Theoretical Solutions of Wave-Induced Seabed Response Under Fully Drained and Undrained Conditions for Verification of a Numerical Analysis Code

Yamamoto’s theoretical solution for a two-dimensional wave-induced response of an elastic seabed with finite permeability needs a simultaneous equation to be solved. Analysis of the dimensionless simultaneous equation demonstrated that it becomes unsolvable due to the singularity of its matrix when the permeability coefficient of the seabed approaches infinity and zero, representing (elementwise) fully drained and undrained conditions, respectively. To address this limitation and thus expand the verifiable drainage condition for a finite element analysis code, theoretical solutions for seabed responses under the fully drained and undrained conditions were derived. The feasibility of these solutions was discussed through comparison of the forms of these solutions with the one of Yamamoto. Furthermore, characteristics of seabed behaviors explained by these solutions were obtained. Finally, these theoretical solutions and Yamamoto’s solution were utilized to verify a finite element analysis code by considering horizontally periodic seabed behavior in the numerical analysis. It turned out that the numerical code was capable of expressing seabed behavior in any drainage condition without any approximation to a governing equation as made in the derivation of the fully drained and undrained solutions. Therefore, the numerical analysis code is now reliably used for further studies on wave-induced seabed behaviors even out of the verifiable range of drainage conditions by Yamamoto’s solution.