An Analytical Solution for Wave-Induced Soil Response and Seabed Liquefaction

2010 ◽  
Author(s):  
Xiang-Lian Zhou ◽  
Jian-Hua Wang ◽  
Yun-Feng Xu
Keyword(s):  
Shear Modulus ◽  
Pore Pressure ◽  
Effective Stress ◽  
Fourier Transformation ◽  
Saturated Porous Medium ◽  
Helmholtz Equations ◽  
Soil Response ◽  
Depth Increase ◽  
Vertical Effective Stress ◽  
Wave Induced

In this study, an analytical method to solve the wave-induced pore pressure and effective stress in a saturated porous seabed is proposed. The seabed is considered as a saturated porous medium and characterized by Biot’s theory. The displacements of the solid skeleton and pore pressure are expressed in terms of two scalar potentials and one vector potential. Then, the Biot’s dynamic equations can be solved by using the Fourier transformation and reducing to Helmholtz equations that the potentials satisfy. The general solutions for the potentials are derived through the Fourier transformation with respect to the horizontal coordinate. Numerical results show that the permeability and shear modulus of the porous seabed has obvious influence on the response of the seabed. The vertical effective stress and attenuation velocity of pore pressure along seabed depth increase as permeability k increases. The liquefaction may be occur at the surface of seabed when shear modulus decreasing.

scholarly journals Wave-Induced Seabed Response around a Dumbbell Cofferdam in Non-Homogeneous Anisotropic Seabed

2019 ◽  
Vol 7 (6) ◽  
pp. 189 ◽  
Author(s):  
Linya Chen ◽  
Dong-Sheng Jeng ◽  
Chencong Liao ◽  
Dagui Tong
Keyword(s):  
Shear Modulus ◽  
Vertical Distribution ◽  
Pore Pressure ◽  
Wave Structure ◽  
Offshore Structures ◽  
Hydrodynamic Process ◽  
Response Analysis ◽  
Depth Function ◽  
Wave Induced ◽  
The Vertical Distribution

Cofferdams are frequently used to assist in the construction of offshore structures that are built on a natural non-homogeneous anisotropic seabed. In this study, a three-dimensional (3D) integrated numerical model consisting of a wave submodel and seabed submodel was adopted to investigate the wave–structure–seabed interaction. Reynolds-Averaged Navier–Stokes (RANS) equations were employed to simulate the wave-induced fluid motion and Biot’s poroelastic theory was adopted to control the wave-induced seabed response. The present model was validated with available laboratory experimental data and previous analytical results. The hydrodynamic process and seabed response around the dumbbell cofferdam are discussed in detail, with particular attention paid to the influence of the depth functions of the permeability K i and shear modulus G j . Numerical results indicate that to avoid the misestimation of the liquefaction depth, a steady-state analysis should be carried out prior to the transient seabed response analysis to first determine the equilibrium state caused by seabed consolidation. The depth function G j markedly affects the vertical distribution of the pore pressure and the seabed liquefaction around the dumbbell cofferdam. The depth function K i has a mild effect on the vertical distribution of the pore pressure within a coarse sand seabed, with the influence concentrated in the range defined by 0.1 times the seabed thickness above and below the embedded depth. The depth function K i has little effect on seabed liquefaction. In addition, the traditional assumption that treats the seabed parameters as constants may result in the overestimation of the seabed liquefaction depth and the liquefaction area around the cofferdam will be miscalculated if consolidation is not considered. Moreover, parametric studies reveal that the shear modulus at the seabed surface G z 0 has a significant influence on the vertical distribution of the pore pressure. However, the effect of the permeability at the seabed surface K z 0 on the vertical distribution of the pore pressure is mainly concentrated on the seabed above the embedded depth in front and to the side of the cofferdam. Furthermore, the amplitude of pore pressure decreases as Poisson’s ratio μ s increases.

Dynamic Response of a Circular Tunnel Embedded in a Saturated Poroelastic Medium due to a Moving Load

2006 ◽  
Vol 128 (6) ◽  
pp. 750-756 ◽  
Author(s):  
Jian-Fei Lu ◽  
Dong-Sheng Jeng
Keyword(s):  
Porous Medium ◽  
Dynamic Response ◽  
Closed Form ◽  
Pore Pressure ◽  
Fourier Transformation ◽  
Moving Load ◽  
Wave Number ◽  
Circular Tunnel ◽  
Soil Response ◽  
General Solutions

Dynamic response of a circular tunnel embedded in a porous medium and subjected to a moving axisymmetric ring load is investigated in this paper. In this study, two scalar potentials and two vectorial potentials are introduced to represent the displacements for the solid skeleton and the pore fluid. Based on Biot’s theory and applying the Fourier transformation on time variable, a set of frequency domain governing equations for the potentials are obtained. Performing the Fourier transformation on the axial coordinate, closed-form general solutions for the potentials with arbitrary constants are obtained. Using the closed-form general solutions and boundary conditions along the tunnel surface, the arbitrary constants involved in the potentials are calculated. Representations for the displacements, the stresses and the pore pressure are derived in terms of the closed-form potentials. Analytical inversion of the Fourier transformation with respect to frequency and numerical inversion of the Fourier transformation with respect to the axial wave number lead to numerical solutions for the displacements, the stresses and the pore pressure in the porous medium. Numerical results demonstrate the soil response due to a high speed load is quite different from those due to a static load or a lower speed load. These differences become more pronounced when the velocity of moving load approaches the velocities of elastic waves of a porous medium.

Modeling wave-induced pore pressure and effective stress in a granular seabed

2014 ◽  
Vol 27 (1-2) ◽  
pp. 305-323 ◽  
Author(s):  
Luc Scholtès ◽  
Bruno Chareyre ◽  
Hervé Michallet ◽  
Emanuele Catalano ◽  
Donia Marzougui
Keyword(s):  
Pore Pressure ◽  
Effective Stress ◽  
Wave Induced

Wave-Induced Pore Pressure and Effective Stresses in a Porous Seabed With Variable Permeability

1997 ◽  
Vol 119 (4) ◽  
pp. 226-233 ◽  
Author(s):  
D. S. Jeng ◽  
B. R. Seymour
Keyword(s):  
Pore Pressure ◽  
Offshore Structures ◽  
Soil Permeability ◽  
Soil Response ◽  
Mathematical Procedure ◽  
Effective Stresses ◽  
Variable Permeability ◽  
Seabed Interaction ◽  
Wave Induced ◽  
Interaction Problem

An evaluation of wave-induced soil response is particularly important for marine geotechnical engineers involved in the design of foundations for offshore structures. To simplify the mathematical procedure, most theories describing the wave-seabed interaction problem have assumed a porous seabed with uniform permeability, despite strong evidence of variable permeability. This paper presents an analytical solution for the wave-induced soil response in a porous seabed with variable permeability. Verification is available through a reduction to the simple case of uniform permeability. The results indicate that the effect of variable soil permeability on pore pressure and effective stresses is significant.

Response of Pore Pressure and Effective Stress in Seabed to Waves Around a Permeable Submerged Breakwater

2015 ◽  
Author(s):  
Hao Chen ◽  
Jinhai Zheng ◽  
Qianzhen Li ◽  
Naiyu Zhang ◽  
Hanyi Chen ◽  
...  
Keyword(s):  
Pore Pressure ◽  
Effective Stress ◽  
Fluid Pressure ◽  
Wave Model ◽  
Pore Fluid Pressure ◽  
Submerged Breakwater ◽  
Great Ability ◽  
Wave Induced ◽  
Foundation Failure ◽  
Dynamic Wave

As the unexpected wave-induced seabed instability may cause foundation failure, the evaluation of wave-induced pore pressure and effective stress in seabed plays an important role in the design of the foundation of marine structures. In this study, a two-dimensional integrated mathematical model, based on COBRAS wave model and SWANDYNE seabed model is developed to numerically investigate the mechanism of wave-induced seabed response in the vicinity of a permeable submerged breakwaters. Numerical results indicate that this model has a great ability in predicting the dynamic response of the pore pressure and effective stress around the breakwater. Both the pore fluid pressure and effective stress in seabed largely changes with an increasing water depth. It is also found that the responses of the pore pressure and effective stress of different locations to the dynamic wave loading are significantly different in the cases with variable top width of the breakwater.

Wave Transformation and Soil Response Due to Submerged Permeable Breakwater

2006 ◽  
Author(s):  
Ching-Piao Tsai ◽  
Hong-Bin Chen ◽  
Dong-Sheng Jeng ◽  
Kuan-Hong Chen
Keyword(s):  
Pore Pressure ◽  
Wave Spectrum ◽  
Experimental Results ◽  
Wave Transformation ◽  
Harmonic Mode ◽  
Submerged Breakwater ◽  
Soil Response ◽  
Higher Harmonic ◽  
Wave Induced ◽  
The Waves

This study reports the experimental results of the wave transformation and the wave-induced soil response when the waves pass through the submerged permeable breakwater. The model of the submerged breakwater was built on a horizontal sandy bottom. The experimental results of the spectrum of the wave transformation and the wave-induced pore-pressure are first analyzed in this paper. It is found that the wave spectrum is similar to the condition of the impermeable bottom that the higher harmonic mode appears when the waves pass over the submerged structure. However, the higher harmonic mode is not found in the spectrum of the wave-induced pore pressure, showing that the nonlinearity of the pore pressure is damped by the porous bed. The influences of the geometry of the submerged breakwater to the transformation of the wave height and the pore-pressure are also investigated. Based on the experimental results, the regression formulas for the coefficients of the wave reflection, the wave transmission and the wave energy dissipation are obtained in the paper.

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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