A finite element model for the analysis of wave induced stresses, displacements and pore pressures in an unsaturated seabed I: theory

Abstract This paper presents the theoretical development of the differential equations governing wave induced stresses, displacements and pore pressures in an unsaturated seabed. These governing coupled flow and deformation equations are presented for plane strain conditions subject to a sinusoidal wave loading on the seabed. The finite element formulation of the resulting equations is also presented. The governing flow and deformation equations, reduced by assuming that all variables behave in simple harmonic form, are discretized in one-dimensional vertical space using the Galerkin finite element method. Simple linear two-noded elements are used to which closed form solutions of the element stiffness matrices and load vectors are presented. Solution algorithms for the flow and deformation equations are described. Nodal values of horizontal displacement, vertical displacement and pore water pressure are output in simple harmonic form, as are the total and effective components of stress at the element centroids.

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