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.     

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.     

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。     

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.     

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.     

The effect of structures on the wave-induced liquefaction potential of seabed sand deposits

One of the important design considerations for marine structures situated on sand deposits is the potential for instability caused by the development of excess pore pressure as a result of wave loading. A build-up of excess pore pressure may lead to initial liquefaction. The current practice of liquefaction analysis in marine deposits neglects the effects of structures over seabed deposits. However, analyses both in terrestrial and marine deposits have shown that the presence of a structure, depending on the nature of the structure and initial soil conditions, may decrease or increase the liquefaction potential of underlying deposits. In the present study, a wave-induced liquefaction analysis is carried out using mechanisms similar to earthquake-induced liquefaction. The liquefaction potential is first evaluated using wave-induced liquefaction analysis methods for a free field. Then by applying a structure force on the underlying sand deposits, the effect of the structure on the liquefaction potential is evaluated. Results showed that depending on the initial density of the sand deposits and different structures, water depths and wave characteristics, the presence of a structure may increase or decrease the liquefaction potential of the underlying sand deposits.     

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.     

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.     

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.     

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.     

The effects of variable permeability on the wave-induced seabed response

The topic of wave-seabed interaction is important for civil engineers with regard to stability analysis of foundations for offshore structures. Most previous investigations of such problems have simply assumed a seabed with uniform permeability, even if the evidence of variable permeability has been reported in the literature. This paper presents a finite-element model for investigating the wave-induced seabed response in a porous seabed, with variable permeability as a function of burial depth. The present finite formulation is established by using a combination of semi-analytical techniques and the Galerkin method. Based on the present numerical model, together with the Mohr-Coulomb failure criterion, the wave-induced seabed instability is estimated. The numerical results indicate that variable permeability affects the wave-induced seabed instability significantly, especially for gravelled seabeds.     

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。     

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.     

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.     

Numerical analysis on random wave-induced porous seabed response

Research on the response of random wave on offshore structures has received great deal of attention of many researchers and engineers in the design of marine structures. Most previous investigations have been limited to the regular waves. In this paper, based on Longuet–Higgins random wave theory and finite element method, a numerical model for random wave-induced seabed response is established. The seabed is treated as poroelastic medium and characterized by Biot’s partly dynamic equations (u–p model). The JONSWAP spectrum is adopted in Longuet–Higgins model, which is based on the cumulative superposition of linear diffraction solution. Based on the numerical results, the effects of random wave on seabed response are investigated by comparing with the corresponding Stokes wave and cnoidal wave. Then, a parametric study is conducted to examine the effect of wave and soil characteristic on the seabed.     

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.     

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。     

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,讨论了已液化和未液化海底粉土在孔压增长模式和轴向动应变发展趋势方面的异同,对比分析了二者的液化势。研究结果表明:应变标准比孔压标准更适用于评估黄河三角洲地区海底粉土的液化势;孔压和动应变发展模式均表明与未液化粉土相比,已液化海底粉土再次发生液化的抗力有所提高;已液化和未液化海底粉土归一化孔压比u_d/σ₃与循环加载次数比N/N_f间相关关系可采用双曲线或指数函数模型进行定量化描述;未液化海底粉土的波致液化临界循环应力比约为0.20,已液化海底粉土的临界循环应力比约为0.35。研究成果有助于加深对海底粉土波致液化特性的认识,亦可为循环应力历史影响下的土体力学性质研究提供参考。