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.     

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.     

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.     

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.     

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.     

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。     

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.     

Propagating buckles in corroded pipelines

Rigid–plastic solutions for the steady-state, quasi-static buckle propagation pressure in corroded pipelines are derived and compared to finite element predictions (ABAQUS). The corroded pipeline is modeled as an infinitely long, cylindrical shell with a section of reduced thickness that is used to describe the corrosion. A five plastic hinge mechanism is used to describe plastic collapse of the corroded pipeline. Closed-form expressions are given for the buckle propagation pressure as a function of the amount of corrosion in an X77 steel pipeline. Buckles that propagate down the pipeline are caused by either global or snap-through buckling, depending on the amount of corrosion. Global buckling occurs when the angular extent of the corrosion is greater than 90°. When the angular extent is less than 90° and the corrosion is severe, snap-through buckling takes place. The buckle propagation pressure and the corresponding collapse modes also compare well to finite element predictions.     

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.     

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.     

海底管道腐蚀后的剩余强度评价

海底管道通常会因腐蚀而形成各种不同类型的缺陷,影响管道的承载能力和使用寿命。本研究在准确掌握管道缺陷发展情况的基础上,分别根据行业规范和采用有限元方法对海上油田含有腐蚀缺陷的原油管线进行剩余强度评价,判定海底管道修复的必要性和修复的紧迫程度,以确定最终的管线修复方案,可供类似海底管道修复工程参考。     

Symmetric and anti-symmetric buckle propagation modes in subsea corroded pipelines

Solutions for the steady-state buckle propagation modes and pressures in a corroded pipeline subjected to external hydrostatic pressure are presented. The buckle propagation pressure of a corroded pipeline is obtained analytically with a rigid-plastic analysis and numerically from finite element analysis (ABAQUS). Both the rigid-plastic analysis and ABAQUS program reveal symmetric and anti-symmetric buckling modes, depending on the depth and angular extent of the corrosion. Snap-through and global buckling of the pipeline are also distinguished in both solutions. The rigid-plastic solutions for buckle propagation pressure and corresponding collapse modes are found to be within 15% with numerical solutions.     

Controlled pipeline lateral buckling by reeling induced curvature imperfections

Expansion of pipelines installed on the sea floor due to the passage of high temperature and pressure hydrocarbons leads to lateral buckling. Interaction with a frictional sea floor can result in localization of such buckles, which must be controlled to ensure that the local bending is within acceptable limits. Periodic geometric imperfections introduced to a pipeline installed by reeling using the Residual Curvature Method are modeled and their effectiveness as expansion loops is evaluated. The imperfections are generated by allowing chosen lengths of the line to retain a small curvature by judicious action at the straightener. The model properly accounts for the complex interactions between geometric and material nonlinearities with frictional forces. It is demonstrated that as the temperature increases, the line can buckle in a snap-through manner, or can grow stably usually causing plastic deformation in its crest. The behavior is governed by the length, curvature, amplitude and periodicity of the imperfection, and by the lateral and axial frictional forces that develop. The effect of each of these variables is studied parametrically. Overall, the Residual Curvature Method is found to be a viable and effective method of controlling lateral buckling. The results provide guidance on the optimal periodicity, how to avoid snap-through buckling, and how to simultaneously minimize plastic bending.     

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。     

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.     

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。     

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.     

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.     

船体结构屈曲强度评估方法的规范研究及应用

论述了船舶结构规范中应用的结构屈曲强度评估方法的规范,如二维屈曲规范指定性要求,三维有限元模型中高级屈曲方法及其技术发展等。对其中的高级屈曲方法中的两种不同方法论的技术背景,包括理论基础和实际应用情况做了阐述,并对其中的非线性有限元加筋板格极限强度分析工作做了阐述,及时掌握目前国际领域新技术新标准发展信息。     

Reliability-based design of subsea light weight pipeline against lateral stability

The application of non-metallic light weight pipeline (LWP) in subsea oil/gas transmission system is subject to subsea pipeline on-bottom stability problem because of their light weight. Additional weight required for the stabilization of subsea LWP is a critical item to consider when decreasing the cost of the pipeline system. This paper presents an effective approach to determine the additional weight by utilizing a reliability-based assessment of subsea LWP against on-bottom stability. In the approach, a dynamic non-linear finite element model (FEM), including a model of fluids-pipe-soil interaction for the subsea pipeline, is used to study the pipeline displacement response. In-place analysis of a flexible pipe is presented as an example of the authors' methodology. Results show that displacements are largely affected with and without considering the lift force. Additionally, the uncertainties of all parameters used in the model are considered. With 145 cases of FEM calculations being the samples, a response surface model (RSM) is developed to predict the pipeline lateral displacement using the software Design-Expert. Combing with the RSM equation, the Monte Carlo simulation method is employed to estimate the probability of exceeding pipeline stability. To calculate the reliability of LWP for different submerged weights, the method introduces a calibrated factor into the serviceability limit state (SLS) function. The proposed approach can be used to determine the additional weight required for the on-bottom stability of subsea pipelines while considering the uncertainties of all relevant parameters.