Three-Dimensional Wave-Induced Dynamic Response in Anisotropic Poroelastic Seabed

Cheng-Jung Hsu,Ching Hung

doi:10.3390/w12051465

Abstract

This paper presents a novel analytical solution, which is developed for investigating three-dimensional wave-induced seabed responses for anisotropic permeability. The analytical solution is based on the assumption of the poroelastic and the u − p dynamic form, which considers the inertia force of the soil skeleton. In this paper, the problem is regarded as an eigenvalue problem through a first-order ordinary differential equation in matrix form. The problematic eigenvector involved in the solution is dealt with using numerical computation, and a process is proposed to implement the present solution for the desired dynamic response. A verification, which is compared with two existing solutions, demonstrates an agreement with the present solution. The results show that the amplitude profile of seabed response for a shorter wave period varies significantly. A comparison between the anisotropic and transverse isotropic, as well as isotropic permeabilities reveals that the error of vertical effective stress on the seabed bottom can reach 74 . 8 % for the isotropic case. For anisotropic permeability, when the wave direction is parallel to the higher horizontal permeability direction, the amplitude profiles of pore pressure and vertical effective stress exhibit the greatest dissipation and increment, respectively. For transverse isotropic permeability, the vertical effective stress is independent of the wave direction, which results in the two horizontal effective stresses on the seabed bottom being identical to each other and independent of the wave direction. Our comprehensive analysis provides insight into the effect of anisotropic permeability on different wave periods and wave directions.

Highlights

The dynamic response caused by pore fluid movement in a soil matrix under cyclic loads is a practical issue in geotechnical engineering and has been intensively studied, based on the theory of soil consolidation [1,2,3,4]
As the anisotropic permeability of soil is common in a natural environment, the present solution was suitable for investigating the effect of anisotropy on a three-dimensional dynamic seabed response for rapid soil behavior
The seabed response for anisotropic permeability was compared with the results of isotropy and transverse isotropy to evaluate the error when the accurate directional permeability failed to be acquired

Summary

Introduction

The dynamic response caused by pore fluid movement in a soil matrix under cyclic loads is a practical issue in geotechnical engineering and has been intensively studied, based on the theory of soil consolidation [1,2,3,4]. Since the pioneering work of Biot on the three-dimensional consolidation theory of a poroelastic medium [11], as well as the storage equation of Verruijt [12], the wave-induced seabed response problem had been intensively investigated. Among these studies, the quasi-static seabed responses considered in two-dimensional space [13,14,15,16] and three-dimensional space [17,18], as well as the effect of inertia forces of both the soil skeleton and pore fluid [19,20,21,22] were investigated. Depending on the consideration of the inertia forces of the soil skeleton and pore fluid in momentum equations, two types of simplified soil behaviors can be assumed for the approximation

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Results

Conclusion