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.     

波浪作用下粉土中的孔压响应及其在粉土海床稳定性评价中的应用

粉土在波浪等动荷载作用下极易发生液化破坏,而孔隙水压力在粉土动力学行为中扮演了一个很重要的角色,其发展变化会直接影响到土体的稳定性。因此,通过室内波浪作用下的粉土孔压响应模型试验探讨了孔压与波浪之间的响应情况,发现波浪能量的影响沿土层深度递减,水深条件相同时,响应的孔压随波高的增大而增加,当波浪作用足够长时间后粉土发生液化破坏,此时粉土内累积的孔压小于上覆土体的自重应力。根据结果提出了1种评价粉土海床稳定性的方法。     

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.     

The influence of nonlinear hysteretic seabed interaction on slug-induced stress oscillations in steel catenary risers

Steel catenary risers (SCRs) are usually cost-effective solutions in the development of offshore fields and the transferring of the hydrocarbons from the seabed to the floating facilities. These elements are subjected to the fatigue loads particularly in the touchdown zone (TDZ), where the oscillating SCR is exposed to cyclic contact with the seabed. The slug-induced oscillation is a significant contributor to the fatigue loads in the TDZ. The cyclic seabed soil softening under the wave-induced riser oscillations and the gradual penetration of the SCR into the seabed are widely accepted to have a significant influence on SCR fatigue performance. However, this has never been investigated for slug-induced oscillations due to the lack of integrated access to comprehensive numerical models enabling the simulation of the riser slugging and nonlinear hysteretic riser-seabed interaction at the same time. In this paper, an advanced interface was developed and verified using the multi-point moving tie constraint in order to examine the influence of cyclic seabed soil softening on slug-induced oscillations of SCR. The interface was integrated with a pre-developed user subroutine for modeling of the nonlinear hysteretic riser-seabed interaction and incorporated into a global SCR model in ABAQUS. A comprehensive parametric study was conducted to investigate the influence of slug characteristics and nonlinear seabed soil model on slug-induced, wave-induced, and combined wave/slug induced oscillations of SCR in the TDZ. It was observed that the nonlinear seabed model could significantly affect the embedment of the SCR into the seabed under the slug-induced oscillations and consequently improve the fatigue life. The developed user interface was found to be a strong framework for modeling riser slugging.     

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.     

波浪荷载及土体特性对风电单桩基础水平变形影响规律

大直径单桩基础是海上风电应用广泛的一种基础形式,严格控制桩基泥面处的位移是保证基础稳定和风机安全运营的关键因素.通过数值方法建立了单桩—海床的三维模型,将可以描述海洋砂土超固结性和结构性的弹塑性本构模型通过UMAT子程序嵌入有限元软件ABAQUS中,桩基承受的波浪荷载通过Morison方程进行计算模拟.针对无波浪荷载、仅作用于海床的波浪荷载、同时作用于桩基和海床的波浪荷载三种情况,分析了海床土的动力响应以及桩基的水平位移之间的差异,探讨了海床土体参数对桩基水平变形的影响.研究结果表明海床土体液化会导致桩基水平变形增加,海床土渗透性、超固结性、结构性对桩基水平位移影响显著,研究成果可为海上风电单桩基础的设计与运维提供参考.     

Centrifuge modelling of SCR vertical motion at touchdown zone

Steel catenary risers (SCR) connect seabed pipelines and flow lines to floating structures used for oil and gas production in deep waters. Waves and currents induce motions of the structure and the risers. The repeated motions of the risers at the touchdown zone in turn induce loads on the seabed soil and might eventually cause fatigue damage to the risers. The analysis of riser fatigue damage is heavily dependent on the soil model. Soil behaviour at touchdown zone such as soil remoulding, stiffness degradation and deformation of the seabed at the touchdown zone further complicate the accurate assessment of riser fatigue damage, which is currently not appropriately quantified in existing design methods. This paper presents centrifuge model tests simulating the repeated vertical movement of a length of riser on clay seabed with increasing undrained shear strength with depth. During the tests, the pipe was subject to cyclic motion over fixed vertical displacement amplitude from an invert embedment of 0.5-3.5 pipe diameters into the soil. The test results show a significant progressive degradation of soil strength and diminution of excess pore water pressure with increasing number of riser penetration/uplift cycle. In view of the different types of environment loadings experienced by floating platforms and various soil conditions, tests were also conducted to investigate the effect of soil strength, riser displacement rate and loading mode on riser-soil interaction during repetitive penetration/uplift motion of the riser.     

The numerical study of wave-induced pore water pressure response in highly permeable seabed

The coupling numerical model of wave interaction with porous medium is used to study waveinduced pore water pressure in high permeability seabed.In the model,the wave field solver is based on the two dimensional Reynolds-averaged Navier-Stokes(RANS) equations with a k-ε closure,and Forchheimer equations are adopted for flow within the porous media.By introducing a Velocity-Pressure Correction equation for the wave flow and porous flow,a highly efficient coupling between the two flows is implemented.The numerical tests are conducted to study the effects of seabed thickness,porosity,particle size and intrinsic permeability coefficient on regular wave and solitary wave-induced pore water pressure response.The results indicate that,as compared with regular wave-induced,solitary wave-induced pore water pressure has larger values and stronger action on seabed with different parameters.The results also clearly show the flow characteristics of pore water flow within seabed and water wave flow on seabed.The maximum pore water flow velocities within seabed under solitary wave action are higher than those under regular wave action.     

Subsea pipeline walking with velocity dependent seabed friction

With the increase in demand and supply gap in the oil and gas industry, new developments of oil and gasinfrastructure are moving into deeper water. This requires design and construction of long high temperature and high pressure pipelines from deep sea to shore. These pipelines are subjected to cyclic expansion during operating cycles. Accumulated axial movement due to repeated thermal cycles may lead to global displacement referred to as ‘walking’. Walking rates depend on the restraint associated with seabed friction. In conventional analyses, seabed friction is independent of the rate of thermal loading and expansion but it has been recognised that the sliding resistance between a pipe and the seabed varies with velocity, partly due to drainage effects. In this paper a numerical model is used to explore the effect of velocity-dependent seabed friction. A velocity-dependent friction model is implemented in commercial software ABAQUS and validated via single element and simple (flat seabed) pipeline cases. This model features upper and lower friction limits, with a transition that occurs as an exponential function of velocity. A parametric study is performed using differing rates of heating and cool-down in walking situations driven by seabed slope, SCR end tension and the difference between heat up and cool down rates. The walking behaviour is compared to cases with constant friction and solutions are proposed to express the velocity-dependent response in terms of an equivalent constant friction. These equivalent friction values can then be applied in existing simple solutions or more complex numerical analyses, as a short cut method to account for velocity-dependent friction.     

波致海床滑动稳定性计算方法及滑动失稳特征研究

波浪引起的海床不稳定性是海洋工程中需要考虑的重要问题。在对现有波致海床滑动稳定性计算方法进行分析的基础上,提出了一种波致海床滑动稳定性计算的全应力状态法,将其与现有计算方法进行了对比分析,并进一步研究了波致砂土海床和软土海床的滑动失稳特征。结果分析表明,全应力状态法在波致海床滑动稳定性分析中具有较好的适用性。对于砂土海床,其滑动稳定性受饱和度的影响较大,且当海床计算厚度约为0.2倍波长时对应的滑动深度最大。波浪作用下坡度不超过2°的均质软土海床,其最危险滑动面的位置仅与波长有关,其滑动深度约为0.21倍波长,滑动面半弦长约为0.33倍波长;海床表面的波压力数值只影响其安全系数的大小,而不影响其滑动深度。     

埕岛油田海底管线在位稳定性的计算分析

埕岛油田主要分布粉土和淤泥质软土2类典型的海床.通过建立海床与其上裸置管线相互作用的有限元计算模型,对埕岛油田2类典型海床上裸置管线的在位稳定性进行了数值计算分析,并与现行常用的DNV(挪威船级社)管道设计方法的计算结果进行了对比.分析表明,对于埕岛油田粉土海床上裸置管线的在位稳定性分析,数值计算结果与DNV简化分析方法的结果较为一致;对于埕岛油田淤泥质软土海床上裸置管线的在位稳定性分析,DNV简化分析得到的裸置管线的在位稳定性一般高于相应的数值计算结果.     

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.     

An experimental study on non-linear progressive wave-induced dynamic stresses in seabed

In this study, the dynamic stresses within the seabed induced by non-linear progressive waves were explored through a series of hydraulic model tests on a movable bed within a wave flume. By comparing Stokes’ 2nd-order wave theory with the theory of wave-induced dynamic stresses within the seabed as proposed by Yamamoto et al. [1978. On the response of a poro-elastic bed to water waves. Journal of Fluid Mechanics 87 (1), 193–206.] and Hsu and Jeng [1994. Wane-induced soil response in an unsaturated anisotropic seabed of finite thickness. International Journal for Numerical and Analytical Methods in Geomechanics 18, 785–807], the experimental results show that the pressure on the seabed surface, the pore water pressure within the seabed as well as the vertical and the horizontal stresses are all smaller than their theoretical values. If we were to obtain the characteristics of seabed soil, the analytical solution of Hsu and Jeng [1994. Wane-induced soil response in an unsaturated anisotropic seabed of finite thickness. International Journal for Numerical and Analytical Methods in Geomechanics 18, 785–807] might agree to the simulation of the wave-induced effective stresses and shear stress in the sandy seabed. A different phase shift exists among all the three soil stresses. Their influences on the three dynamic stresses within seabed soil are important for seabed stability, and can be used in the verification of numerical models. In the whole, the non-linear progressive waves and the naturally deposited seabed are found to have a strong interaction, and the behavior of the induced dynamic stresses within the seabed is very complicated, and should be investigated integrally.     

浅水区波浪非线性效应对砂质海床动力响应的影响

以广义Biot动力固结理论为基础,运用一阶椭圆余弦波和二阶Stokes波等非线性波浪理论考虑浅水区波浪荷载的非线性效应,在时域上采用有限元方法对非线性波浪力作用下饱和砂质海床的动力响应进行了数值求解,并与线性波浪作用下海床动力响应特性进行了对比分析。结果表明,随着波长与水深之比L／d及无量纲参数T(g/d)^1/2的增大,非线性波浪对海床动力响应的影响增大。与线性波浪理论相比,孔隙水压力与有效应力幅值的增大效应非常显著。因此在近海海洋建筑物设计与工程场地评价中,波浪力的非线性特性必须引起注意。     

波浪作用下孔隙海床-管线动力相互作用分析

波浪作用下海床中的孔隙水压力与有效应力是影响海底管线稳定性的主要因素。然而,在目前的海床响应分析中一般将管线假定为刚性,并不能合理地考虑海床与管线之间的相互作用效应,同时也没有考虑土体和管线加速度对海床动力响应的惯性影响,从而无法确定由此所引起的管线内应力。为此考虑管线的柔性,分别采用饱和孔隙介质的Biot动力固结理论和弹性动力学理论列出了海床与管线的控制方程,进而采用摩擦接触理论考虑海床与管线之间的相互作用效应,基于有限元方法建立了海床-管线相互作用的计算模型及其数值算法。通过变动参数对比计算讨论了管线几何尺寸、海床土性参数对波浪所引起的管线周围海床孔隙水压力和管线内应力的影响。     

Penetration depth of the dynamic response of seabed induced by internal solitary waves

We use flume experiments and numerical modeling to examine the penetration depth of internal solitary waves (ISWs) on partially saturated porous sandy silt and clayey silt seabed. The results of the experiment and model showed that the instantaneous excess pore water pressure in both the sandy silt and clayey silt seabed followed the same trend of decreasing with the seabed depth. In general, the excess pore water pressure generated by the sandy silt was bigger than that by clayey silt at the same depth. The ISW-induced excess pore water pressure greatly influenced the surface seabed and showed a linear relationship. The penetration depth was approximately one order of magnitude smaller than the half-wavelength of the ISWs, which might be larger than the penetration depth induced by surface waves. Our study results are helpful for understanding the damage that ISWs inflict upon the seabed and for informing future field experiments designed to directly measure the interaction between ISWs and seabed sediments.     

海底输油管道底砂床冲刷机理研究

设计了海底输油管道水槽冲刷试验模型,研究了海底输油管道与砂床处于不同相对位置情况下床砂起动流速的变化,采用理想流体映射定理对其进行了理论分析,探讨起动流速变化规律。结合有限元数值模拟对试验进行细化分析,研究了海底管道底砂床砂粒起动的产生机理,根据研究结果将冲刷过程划分为五个阶段。阐明了海底管道暴露冲刷的危害性和实时监测的重要性。     

Numerical Simulation of Wave Forces on Seabed Pipelines

A three-step finite element method(FEM)together with Large Eddy Simulation(LES)is ap-plied to incompressible turbulent flow around seabed pipelines at relatively high Reynolds numbers.Bothtwo-dimensional and three-dimensional numerical simulation is carried out to determine thethree-dimensional effect.The results of numerical simulation agree quite well with the wave forces actingon pipeline models measured in physical model test.     

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。     

Analysis of wave-induced liquefaction in seabed deposits of silt

The dynamic stress introduced in half elastic space by wave loading is characterized by the equation between the magnitude of half cyclic axial stress and cyclic torsion shear stress and the principal stress,whose direction rotates continuously and compression stress on seabed can be calculated by the use of small amplitude wave theory.With relationship curves of saturated silt of liquefaction cycles and cyclic stress ratios obtained by cyclic triaxial-torsional coupling shear tests and curve fitting method to different data points of relative density,it is suggested that the cyclic stress ratio corresponding to constant liquefaction impedance be taken as the critical cyclic stress ratio which implies liquefaction.There exists a linear relationship between critical cyclic stress ratio and relative density under different relative densities.Empirical formula for critical cyclic stress ratios of seabed liquefaction induced by wave loading under different relative densities is established.The possibility of seabed silt liquefaction and its influence factors are analyzed based on the small-amplitude wave theory and the data acquired in laboratory tests.