Wave-induced Seabed Response Research Articles

Two-Dimensional Model for Pore Pressure Accumulations in the Vicinity of a Buried Pipeline

In this paper, we presented an integrated numerical model for the wave-induced residual liquefaction around a buried offshore pipeline. In the present model, unlike previous investigations, two new features were added in the present model: (i) new definition of the source term for the residual pore pressure generations was proposed and extended from 1D to 2D; (ii) preconsolidation due to self-weight of the pipeline was considered. The present model was validated by comparing with the previous experimental data for the cases without a pipeline and with a buried pipeline. Based on the numerical model, first, we examined the effects of seabed, wave and pipeline characteristics on the pore pressure accumulations and residual liquefaction. The numerical results indicated a pipe with a deeper buried depth within the seabed with larger consolidation coefficient and relative density can reduce the risk of liquefaction around a pipeline. Second, we investigated the effects of a trench layer on the wave-induced seabed response. It is found that the geometry of the trench layer (thickness and width), as well as the backfill materials (permeability K and relative density Dr) have significant effect on the development of liquefaction zone around the buried pipeline. Furthermore, under certain conditions, partially backfill the trench layer up to one pipeline diameter is sufficient to protect the pipelines from the wave-induced liquefaction.

Numerical study for wave-induced seabed response around offshore wind turbine foundation in Donghai offshore wind farm, Shanghai, China

Analysis of the wave–seabed–structure interaction is of great importance for the design and construction of marine structures. In this paper, a three-dimensional porous model, based on Reynolds-Averaged Navier–Stokes equations and Biot׳s poro-elastic theory, is developed by integrating 3D wave and seabed models to simulate the wave–seabed–structure interaction around the high-rising structure foundation used in the Donghai offshore wind farm. Then parametric studies for wave and seabed characteristics on soil response around the wind turbine foundation are conducted. Liquefaction potential and seabed protection methodology are investigated in the last section. The main results concluded from the numerical analysis are as follows: (i) both larger wave height and longer wave period will result in higher wave pressure on the structure and seabed; (ii) the existence of the structure has a significant effect on the wave transformation and the distribution of wave-induced pore pressure; (iii) wave height, wave period, soil permeability and degree of saturation play critical roles on dynamic soil behavior; and (iv) original seabed can be protected from liquefaction by replacing the existing layers.

Soil response around Donghai offshore wind turbine foundation, China

Donghai offshore wind farm next to Shanghai is the first and largest commercial operating offshore wind energy system in China that adopts a high-rising structure foundation. This paper consists of two parts. Details are presented of this wind farm project, site conditions and related engineering solutions in the first part. Then, in the second part, a three-dimensional porous model, based on Reynolds-averaged Navier–Stokes equations and Biot's poro-elastic theory, is developed by integrating three-dimensional wave and seabed models to simulate the wave-induced seabed response around the high-rising structure foundation. A parametric study of the effects of the wave and seabed characteristics on the soil response around the wind turbine foundation is conducted. Results concluded from the numerical analysis are as follows: (a) the existence of the structure has a significant effect on the wave transformation and the distribution of wave-induced pore pressure; (b) the magnitude of wave-induced pore pressure increases as wave height or wave period increases. In addition to the current design of the Donghai offshore wind farm with high-rising structure foundation, a gravity-based foundation is also considered and results are compared with those for the high-rising structure foundation.

3D numerical model for wave-induced seabed response around breakwater heads

This paper presents a three-dimensional (3D) integrated numerical model where the wave-induced pore pressures in a porous seabed around breakwater heads were investigated. Unlike previous research, the Navier-Stokes equation is solved with internal wave generation for the flow model, while Biot's dynamic seabed behaviour is considered in the seabed model. With the present model, a parametric study was conducted to examine the effects of wave and soil characteristics and breakwater configuration on the wave-induced pore pressure around breakwater heads. Based on numerical examples, it was found that the wave-induced pore pressures at breakwater heads are greater than that beneath a breakwater. The wave-induced seabed response around breakwater heads become more important with: (i) a longer wave period; (ii) a seabed with higher permeability and degree of saturation; and (iii) larger angle between the incident waves and breakwater. Furthermore, the relative difference of wave-induced pore pressure between fully-dynamic and quasi-static solutions are larger at breakwater heads than that beneath a breakwater.

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.

Wave-induced multi-layered seabed response around a buried pipeline

The subject of the wave–seabed–structure interaction is important for geotechnical and coastal engineering regarding stability analysis of foundations for offshore structures. Most previous theoretical investigations available concerned only with such a pipeline in a uniform single layer seabed. In this paper, a wave–seabed–pipeline system is modeled using finite elements. The seabed is treated as porous medium and characterized by Biot's dynamic equations. To explore the mechanism of the seabed instability, the two possible formulations: partly dynamic (u–p model) and fully dynamic (u–w model) for the wave-induced seabed response are considered. Verification of the proposed model is performed against the previous analytical result and experimental data. Based on the numerical results, the effects of wave and seabed characteristics, such as water depth, permeability, shear modulus, degree of saturation, and pipeline buried depth, on the wave-induced excess pore pressure and vertical effective stress will be examined. Finally, a parametric study will be conducted to examine the effects of wave and soil characteristics on the liquefaction potential. It is worth noting that soil permeability has a very significant influence on the pore pressure generation and liquefaction.

An integrated model for the wave-induced seabed response around marine structures: Model verifications and applications

In this study, an integrated model (PORO-WSSI II) for wave–seabed–structure interactions (WSSI) is developed by combining (i) the Volume-Averaged Reynolds-Averaged Navier–Stokes (VARANS) equations for wave motions in a fluid domain and the porous media flows in porous structures, and (ii) the dynamic Biot's equations for a porous elastic seabed. The effects of the porous flow in seabed and marine structures, and the fluid exchange at the interface between the fluid domain and solid domain on wave characteristics are considered. The finite difference two-step projection method and the forward time difference method are adopted to solve the VARANS equations. The volume of fluid (VOF) method is applied to track water free-surface. The finite element method and the Generalized Newmark method are respectively adopted for the space discretization and time discretization of the dynamic Biot's equations. A one-way integrating method is developed to integrate the VARANS equations with the dynamic Biot's equations. Several experimental data available in the literature are used to validate the integrated model. An overall agreement between the numerical results and the experiment data indicates that the integrated model developed for the WSSI problem is highly reliable. The integrated model is then applied to investigate the dynamic response of a large-scale composite breakwater on a seabed, and the mechanism of WSSI. Numerical results indicate that there are intensive fluid exchanges between the water body and the seabed and strong seepage forces in the seabed under the ocean wave loading. The excessive upward seepage force leads to the liquefaction of the seabed in the region under wave trough. There is a liquefaction zone in the seabed close to the bottom corner of the rubble mound, which may lead to foundation instability of the composite breakwater. The parametric study indicates that the wave characteristics have a significant impact on the liquefaction properties (depth, width and area).

Response of a porous seabed to water waves over permeable submerged breakwaters with Bragg reflection

An integrated model is developed for the investigation of wave motion and seabed response around multiple permeable submerged breakwaters subject to different levels of Bragg reflection. In this study, the Volume-Averaged Reynolds-Averaged Navier–Stokes (VARANS) equations are used to describe the non-linear interaction between waves and permeable structures, while Biot's “u−p” approximation theory is adopted for predicting the wave-induced seabed response. The numerical results show that the reflection coefficient is highly dependent on the wave period and the configuration/number of arrayed breakwaters. Wave motion and its induced seabed response (in terms of pore fluid pressure, vertical effective stress and liquefaction potential) around breakwaters can be largely changed due to Bragg reflection and energy dissipation of permeable structures. With the same incident wave conditions, the maximum liquefaction area decreases in size with an increasing soil permeability or degree of saturation.

An analytical solution for wave-induced seabed response in a multi-layered poro-elastic seabed

In this study, a new analytical solution for the wave-induced seabed response in a multi-layered poro-elastic seabed is developed. The seabed is treated as a multi-layered porous medium and characterized by Biot’s theory. The displacements of the solid skeleton and the pore pressure are expressed in terms of two scalar potentials and one vector. Then, the Biot’s dynamic equation can be solved using Fourier transformation and reducing to Helmholtz equations. To obtain the general solutions for the multi-layered poro-elastic seabed in the frequency-wave-number domain, the transmission and reflection matrices (TRM) method is used to form the equivalent stiffness. Using the boundary conditions and continuous conditions, the frequency-wave-number domain solutions are obtained. Finally, the time-space domain solutions for the multi-layered poro-elastic seabed are obtained by means of the inverse Fourier transformation with respect to the horizontal coordinate. Based on the new solution, a parametric study is carried out to examine the effects of soil characteristics (number of layers, permeability and shear modulus) and wave characteristics (water depth and wave steepness) on seabed responses. The results indicate that the seabed response is affected significantly by permeability, shear modulus and relative water depth.

3D models for wave-induced pore pressures near breakwater heads

Wave-induced pore pressure is one of the important factors in the analysis of foundation stability around coastal structures. Existing models for the wave-induced seabed response around breakwater heads have been limited to poro-elastic soil behavior and de-coupled oscillatory and residual mechanisms for the rise in excess pore water pressure. To overcome the shortcoming of the existing models, in this study a new three-dimensional poro-elastoplastic model is established, in which both oscillatory and residual mechanisms can be simulated simultaneously. The reduced cases of the proposed model are verified with existing 2D experimental data available and a 3D poro-elastic analytical solution in front of a breakwater. With the proposed new model, a parametric study is conducted to investigate the relative differences of the predictions of the wave-induced pore pressure and liquefaction with poro-elastic and poro-elasto-plastic models. Based on numerical examples, it can be concluded that relative differences between elastic and elasto-plastic models are significantly affected by wave periods and water depths. Wave height significantly affects the development of residual pore pressure versus time. Plastic soil behavior plays an important role in a seabed of low permeability. Plastic soil behavior has more significant influence on wave-induced residual pore pressure than the amplitude of the oscillating pore pressure. Furthermore, poro-elastic analysis tends to under-estimate the size of the liquefaction regions around breakwater heads.

Wave-induced response of seabed: Various formulations and their applicability

In this study, a set of generalized analytical solutions are developed for the wave-induced response of a saturated porous seabed under plane strain condition. When considering the water waves originating in deep water and travelling towards the shore, their velocities, lengths and heights vary. Depending on the characteristics of the wave and the properties of the seabed, different formulations (fully dynamic, partly dynamic, quasi-static) for the wave-induced response of the seabed are possible. The solutions for the response with these formulations are established in terms of non-dimensional parameters. The results are presented in terms of pore pressure, shear stress and vertical effective stress distributions within the seabed. For typical values of wave period and seabed permeability, the regions of applicability of the three formulations are identified and plotted in parametric spaces. With given wave and seabed characteristics, these regions provide quick identification of the appropriate formulation for an adequate evaluation of the wave-induced seabed response.

An integrated three-dimensional model for wave-induced seabed response in a porous seabed. I. A sloping seabed

In this paper, an integrated model for the wave-induced seabed response in a porous seabed is proposed. Most previous studies have considered two-dimensional cases and a flat seabed. In this study, a full three-dimensional case is considered as well as a sloping seabed. The wave model (SWAN) and soil model (PORO-WSI) is coupled into one model. With the new model, the effects of wave and soil characteristics on the ocean waves-induced seabed response (including pore pressure and stresses) are investigated. Based on numerical results, the following conclusions can be drawn: (1) the magnitude of the wave-induced soil response in a sloping seabed is much smaller than that in a flat seabed (2) the wave-induced pore pressure decreases as the slope of the seabed increases.

Effects of dynamic soil behavior and wave non-linearity on the wave-induced pore pressure and effective stresses in porous seabed

Most previous investigations for the wave-induced soil response have only considered the quasi-static soil behavior under linear wave loading. However, it is expected that the dynamic soil behavior and wave non-linearity will play an important role in the evaluation of wave-induced seabed response. In this paper, we include dynamic soil behavior and wave non-linearity into new analytical models. Based on the analytical solution derived, the effects of wave non-linearity on the wave-induced seabed response with dynamic soil behavior are examined. Numerical results demonstrate the significant effects of wave non-linearity and dynamic soil behavior on the wave-induced effective stresses. The applicable range of dynamic and quasi-static approximations is also clarified for engineering practice.

Numerical study on the interaction between non-linear wave, buried pipeline and non-homogenous porous seabed

The wave-seabed-pipeline interaction problem is particularly important for coastal geotechnical engineers involved in the design of submarine pipelines. Most previous investigations have only concerned with the soil response due to linear progressive ocean waves, even though strong evidence of wave non-linearity has been reported in the literature. In this study, the finite element model (GFEM-WSSI) proposed by the first author is adopted to investigate the interaction between nonlinear ocean waves, a buried pipelines and a porous seabed. Unlike previous models, the deformation of pipeline and non-homogeneous soil behavior are also considered in the new model. Numerical results demonstrate that the influence of non-linear wave components can not always be ignored without committing substantial error, especially for the case of large waves in shallow water. Also, revealed is that nonlinear wave-induced seabed response is affected significantly by variable permeability and shear modulus. Moreover, the internal stresses of buried pipeline increase significantly with a decrease of pipeline thickness.

Ocean waves propagating over a porous seabed of finite thickness

In the past few decades, considerable efforts have been devoted to the phenomenon of wave-seabed interaction. However, conventional investigations for determining wave characteristics have been focused on the wave nonlinearity. On the other hand, most previous works have been only concerned with the seabed response under the wave pressure, which was obtained from the assumption of a rigid seabed. In this paper, the inertia forces and employing a complex wave number are considered in the whole problem. Based on Biot’s poro-elastic theory, the problem of wave-seabed interaction is first treated analytically for a homogeneous bed of finite thickness and a new wave dispersion relationship is also obtained, in which the soil characteristics are included. The numerical results indicate that the effects of soil parameters significantly affect the wave characteristics (such as the damping of water wave, wave length and wave pressure). Furthermore, the effects of inertia forces on the wave-induced seabed response cannot always be ignored under certain combination of wave and soil conditions.

Ocean waves propagating over a Coulomb-damped poroelastic seabed of finite thickness: an analytical solution

Abstract In this paper, the Coulomb-damping friction is considered in the problem of the wave–seabed interaction in a porous seabed of finite thickness. A closed-form analytical solution will be presented here. In the model, we couple the water waves and porous seabed with a complex wave number. Thus, the effects of soil properties on the wave characteristics can be examined. The numerical results indicate that the coulomb-damping friction significantly affects the wave-induced pore pressure in a finer seabed (such as fine sand and clay). Also, the wave characteristics have been significantly affected by the wave-induced seabed response.

A New Wave Dispersion Equation: Effects of Soil Characteristics

The evaluation of wave characteristics has been widely studied by ocean engineers in the past. However, conventional investigations for determining wave characteristics have been focused on the nonlinear wave effects in a rigid seabed. On the other hand, most previous investigations for the wave-induced seabed response in a porous seabed have been only concerned with the soil response after wave pressure penetrate into seabed. In this paper, employing a complex wave number, the whole wave-seabed interaction problem will be re-examined. Based on the new closed-form analytical solution, a new wave dispersion equation is derived, including the seabed characteristics. The numerical results indicate that the wave characteristics (such as the wavelength, wave pressure and wave profile) are affected by the soil permeability and shear modulus in a shallow water.

Effective stresses in a porous seabed of finite thickness: inertia effects

The evaluation of wave-induced pore pressure and effective stresses is an important factor in the design of offshore installations. However, to simplify a complicated problem, most previous investigations have ignored the effects of inertia forces. This paper presents a new semi-analytical solution to the equations governing the wave-induced seabed response, including inertia terms for the whole problem. The numerical results show that the inertia forces cannot always be ignored. The relative difference between the present solution (with inertia items) and the previous solution (without inertia items) may reach 17% of po under certain combinations of wave and soil conditions. Key words: inertia force, pore pressure, effective stresses.

Water wave-driven seepage in marine sediments

The action of water waves moving over a porous seabed drives a seepage flux into and out of the marine sediments. The volume of fluid exchange per wave cycle may affect the rate of contaminant transport in the sediments. In this paper, the dynamic response of the seabed to ocean waves is treated analytically on the basis of poro-elastic theory applied to a porous seabed. The seabed is modelled as a semi-infinite, isotropic, homogeneous material. Most previous investigations on the wave–seabed interaction problem have assumed quasi-static conditions within the seabed, although dynamic behaviour often occurs in natural environments. Furthermore, wave pressures used in the previous approaches were obtained from conventional ocean wave theories, which are based on the assumption of an impermeable rigid seabed. By introducing a complex wave number, we derive a new wave dispersion equation, which includes the seabed characteristics (such as soil permeability, shear modulus, etc.). Based on the new closed-form analytical solution, the relative differences of the wave-induced seabed response under dynamic and quasi-static conditions are examined. The effects of wave and soil parameters on the seepage flux per wave cycle are also discussed in detail.

Short-Crested Wave-Induced Liquefaction in Porous Seabed

To simplify a complicated problem, most previous investigations of wave-induced seabed response have been concerned with an isotropic seabed with uniform soil characteristics, even though strong evidence of anisotropic soil behavior and variable soil characteristics has been reported in soil mechanics literature. This paper proposes a finite-element model to investigate the response of a cross-anisotropic seabed with variable soil characteristics subjected to a three-dimensional short-crested wave system. Based on the present model, together with the liquefaction criterion, the wave-induced liquefaction potential can be estimated. The numerical results indicate that the influence of cross-anisotropic soil behavior and variable soil characteristics on the wave-induced seabed response (including liquefaction potential) cannot always be ignored without committing substantial errors.