Fully Coupled Simulation of Interactions Among Waves,Permeable Breakwaters and Seabeds Based on N−S Equations

Interstitial flows in breakwater cores and seabeds are a key consideration in coastal and marine engineering designs and have a direct impact on their structural safety.In this paper,a unified fully coupled model for wave?permeable breakwater?porous seabed interactions is built based on an improved N?S equation.A numerical wave flume is constructed,and numerical studies are carried out by applying the finite difference method.In combination with a physical model test,the accuracy of the numerical simulation results is verified by comparing the calculated and measured values of wave height at measurement points and the seepage pressure within the breakwater and seabed.On this basis,the characteristics of the surrounding wave field and the internal flow field of the pore structure,as well as the evolution process of the fluctuating pore water pressure inside the breakwater and seabed,are further analyzed.The spatial distribution of the maximum fluctuating pore water pressure in the breakwater is compared between two cases by considering whether the seabed is permeable,and then the effect of seabed permeability on the dynamic pore water pressure in the breakwater is clarified.This study attempts to provide a reference for breakwater design and the protection of nearby seabeds.     

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.     

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.     

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.     

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.     

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。     

Parametric study of the wave-induced residual liquefaction around an embedded pipeline

Wave-induced liquefaction in a porous seabed around submarine pipeline may cause catastrophic consequences such as large horizontal displacements of pipelines on the seabed, sinking or floatation of buried pipelines. Most previous studies in relation to the wave and seabed interactions with embedded pipeline dealt with the wave-induced instaneous seabed response and possible resulting momentary liquefaction (where the soil is liquefied instantaneously during the passage of a wave trough), using theory of poro-elasticity. Studies for the interactions between a buried pipeline and a soil undergoing build-up of pore pressure and residual liquefaction have been comparatively rare. In this paper, this complicated process was investigated by using a new developed integrated numerical model with RANS (Reynolds averaged Navier–Stokes) equations used for governing the incompressible flow in the wave field and Biot consolidation equations used for linking the solid–pore fluid interactions in a porous seabed with embedded pipeline. Regarding the wave-induced residual soil response, a two-dimensional poro-elastoplastic solution with the new definition of the source term was developed, where the pre-consolidation analysis of seabed foundation under gravitational forces including the body forces of a pipeline was incorporated. The proposed numerical model was verified with laboratory experiment to demonstrate its accuracy and effectiveness. The numerical results indicate that residual liquefaction is more likely to occur in the vicinity of the pipeline compared to that in the far-field. The inclusion of body forces of a pipeline in the pre-consolidation analysis of seabed foundation significantly affects the potential for residual liquefaction in the vicinity of the pipeline, especially for a shallow-embedded case. Parametric studies reveal that the gradients of maximum liquefaction depth with various wave and soil characteristics become steeper as pipeline burial depth decreases.     

Standing wave induced pore pressures in a porous seabed

Incident waves reflecting normally from a breakwater produce standing waves; they are more conducive in terms of scouring of the seabed than the action of progressive waves. Employing Biot's theory of consolidation, the pore pressure response within a porous seabed induced by the standing wave is analytically presented. Experiments for the response are also conducted in a wave flume. Unlike the progressive wave, the variation of standing-wave induced soil response is temporal and spatial. The theories compare well with the experiments.     

随机波作用下埋管海床动态响应及液化研究

基于广义Biot动力理论和Longuet-Higgins线性叠加模型,构建波浪-海床-管线动态响应的有限元计算模型,求解随机波作用下,多层砂质海床中管线周围土体孔隙水压力和竖向有效应力的分布。采用基于超静孔隙水压力的液化判断准则,得出液化区的最大深度及横向范围,从而判断海床土体液化情况。考虑海洋波浪的随机性,将海床视为多孔介质,海床动态响应计算模型采用u-p模式,孔隙水压力和位移视为场变量。并考虑孔隙水的可压缩性、海床弹性变形、土体速度、土体加速度以及流体速度的影响,忽略孔隙流体惯性作用。参数研究表明:土体渗透系数、饱和度以及有效波高等参数对海床土体孔隙水压力、竖向有效应力和液化区域分布有显著影响。     

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.     

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.     

Wave transformation over submerged permeable breakwater on porous bottom

A numerical model is presented in this study to investigate the wave transformation over a submerged permeable breakwater on a porous slope seabed. For this purpose, the time-dependent mild-slope equation is newly derived for waves propagating over two layers of porous medium. This new mild-slope equation involves the parameters of the porous medium, and it is a type of hyperbolic differential equation, therefore numerically efficient. The validity of the present model is verified based on the comparisons with the previous experiments. The effects of the permeable properties of both the porous seabed and the submerged permeable breakwater are discussed in detail. The geometry of the submerged permeable breakwater to the wave transformation is also investigated based on the numerical solutions.     

Numerical evaluation of liquefaction-induced damages in composite breakwaters and its application for performance-based improvement design

Breakwaters provide a calm sea basin for ships and protect harbor facilities by reflecting wave energy toward the open sea area. Their performance under environmental loadings is the main concern for coastal engineers. Liquefaction susceptibility of loose sediments of seabed threatens performance of these structures. The article investigates soil liquefaction effects on the seismic performance of Iran liquefied natural gas (LNG) composite breakwater. Performance-based design method, considering both grade of the breakwater and acceptable level of damages, was selected as design philosophy. Liquefaction-induced damages to the breakwater were determined by numerical analysis. Since the obtained level of deformations did not meet allowable damages, soil improvement against liquefaction was considered. Different improvement patterns were proposed based on distribution of pore pressure ratio (r_u) beneath the breakwater to control its seismic performance. This investigation revealed that the most important area for soil improvement is located near the toes of breakwater to control the slope instability and performance of the breakwater.     

随机波作用下海床动态响应分析

真实的海洋波浪是随机的,而前人对海床的动态响应分析大都是选用线性波或者Stokes波理论,对海床的模拟大都采用Biot拟静力模型,忽略了流体速度及土体位移加速度的影响。联合使用Longuet-Higgins随机波模型(采用Jonswap谱)以及动力u-p形式的海床响应计算模型,使用COMSOL Multiphysics多场耦合软件的PDE模块输入方程进行有限元计算,得到随机波作用下整体海床动态响应结果。将随机波结果与一阶Stokes波和椭圆余弦波结果进行对比,并对渗透系数和饱和度进行参数分析,研究表明渗透系数和饱和度对于随机波作用下海床动态响应影响显著。     

Wave interaction with a wave absorbing double curtain-wall breakwater

This study examines the hydrodynamic performance of a wave absorbing double curtain-wall breakwater. The breakwater consists of a seaward perforated wall and a shoreward impermeable wall. Both walls extend from above the seawater to some distance above the seabed. Then the below gap allows the seawater exchange, the sediment transport and the fish passage. By means of the eigenfunction expansion method and a least square approach, a linear analytical solution is developed for the interaction of water waves with the breakwater. Then the reflection coefficient, the transmission coefficient and the wave forces acting on the walls are calculated. The numerical results obtained for limiting cases agree very well with previous predictions for a single partially immersed impermeable wall, the double partially immersed impermeable walls and the bottom-standing Jarlan-type breakwater. The predicted reflection coefficients for the present breakwater also agree reasonable with previous experimental results. Numerical results show that with appropriate structure parameters, the reflection and transmission coefficients of the breakwater may be both below 0.5 at a wide range of the relative water depth. At the same time, the magnitude of wave force acting on each wall is small. This is significant for practical engineering.     

植物对孤立波作用下直立堤局部冲刷影响实验研究

基于水槽实验,研究植物对孤立波作用下直立堤局部冲刷的影响。通过改变实验入射波高、植物带的宽度和密度,分析各要素对直立堤局部冲刷的影响。实验对波高沿程变化、孤立波越堤、回落过程以及地形演变进行全程的测量和记录,并进行有无植物带保护的直立堤局部冲刷对比分析。结果表明,植物带的存在,使得堤后相对最大冲刷深度显著减小,堤前冲刷形态由单峰式"L"型变为双峰式淤积沙坝形态,且冲刷位置由原堤脚前移至植物带所在位置,冲刷范围大幅增加。减小植物带密度或者植物带宽度会使近岸侧或是离岸侧的相对最大冲刷深度和相对最大淤积高度有增大的趋势,但是当入射波高增大时,二者的影响不显著。该研究对实际工程中植物带的合理布置提出了具有参考性的建议,对减少堤防工程的冲刷和损失有一定现实意义。     

新型开孔工字板组合式防波堤波浪力特性试验研究

开孔工字板组合式防波堤是基于透空板式防波堤的一种新型结构形式,具有自重轻、材料省的特点。为充分了解新型开孔组合式防波堤的受力特性,基于室内水槽物理模型试验,测量新型开孔工字板组合式防波堤上的波压力与结构总力,研究相对波高H/d、相对波长L/B对该新型防波堤结构表面压力的影响,讨论了该新型防波堤所受波浪力荷载与相对波高H/d、相对波长L/B的关系。结果表明,相对波高H/d是决定新型防波堤结构表面波压力和结构总力的主要影响因素。该新型防波堤结构波浪力荷载以垂直方向受力为主,新型防波堤结构所受竖向总力远大于水平总力,最大可达到15倍。新型防波堤水平总力随相对波长L/B先增大后趋于稳定。相对波长L/B=3.617是防波堤结构水平总力变化幅度的分界点。     

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.     

Theoretical and experimental study on wave damping inside a rubble mound breakwater

Wave decay in a rubble mound breakwater has been analysed theoretically for various types of damping functions (linear, quadratic and polynomial). The applicability of these damping functions for wave decay in the landward part of the breakwater core has been investigated in large scale model tests. The properties of the rock materials that have been used in the model tests have been determined to provide a rational basis for the damping coefficients. The analysis is based on detailed measurements of wave conditions and pressure distributions inside the breakwater. The theoretical approaches have been validated and where necessary extended by empirical means. The wave decay inside the breakwater can be reasonably approximated by the commonly applied linear damping model (resulting in exponential wave height attenuation). An extended polynomial approach provides a slightly better fit to the experimental results and reflects more clearly the governing physical processes inside the structure.     

The role of submerged berms on the momentary liquefaction around conventional rubble mound breakwaters

Berms deployed at the toe of conventional rubble mound breakwaters can be very effective in improving the stability of the armor layer. Indeed, their design is commonly tackled by paying attention to armor elements dimensioning. Past research studies showed how submerged berms can increase the stability of the armor layer if compared to straight sloped conventional breakwaters without a berm. To fill the gap of knowledge related to the interaction between breakwaters with submerged berm, waves and soil, this research aims to evaluate how submerged berms configuration influences the seabed soil response and momentary liquefaction occurrences around and beneath breakwaters foundation, under dynamic wave loading. The effects of submerged berms on the incident waves transformation have been evaluated by means of a phase resolving numerical model for simulating non-hydrostatic, free-surface, rotational flows. The soil response to wave-induced seabed pressures has been evaluated by using an ad-hoc anisotropic poro-elastic soil solver. Once the evaluation of the seabed consolidation state due to the presence of the breakwater has been performed, the dynamic interaction among water waves, soil and structure has been analyzed by using a one-way coupling boundary condition. A parametric study has been carried out by varying the berm configuration (i.e. its height and its length), keeping constant the offshore regular wave condition, the berm and armor layer porosity values, the water depth and the elastic properties of the soil. Results indicate that the presence of submerged berms tends to mitigate the liquefaction probability if compared to straight sloped conventional breakwater without a berm. In addition, it appears that the momentary liquefaction phenomena are more influenced by changing the berm length rather than the berm height.