Laboratory tests and thermal buckling analysis for pipes buried in Bohai soft clay

Upheaval buckling of submarine pipelines occurs due to relative movement of pipeline and surrounding soil and is often triggered by high operational temperature of the pipeline, initial imperfection of the pipeline, or a combination of both. Since buckling can jeopardize the structural integrity of a pipeline, it is a failure mode that should to be taken into account for the design and in-service assessment of trenched and buried offshore pipelines. In this study, a series of vertical (uplift) and axial pullout tests were carried out on model pipe segments buried in soft clay deposit similar to that present in Bohai Gulf, China. Pipe segments with three different diameters (= 30 mm, 50 mm and 80 mm) were buried in different depth-to-diameter ratios ranging from 1 to 8. Based on the results of laboratory tests, nonlinear force–displacement relations are proposed to model soil resistance mobilized during pipeline movement. The proposed nonlinear soil resistance models are employed in finite element analysis of buried pipelines with different amplitudes of initial geometric imperfections. Thermal upheaval buckling behavior of pipelines operating at different temperatures is studied. Results show that the capacity of pipeline against thermal buckling increases with the burial depth and decreases with the amplitude of initial imperfection.     

Analytical study on controlled lateral thermal buckling of antisymmetric mode for subsea pipelines triggered by sleepers

Subsea pipelines exposed to high temperature and high pressure (HTHP) conditions is susceptible to lateral buckling. In order to control lateral buckling, engineered buckle initiators, such as sleepers, are introduced to initiate planned lateral buckles along the pipeline at specific locations in order to ensure that the stress in each lateral buckle remains acceptable. In this study, taking the interaction of adjacent buckles into account, analytical solutions of antisymmetric lateral buckling mode triggered by sleepers are derived. With the proposed formulations, the method to obtain the accurate locations of lateral displacement amplitude and maxima of bending stress is presented and discussed. And a detailed comparison between symmetric and antisymmetric mode of lateral buckling triggered by single sleeper is presented. Moreover, the influence of the sleeper spacing on controlled lateral buckling behaviour with the consideration of axial interaction between adjacent buckles is conducted. Finally, a detailed analysis about the influence of the sleeper height, lateral frictional coefficient and submerged weight of the pipeline on the controlled post-buckling behaviour is presented. Our results show that, for smaller sleeper friction or smaller sleeper height, the symmetric mode is more likely to happen, while the antisymmetric mode is prone to occur for larger sleeper friction and larger sleeper height. One effective method to reduce displacement amplitude and maximum stress is to decrease the sleeper spacing. The minimum critical temperature difference decreases with increasing sleeper height and increases with increasing lateral friction coefficient or submerged weight of the pipeline. And an alternative way to reduce the maximum stress is to reduce the lateral friction coefficient or submerged weight of the pipeline even though the displacement amplitude increases.     

Imperfection study on lateral thermal buckling of subsea pipeline triggered by a distributed buoyancy section

Controlled lateral buckling is triggered by distributed buoyancy section at predesigned sites to release the axial force induced by high temperature and high pressure in subsea pipelines. Due to the larger diameter and smaller submerged weight of distributed buoyancy section, compared to the normal pipe section, imperfections are more easily introduced at the location of distributed buoyancy section. In this study, an analytical model is proposed to simulate lateral buckling triggered by a distributed buoyancy section for an imperfect subsea pipeline, which is validated by test data. Semi-analytical solutions are derived. First, snap-through buckling behaviour is discussed. Then the influence of initial imperfections on buckled configurations, post-buckling behaviour, displacement amplitude and maximum stress is discussed in detail. The results show that there is no snap-through phenomenon for large amplitude of initial imperfections, which appears only when the amplitude of imperfection is small enough. The displacement amplitude increases with the amplitude of initial imperfections, and it first increases and then decreases with wavelength of initial imperfection. Compared to a perfect pipeline, the maximum stress amplifies for relative small wavelength of initial imperfections. Therefore, a large enough wavelength of initial imperfection should be introduced.     

Modelling upheaval buckling in marine buried pipelines by coupling the shear stresses and soft soil stiffness

Buried marine pipelines employed in the Oil & Gas industry are subjected to pressure and temperature gradients, which cand produce local high compression loads leading to the onset of upheaval buckling failure. Upheaval buckling occurs when the localized stresses across the pipeline are high enough to induce constant deformation due to the low soil restriction in the upward direction. Therefore, models to predict upheaval buckling in buried marine pipes caused by high pressure and high temperature (HP/HT) and soil stiffness have been developed based on Euler-Bernoulli beam theory (EBT). However, this theory does not consider stresses and strains due to shear stresses which can play an important role in upheaval buckling failure. Therefore, in this work an analytical model that takes into account Engesser-Timoshenko beam theory (TBT) and considers the shear effects on pipelines was developed to predict upheaval buckling in buried marine pipelines. Furthermore, equations that govern vertical buckling of buried pipelines considering a plastic soil with initial imperfection were considered. Analytical results were compared with finite element models of buried pipeline and other models reported in the literature, and it was observed that analytical results fall in the range of those reposted in the literature. It was also observed that the incorporation of shear stresses in buried marine pipelines has low effect on upheaval buckling onset and propagation, but the soil stiffness has a strong influence on upheaval failure in buried marine pipelines.     

Experimental and theoretical studies on lateral buckling of submarine pipelines

Global buckling of a submarine pipeline during high pressure/high temperature (HP/HT) operation results in a loss of pipeline stability that is similar to a bar in compression; this phenomenon constitutes one of the key factors affecting pipeline integrity and design. To intuitively study the buckling response, a test system was designed that can account for thermal loading and pipe-soil interactions, and this system was used to perform a series of small-scale model tests on the lateral buckling of submarine pipelines with different initial imperfections. Based on the hat-shaped buckling profiles of the test pipelines, a new buckling mode called "hat-shaped buckling" was proposed. In an attempt to study the conditions under which the pipeline exhibits this hat-shaped buckling mode, the changing law of the buckling mode was investigated through finite element analyses of pipelines with different parameters, including the length of the pipeline and the amplitude and wavelength of the initial imperfection. Subsequently, an analytical solution for calculating the buckling amplitude of a pipeline with a hat-shaped buckling profile was proposed. The theoretical solution was compared to the experimental data, which verified the feasibility of the model in calculating pipeline buckling deformation. The experimental data, the buckling mode based on these data and the corresponding analytical model discussed herein may provide a reference for future experimental studies of pipeline buckling.     

Mode jumping in the lateral buckling of subsea pipelines

Unburied subsea pipelines under high-temperature conditions tend to relieve their axial compressive stress by forming localised lateral buckles. This phenomenon is traditionally studied under the assumption of a specific lateral deflection profile (mode) consisting of a fixed number of lobes. We study lateral thermal buckling as a genuinely localised buckling phenomenon by applying homoclinic (‘flat’) boundary conditions. By not having to assume a particular buckling mode we are in a position to study transitions between these traditional modes in typical loading sequences. For the lateral resistance we take a realistic nonlinear pipe-soil interaction model for partially embedded pipelines. We find that for soils with appreciable breakout resistance, i.e., nonmonotonicity of the lateral resistance characteristic, sudden jumps between modes may occur. We consider both symmetric and antisymmetric solutions. The latter turn out to require much higher temperature differences between pipe and environment for the jumps to be induced. We carry out a parameter study on the effect of various pipe-soil interaction parameters on this mode jumping. Away from the jumps post-buckling solutions are reasonably well described by the traditional modes whose analytical expressions may be used during preliminary design.     

On maximum forces exerted by floating ice on a structure due to constrained thermal expansion of ice

The problem of interaction between a floating ice cover and an engineering structure is considered, in which the ice–structure contact forces are caused by an increase in ice temperature due to solar radiation in situations, when the lateral thermal expansion of ice is constrained. The focus is on the determination of the maximum thermally-induced horizontal force exerted on a structure wall, assuming that the magnitude of this force is bound by the smallest force capable of fracturing the ice cover due to its buckling. The ice cover is modelled as a rectangular plate of uniform thickness, with its four edges being constrained by vertical rigid walls, and it is assumed that ice deforms, and eventually fails, by the mechanism of viscous creep buckling. The plate is subjected to in-plane axial compressive stresses developing in ice to prevent its thermal expansion due to solar heating, and is transversely (vertically) bent by the forces caused by the reaction of underlying water. The floating ice is treated as a material whose elastic and viscous properties depend on temperature and the ice porosity, and therefore they vary with time and the depth of ice. The results of numerical simulations, conducted for a variety of the ice plate horizontal dimensions, thicknesses and daytime temperature-change scenarios, illustrate the evolution of the plate deflection surface prior to its failure, and show the time variation of the maximum forces exerted by ice on a structure wall as functions of the ice thickness and maximum daytime temperature rise at the top surface of ice.     

Antisymmetric thermal buckling triggered by dual distributed buoyancy sections

Rogue buckles may occur for unburied subsea pipelines operating under high temperature and high pressure conditions. Distributed buoyancy section (DBS) is often installed to trigger pipeline lateral buckling. Single distributed buoyancy section (SDBS) is normally adopted to trigger a symmetric lateral buckling mode. But in some cases, dual distributed buoyancy sections (DDBS) with a gap between them are utilised to trigger an antisymmetric lateral buckling mode. This paper concerns the behaviour of antisymmetric lateral buckling triggered by DDBS. First, the locations of the maxima of the deflection and bending stress are determined. Then, comparisons of the post-buckling behaviour between antisymmetric buckling mode, triggered by DDBS, and symmetric buckling mode, triggered by SDBS, are presented and discussed. The influences of the spacing between dual buoyancy sections and the parameters of the DBS on the buckled configuration and post-buckling behaviour are presented. Finally, the effects of the DBS on the minimum critical temperature difference, the maxima of the deflection and stress are discussed. The results show that the maxima of the deflection and stress of the antisymmetric mode are much smaller than that of the symmetric mode under the same operating conditions. During the design process, the spacing between dual buoyancy sections, the length and the weight ratio coefficient of the DBS should be determined in sequence.     

Ultimate torsional strength of flat-bar stiffeners attached to flat plating under axial compression

A parametric study based on numerical analysis using an efficient non-linear finite element method code is presented for the simulation of the interactive flexural-torsional failure behaviour of flat-bar stiffeners in plates under uniform axial compression. The restraining effect of the structural components on one another is investigated by varying the plate and stiffener slenderness. Initial imperfection levels partinent to marine structures have been accounted for. Strength curves for the allowable stress at the top of the stiffener due to elasto-plastic torsional buckling are given for use with approximate design formulas.     

Finite element study on circular armour wire lateral buckling in umbilicals

The present paper addresses the circular armour wire lateral buckling in umbilicals. An asymmetric non-linear finite element model is developed to analyze a single armour wire subjected to combined constant axial compression and uniform cyclic curvatures. A parametric case study is performed for an armour wire from a nine-hose umbilical cable, where the armour wire pitch number, applied axial compressive load and minimum and maximum curvatures in the applied cyclic bending are varied. The armour wire end shortenings, transverse sliding in cyclic bending, the buckling shapes and equilibrium paths after numerous bending cycles, the critical buckling loads, the stress states at the onset of lateral buckling, and the required number of bending cycles that triggers lateral buckling are obtained and extensively discussed. The critical buckling loads given by the FE model have been compared with an existing analytical formulation, indicating that the analytical model is reliable for small cyclic curvatures. Moreover, an empirical model is proposed for the required number of bending cycles to trigger the lateral buckling and good correlation with the FE results has been observed.     

含缺陷海底管道横向屈曲理论研究

考虑了初始几何缺陷对管道屈曲临界载荷的影响,基于经典热屈曲理论,推导了平坦海床上裸铺管道横向屈曲临界载荷的理论公式,给出了无限远处管道轴向力的计算公式及临界温度的计算公式。建立了平坦海床上裸铺管道的非线性有限元模型,并将有限元结果与解析结果进行了对比,验证了解析公式的合理性。     

国外海底管道局部屈曲研究综述

海底管道是海洋油气集输系统中最重要的组成部分之一,从铺设到服役都将承受多种载荷的作用,并可能发生局部屈曲且沿管道传播开来,由此造成严重的后果。海底管道的局部屈曲在管道安全性方面具有重要意义,已成为海底管道设计与评估中重要的内容。详细阐述了国外关于海底管道受外压、弯矩和轴力作用下的局部屈曲研究成果,论述了在单个载荷和多个载荷联合作用下的局部屈曲破坏机理,并提出了未来研究的建议。     

特征载荷下海工管状结构屈曲临界载荷分析

圆柱形管状结构在海洋工程领域中应用较多，在进行结构设计时，需重点关注其侧向受载时的屈曲强度问题。通过理论分析和数值模拟，对比研究径向线性载荷变化下圆柱壳的屈曲行为，以经典的Donnell壳体理论为基础，得到圆柱壳的屈曲控制方程，并通过本征值分析方法得到结构屈曲的临界条件。采用有限元软件ABAQUS对线性变化径压下圆柱壳的屈曲进行数值仿真。分析得出径厚比是径向线性分布载荷下圆柱壳屈曲临界载荷的主要影响因素，三角形径压下屈曲临界载荷值约为均布径压下屈曲临界载荷值的2倍。     

复杂悬跨条件下的管线涡激振动分析(英文)

Spans occur when a pipeline is laid on a rough undulating seabed or when upheaval buckling occurs due to constrained thermal expansion. This not only results in static and dynamic loads on the flowline at span sections, but also generates vortex induced vibration (VIV), which can lead to fatigue issues. The phenomenon, if not predicted and controlled properly, will negatively affect pipeline integrity, leading to expensive remediation and intervention work. Span analysis can be complicated by: long span lengths, a large number of spans caused by a rough seabed, and multi-span interactions. In addition, the complexity can be more onerous and challenging when soil uncertainty, concrete degradation and unknown residual lay tension are considered in the analysis. This paper describes the latest developments and a .state-of-the-art. finite element analysis program that has been developed to simulate the span response of a flowline under complex boundary and loading conditions. Both VIV and direct wave loading are captured in the analysis and the results are sequentially used for the ultimate limit state (ULS) check and fatigue life calculation.     

Lateral buckling of subsea pipelines triggered by combined sleeper and distributed buoyancy section

In order to release the axial compressive force resulting from high-temperature conditions, sleepers or distributed buoyancy sections are usually installed along the route of the subsea pipeline as the buckle initiation facilities to trigger lateral buckles. DNV-RP-F110 suggests that the individual buckle initiators can be combined to further increase the reliability of buckle formation. In this study, an improved buckle initiation technique, called the combined sleeper and distributed buoyancy section, is investigated. A generalised mathematical model is proposed to simulate lateral buckling triggered by the combined sleeper and distributed buoyancy section, and it can also be applied to simulate lateral buckling triggered by an individual technique, such as triggered only by sleeper or only by distributed buoyancy section. The mathematical model is verified by comparing with the solutions in the literature. The parametric analysis shows that the buckle formation reliability can be improved when the combined sleeper and distributed buoyancy section is employed. Moreover, both the axial force and the maximum stress along the buckled pipeline in the post-buckling stage are at a lower level, so the pipeline will be safer when the combined sleeper and distributed buoyancy section is utilised as the triggers.     

Three-dimensional pipeline element formulation for global buckling analysis of submarine pipelines with sleeper

Submarine pipelines can utilize sleepers to control global buckling location, which mitigates potential risks under high temperature and pressure. However, pipelines with sleepers require execution in three-dimensional space and experience lateral buckling modes. As such, this paper proposes a 3D pipeline element for lateral buckling analysis, building on previous 2D element formulations. This new element considers non-linear pipe-soil interactions, thermal expansion, axial load, initial imperfections, large deflection, and other major factors that affect lateral buckling. The derivations of the 3D pipeline element are provided in detail, and the numerical analysis procedure is elaborated. To validate the accuracy and efficiency of the proposed 3D pipeline element, several examples are presented.     

Interactive flexural-torsional buckling behaviour of stiffened plating

Results from a series of studies on stiffened plates under axial compression are presented in this paper. The large-deflection elasto-plastic behaviour of each panel component is described by the von Karman equations, thus enabling the lateral-torsional buckling of the stiffener to be modelled in a rigorous manner. Material nonlinearity is represented using the von Mises yield criterion in conjunction with the Prandtl-Reuss flow rule. Results are presented in the form of average stress-strain curves which are used to generate maximum strength curves for the stiffener and plate.     

组合应力作用下含腐蚀缺陷海管安全工作压力评价方法

在较高温度和压力作用下,由于土壤的摩擦阻力,海管会产生很大的轴向压力,以及由侧向屈曲引发的弯矩。因此对含腐蚀缺陷管道安全工作压力的评价,须考虑轴向压应力的影响。对目前工程界的评价方法进行对比分析,在内压和轴向压应力组合作用下,含腐蚀缺陷海管的安全压力评价方法还很不完善,尤其是复杂缺陷,目前的规范还不完全适用。通过对许用应力法安全系数的讨论和分析,基于Von Mises准则和有限元分析,提出了组合应力作用下含腐蚀缺陷海管的安全工作压力评价方法。通过该方法对某运行了近三十年的管道进行了安全工作压力的评估,同时考察了轴向压应力对安全工作压力的影响。此方法对应的轴向压应力限值和安全等级以及安全系数相关,当安全等级低时,其值和DNV-RP-F101规范值基本一致,当安全等级高时,其值比DNV-RP-F101规范值大。     

海底埋设管线屈曲剧变理论研究综述

海上生产的烃类必须在高温高压下运输以使流体舒缓而避免蜡组分的凝固。由于内外压差和温差引起强制膨胀导致轴向压缩力,此时便产生了海底管线的屈曲。此压缩力既能引起管线在海床平面内的侧向屈曲,也能造成垂向屈曲。通常将管线埋于沟槽内从而确保与其它海洋活动的干扰最小化。在此情况下,侧向土约束超过了由管线浮重造成的垂向隆起约束。因此,要特别注意挖沟埋设管线的垂向屈曲。最近对中国高温管线和渤海湾几起事故的关注引发中国海洋工程师对此现象的强烈兴趣。文章综述了海底埋设管线垂向屈曲的理论研究历史,以及作者对此问题的一些经验。希望海洋工程师能从本领域的文献综述和总结中受益。文中同时研究了管线的防护层设计,最后明确了未来发展的方向。     

壁厚所致几何不连续性对卷管法安装管道的影响

对于深水管道,止屈器起到了很好的防止屈曲传播的作用,但是在卷管法安装中,管道在上卷和退卷的过程中将产生塑性变形,而由于止屈器导致的管道壁厚几何不连续性将使局部管段的变形增大,可能加剧塑性变形的影响。针对这个问题,建立ABAQUS非线性有限元模型模拟管道安装过程,研究上述问题对卷管铺管中管道性能的影响并作参数敏感性分析。结果表明,壁厚所致几何不连续性的存在导致卷管安装时管道局部曲率及应变明显增大;回拉力、管径与卷筒直径之比及管道壁厚等参数也将产生影响。另外,增加回拉力可降低上述不连续性的影响,但管道残余椭圆度也将增加;增大卷筒半径（或减小管道直径）将使不连续性的影响降低;增大管道壁厚可降低不连续性影响,但随之建造成本也将增加。本文研究结论可为卷管法安装中管道设计提供理论指导。