Wave-induced seabed response in a cross-anisotropic seabed in front of a breakwater: An analytical solution

To simplify the complicated mathematical process, most previous investigations for the water waves-seabed interaction problem have assumed a porous seabed with isotropic soil behavior, even though strong evidence of anisotropic soil behavior has been reported in soil-mechanics literature. This paper proposes an analytical solution of the short-crested wave-induced soil response in a cross-anisotropic seabed. As shown in the numerical results presented, the wave-induced seabed response, including pore pressure, effective stresses and soil displacements, is affected significantly by the cross-anisotropic elastic constants. A parametric study is performed to clarify the relative differences in pore pressure between isotropic and cross-anisotropic solutions.     

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.     

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.     

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.     

Wave-induced seabed response in shallow water

To simulate the wave-induced response of coupled pore fluids and a solid skeleton in shallow water, a set of solutions with different formulations (fully dynamic, partly dynamic, and quasi-static) corresponding to each soil behavior assumption is presented. To deal with Jacobian elliptic functions involved in the cnoidal theory, a Fourier series approximation is adopted for expanding the boundary conditions on the seabed surface. The parametric study indicates the significant effect of nonlinearity for shallow water wave, which also enhances the effect of soil characteristics. The investigation of the applicability of reduced formulations reveals the necessity of a partly or even fully dynamic formulation for the wave-induced seabed response problem in shallow water, especially for thickened seabed. The analysis of liquefaction in the seabed indicates that the maximum depth of liquefaction is shallower, and the width of liquefaction is broader under cnoidal wave loading. The present analytical model can provide more reasonable result for the wave-induced seabed response in the range of shallow water wave.     

波浪诱发松散海床渐进式液化的数值分析

近海区域广泛分布着第四纪新沉积的松散海洋土,波浪荷载作用下松散海床会发生液化进而对近海结构物的稳定性存在巨大威胁。本文采用中国科学院流体-结构-海床相互作用数值计算模型FSSI-CAS 2D,选用Pastor-Zienkiewicz-Mark Ⅲ（PZⅢ）弹塑性本构研究了波浪诱发的松散海床液化问题。分析了波浪荷载引起的松散海床内超孔隙水压力、有效应力以及应力角的时程变化特性,并预测了松散海床的渐进液化过程。计算结果表明,波浪荷载作用下松散海床内残余孔压会累积增长,海床表面最先发生液化,然后逐渐向下发展至液化最大深度。同时指出海床内超孔隙水压力的竖向分布特征和应力角的变化时程均可以作为判断海床液化的间接参数。最后,通过应力状态分析,讨论了海床渐进式液化的发展过程和趋势。     

Wave-induced porewater pressure in a seabed with inhomogeneous permeability

We have developed an analytical treatment for the wave-induced response of a seabed with inhomogeneous permeability, by employing the boundary layer approximation. By assuming an exponential function for vertically distributed permeability, the inhomogeneous consolidation equation was formulated as Bessel's differential equation. Subsequently, we proposed some representative quantities for examining the effects of inhomogeneity of permeability. The main effects of inhomogeneity are that the boundary layer becomes thinner and the phase delay in the direction of depth becomes larger as the inhomogeneity becomes significant. In addition, it was shown that the boundary layer is properly evaluated by using the averaged permeability.     

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.     

Wave-induced uplift force on a submarine pipeline buried in a compressible seabed

A two-dimensional finite-element simulation of the wave-induced hydrodynamic uplift force acting on a submarine pipeline buried in sandy seabed sediments subject to continuous loading of sinusoidal surface waves is presented. Neglecting inertia forces, a linear-elastic stress-strain relationship for the soil and Darcy's law for the flow of pore fluid are assumed. The model takes into account the compressibility of both components (i.e., pore fluid and soil skeleton) of the two-phase medium.The results of numerical analysis are presented and discussed with respect to soil and pore fluid parameters where special attention is paid to the question of soil saturation conditions. The meaning of the results is also related to surface wave conditions. As a general conclusion, the practical, engineering recommendation is given in order to make a realistic, safe and economic estimation of the wave-induced uplift force acting on a buried submarine pipeline.     

波浪作用下单桩基础周围海床液化机制研究

建立波浪作用下单桩周围三维海床动力响应模型,考虑自重影响下的海床长时间固结过程。采用已有物理模型试验数据对模型进行验证,证实其具有较好的适用性。模拟波浪作用下单桩周围三维海床液化区域,通过定量分析超孔隙水压力和土体初始有效应力的变化,讨论单桩插入深度对海床液化的影响机制。研究表明,单桩插入深度发生变化时,土体初始有效应力对海床液化的影响要大于超孔隙水压力,且影响程度随着插入深度的增加而逐渐增大。     

Wave-induced pore pressures and effective stresses in inhomogeneous seabed foundations

Stability analyses of homogeneous and inhomogeneous seabed foundations under attack by storm waves are made by calculating the wave-induced effective stresses. Wave-induced effective stress analysis of homogeneous seabed is made using the theory previously developed by the author which is based on the poro-elastic theory of Biot. Effective stresses in inhomogeneous seabeds induced by waves are calculated by approximating aa inhomogeneous bed by many layers of homogeneous soils each of which has different geotechnical soil properties. A good agreement is obtained between the theory and the pore pressure data from in situ field measurements. For a given wavelength, it is found that there exists a most unstable thickness of homogeneous seabed when the thickness is one-fifth of the wave length. As a realistic example of an inhomogeneous bed, the effective stresses in a typical seabed formation at the Mississippi Delta area of the Gulf of Mexico under the attack of design storm waves are calculated. The numerical results indicate that the storm waves induce a continuous submarine landslide which extends as deep as 9 m from the mud line. Numerical calculations also indicate that such landslides and liquefaction of seabeds can be prevented by placing a layer of concrete blocks or rubble on top of the seabeds.     

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.     

Wave-induced seabed response analysis by radial point interpolation meshless method

Wave-induced transient response of seabeds is numerically analyzed through a radial point interpolation meshless method (radial PIM). The Biot’s consolidation theory is employed and incorporated with virtual boundary conditions to describe this wave-induced transient response of the seabed. Displacement and pore water pressure are spatially discretized by the radial PIM with the same shape function. Compactly supported basis functions are proposed to obtain a banded system equation. Because the radial PIM passes through all nodal points within an influence domain, essential boundary conditions as well as virtual boundary conditions can be easily implemented at local level. Fully implicit integration scheme is used in time domain to avoid spurious ripple effect. The proposed algorithm is assessed through the comparison of numerical results with closed-form solution or finite element solutions.     

Numerical study of wave-induced soil response in a sloping seabed in the vicinity of a breakwater

In this study, a mathematical integrated model is developed to investigate the wave-induced sloping seabed response in the vicinity of breakwater. In the present model, the wave model is based on the Volume-Averaged/Reynolds Averaged Navier–Stokes (VARANS) equations, while Biot's consolidation equation is used to govern the soil model. The influence of turbulence fluctuations on the mean flow with respect to the complicated interaction between wave, sloping seabed and breakwater are obtained by solving the Volume-Averaged k − ϵ model. Unlike previous investigations, the phase-resolved absolute shear stress is used as the source of accumulation of residual pore pressure, which can link the oscillatory and residual mechanisms simultaneously. Based on the proposed model, parametric studies regarding the effects of wave and soil characteristics as well as bed slopes on the wave-induced soil response in the vicinity of breakwater are investigated. Numerical results indicate that wave-induced seabed instability is more likely to occur in a steep slope in the case of soil with low relative density and low permeability under large wave loadings. It is also found that, the permeability of breakwater significantly affect the potential for liquefaction, especially in the region below the breakwater.     

直立堤前海床的局部冲刷

对不规则波作用下直立堤前海床的局部冲刷进行了研究。研究了由于波浪作用导致床面的底沙运动,从而造成提前海床的局部冲刷,即所谓的“相对粒沙”的情况。报导了;(1)堤前海床面为水平、堤下无基床情况下的堤前局部冲刷,以及堤下有明基床时基床尺度对堤前局部冲刷的影响;(2)堤前海床面为斜坡面时堤前的局部冲刷,以及当堤下有明基床时基床尺度对堤前局部冲刷的影响;(3)从波浪作用下床面边界层的理论分析出发,对于在不规则波作用下,离堤面愈远处的冲刷坑深度愈小的事实给出了解释。     

Laboratory experiments for wave motions and turbulence flows in front of a breakwater

In this paper, laboratory data for free surface displacements and velocity fields in front of a caisson breakwater covered with wave-dissipating blocks, together with wave pressures acting on the caisson, are presented and discussed. The core of the breakwater is made of a concrete caisson with a vertical front wall. The caisson is protected by a thick layer of tetrapods and is supported by a rubble mound. The breakwater is placed on the 1/25 impermeable slope. Two types of incident waves are used in the experiments: nonbreaking waves and spilling-type breaking waves. In the breaking wave case, the incident wave breaks offshore before it reaches the breakwater. The velocity data are obtained by using both the Laser Doppler Velocimeter (LDV) and the Electromagnetic Current Meter (EMCM). The raw data are analyzed using a numerical-filtering scheme so that turbulent fluctuations are separated from the phase-dependent wave motions. The vertical profiles of the time-averaged (over a wave period) turbulent velocity components at several vertical cross-sections in front of the breakwater are then analyzed. The spatial variations of the time-averaged turbulence velocity suggest that turbulence is generated inside the protective armor layer and transported into the flow region in front of the breakwater. The wave pressures on the vertical face and on the bottom of the caisson are also reported.     

Simulation of the nonlinear dynamic interactions between waves, a submerged breakwater and the seabed

This study employed direct numerical simulation to simulate the fully nonlinear interaction between the water waves, the submerged breakwater, and the seabed under differing wave conditions. In the numerical simulation, the laminar flow condition in the seabed was applied to evaluate the more exact fluid resistance acting on the porous media. Varying incident wave conditions were applied to the flow field resulting from the wave–structure–seabed interaction, and the variation in the pore water pressure beneath the submerged breakwater was investigated along the cross-section of the submerged breakwater. Structural safety and scouring were also considered on the basis of the numerical results for the flow field around the structure and the variation of the pore water pressure.     

Numerical study on the interaction among a nonlinear wave,composite breakwater and sandy seabed

Most previous investigations related to composite breakwaters have focused on the wave forces acting on the structure itself from a hydrodynamic aspect. The foundational aspects of a composite breakwater under wave-induced cyclic loading are also important in studying the stability of a composite breakwater. In this study, numerical simulations were performed to investigate the wave-induced pore water pressure and flow changes inside the rubble mound of the composite breakwater and seabed foundation. The validity and applicability of the numerical model were demonstrated by comparing numerical results with existing experimental data. Moreover, the present model clearly has shown that the instantaneous directions of pore water flow motion inside the seabed induced by surface waves are in good agreement with the general wave-induced pore water flow inside the seabed. The model is further used to discuss the stability of a composite breakwater, i.e., the interaction among nonlinear waves, composite breakwater and seabed. Numerical results suggest that the stability of a composite breakwater is affected by not only downward shear flow generating on the seaward slope face of the rubble mound but, also, a high and dense pore water pressure gradient inside the rubble mound and seabed foundation.     

A numerical model for wave motions and turbulence flows in front of a composite breakwater

A mathematical model based on the Volume-Averaged/Reynolds Averaged Navier-Stokes (VARANS) equations is developed to describe surface wave motions in the vicinity of a coastal structure, which could be either a rigid solid structure or a permeable structure or a combination of both. In the VARANS equations, the volume-averaged Reynolds stress is modeled by adopting the nonlinear eddy viscosity assumption. The model equations for the volume-averaged turbulent kinetic energy and its dissipation rate are derived by taking the volume-average of the standard k−ϵ equations. Because of the volume-averaging process, the effects of the small-scale turbulence in porous media are introduced. The performance of the model is checked by comparing numerical solutions with the experimental data related to a composite breakwater reported by Sakakiyama and Liu [Coast. Eng. 121 (2001) 117].     

部分反射直墙前潜堤水动力特性研究

基于线性势流理论,对部分反射直墙前潜堤的水动力特性进行了理论研究。利用匹配特征函数展开法给出了潜堤透射系数和反射系数的计算方法,计算结果与边界元方法的计算结果一致。利用数值算例分析了潜堤透射系数和反射系数的主要影响因素。增大部分反射直墙的反射系数,将加大潜堤的透射系数。随着潜堤相对宽度或潜堤与直墙之间相对间距的增加,潜堤透射系数和反射系数呈周期性变化,但变化规律相反。