Anisotropic Seabed Research Articles

Numerical study of scour depth effect on wave-induced seabed response and liquefaction around a pipeline

Wave-induced liquefaction depth is a key factor in providing the safe design of submarine pipelines. However, existing numerical studies simplify the seabed as a flat foundation and ignore the effect of scour depth on wave-induced seabed response and liquefaction depth. The effects of scour depth on wave-induced seabed response and liquefaction depth around a submarine pipeline are investigated, and a three-dimensional hybrid model combining Reynolds-averaged Navier-Stokes (RANS) equations with Biot's poroelastic theory for wave propagation and anisotropic seabed is proposed in this study. Numerical results indicate that local scour leads to the redistribution of the initial effective stress within the seabed around the pipeline. With increasing scour depths, the maximum liquefaction depth beneath the pipeline simultaneously decreases. When the scour depth reaches a certain depth, the seabed seems to no longer liquefy. Parametric studies indicate that the liquefaction depth increases by either decreasing the saturation degree or increasing the wave height. Under anisotropic seabed conditions, a nonlinear relationship exists between the maximum liquefaction depth of the seabed and the seabed permeability.

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

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.

Numerical simulation of the nonlinear wave-induced dynamic response of anisotropic poro-elastoplastic seabed

In this paper, a 2D poro-elastoplastic model for wave-induced dynamic response in an anisotropic seabed is derived analytically. The seabed is treated as a porous medium and characterized by Biot’s consolidation equations. The soil plasticity and wave non-linearity are included in the model and both the pore fluid and the soil skeleton are assumed to be compressible. The nonlinear ocean waves are respectively considered as progressive and standing waves. The previous experimental data is used to validate the proposed model. Numerical results demonstrate that the influence of nonlinear wave components should not be ignored without committing substantial error. A significant difference between progressive and standing waves is also observed for the development of residual pore pressure, as well as the distribution of liquefied zone. A detailed parametric investigation reveals that the nonlinear wave-induced seabed response is also affected significantly by cross-anisotropic soil parameters.

Principal stress rotation and cyclic shear strength for an elliptical rotation stress path

ABSTRACTBased on the analytical solutions for wave-induced soil response in an unsaturated anisotropic seabed of finite thickness, an elliptical, i.e., noncircular rotation stress path is proven to be a more common state in a soil element with the cyclic shear stresses due to the traveling linear wave. The influence of an elliptical stress path on the characterization of failure strength is analyzed using three new parameters representing the shape, size, and the orientation of the ellipse. A series of cyclic rotational shear tests on the reconstituted specimens of Chinese Fujian Standard Sand have been performed to investigate the effect of elliptical stress path. A strength function in term of failure cycles is derived to quantify the failure strength of a given sand within a seabed subjected to regular wave loading. The results provide a basis for the evaluation of liquefaction potential of seabed but also point to a unique backbone cycle shear strength curve for soil under principal stress rotation.

Wave and current induced seabed response around a submarine pipeline in an anisotropic seabed

A better understanding of the phenomenon of wave–seabed-structure interactions is essential for the evaluation of the liquefaction of seabed foundation under dynamic loading in the ocean environments. However, only a few investigations have been conducted for the cross-anisotropic seabed under wave pressure and marine structures, despite the fact that most seabeds are anisotropic medium. Furthermore, most previous numerical models for Biot's consolidation theory were only considered wave loading. In this study, based on Biot's partly dynamic poroelastic theory (“u-p” approximation), a two-dimensional FEM seabed model is adopted to investigate the wave and current induced seabed response around a submarine pipeline. The third-order solution of wave-current interactions is used to determine the dynamic pressure acting on the seabed. Verification of the proposed model is performed against the previous experimental data and analytical result. With the proposed numerical model, the effects of wave, current and seabed characteristics, such as Poisson's ratio, Young's modulus, degree of saturation, and pipeline buried depth on the wave-induced seabed response will be examined. Then, the wave-current induced seabed liquefaction is also discussed. The numerical results demonstrate significant effects of anisotropic soil behavior on seabed liquefaction.

Three-dimensional numerical modeling of marine controlled-source electromagnetic responses in a layered anisotropic seabed using integral equation method

We perform a numerical simulation of marine controlled-source electromagnetic （MCSEM） responses in a layered anisotropic seabed using integral equation method. Firstly, we use the operator theory to deduce the contraction integral equation, which is always convergent regardless of any parameters, for it satisfies the contraction mapping condition. Then we introduce the subdomain multigrid and quasi-linear approximation to improve the computation efficiency. We also validate the accuracy and efficiency of the algorithm by synthetic numerical modelings. Finally, we simulate the three-dimensional MCSEM responses in the layered anisotropic seabed, and investigate the effects of anisotropy.

An experimental study on non-linear progressive wave-induced dynamic stresses in seabed

In this study, the dynamic stresses within the seabed induced by non-linear progressive waves were explored through a series of hydraulic model tests on a movable bed within a wave flume. By comparing Stokes’ 2nd-order wave theory with the theory of wave-induced dynamic stresses within the seabed as proposed by Yamamoto et al. [1978. On the response of a poro-elastic bed to water waves. Journal of Fluid Mechanics 87 (1), 193–206.] and Hsu and Jeng [1994. Wane-induced soil response in an unsaturated anisotropic seabed of finite thickness. International Journal for Numerical and Analytical Methods in Geomechanics 18, 785–807], the experimental results show that the pressure on the seabed surface, the pore water pressure within the seabed as well as the vertical and the horizontal stresses are all smaller than their theoretical values. If we were to obtain the characteristics of seabed soil, the analytical solution of Hsu and Jeng [1994. Wane-induced soil response in an unsaturated anisotropic seabed of finite thickness. International Journal for Numerical and Analytical Methods in Geomechanics 18, 785–807] might agree to the simulation of the wave-induced effective stresses and shear stress in the sandy seabed. A different phase shift exists among all the three soil stresses. Their influences on the three dynamic stresses within seabed soil are important for seabed stability, and can be used in the verification of numerical models. In the whole, the non-linear progressive waves and the naturally deposited seabed are found to have a strong interaction, and the behavior of the induced dynamic stresses within the seabed is very complicated, and should be investigated integrally.

Closure to “Simplified Solutions for Wave-Induced Response of Anisotropic Seabed” by Masatoshi Yuhi and Hajime Ishida

Closure to “Simplified Solutions for Wave-Induced Response of Anisotropic Seabed” by Masatoshi Yuhi and Hajime Ishida

Discussion of “Simplified Solutions for Wave-Induced Response of Anisotropic Seabed” by Masatoshi Yuhi and Hajime Ishida

Discussion of “Simplified Solutions for Wave-Induced Response of Anisotropic Seabed” by Masatoshi Yuhi and Hajime Ishida

Simplified Solutions for Wave-Induced Response of Anisotropic Seabed

Simplified analytical solutions have been developed for the wave-induced response of a cross-anisotropic seabed of infinite thickness. These solutions deal with the seabed in two conditions: slightly unsaturated and fully saturated. In the limiting cases of full saturation, the solutions are described in extremely clear forms. By employing these solutions, we examine the transmission of the pore-pressure. It is shown that the vertical attenuation of the amplitudes of pressure fluctuations can be correlated fairly well by a nondimensional parameter that corresponds to the stiffness ratio of the soil skeleton to the pore-water. The attenuation of the pore-pressure becomes significant as this value increases. Mechanical anisotropy effects are deduced qualitatively from the relation between this parameter and the anisotropic Young's moduli and Poisson's ratios.

Effects of a cover layer on wave-induced pore pressure around a buried pipe in an anisotropic seabed

In engineering practice, a cover layer of coarser material has been used to protect a buried marine pipeline from wave-induced seabed instability. However, most previous investigations of the wave–seabed–pipe interaction problem have been concerned only with such a problem either in an isotropic single layer or a rigid pipe. This paper proposes a two-dimensional finite element model by employing the principle of repeatability to investigate the wave-induced soil response around a buried pipeline. The elastic anisotropic soil bahavior and geometry of cover layer are included in the present model, while the pipe is considered to be an elastic medium. This study focuses on the effects of a cover layer (including thickness B and width W of the cover layer) on the wave-induced pore pressure in the vicinity of a buried pipeline.

Boundary-Layer Theory for Anisotropic Seabed Response to Sea Waves

By employing a boundary-layer concept, the wave-induced fluctuation of pore-water pressure in an anisotropic seabed of semi-infinite depth is derived in a simple form, which contains the solution of the isotropic case. The solution of pore-water pressure consists of the two exponential terms with the different decay rates, and it is characterized by two factors: The boundary-layer thickness and weights of the two terms. The boundary-layer approximation shows that the two factors are dominated by two dimensionless parameters: One is a kind of Terzaghi's consolidation coefficient represented by properties of waves and soil, and the other is the stiffness ratio related to the saturation of pore water. These two factors can be expressed simply by modifying those of the isotropic case.

Wave-induced soil response in an unsaturated anisotropic seabed of finite thickness : J. R. C. Hsu & D. S. Jeng, International Journal for Numerical & Analytical Methods in Geomechanics, 18(11), 1994, pp 785–807

An analytical solution for the wave-induced soil response is developed for a seabed of finite thickness subject to a three-dimensional (3-D) wave system produced by two intersecting waves of equal properties. These 3-D exact solutions for the pore pressure and effective stresses, proposed for a non-cohesive soil matrix of finite depth in a homogeneously unsaturated and anisotropic condition, are readily reducible to the limiting two-dimensional cases of progressive and standing waves, for which no explicit solutions are available for finite thickness. The effects of soil isotropy, degree of saturation, seabed thickness and grain size on the wave-induced pore pressure are discussed in detail. The explicit solutions presented in this study for the wave-induced pore pressure and effective stresses should benefit the laboratory experiments and field monitoring programs carried out in soil of finite depth.

Wave‐induced soil response in an unsaturated anisotropic seabed of finite thickness

AbstractAn analytical solution for the wave‐induced soil response is developed for a seabed of finite thickness subject to a three‐dimensional (3‐D) wave system produced by two intersecting waves of equal properties. These 3‐D exact solutions for the pore pressure and effective stresses, proposed for a non‐cohesive soil matrix of finite depth in a homogeneously unsaturated and anisotropic condition, are readily reducible to the limiting two‐dimensional cases of progressive and standing waves, for which no explicit solutions are available for finite thickness. The effects of soil isotropy, degree of saturation, seabed thickness and grain size on the wave‐induced pore pressure are discussed in detail. The explicit solutions presented in this study for the wave‐induced pore pressure and effective stresses should benefit the laboratory experiments and field monitoring programs carried out in soil of finite depth.

Effects of seabed properties on acoustic normal mode propagation in a stratified shallow ocean

The pressure field of a point source in a shallow stratified ocean over a nonhomogeneous anisotropic seabed is calculated using normal modes. The sediment is modeled using the Biot‐Yamamoto theory of poro‐elastic media. The influence of geoacoustic properties of sediments on low‐frequency transmission loss is investigated. It is found that the variation of permeability has large influence on acoustic wave attenuation, whereas the elastic properties variation has lesser effect. Finally, the existing model is used in an attempt to extract the depth structure of permeability and porosity of the seabed. [Work supported by ONR.]