Stability analysis on a porous seabed under wave and current loadings

The stability of a porous seabed under wave and current loadings is particularly important for engineers to design marine structures such as submarine pipelines, breakwaters, and offshore platform foundations. Most previous investigations of dynamic response of marine structures and seabed have only considered the influence of wave loading, but the important influence of current is ignored. Even if the influence of current is considered, the interaction mechanism of both loadings has not been clearly elaborated. Based on the Biot’s dynamic theory and combined two-dimensional nonlinear progressive wave and uniform current theory, the interaction mechanism of wave and current loadings and the influence of current on wave characteristic are analyzed by numerical computations. The influence of current velocity, different permeability, and stratification in seabed on the effective stresses and pore pressures of seabed is discussed in detail. Further, the stability of seabed is evaluated through the liquefaction analysis of seabed, which will provide important reference frames to improve the design and construction of marine structures.     

Wave-induced seabed instability around a buried pipeline in a poro-elastic seabed

The subject of the wave–seabed–structure interaction is important for civil engineers regarding stability analysis of foundations for offshore installations. Most previous investigations have been concerned with such a problem in the vicinity of a simple structure such as a vertical wall. For more complicated structures such as a pipeline, the phenomenon of the wave–seabed–structure has not been fully understood. This paper proposes a finite-difference model in a curvilinear coordinate system to investigate the wave-induced seabed response in a porous seabed around a pipeline. Based on the present numerical model, mechanism of the wave-induced soil response is examined. Employing Mohr–Coulomb failure criterion, the wave-induced seabed instability is also estimated. The numerical results indicate the importance of the effect of pipeline on the seabed response.     

砂质海床上海底管线的斜向波浪力试验研究

近岸海底管线在波浪作用下的受力情况关系着海底管线的安全运营。本文利用波浪港池物理模型试验,研究了斜向规则波作用下海底管线断面和管线沿程波浪力特性,分析了波浪入射方向与管线轴线夹角α及波浪要素对海底管线所受波浪力的影响,探讨了管线冲刷与所受波浪力之间的关系。试验结果表明:管线水平力在α=60°时达到最大,而上升力在α=45°时达到最大,并且从力的大小来看水平力比上升力大。随着角度增大,管线压力沿程变化幅度先增大再减小,α在60°时管线上游端压力最大;在45°时管线压力沿程变化呈波浪型,从上游往下游增减交替变化。随着冲刷的发展,管线下方受力最大值逐渐增大,管线前后方压力差值也逐渐增大。     

An integrated three-dimensional model of wave-induced pore pressure and effective stresses in a porous seabed: II. Breaking waves

The evaluation of the wave-induced liquefaction potential is particularly important for coastal engineers involved in the design of marine structures. Most previous investigations of the wave-induced liquefaction have been limited to two-dimensional non-breaking waves. In this paper, the integrated three-dimensional poro-elastic model for the wave-seabed interaction proposed by [Zhang, H., Jeng, D.-S., 2005. An integrated three-dimensional model of wave-induced pore pressure and effective stresses in a porous seabed: I. A sloping seabed. Ocean Engineering 32(5/6), 701–729.] is further extended to simulate the seabed liquefaction potential with breaking wave loading. Based on the parametric study, we conclude: (1) the liquefaction depth due to breaking waves is smaller than that of due to non-breaking waves; (2) the degree of saturation significantly affects the wave-induced liquefaction depth, and no liquefaction occurs in full saturated seabed, and (3) soil permeability does not only significantly affect the pore pressure, but also the shear stresses distribution.     

A semi-analytical solution for random wave-induced soil response and seabed liquefaction in marine sediments

In this study, unlike most previous investigations for wave-induced soil response, a simple semi-analytical model for the random wave-induced soil response is established for an unsaturated seabed of finite thickness. Two different wave spectra, the B-M and JONSWAP spectra, are considered in the new model. The influence of random wave loading on the soil response is investigated by comparing with the corresponding representative regular wave results through a parametric study, which includes the effect of the degree of saturation, soil permeability, wave height, wave period and seabed thickness. The maximum liquefaction depth under the random waves is also examined. The difference on the soil response under the two random wave types, B-M and JONSWAP frequency spectra, is also discussed in the present work.     

Unfluidized soil responses of a silty seabed to monochromatic waves

A flume experimental study on unfluidized responses of a silty bed (d₅₀=0.05 mm) to monochromatic water waves had shown that pore pressure variations were generally poro-elastic in the bulk body and displayed two other characteristic features not found in previous laboratory sand tests. They were an immediately fluidized thin surface layer induced by wave stresses inside the seabed's boundary layer and a porous skeleton with internally suspended sediments due to channeled flow motions. The analyses verified that on soils beneath the measurement points, both features resulted in relatively small-step pore pressure build-ups, while the former played a primary role. Besides, laboratory observations confirmed that there were some near-bed sediment suspensions during wave actions resulting in a flat bed form over a silty bed compared to small-scaled ripples over a sandy bed with no clearly identified suspended sediments. These characteristic silt responses suggest that sediment transport is critically associated with the internal soil responses and some field-observed sediment suspensions near above sandy beaches can further be approached in the laboratory by utilizing fine-grained soils.     

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.     

Stability and liquefaction analysis of porous seabed subjected to cnoidal wave

Cnoidal wave theory is appropriate to periodic wave progressing in water whose depth is less than 1/10 wavelength. However, the cnoidal wave theory has not been widely applied in practical engineering because the formula for wave profile involves Jacobian elliptic function. In this paper, a cnoidal wave-seabed system is modeled and discussed in detail. The seabed is treated as porous medium and characterized by Biot's partly dynamic equations (u–p model). A simple and useful calculating technique for Jacobian elliptic function is presented. Upon specification of water depth, wave height and wave period, Taylor's expression and precise integration method are used to estimate Jacobian elliptic function and cnoidal wave pressure. Based on the numerical results, the effects of cnoidal wave and seabed characteristics, such as water depth, wave height, wave period, permeability, elastic modulus, and degree of saturation, on the cnoidal wave-induced excess pore pressure and liquefaction phenomenon are studied.     

Three-dimensional poro-elastic integrated model for wave and current-induced oscillatory soil liquefaction around an offshore pipeline

To obtain a better understanding of the oscillatory soil liquefaction around an offshore pipeline, a three-dimensional integrated model for the wave–seabed–pipeline interaction (WSPI) is proposed by combining the Reynolds-Averaged Navier–Stokes equations for flow simulations and the dynamic Biot’s equation (“u-p” approximation) for the poro-elastic seabed model. Compared with previous investigations, the wave–current interaction is included in the present WSPI system. At a given time step, the wave pressure extracted from the flow model is applied on the seabed surface to determine the corresponding oscillatory seabed response around an offshore pipeline. The integrated numerical model is first validated using previous laboratory experiments. Then, a parametric study is conducted to examine the effects of flow obliquity and pipeline burial depth on the soil response around an offshore pipeline. Numerical results indicate that the soil under the pipeline is more susceptible to liquefaction at a reduced flow obliquity and pipeline burial depth. Moreover, the liquefaction depth in the case where the wave travels along the current can increase by 10%–30% compared to that in the case where the wave travels against the current, when the magnitude of the current velocity is 1 m/s.     

Non-linear wave-induced transient response of soil around a trenched pipeline

Submarine pipelines are always trenched within a seabed for reducing wave loads and thereby enhancing their stability. Based on Biot's poroelastic theory, a two-dimensional finite element model is developed to investigate non-linear wave-induced responses of soil around a trenched pipeline, which is verified with the flume test results by Sudhan et al. [Sudhan, C.M., Sundar, V., Rao, S.N., 2002. Wave induced forces around buried pipeline. Ocean Engineering, 29, 533–544] and Turcotte et al. [Turcotte, B.R., Liu, P.L.F., Kulhawy, F.H., 1984. Laboratory evaluation of wave tank parameters for wave-sediment interaction. Joseph H. Defree Hydraulic Laboratory Report 84-1, School of Civil and Environmental Engineering, Cornell University]. Non-linear wave-induced transient pore pressure around pipeline at various phases of wave loading is examined firstly. Unlike most previous investigations, in which only a single sediment layer and linear wave loading were concerned, in this study, the influences of the non-linearity of wave loading, the physical properties of backfill materials and the geometry profile of trenches on the excess pore pressures within the soil around pipeline, respectively, were explored, taking into account the in situ conditions of buried pipeline in the shallow ocean zones. Based on the parametric study, it is concluded that the shear modulus and permeability of backfill soils significantly affect the wave-induced excess pore pressures around trenched pipeline, and that the effect of wave non-linearity becomes more pronounced and comparable with that of trench depth, especially at high wave steepness in shallow water.     

Wave-induced pore pressure around a composite breakwater

The interaction between wave, seabed and marine structure is a vital issue in coastal engineering, as well as marine geotechnical engineering. However, most previous investigations have been focused on the wave forces acting on the structure from the aspect of hydrodynamics. In this study, we will examine the problem of wave-seabed-caisson interaction from the aspect of marine geotechnical engineering. Based on Biot's poro-elastic theory (Biot, M.A., 1941. General theory of three-dimensional consolidation. Journal of Applied Physics 12, 155–164), a two-dimensional finite element model is proposed to investigate the wave-induced soil response in the vicinity of a caisson. Based on the numerical model, the water wave driven pore pressure around a caisson will be examined through a parametric analysis.     

Response of a porous seabed around breakwater heads

The evaluation of wave-induced pore pressures and effective stresses in a porous seabed near a breakwater head is important for coastal engineers involved in the design of marine structures. Most previous studies have been limited to two-dimensional (2D) or three-dimensional (3D) cases in front of a breakwater. In this study, we focus on the problem near breakwater heads that consists of incident, reflected and diffracted waves. Both wave-induced oscillatory and residual liquefactions will be considered in our new models. The mistake in the previous work [Jeng, D.-S., 1996. Wave-induced liquefaction potential at the tip of a breakwater. Applied Ocean Research 18(5), 229–241] for oscillatory mechanism is corrected, while a new 3D boundary value problem describing residual mechanism is established. A parametric study is conducted to investigate the influences of several wave and soil parameters on wave-induced oscillatory and residual liquefactions around breakwater heads.     

波浪作用下粉土海床中的孔压响应试验研究

海床在波浪作用下是否稳定对海底工程的安全至关重要,海床的稳定性与土体中的孔压响应密切相关。水槽模拟试验表明:在波浪的作用下,黄河三角洲粉土海床中将产生振荡孔隙水压力和累积孔隙水压力。振荡孔隙水压力大小与土层深度、波高和粘粒含量有关,其振幅(能量)在土层中随深度的增加呈指数衰减,且粘粒含量越高衰减越快;加载波高越大,能量衰减越快。而累积孔压响应模式表现为在波浪作用最初的一段时间内,孔隙水压力快速上升,然后逐渐减小而趋于稳定,其大小和速率也与波高、粘粒含量、土层埋深有关,粘粒含量越高,孔压累积速度越低。     

The liquefaction and displacement of highly saturated sand under water pressure oscillation

In order to investigate the characteristics of water wave induced liquefaction in highly saturated sand in vertical direction, a one-dimensional model of highly saturated sand to water pressure oscillation is presented based on the two-phase continuous media theory. The development of the effective stresses and the liquefaction thickness are analyzed. It is shown that water pressure oscillating loading affects liquefaction severely and the developing rate of liquefaction increases with the decreasing of the sand strength or the increasing of the loading strength. It is shown also that there is obvious phase lag in the sand column. If the sand permeability is non-uniform, the pore pressure and the strain rise sharply at which the smallest permeability occurs. This solution may explain why the fracture occurs in the sand column in some conditions.     

Analysis on pore pressure in an anisotropic seabed in the vicinity of a caisson

This paper presents an analysis of pore pressure around a caisson-type breakwater subjected to dynamic wave loading. Unlike previous investigations for wave-seabed-caisson interaction, cross-anisotropic soil behaviour is considered in this paper. Based on a linear poro-elastic theory, a finite element model is developed. A parametric study related to the effects of wave parameters, soil characteristics and geometry of caisson and rubble mound base on the pore pressure around a caisson is performed. The numerical results indicate that the effects of anisotropic soil behaviour on the wave-induced pore pressure in a sandy bed beneath a caisson are not negligible.     

Mechanism of the wave-induced seabed instability in the vicinity of a breakwater: a review

A detailed knowledge of the wave-induced seabed instability is particularly important for engineers involved in the design procedure of many marine structures and offshore installations. In this paper, the basic aspects of such instability will be examined. The current understanding of the mechanism of the wave–seabed interaction phenomenon and available approaches will be reviewed. Based on the framework of simplified analysis, the potential for such instability will be formulated that will help engineers to identify potential unstable sediments in the vicinity of a marine structure.     

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.     

波浪作用下粉质土海床液化界面波压力的研究

波浪作用下粉质土海床的液化是影响海上平台、海底管线等海洋构筑物安全的灾害之一。在进行构筑物设计中应考虑海床液化的深度问题,而液化土体对下部海床的界面波压力是计算海床孔隙水压力增长以及液化深度的重要参量。本文基于波致粉土海床自上而下的渐进液化模式,利用双层流体波动理论,推导了考虑海床土体黏性的海床界面波压力表达式,并与不考虑黏性时的界面波压力进行了比较分析。结果表明,计算液化后土体界面波压力时,是否考虑液化土体的黏性对结果影响较大,进而可能影响粉质土海床液化深度的确定。     

Comparison of existing poroelastic models for wave damping in a porous seabed

Mechanism of wave–seabed interaction has been extensively studied by coastal geotechnical engineers in recent years. Numerous poro-elastic models have been proposed to investigate the mechanism of wave propagation on a seabed in the past. The existing poro-elastic models include drained model, consolidation model, Coulomb-damping model, and full dynamic model. However, to date, the difference between the existing models is unclear. In this paper, the fully dynamic poro-elastic model for the wave–seabed interaction will be derived first. Then, the existing models will be reduced from the proposed fully dynamic model. Based on the numerical comparisons, the applicable range of each model is also clarified for the engineering practice.     

Coupled analysis for response and instability of sloping seabed under wave action

Wave-induced instability of seabed may cause damage to coastal and offshore structures. This issue has been investigated mostly for mildly sloping ($<5^{°}$) seabed considering uncoupled or one-way coupled response of wave and seabed interaction. However, some of the marine structures are founded on seabed with steeper slopes. In this study, the wave-induced response and instability of sloping seabed are evaluated using a coupled finite element model. The interaction between fluid and porous seabed accounting for the effect of fluid motion on the seabed response, and conversely the effect of seabed response on the fluid motion (but not on the surface wave profile) is considered. The results indicate that the system response (fluid pressure, stresses, etc.) and the extent of instantaneously liquefied zone within the sloping seabed with significant steepness are lesser than those for horizontal seabed. Moreover, for typical sediment and wave characteristics, for the flat seabed, the response obtained from fully coupled analysis is not significantly different from those obtained by uncoupled analysis. For the sloping bed, such difference is slightly greater as compared to that for the flat bed.