously higher than the liquefaction depth below the trough of wave. However, the liquefaction occurs between phase angles of p/2 and 3p/2, instead of just under the wave crest, which indicates the existence of phase lags under wave actions. Unlike the variation of pore water pressure, the change of shear stress is relatively linear to the wave propagation. The proposed model will provide a better understanding of the mechanism of soil-wave interaction.