Analytical solution based on spatial distortion for a time-harmonicdipole source in a transverse isotropic viscoelastic solid

2020 ◽  
Vol 148 (4) ◽  
pp. 2522-2522
Author(s):  
Thomas Royston
Keyword(s):  
Analytical Solution ◽  
Viscoelastic Solid ◽  
Spatial Distortion ◽  
Transverse Isotropic

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

Water ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 1465 ◽  
Author(s):  
Cheng-Jung Hsu ◽  
Ching Hung
Keyword(s):  
Analytical Solution ◽  
Effective Stress ◽  
Three Dimensional ◽  
Wave Direction ◽  
Anisotropic Permeability ◽  
Present Solution ◽  
Transverse Isotropic ◽  
Vertical Effective Stress ◽  
Wave Induced ◽  
Dimensional Wave

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.

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