Numerical Simulation of Seabed Response and Liquefaction due to Nonlinear Waves

Based on Biot＇s consolidation theory, a two-dimensional model for computation of the seabed response to waves is presented with the finite element method. Numerical results for different wave conditions are obtained, and the effects of wave non-lineafity on the wave-induced seabed response are examined. Moreover, the wave-induced momentary liquefaction in uniform and inhomogeneous seabeds is investigated. It is shown that the wave non-linearity affects the distribution of the wave-induced pore pressure and effective stresses, while the influence of wave non-linearity on the seabed liquefaction potential is not so significant.     

Evaluation of storm wave-induced silty seabed instability and geo-hazards: A case study in the Yellow River delta

Models based on the theoretical framework of soil mechanics are presented to evaluate storm wave-induced silty seabed instability and geo-hazards through a case study in the Yellow River delta. First, the transient and residual mechanisms of wave-induced pore pressure are analyzed. Three typical models (i.e., elastic model, pore pressure development mode and elasto-plastic model) are proposed to calculate wave-induced stresses in the seabed. Next, mechanisms and calculation methods of wave-induced seabed instability modes such as scour, liquefaction, seepage instability and shear slide are proposed. Typical results of storm wave-induced excess pore pressure and seabed instability are given and relevant discussions are made. At last, the formation mechanism of geo-hazards in the Yellow River delta is analyzed based on the proposed mechanism and calculated results. Results and analysis indicate that both transient and residual mechanisms are important to storm wave-induced response of silty seabed and hence the elasto-plastic model is more appropriate. Complete liquefaction does not happen, while other types of instability occur mostly within 2–6 m under the seabed surface. Wave-induced scour, seepage instability and shear slide are all possible instability modes under the 1-year storm waves, and scour is predominant for the 50-year storm waves. The formation mechanism of geo-hazards such as shallow slide and storm wave reactivation, pockmarks, silt flow and gully, disturbed stratum and hard crust in the Yellow River are well explained based on the proposed mechanisms and calculated results of storm wave-induced silty seabed instability.     

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。     

A probabilistic analysis of random wave-induced liquefaction

Seabed instability caused by soil liquefaction due to build-up of excess pore pressure within the sedimentary seabed represents a serious threat to coastal structures. Models of varying sophistication exist for predicting the liquefaction process but most previous calculations are limited to regular waves while the real waves are random. In this study, a numerical study of liquefaction potential of a sand bed under narrow-band random waves is carried out employing ensemble modelling techniques. The aim of the work is to investigate the effect of random waves on excess pore pressure build-up and liquefaction processes and study the probability distribution of the maximum liquefaction depth. The computational results using a 1D liquefaction model indicate that the random wave-induced liquefaction can be much deeper than that of the corresponding regular waves with the largest individual waves in the random wave time series playing a dominant role in determining the maximum liquefaction depth. It is also found that the time for the maximum liquefaction depth to be reached can vary considerably from one random wave series to another, which suggests that in random waves notable densification may occur within the same timeframe as that for liquefaction.     

Effects of cross-correlated multiple spatially random soil properties on wave-induced oscillatory seabed response

The evaluation of seabed response under wave loading is important for prediction of stability of foundations of offshore structures. In this study, a stochastic finite element model which integrates the Karhunen-Loève expansion random field simulation and finite element modeling of wave-induced seabed response is established. The wave-induced oscillatory response in a spatially random heterogeneous porous seabed considering cross-correlated multiple soil properties is investigated. The effects of multiple spatial random soil properties, correlation length and the trend function (the relation of the mean value versus depth) on oscillatory pore water pressure and momentary liquefaction are discussed. The stochastic analyses show that the uncertainty bounds of oscillatory pore water pressure are wider for the case with multiple spatially random soil properties compared with those with the single random soil property. The mean pore water pressure of the stochastic analysis is greater than the one obtained by the deterministic analysis. Therefore, the average momentary liquefaction zone in the stochastic analysis is shallower than the deterministic one. The median of momentary liquefaction depth generally decreases with the increase of vertical correlation length. When the slope of the trend function increases, the uncertainty of pore water pressure is greatly reduced at deeper depth of the seabed. Without considering the trend of soil properties, the wave-induced momentary liquefaction potential may be underestimated.     

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.     

Wave-induced seabed instability in front of a breakwater

The wave-induced soil response in a porous seabed has become an important factor for the stability of offshore facilities, because many marine structures may have failed due to seabed instability and concomitant subsidence. An analytical solution is presented for the wave-induced soil response under the action of a three-dimensional wave system. Based on this general solution, the mechanism of seabed instability is then investigated. The general solutions for pore pressure and effective stresses are readily reducible to two dimensions for progressive waves, and are compared to theoretical and experimental work available. Some dominant factors affecting the wave-induced seabed instability are discussed; including permeability, seabed thickness and degree of saturation.     

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.     

A 3-D model for ocean waves over a Columb-damping poroelastic seabed

The evaluation of the wave-induced seabed instability in the vicinity of a breakwater is particularly important for coastal and geotechnical engineers involved in the design of coastal structures. In this paper, an analytical solution for three-dimensional short-crested wave-induced seabed instability in a Coulomb-damping porous seabed is derived. The partial wave reflection and self-weight of breakwater are also considered in the new solution. Based on the analytical solution, we examine (1) the wave-induced soil response at different location; (2) the maximum liquefaction and shear failure depth in coarse and fine sand; (3) the effects of reflection coefficients; and (4) the added stresses due to the self-weight of the breakwater.     

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。     

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。     

波浪作用下黄河三角洲海底粉土液化特征对比研究

作为一种常见的近海海底灾害地质现象,波致海床液化严重威胁着黄河三角洲地区海底工程设施的安全.粉质海床液化后,海底粉土的结构、物理和力学性质均发生了改变,研究该变化规律尤其是评估液化后海底粉土再次发生液化的可能性具有重要的理论意义和应用价值.本文利用室内动三轴仪对取自黄河三角洲已液化和未液化海底粉土开展了液化试验对比研究...     

Experimental investigation on the wave-induced pore pressure around shallowly embedded pipelines

A series of regular wave experiments have been done in a large-scale wave flume to investigate the wave-induced pore pressure around the submarine shallowly embedded pipelines.The model pipelines are buried in three kinds of soils,including gravel,sand and silt with different burial depth.The input waves change with height and period.The results show that the amplitudes of wave-induced pore pressure increase as the wave period increase,and decay from the surface to the bottom of seabed.Higher pore pressures are recorded at the pipeline top and the lower pore pressures at the bottom,especially in the sand seabed.The normalized pressure around pipeline decreases as the relative water depth,burial depth or scattering parameters increase.For the silt seabed,the wavelet transform has been successfully used to analyze the signals of wave-induced pore pressure,and the oscillatory and residual pore pressure can be extracted by wavelet analysis.Higher oscillatory pressures are recorded at the bottom and the lower pressures at the top of the pipeline.However,higher residual pressures are recorded at the top and the lower pressures at the bottom of the pipeline.     

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.     

Transient soil response in a porous seabed with variable permeability

The soil permeability of many natural marine sediments decreases with depth because of consolidation under overburden pressure. This is accompanied by a decrease in porosity and void ratio that also affect the permeability. Conventional theories for wave-induced soil response have assumed a homogeneous porous seabed. This paper presents a new approach for the wave-induced response in a soil matrix, with variable permeability as a function of burial depth. The soil matrix considered is unsaturated and anisotropic, and is subject to a three-dimensional wave system. The pore pressure and effective stresses induced by such a system are obtained from a set of equations incorporating a variable permeability. Verification is available through reduction to the simple case of uniform permeability. The results indicate that the effect of variable soil permeability on pore pressure and vertical effective stress may be significant, especially in a gravelled seabed and for unsaturated sandy soils.     

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.     

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.     

Pore pressure response of seabed in standing waves and its mechanism

Experiments were carried out in a newly-developed rectangular flume to investigate the pore pressure response of silty seabed in standing waves, and to emphatically discuss the physical mechanism of wave-induced pore pressure. We first analyzed the features of wave-induced stress, laid out the experimental setup, and particularly monitored the temporal and spatial variation of pore pressure. Then, we summarized the physical essence of wave-induced pore pressure, discussed the applicability of the existing models, and proposed several key points about developing new models. Results indicate that regular standing waves were obtained in the rectangular flume. The oscillating pore pressure (OPP) and the residual pore pressure (RPP) were observed simultaneously in the seabed under wave nodes or antinodes, and were found with coupling effect. The OPP and RPP were related to the elastic and plastic volumetric strains, respectively. Both elastic and plastic volumetric strains may be caused by the wave-induced cyclic spherical stress or deviatoric stress. The elastic model could only simulate the OPP and the pore pressure development mode could only simulate the RPP. The yielding under isotropic compression and the shear expansion of geotechnical materials, as well as the wave-induced stress paths, should be considered in the elastoplastic model to simulate the wave-induced pore pressure accurately.     

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.     

Analysis of seabed instability using element free Galerkin method

Wave-induced seabed instability, either momentary liquefaction or shear failure, is an important topic in ocean and coastal engineering. Many factors, such as seabed properties and wave parameters, affect the seabed instability. A non-dimensional parameter is proposed in this paper to evaluate the occurrence of momentary liquefaction. This parameter includes the properties of the soil and the wave. The determination of the wave-induced liquefaction depth is also suggested based on this non-dimensional parameter. As an example, a two-dimensional seabed with finite thickness is numerically treated with the EFGM meshless method developed early for wave-induced seabed responses. Parametric study is carried out to investigate the effect of wavelength, compressibility of pore fluid, permeability and stiffness of porous media, and variable stiffness with depth on the seabed response with three criteria for liquefaction. It is found that this non-dimensional parameter is a good index for identifying the momentary liquefaction qualitatively, and the criterion of liquefaction with seepage force can be used to predict the deepest liquefaction depth.