Reverse catenary equation of the embedded installation line and application to the kinematic model for drag anchors

The penetration behavior and trajectory of the drag anchor in seabed soils are not only determined by properties of the anchor and soil, but also controlled by the installation line especially the segment embedded in the soil. Correctly understanding and describing reverse catenary properties of the embedded line are crucial for improving the drag embedment performance, precisely predicting the anchor trajectory, and solving the positioning problem in offshore applications. The investigation on reverse catenary problems demonstrates that, the reverse catenary shape of the embedded line has to be solved almost through numerical incremental methods. In the present study, based on the mechanical model for the embedded line, the relationship between the tension and geometry of the embedded line, and the interactional equation between the anchor and embedded line are derived. By introducing the concept of the initial embedment depth of the installation line, the reverse catenary equation and the expression for calculating the length of the embedded line are obtained for soils with a linear strength, and the position of the embedment point can be reasonably solved through the derived reverse catenary equation. The reverse catenary equation is then introduced into the kinematic model for drag anchors, which combines the drag anchor, the installation line and the movement of the anchor handling vessel being an interactional system. More information related to the drag embedment problem can be definitely gained through the present work, including not only the anchor behaviors such as the trajectory, penetration direction and ultimate embedment depth, but also the properties of the installation line for both the embedded and horizontal segments. By comparing with drum centrifuge tests and model flume experiments, the efficiency of the theoretical method for predicting the anchor trajectory is well verified.     

法向承力锚拖曳安装过程的整体模拟

法向承力锚(Vertically Loaded Plate Anchor,VLA)是一种适用于深水的新型系泊基础,它的拖曳安装过程直接决定了其系泊定位的精度和锚体的最终承载能力。综合考虑VLA锚体、锚泊线和上部船体的运动,建立了一种新的准静力整体分析模型。模型包括不断贯入海床的锚体、锚泊线(土中反悬链段和水中悬链段)和安装船体三部分,针对确定的锚泊线长度,安装船运动张紧锚泊线进行安装的过程,计算了此过程中锚体的运动轨迹、锚泊线形态和作用在船体上的锚泊线张力矢量的变化,重点分析了不同抛链长度和海床土体的参数对安装过程控制的影响,发现链长与水深之比达到5时,接近极限贯入深度。     

Anchor loads in taut moorings: The impact of inverse catenary shakedown

Taut mooring systems have become prospective alternatives for the station keeping of offshore floating facilities in deep water. The associated embedded anchors cause a part of the mooring line to be buried in the seabed − the inverse catenary − which introduces a requirement to predict the load and uplift angle at the padeye, where the chain is connected to the anchor. The padeye load and angle depend on the shape and tension profile of the inverse catenary, which must be assessed in the mooring system design. The dynamic interaction between the embedded chain and the soil in the inverse catenary is not usually considered in this analysis. Instead, the inverse catenary is assessed statically, albeit potentially using cyclically-degraded soil strength parameters. The present study employs the lumped mass method to simulate the dynamic response of mooring lines under different imposed oscillations at the fairlead, where the chain is connected to the floating facility. A new chain-soil interaction model, which includes hysteresis effects associated with irrecoverable relative chain-soil displacement is calibrated by experimental results. Simulations of cyclic vessel motion are then performed, and the resulting chain-seabed interaction is observed. During constant-amplitude vessel motion cycles, the load angle at the padeye significantly decreases due to progressive ratcheting or ‘shakedown’ of the inverse catenary from the initial static profile towards a straighter profile. This effect is due to the hysteretic soil response and creates a less onerous loading condition for the anchor which may be beneficial, but is conventionally overlooked in design. At the end of the present study, an elastic bound method is proposed to estimate the profile of the inverse catenary after shakedown. A parametric study illustrates the performance of this simple method for predicting the steady state condition.     

A modified method to estimate chain inverse catenary profile in clay based on chain equation and chain yield envelope

Offshore floating facilities are fixed by anchoring systems embedded in seabed soils through chains or ropes. The chain inverse catenary profile embedded in soils influences both the anchor failure mechanism and the anchor holding capacity. The chain mobilizes varying soil normal and tangential resistances during motion, hence it is with difficulty to depict the chain profile. The present work proposed a modified method to estimate the chain inverse catenary profile with high accuracy based on the chain equations and the chain yield envelope. A testing arrangement with three load cells and two MEMS (Micro-electromechanical systems) accelerometers included was designed in model tests. By model tests, the loading combinations of the soil tangential and normal resistances on the chain were obtained and the yield envelopes for both chain and rope were determined. In addition, supplemental model tests were performed to validate the modified method proposed in this study, and the testing results indicated that the estimated chain inverse catenary profile was in good agreement with the actual one. Moreover, the testing arrangement is beneficial in investigating the chain-soil-anchor interaction.     

Analytical study on comprehensive behaviors of drag anchors in the seabed

Attributed to good performance in the seabed, drag anchors are adopted as an effective anchoring solution in deepwater mooring systems. This type of anchors is drag installed, companying with comprehensive behaviors during movement of the anchor in the seabed, which make the anchor trajectory and therefore the final embedment position difficult to be predicted. On the basis of the mechanical model and analytical procedure, an analytical method is proposed for exploring comprehensive behaviors of drag anchors in both clay and sand. The anchor behaviors are classified as keying, pulling out and diving. The bearing capacity and the trajectory of the anchor can be predicted through the combination of the three behaviors. By comparing analytical predictions with experimental data and other predictions, the efficiency and veracity of the theoretical model are validated. A parametric study is also performed to investigate the effects of different parameters, and to further understand the comprehensive anchor behaviors in the seabed. The present work provides an efficient theoretical tool for analyzing comprehensive behaviors of drag anchors in either clayey or sandy seabed.     

拖曳锚在海床中运动特性的大变形有限元分析

拖曳锚由于其承载性能和深水中便于安装被广泛应用于海洋工程系泊系统中,如:适用于悬链式系泊系统的传统拖曳锚和适用于绷紧式系泊系统的法向承力锚。拖曳锚安装过程中涉及诸多运动特性:锚板运动方向、系缆点处拖曳力和拖曳角及运动轨迹。基于大变形有限元分析技术耦合的欧拉-拉格朗日法,并引入缆绳方程,建立起锚-缆绳-海床土耦合作用的有限元分析模型;模拟了拖曳锚在均质和线性强度黏土中的嵌入安装过程,研究了锚板运动方向、系缆点处拖曳力和拖曳角及运动轨迹等运动特性;通过与已有的有限元分析方法及理论方法进行对比,验证了该分析模型的有效性;与已有的有限元分析方法相比,提出的分析模型有效地提高了计算效率。     

Influence of Kinematic Analysis Parameters of Drag Anchor Trajectory Prediction Using Yield Envelope Method

Drag anchor is widely applied in offshore engineering for offshore mooring systems. The prediction of the invisible trajectory during its drag-in installation is challenging for anchor design in determining the anchor final position for ensuring sufficient holding capacity. The yield envelope method based on deep anchor failure for kinematic analysis was proposed as a promising trajectory prediction method for drag anchor. However, there is a lack of analysis on the effects of the parameters applied in the kinematic analysis. The current work studies the effects of the yield envelope parameters, anchor line bearing capacity factor and the anchor/soil interface friction. It is found that the accuracy of the yield envelope parameters has large impact on the prediction results based on deep yield envelopes.Analyses of cases with smooth fluke predict deeper embedment depth than that from analyses of cases with rough fluke. The decrease of the capacity factor results in the increase of the anchor embedment depth, the anchor line load,the anchor chain angle and the stable value of the normalized horizontal load component for the same drag length,while the stable value of the normalized vertical load component decreases when the capacity factor decreases. This illustrates the importance in applying reasonable parameters and improving the method for more reliable prediction of the anchor trajectory.     

新型铰接式重力锚的设计及其性能研究

重力锚锚固是一种常见的锚固形式。为了能够提供足够的水平承载力,传统型式的重力锚普遍比较笨重,在上拔回收时会产生较大的竖向吸附力,不利于重复利用。针对此问题,设计了一种新型铰接式重力锚,并阐述了其铺设与回收方案。其次采用有限元方法对其整体强度进行了校核,结果均符合规范。最后基于模型试验,对铰接式重力锚在黏土中的运动过程进行了研究,进而确定了其在黏土中的水平承载力和回收时的上拔力。结果表明：相较于传统重力锚,新型铰接式重力锚在确保水平承载性能的基础上,能够大幅减小上拔力,从而有效地降低铺设和回收作业的难度,且可适应多种海底土质,但该锚型仅适用于悬链线式系泊系统。相关研究结果可为实际工程中铰接式重力锚的设计提供参考。     

Numerical implementation of the installation/mooring line and application to analyzing comprehensive anchor behaviors

With the application of innovative anchor concepts and advanced technologies in deepwater moorings, anchor behaviors in the seabed are becoming more complicated and pose a great challenge to the analytical methods. In the present work, a large deformation finite element (FE) analysis employing the coupled Eulerian–Lagrangian technique is performed to simulate the installation/mooring line, and then is applied to analyzing comprehensive anchor behaviors in the seabed. By connecting cylindrical units with each other using connector elements, the installation/mooring line is constructed. With the constructed installation/mooring line, FE simulations are carried out to investigate comprehensive anchor behaviors in the seabed, including long-distance penetration of drag anchors, keying of suction embedded plate anchors and non-catastrophic behavior of gravity-installed anchors. Through comparative studies, the accuracy of the proposed method is well examined. A parametric study is also undertaken to quantify the effects of the frictional coefficient, initial embedment depth, and soil weight on the profile of the embedded anchor line and the shackle load. The present work demonstrates that the proposed FE model, which incorporates the installation/mooring line and the anchor, is effective in analyzing the comprehensive anchor behaviors in the seabed.     

深水系泊新型拖曳锚研发关键技术

作为深海工程应用中一种新型的拖曳嵌入式系泊基础,法向承力锚与目前新型的深水绷紧索系泊方式结合,在深水条件下的优势非常明显.综合比较了新型拖曳锚、吸力锚以及桩锚在施工、性能以及经济性等多方面的特点.提出了开展新型拖曳锚研发的若干关键技术.在对国外的实验研究现状进行综合评述的基础上,重点介绍了在构建新型拖曳锚模型实验平台方面取得的成果,涉及模型水槽、拖曳与回收系统、测量系统、模型锚板设计以及拖曳-系泊转换机构等关键技术.     

Numerical study of effect of fluke inclination on behavior of drag anchor in clay with linearly increasing shear strength under unidirectional and combined loading

Drag anchor is a widely used anchor type in offshore engineering for the mooring system. The prediction of the anchor trajectory installation and the final position is important for anchor selection in design. The existing method using yield envelope method for trajectory prediction ignored the shallow anchor behavior but applied the deep yield envelope from a deeply embedded horizontal fluke in uniform clay for the whole drag-in installation process. However, the anchor fluke embedment depth and inclination angle change continually during installation in clay with linearly increasing shear strength soil profile in practice. Studies on the effect of fluke inclination angle on the anchor behavior in clay with such non-uniform soil profile under unidirectional and combined loading are important and necessary for the improvement of the yield envelope method to ensure a reasonable prediction. The current 2D finite element studies investigate the anchor behavior for inclined fluke in clay with linearly increasing shear strength under unidirectional vertical, horizontal and rotational loadings first. Then the effects of the fluke inclination angle, soil non-homogeneity and embedment depth ratio on the shallow yield envelopes are investigated. It is found that the effect of fluke inclination angle on the vertical capacity factors for anchor in clay with non-uniform and uniform soil profile is largely different. The resultant large impact on the yield envelopes shown here illustrates the importance of considering the fluke inclination angle and soil non-homogeneity in the prediction of anchor trajectory using yield envelope method.     

Effect of Failure Mode of Taut Mooring System on the Dynamic Response of A Semi-Submersible Platform

Mooring system failure can lead to largely different dynamic response of floating structures when compared to the response under the condition of intact mooring system. For a semi-submersible platform with taut mooring system under extreme environmental conditions, the typical mooring system failure includes anchor line breaking failure due to the broken anchor line, and the anchor dragging failure caused by the anchor failure in the seabed soil due to the shortage of the anchor bearing capacity. However, study on the mooring failure caused by anchor failure is rare. The current work investigates the effect of three failure modes of taut mooring system on dynamic response of a semi-submersible platform, including one line breaking failure, two lines breaking failure, and one line breaking with one line attached anchor dragging failure. The nonlinear polynomial mooring line model in AQWA was used with integrating the load and displacement curve from the anchor pulling study to characterize the anchor dragging behavior for mooring system failure caused by the anchor failure. The offsets of the platform and the tension of mooring lines were analyzed for mooring system failure with 100-year return period. It is found that the mooring failure of one line breaking with one line attached anchor dragging is a case between the other two mooring failures. The traditional mooring analysis considering only the damaged condition with one line breaking is not safe enough. And the simple way of mooring analysis of two lines breaking is too conservative for the costly offshore engineering.

     

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.     

Behavior of drag anchor in clay with linearly increasing shear strength under unidirectional and combined loading

Drag anchor is a widely used economical anchor option for offshore floating structures. The anchor behavior under unidirectional loading and combined loading is important for anchor selection. The anchor behavior under combined loading, characterized by the yield envelope, can also be used for the prediction of anchor installation, which is still an issue in anchor design. However, most existing studies on anchor capacity are for plate anchors which focused only on the anchor pullout capacity in soil with uniform shear strength. The behavior of drag anchor under unidirectional and combined loading in soil with linearly increasing shear strength profile is seldom investigated. The current 2D finite element studies investigate the anchor behavior for a horizontal anchor fluke in clay with linearly increasing shear strength under unidirectional vertical, horizontal and rotational loadings first. Then based on the results of anchor unidirectional loading behavior, the yield envelopes for anchor under combined loading for both shallow and deep embedded flukes are studied. The effect of anchor embedment depth, soil non- homogeneity, soil overburden pressure and the soil/anchor interface breakaway conditions are studied to provide insight for drag anchor design.     

法向承力锚极限抗拔力特性

法向承力锚是一种新型的适用于深海工程的系泊基础,其极限抗拔力是锚在工程应用中的关键指标。尝试用两种不同的方法评估法向承力锚的极限抗拔力,其一是基于塑性上限分析理论;其二是运用非线性有限元数值方法。与已有的经验公式相比,所建立的计算模型不仅可考虑海床土性质,还能反映锚板定位(嵌入深度及角度)以及系缆力角度对锚极限抗拔力的影响。在与已有评估方法进行比较的基础上,还特别对锚板的嵌入深度、角度以及系缆力角度变化对极限抗拔力的影响规律进行了分析,对三种方法的适用性进行了评述。     

Quasi-static three-dimensional analysis of suction anchor mooring system

The suction anchor has been widely used in taut or semi-taut mooring systems as an effective and economical solution to anchoring problems. To ensure high reliability, the profile of the mooring cable connecting the fairlead and the pad-eye must be accurately designed. However, previous studies have rarely considered the effect of cable slippage in soil on the mooring behavior, or embedded cables have been studied with an assumed tension at the seabed. This paper, by treating the cable suspended in water and the cable embedded in soil as a single cable, presents a two-dimensional (2D) static model and a three-dimensional (3D) quasi-static model for the cable during pretensioning and in service, respectively. The two models take into account the comprehensive effects of ocean currents, soil resistance and cable elasticity, all of which are critical for the design of a mooring system. Three examples are analyzed using the models and some useful conclusions are drawn.     

Simplified limit solutions for the capacity of suction anchors under undrained conditions

Upper bound plastic limit analyses (PLA) can provide a useful framework for estimating the load capacity of suction caisson anchors in purely cohesive soils. Since arbitrary assumptions regarding the soil stress state are not required in the PLA formulation, it may be used with greater consistency compared to other simplified approaches such as limit equilibrium methods. While PLA methods do not attempt to include all of the complexities of anchor behavior, they can provide a relatively simple framework for visualizing anchor kinematics leading to an understanding of the relative importance of various parameters on suction anchor load capacity. The most rigorous PLA formulations involve postulating a three-dimensional anchor-soil failure mechanism and deriving expressions for internal energy dissipation throughout the mechanism. This approach can involve extensive numerical integrations and a relatively complex scheme for optimizing the failure mechanism to obtain a least upper bound collapse load. Considerable simplification is possible if the problem is formulated in terms of ultimate unit resistances (lateral, axial, and their interaction) that can be exerted by the soil on the caisson. In this case, the caisson failure mechanism can be characterized in terms of one or two optimization variables. Simple expressions for the ultimate unit resistances acting on the caisson can be obtained from several sources including rigorous PLA solutions, finite element techniques, or experimental measurements. General expressions are possible by limiting consideration to common, idealized strength profiles such as uniform or constant gradient. Such simplified formulations are particularly valuable for providing an analysis tool accessible to practicing engineers. Suction caisson anchors can be subjected to a variety of load orientations including nearly vertical uplift forces imposed by the vertical tendons of tension leg platforms, horizontal loads imposed by catenary mooring systems, and inclined loads imposed by taut moorings. Recently, PLA methods have been applied to the analysis of suction caissons subjected to this range of loading conditions. This paper reviews the formulation of these analyses and summarizes the most significant findings.     

Experimental investigation of the keying process of OMNI-Max anchor

ABSTRACT

The OMNI-Max anchors are newly developed dynamically installed anchors for deep water mooring systems. After installation, the anchor is keyed to a new orientation and position by tensing the attached mooring chain, which is known as the “keying process”. This study conducted 1g model tests to study the trajectories and capacity developments of OMNI-Max anchors in homogeneous and lightly overconsolidated (LOC) clays. A testing arrangement was designed to simulate the anchor keying process with a constant pullout angle at the mudline. A half model anchor which could move against the box glass was used to determine the anchor trajectory in the soil. The effects of padeye offset angle, uplift angle at the mudline, anchor fluke thickness, anchor initial embedment depth, and soil strength on the anchor trajectory and capacity were systematically investigated. Moreover, the critical uplift angle at the padeye and the anchor critical initial embedment depth were discussed. The results indicate that the anchor can dive both in homogeneous and LOC clays under certain conditions. A padeye offset angle of 24–30° is recommended for the OMNI-Max anchor to maintain high capacity and diving trend simultaneously. Besides, the anchor diving trend can be improved with small uplift angles at the mudline and with thick anchor flukes. A critical initial embedment depth of 1.3 times the anchor length is recommended to preclude the anchor from being pulled out.     

Numerical investigation on the penetration of gravity installed anchors by a coupled Eulerian–Lagrangian approach

Gravity installed anchors (GIAs) are released from a height of 30–150 m above the seabed, achieving velocities up to 19–35 m/s at the seabed, and embed to depths of 1.0–2.4 times the anchor length. Challenges associated with GIAs include the prediction of anchor initial embedment depth, which determines the holding capacity of the anchor. Based on the coupled Eulerian–Lagrangian approach, a numerical framework is proposed in this paper to predict the embedment depth of GIAs, considering the effects of soil strain rate, soil strain-softening and hydrodynamic drag (modeled using a concentrated force), with the anchor-soil friction described appropriately. GIAs are influenced by the hydrodynamic drag before penetrating into the soil completely, hence the anchor accelerates less than the previous investigations in shallow penetration, even decelerates directly at the terminal impact velocity. The hydrodynamic drag has more influence on OMNI-Max anchors (with an error of ∼4.5%) than torpedo anchors, and the effect becomes more significant with increasing impact velocity. An extensive parametric study is carried out by varying the impact velocity, strain rate and strain-softening parameters, frictional coefficient, and soil undrained shear strength. It is concluded that the dominant factor affecting the penetration is the soil undrained shear strength, then are the impact velocity, strain rate dependency and frictional coefficient, and the minimal is the strain-softening of soil. In addition, although the strain rate dependency is partly compensated by the softening, the anchor embedment depth accounting for the effects of strain rate and strain-softening is lower than that for ideal Tresca soil. Strain rate dependency dominates the combined effects of strain rate and strain-softening in the dynamic installation of GIAs, on which should pay more attention, especially for the calibration of the related parameters and the measured solutions. In the end, the theoretical model based on the bearing resistance method is extended by accounting for the hydrodynamic drag effect.     

An Analytical Method for Positioning Drag Anchors in Seabed Soils

Positioning drag anchors in seabed soils are strongly influenced not only by the properties of the anchor and soil,but also by the characteristics of the installation line.The investigation on the previous prediction methods related to anchor positioning demonstrates that the prediction of the anchor position during dragging has inevitably introduced some key and unsubstantiated hypotheses and the applicability of these methods is limited.In the present study,the interactional system between the drag anchor and installation line is firstly introduced for the analysis of anchor positioning.Based on the two mechanical models for embedded lines and drag anchors,the positioning equations for drag anchors have been derived both for cohesive and noncohesive soils.Since the drag angle at the shackle is the most important parameter in the positioning equations,a novel analytical method that can predict both the variation and the exact value of the drag angle at the shackle is proposed.The analytical method for positioning drag anchors which combines the interactional system between the drag anchor and the installation line has provided a reasonable theoretic approach to investigate the anchor behaviors in soils.By comparing with the model flume experiments,the sensitivity,effectiveness and veracity of the positioning method are well verified.