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.     

Snap behaviour in the upheaval buckling of subsea pipelines under topographic step imperfection

Pipelines exposed to high temperature and high pressure with a topographic step imperfection are susceptible to the phenomenon of upheaval buckling potentially leading to a hazard for the structural integrity of the pipeline. To analyse this problem we derive analytical upheaval buckling solutions and obtain the locations of maximum displacement and maximum axial compressive stress. We also analyse the typical post-buckling behaviour and its dependence on step height, axial soil resistance and wall thickness. The difference in behaviour between a pipeline with step imperfection and one with a symmetric prop imperfection is discussed. Our results show that a pipeline with a step imperfection is more prone to upheaval buckling than a perfect pipeline. For sufficiently small step heights the pipeline may suffer a snap-back instability under decreasing thermal loading, raising the possibility of hysteretic snap behaviour under cyclic thermal loading (for instance caused by periodic start-ups and shut-downs). The snap-back buckling disappears for large enough step height and the minimum critical temperature difference decreases with increasing step height and wall thickness or with decreasing axial soil resistance. The maximum compressive stress decreases with increasing step height and axial soil resistance or with decreasing wall thickness. A pipeline with step imperfection is safer than one with a symmetric prop imperfection.     

小径厚比深水管道的压溃屈曲研究

深水管道所处的特殊海洋环境极易导致其发生压溃屈曲破坏.通过深入分析不同径厚比深水管道的压溃屈曲特点,并对具有不同径厚比及初始椭圆度的深水管道模型进行了压溃屈曲及后屈曲行为的计算分析.研究发现,压溃屈曲的经典理论公式并不适用于小径厚比深水管道.文章基于经典理论和数值模拟结果,得到了适用于小径厚比深水管道压溃屈曲分析的临界压力修正公式,进而对小径厚比深水管道的压溃屈曲评估提供理论支撑和工程推荐.     

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.     

大面积地表荷载作用下的埋深管线的应力分析

当地下埋深管线两侧受到不同的附加压力时,由于压差的存在使管线发生了弯曲变形。弯矩的产生可能导致管线的破坏。根据埋深管线的受力特点,采用弹性地基梁的短梁初端参数法对渤西管线的应力进行了分析。根据管线的埋深条件对边界条件进行了正确的处理,求得了管线的位移,弯矩及剪力方程,并绘制了位移,弯矩及剪力方程曲线,曲线之间具有一一对应的关系,计算的结果表明了对边界处理的正确性及理论选择的合理性。     

Large deformation coupled analysis of embedded pipeline – Soil lateral interaction

Subsea pipelines buried in the seabed may undergo large lateral displacement under environmental, operational, and accidental loads at different interaction rates and hence different drainage conditions. The undrained shear strength is commonly used in practice to assess the pipe-soil interaction assuming a sufficiently high displacement rate. This approach neglects consolidation effects and the rate-dependent response of the soil and may significantly underestimates the lateral resistance for a pipeline moving slowly relative to the ground. In this study, a coupled large deformation finite element (LDFE) framework is developed via a remeshing and interpolation technique with small strain (RITSS). A Modified Cam-Clay (MCC) model with efficient numerical integration is used. The proposed coupled LDFE framework is verified against selected physical model tests. Effects of the interaction rate and hence drainage condition on the p-y curve, excess pore pressure generation and dissipation, and failure mechanisms are discussed. An empirical relationship between the ultimate resistance and the normalized velocity of the pipe (denoting the drainage condition) is proposed, which may be applied for the integrity and safety analysis of buried pipes in landslide or fault-crossing regions.     

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.     

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。     

回填刚度对深埋管道横向响应影响的试验研究（英文）

Subsea pipelines passing through the shallow area are physically protected against the environmental, accidental, and operational loads by trenching and backfilling. Depending on construction methodology, environmental loads, and seabed soil properties, the stiffness of backfilling material may become largely different from the native ground(softer than native ground in most of the cases). The different stiffness between the backfill and native ground affects the soil failure mechanisms and lateral soil resistance against large pipeline displacements that may happen due to ground movement, landslides, ice gouging, and drag embedment anchors. This important aspect is not considered by current design codes. In this paper, the effect of trench-backfill stiffness difference on lateral pipeline-backfill-trench interaction was investigated by performing centrifuge tests. The soil deformations and failure mechanisms were obtained by particle image velocimetry(PIV) analysis. Three experiments were conducted by using three different backfills including loose sand, slurry, and chunky clay that represent the purchased, natural in-fill, and preexcavated materials, respectively. The study shows that the current design codes underestimate the lateral soil resistance for small to moderate pipe displacements inside the trench and overestimate it for large lateral displacement, where the pipeline is penetrating into the trench wall.     

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.     

浅埋海底管线防护的设计方法研究

浅埋海底管线由于外部环境荷载的改变,必然引起一定的附加应力。在这种条件下,必须对管线采取防护措施。提出了浅埋海底管线的防护方案,并应用有限元方法,建立了同时考虑土体-结构-海底管线三者耦合作用的二维有限元分析模型,对采取保护措施的海底管线进行应力的分析计算,计算结果表明所采用的防护方案是合理的。     

Stability of submarine bi-material pipeline-liner system with novel polyhedral composites subjected to thermal and mechanical loading fields

This study is concerned with the thermal and mechanical instability behaviors of composite novel liners encased in deteriorated pipelines. A liner may contain many connected segments, and two adjacent segments may become disconnected after long years of service. In such a case, the single disconnected segment may reduce to a ring. An innovative polyhedral configuration is introduced to improve the bending stiffness of the composite ring that is confined by the pipeline. The radius and bending rigidity of the ring are simplified analytically to facilitate the derivation of the critical buckling load. By employing the classical shell criteria, and defining an admissible displacement function, the expression of the potential energy function is obtained with only two unknown parameters. Taking the first derivative of the energy function to the two unknowns respectively generates two equilibrium equations. By solving the two equations, the analytical buckling load is obtained for a composite polyhedral ring in a thermal variational field. Then, two comparisons are taken between the present analytical predictions and results from elsewhere, and good agreements are obtained. An amplification coefficient is defined as the ratio between the buckling load of the polyhedral and circular rings. Finally, parametric evaluations indicate the amplification coefficient reduces with the increase of thickness-to-radius ratio, the increase of the number of sides, and the increase of the temperature variation, respectively. Therefore, a polyhedral ring with a low thickness-to-radius ratio is recommended in engineering applications.     

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.     

Comparison of computational and analytical methods for evaluation of failure pressure of subsea pipelines containing internal and external corrosions

In the designing stage of subsea pipelines, the design parameters, such as pipe materials, thickness and diameters, are carefully determined to guarantee flow assurance and structural safety. However, once corrosion occurs in pipelines, the operating pressure should be decreased to prevent the failure of pipelines. Otherwise, an abrupt burst can occur in the corroded region of the pipeline, and it leads to serious disasters in the environment and financial loss. Accordingly, the relationship between the corrosion amount and failure pressure of the pipeline, i.e., the maximum operating pressure, should be investigated, and then, the assessment guideline considering the failure pressure should be identified. There are several explicit type codes that regulate the structural safety for corroded subsea pipelines, such as ASME B31G, DNV RF 101, ABS Building and Classing Subsea Pipeline Systems, and API 579. These rules are well defined; however, there are some limitations associated with describing precise failure pressure. Briefly, all of the existing rules cannot consider the material nonlinearity, such as elastoplasticity effect of the pipeline, as well as the actual three-dimensional corrosion shape. Therefore, the primary aim of this study is to suggest a modified formula parameter considering the above-mentioned pipeline and corrosion characteristics. As a result, the material nonlinearity as well as the corrosion configuration, i.e., axial/circumferential corrosion length, width and depth, is reflected in a set of finite element models and a series of finite element analysis considering the operation conditions are followed. Based on the comparative study between the simulation and analytical results, which can be obtained from the classification society rules, the modified formulae for failure pressure calculation are proposed.     

A theory of coupled beams for strength assessment of passenger ships

This paper describes a coupled beam method, which estimates elastic response in the longitudinal bending of a passenger ship with a large multi-deck superstructure. The method can be applied during an early project stage, when detailed three-dimensional finite element modelling is not yet possible. The theory is based on the assumption that each deck in the superstructure and also the main hull can be considered as a thin-walled beam. These beams are coupled to adjacent beams with springs modelling vertical and shear stiffness. The shear effect in the side and deck structures is included with options for large openings. As a result, the method allows for the calculation of the normal stresses and vertical deflections in the arbitrary location of the hull girder. Average longitudinal displacements of deck structures and shear stresses in the side structures can be estimated as well. Simplified structures were analysed in order to validate the coupled beam method against the three-dimensional finite element method.     

Analysis of single pipeline pull-in procedure using small scale models

The structural elastic behaviour of steel pipelines during on-bottom pull-in procedure is investigated experimentally by using small scale models. Despite the lack of a sea-bed soil pipeline interaction effect in the model, it is possible to show that the unevenness of the sea-bed surface and the non-uniform distribution of friction forces can lead to large deflection bending stresses, higher than the numerical results yielded by standard software packages commonly used for design calculations. Due to foreseen difficulties in overcoming the drawbacks in practical and numerical procedures, the off-bottom pull-in operation arises as an attractive alternative even for shallow waters.     

海底多段悬跨管道涡激振动特性分析

深海海底多跨管道相比于单跨,其涡激振动行为却更为复杂。文章考虑了两端跨肩和中间支撑处的管—土作用边界条件,提出了多跨管道涡激振动预报模型,标定了模型参数,并重点分析了跨肩边界条件、中间支撑条件和悬跨长度对管道涡激振动特性的影响。结果表明:较大的两端边界处扭转弹簧弹性系数、较大的中间支撑处扭转和拉伸弹簧弹性系数和较短的悬跨长度,会限制管道结构高阶模态的激发,同时还发现了振动能量会在相邻管跨之间传递的现象。     

基于多种失效模式SPS复合钢板替换船用钢板的优化设计

在SPS复合钢板的设计中获取不同的失效模式。以减重为目标,应用序列二次规划法对SPS复合钢板进行等效船用钢板的优化设计,同时对SPS复合钢板进行多目标优化,应用层次分析法定各目标的权重。在这两种优化方法的基础上,对船用钢板与SPS复合钢板进行了屈曲、弯曲对比数值分析,同时将结果与理论计算结果对比分析。结果表明,SPS复合钢板重量能够减轻37%以上,刚度增加两倍多,但厚度增加70%。     

周期支撑管路横向振动波传播特性分析

管道系统在船舶行业中应用广泛,其振动及声辐射特性一直以来都是研究的热点.基于Timoshenko梁理论,本文首先利用传递矩阵法计算了单根充液管道的横向振动响应,并通过有限元计算和实验对比验证了计算方法.在此基础上,对管道系统的传递矩阵取特征值得到波传播参数,从而进一步分析了周期支撑的充液管道系统的振动波传递特性.由本文的计算结果可见,基于Timoshenko梁理论的横向振动响应比基于Euler-Bernoulli梁理论的结果更为精准,尤其是在较高频域内.此外,弹性支撑的刚度和间距会影响波阻和波传播带.本文工作将为周期支撑管系的减振提供一定的技术参考.     

用于预报离岸管线膨胀的简化技术（英文）

In this study, we propose a method for estimating the amount of expansion that occurs in subsea pipelines, which could be applied in the design of robust structures that transport oil and gas from offshore wells. We begin with a literature review and general discussion of existing estimation methods and terminologies with respect to subsea pipelines. Due to the effects of high pressure and high temperature, the production of fluid from offshore wells is typically caused by physical deformation of subsea structures, e.g., expansion and contraction during the transportation process. In severe cases, vertical and lateral buckling occurs,which causes a significant negative impact on structural safety, and which is related to on-bottom stability, free-span, structural collapse, and many other factors. In addition, these factors may affect the production rate with respect to flow assurance, wax, and hydration, to name a few. In this study, we developed a simple and efficient method for generating a reliable pipe expansion design in the early stage, which can lead to savings in both cost and computation time. As such, in this paper, we propose an applicable diagram, which we call the standard dimensionless ratio(SDR) versus virtual anchor length(LA) diagram, that utilizes an efficient procedure for estimating subsea pipeline expansion based on applied reliable scenarios. With this user guideline,offshore pipeline structural designers can reliably determine the amount of subsea pipeline expansion and the obtained results will also be useful for the installation, design, and maintenance of the subsea pipeline.