In this paper, the phenomenon of solitary waves propagating over a porous seabed is considered. We first re-derive the governing equations for the generalized shallow water problem with variable water depths. Then, we link the wave model with the existing soil model to investigate the wave-induced pore pressure and stresses in marine sediment. The new boundary value problem was solved by the Legendre pseudo-spectral method numerically. Based on the new model, we investigate the effects of soil permeability, seabed bottom function on the pore pressures and vertical effective normal stresses in marine sediment
This paper is primarily concerned with the propagation of solitary waves over a porous seabed with variable water depth. The solitary wave on a constant water depth, ho, is a permanent progressing wave form consisting of a single elevation above the undisturbed surface, whose amplitude a and effective length Lo are such that a / ho and 2 2 h0 / Lo are comparable small quantities. The propagation of solitary wave has been studied since the 1970s. This wave phenomenon attracts more attention again recently due to the tsunami events in Southeastern Asian in December 2004. Grimshaw (1970, 1971, 1999) was one of pioneer researchers, examined the deformation of a solitary wave due to a slow variation of the bottom topography. Later, the reflection of shallow-water solitary waves in channels with decreasing depth was studied by Knickerbocker (1980, 1985). Recently, Killen and Johnson (2001) further establish a model for Korteweg-de Vries equation in cylinder coordinates. Recently, this problem was re-examined by the authors for a rigid bottom with variable water depth (Li and Jeng, 2006). It has been well known that when ocean waves propagate in the ocean, they generate significant dynamic pressures on the sea floor.