1 Introduction

For the deepwater development of oil and gas production,it is well recognized that the effect of severe environmental conditions,i.e.,high pressure and high temperature(HPHT),has caused various difficulties.Recently,several researches have proposed designs for robust offshore and subsea structures that can withstand the abovementioned problems.In HPHT conditions,thermal expansion naturally occurs in structures such as pipelines,subsea systems,and topside facilities.Therefore,engineers must carefully design and confirm the robustness of offshore oil and gas production structures.This is especially true for subsea structures that are difficult to repair and/or replace in response to the occurrence of unexpected problems,the cost of which is much greater than those of onshore or nearshore cases.

To overcome HPHT-related problems of subsea pipelines,i.e.,thermal expansion and global and local buckling,engineers must consider the amount of thermal expansion that may take place.In this regard,numerous studies have been conducted related to the expansion of pipeline in terms of singlewall cases(Palmer and Ling 1981;AGA 1987;Hobbs and Liang 1989;Choi 1995)and pipe-in-pipe(PIP)cases(Choi 2002;Kershenbaum et al.1996;Harrison et al.1997),as well asmany others.Recently,Baiand Bai(2014)widely reviewed and summarized existing methods for the thermal expansion design of subsea pipelines.In real subsea pipeline projects,engineers design the pipeline based on DNV(2011,2013)and API(2015)design codes that establish engineering design standards based on mechanical theories.Furthermore,many kinds of expansion problems,especially those related to HPHT conditions,were addressed in the joint industry project(JIP)SAFEBUCK,which considered the design challenges for pipelines.In addition,the analyses of pipeline expansion extend to structures attached at the end of the pipelines,including risers,manifolds,and pipeline end terminals(PLETs).

以江苏农牧科技职业学院水产科技系为例，三年制学生一般在入学第二年参加实习，系部根据学生的专业，并结合学生的就业方向、个人意愿等将学生分配到不同的企业，这些企业分布在全国各地，学生进入企业后，经过一段时间的培训后，又会将学生分配到不同的养殖销售区域，受时间、地域等多重条件的影响，学校很难将学生聚集起来开展组织生活。而实习企业大多为民营企业，不重视组织生活，也基本不给学生定期开展民主生活会。

Estimations of subsea pipeline expansion are calculated using complex equations and diverse variables,so equations that have been developed based on experience could be simplified for the purposes of structural design at the initial engineering stages(pre-front-end engineering design(Pre-FEED)and FEED).In this study,we found the relationship between the virtual anchor length and the SDR to be exponentially proportional under conditions in which other variables are fixed.On this basis,we propose a simple and reliable diagram,shown as an exponential equation that can easily calculate the pipe expansion length by changing some of the input values.The insights developed in this study will be useful for engineers who are designing and installing subsea pipelines.

2 Method for Expansion Analysis

Before describing our expansion analysis procedure,first,we clearly define the term subsea pipeline expansion.A pipeline is usually installed at the same temperature as the surrounding environment,in this case,the seawater temperature.However,upon becoming operational,the inlet temperature dramatically increases so the temperature of the whole line also changes.At the same time,the pipeline is also pressurized.The expansion of subsea pipeline is related to the increment of difference between the temperature and pressure and is closely related to the global buckling design procedure shown in Fig.1.In this study,we addressed the whole procedure,from “Start” to the“calculation of expansion length” of the subsea pipeline.

It is well recognized that subsea structures must function safely throughout their design life.Generally,if any problem is encountered in the operation of subsea structures,their oil and gas productions should be stopped and inspection and repair processes undertaken.However,it is not easy to undertake repair work.Whereas ship structures can be dry docked(or re-docked)for the purposes of repair and periodic surveys for status monitoring,the suspension of oil and gas production entails great expense and time,which means substantial loss of income.In this regard,subsea pipeline engineering design,installation,and operation must be reliable and must take advantage of proven high-technology solutions.

Fig.1 Overview of global buckling design considering pipe expansion

Currently,the terminologies used in Fig.2 are widely employed in expansion analyses of subsea pipelines(Choi et al.2008).The free expansion analysis case is defined as occurring when the pipe end restraining forces are zero,but the pipe strain at the end is not.Anchor points(Nes et al.1996)are the fixed points presented in Fig.2,where pipe movement due to expansion is stopped.The pipeline portion from the free end to the anchor point is defined as the unrestrained zone.Lastly,the fully restrained zone is the portion between the anchor points.Predicting the position of the anchor points can help guide the formulation of the subsea pipeline route that will minimize and avoid structural problems,especially lateral buckling.

Fig.2 Overview of subsea pipeline expansion and terms(Choi et al.2008)

Strain due to end cap effect(pressure effect)

In this study,we analyzed pipeline expansion with the assumption of free expansion with uniform temperature.This means that we assumed zero restraining forces at the pipe end,but soil friction along the pipe.In this case,the interaction forces at each upper and lower position are zero,as shown in Fig.2.This is called a free expansion problem in which we also assume the temperature difference between the product and environment to be constant along the pipeline.We define the anchor points in Fig.2 as the two points where movement is zero.The anchor lengths at each end side,i.e.,Lu and Ld,are called the moving portions,which include the space from the pipe end to the anchor point.As shown in Fig.2,these two values will be similar due to the constant temperature.Finally,we define the portion in between the anchor points as the fully restrained zone.

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Strain due to mobilization of soil friction

Strain due to residual lay tension

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3 Applied Examples

Using the procedures mentioned in Section 2,in this section,we describe the application studies we conducted using reliable scenarios.Lastly,we propose the use of the SDR versus virtual anchor length diagrams that are derived from the conventional equations.

3.1 Definition of Design Inputs

3.1.1 Structural Characteristics

In general,we adopted outer diameters ranging from 8 to 14 in.to represent flow lines that are especially subject to HPHT fluids from oil wells.To represent reasonable cases,we defined a wall thickness range that satisfies the requirement for a long pipeline(LA＜L total/2)at structural specifications and environmental conditions.Table 1 summarizes the structural characteristics that cover the geometric,mechanical,and material properties.

As presented in Fig.1,if we can apply time-dependent corrosion damage to these pipeline structures,then we can generate accurate and realistic outcomes.The first time dependent corrosion model was proposed by Paik et al.(2003a,b)for tanker/FPSO and bulk carrier structures,respectively.Since then,those corrosion models have been applied by Kim et al.(2012a,b,2014,2015)in the assessment of corrosion conditions of damaged ship structures.Recently,an advanced technique for the development of time-dependent corrosion models was proposed by Paik and Kim(2012)and was then applied to subsea pipeline structures(Mohd Hairil et al.2014).In our study,we selected 100 cases based on a pipe-wall thickness that ranged from 15 to 28 mm for each outer pipeline diameter.We then divided this thickness range into 100 sub-ranges.

3.1.2 Environmental Parameters

The calculation of the virtual anchor length is perform ed in steps 1 and 2,which were presented in Sections 3.1 and 3.2.Figure 3a-e shows the obtained SDR versus LA diagrams.In this paper,we applied five different pressure cases.In addition,each case consists of four sub-cases,which we applied in different temperature conditions.

Table 1 Structural data

API-X65 and 70 are considered as structural data

Type Data Pipe outer diameter/in. 8,10,12,14 Pipe-wall thickness/mm 15-28 Density of steel pipe/(kg m-3) 7850 Poisson’s ratio 0.3 Young’s modulus/GPa 207 Thermal expansion coefficient(1/°C) 1.171 × 10-5 Total installed pipe length/km 100

Table 2 Properties of production fluid and environmental data

Type Data Density of production fluid/(kg m-3) 90 Temperature difference/°C—5 cases 30 to 150 Pressure difference/MPa—5 cases 10 to 90 Water depth/m 1000 Seawater density/(kg m-3) 1025 Friction coefficient of soil 0.6

3.2 Definition of Expansion Parameters

The parameters causing expansion of subsea pipelines can be classified into five components,i.e.,the Poisson effect,thermal effect,pressure effect,soil friction effect,and residual lay tension effect.In this section,we describe these factors in detail.In this study,we derived all the processes using the strain-based approach.The total strain,called the net strain,can be obtained by combining all the parameters,as shown in

Fig.3 LA Calculation results for case 3.a Case 3-1:10 MPa.b Case 3-2:30 MPa.c Case 3-3:50 MPa.d Case 3-4:70 MPa.e Case 3-5:90 MPa

Table 3 Virtual anchor length exponential function information(LA/L= α ⋅e(OD/t)β)

Press./MPa Temp./°C Case 1:OD=8 in. Case 2:OD=10 in. Case 3:OD=12 in. Case 4:OD=14 in.αβR2αβR2αβR2αβR2 10 30 0.01379 0.04477 0.9987 0.01315 0.05241 0.9974 0.01249 0.05784 0.9966 0.01187 0.06197 0.9949 60 0.02920 0.04241 0.9985 0.02770 0.04864 0.9969 0.02620 0.05348 0.9959 0.02482 0.05744 0.9938 90 0.04461 0.04165 0.9984 0.04227 0.04738 0.9967 0.03994 0.05199 0.9956 0.03782 0.05887 0.9934 120 0.06003 0.04128 0.9984 0.05885 0.04675 0.9966 0.05370 0.05123 0.9954 0.05083 0.05506 0.9932 150 0.75442 0.04106 0.9984 0.07143 0.04637 0.9965 0.06746 0.05078 0.9954 0.06384 0.05458 0.9931 30 30 0.01164 0.06931 0.9998 0.01146 0.07388 0.9994 0.01115 0.07741 0.9990 0.01076 0.08039 0.9982 60 0.02670 0.05515 0.9993 0.02554 0.06055 0.9984 0.02433 0.06483 0.9976 0.02317 0.06842 0.9963 90 0.04198 0.05025 0.9990 0.03993 0.05561 0.9978 0.03785 0.05996 0.9969 0.03593 0.06366 0.9953 120 0.05732 0.04777 0.9989 0.05440 0.05304 0.9975 0.05148 0.05738 0.9965 0.04880 0.06111 0.9947 150 0.07270 0.04627 0.9988 0.06891 0.05146 0.9973 0.06516 0.05578 0.9983 0.06173 0.05951 0.9943 50 30 0.01023 0.08918 0.9999 0.01051 0.08989 0.9999 0.01053 0.09125 0.9998 0.01035 0.09296 0.9994 60 0.02469 0.06655 0.9997 0.02396 0.07068 0.9992 0.02308 0.07416 0.9987 0.02214 0.07723 0.9978 90 0.03971 0.05823 0.9994 0.03803 0.06297 0.9986 0.03626 0.06892 0.9979 0.03455 0.07034 0.9966 120 0.05491 0.05391 0.9992 0.05232 0.05881 0.9982 0.04968 0.06291 0.9974 0.04721 0.06647 0.9959 150 0.07019 0.05125 0.9990 0.06671 0.05621 0.9979 0.06322 0.06037 0.9970 0.05999 0.06399 0.9953 70 30 0.00925 0.10570 0.9995 0.00995 0.10237 0.9997 0.01026 0.10161 0.9999 0.01026 0.10213 0.9999 60 0.02306 0.07684 0.9999 0.02278 0.07943 0.9997 0.02222 0.08199 0.9994 0.02150 0.08447 0.9987 90 0.03775 0.06566 0.9997 0.03648 0.06961 0.9992 0.03503 0.07305 0.9986 0.03355 0.07614 0.9976 120 0.05275 0.05971 0.9994 0.05054 0.06414 0.9987 0.04820 0.06793 0.9980 0.04595 0.07127 0.9968 150 0.06790 0.05602 0.9993 0.06477 0.06065 0.9984 0.06157 0.06460 0.9976 0.05855 0.06807 0.9962 90 30 0.00853 0.11972 0.9987 0.00960 0.11242 0.9992 0.01018 0.10968 0.9997 0.01035 0.10915 0.9998 60 0.02171 0.08619 0.9999 0.02187 0.08708 0.9999 0.03407 0.07850 0.9991 0.02112 0.09056 0.9993 90 0.03604 0.07260 0.9999 0.03520 0.07563 0.9995 0.04698 0.07249 0.9986 0.03281 0.08122 0.9983 120 0.05080 0.06522 0.9997 0.04901 0.06907 0.9991 0.06015 0.06852 0.9981 0.04496 0.07558 0.9975 150 0.06580 0.06058 0.9995 0.06306 0.06483 0.9988 0.21627 0.08866 0.9997 0.05736 0.07181 0.9969

Fig.4 Proposed method for estimating pipe expansion length using the LA diagram

Eq.(4).The five parameters can be individually expressed using Eqs.(5.1)to(5.5),respectively.

In general,five types of conditions,i.e.,free expansion with uniform temperature,free expansion with temperature gradient,expansion with end restraints,expansion of pipe-in pipe system,and lateral deviation(so-called snaking),are considered when estimating the expansion of subsea pipelines,which have been widely reviewed by Choi et al.(2008)and Bai and Bai(2014).

Strain due to the Poisson effect

经过7天朝夕相处，两人的感情更加火热，郭启明提出，让关小美和他一起到北京去。他说：“小美，我是公司里的储备人才，现在公司就已经给我分了公寓，配了雅阁小轿车，公司领导承诺，将来还要给我股份，那时，我就可以每年带着你到海滩度假，带你游历世界……”郭启明的话让关小美心潮澎湃，但她还是犹豫着摇头说：“启明，我们的事我还没来得及给我爸爸妈妈说，如果我现在丢了工作跟你到北京去，他们肯定会反对……”

Strain due to thermal effect

A more advanced pipeline expansion calculation method,i.e.,free expansion with a temperature gradient and expansion with temperature gradient,can be found in the paper by Choi et al.(2008).

In this section,we address the calculation of the virtual anchor length(LA)based on Eq.(6).The procedure for developing the diagram,including the required input data and output,can be summarized as follows:

Fig.5 Exponential function indices.a Index(α).b Index(β)

The force equilibrium in the pipeline can be expressed as shown in Eq.(1).The virtual anchor length can be derived once Eq.(1)is solved,as shown in Eq.(2)(Choi et al.2008).The expansion of the pipeline with a free-end condition can be calculated using Eq.(3).

After calculating the total strain of the subsea pipeline,we can estimate the virtual anchor length(LA).Generally,the virtual anchor length is obtained using Eq.(6).Finally,integrating the total strain gives the pipeline expansion length,as shown in Eq.(7).

3.3 Calculation of Virtual Anchor Length

例4.MARY:What is a lie!Now you're talking in riddles like Jamie. Edmund! Don't! There's your father coming up the steps now. I must tell Bridget.

·Step 1:Definition of design input(structural and environmental parameters)

·Step 2:Definition of expansion parameters(Poisson ratio,thermal,pressure,soil friction,residual laying tension)

·Step 3:Calculation of expansion length

·Step 4:Development of SDR versus LA diagram

·Step 5:Investigation of exponential function indices(α and β)

研究搜救国协调权之前，应首先分析该权利产生的理论权源，明确该权利派生的依据。搜救国协调权的理论权源是多元和广泛的，主要有3个方面。

经过专家们的分析，中国的出口图书存在的问题有质量差的语言，翻译生硬，意思走样，甚至还会有政治错误。翻译的质量低下，已经是中国文化走出去的重要瓶颈。特别是近年来，随着出口需求不断增加，一些出版商忽视盲目追求数量和质量，在时间方面，一般只有人翻译了几个月，否则会增加成本，也很难抢占市场。

We assumed deepwater environmental conditions,for which the properties of the seawater,seabed,and production fluid,for example,must be defined.The pressure and temperature difference properties refer to the different conditions between the production fluid and the environment,so we omitted some product and environmental properties with respect to the temperature and pressure conditions.Table 2 show s theproduction fluid properties and the environmental conditions surrounding the subsea pipeline.

Figure 3 shows the virtual anchor length calculation results for a pipe 12 in.in diameter.Based on these results,we can develop the empirical formula using the curves mentioned in step 5 and Eq.(8).Then,we can define the obtained empirical formula as the SDR versus anchor length diagram.We can determine the linear trend by the exponential function indices and the pipe diameter based on the coefficient of determination(R2).

where α and β can be defined as exponential function indices.

Table 3 lists the exponential function information derived from all the expansion analysis cases for the virtual anchor length.

科学家研究发现，如果小学生连续20分钟背着一个重量超过自身体重15%的书包，其脊椎就会萎缩6～8毫米，长期如此还会导致腰背疼、脊柱侧弯，造成长得慢，缩得快的严重后果。因此，大家应该尽量选择棉麻或帆布材质的书包。它们耐磨又轻巧，即使加上书本、文具等物品，整个书包的重量也容易控制在合理的范围内。举个例子，如果你的体重是20千克，那你的书包装满后的总重量最好低于3千克。同时，各位同学也应该养成每天整理书包的好习惯，把暂时用不上的书从书包里拿出去，以此减重，避免书包超负荷。

3.4 Estimation of Pipeline Expansion Length by Developed Diagrams

We propose a new method for estimating the virtual anchor length of subsea pipelines and investigate its potential applicability to various diameters and wall thicknesses.In this section,we offer guidelines for applying the SDR and LA diagram,as illustrated in Fig.4.

Fig.6 Index functions forαandβexponential functions shown in Fig.5.a α-power function index aα.b α-power function index bα.c βpolynomial function index aβ.d β-polynomial function index bβ.e βpolynomial function index cβ

Table 4 Verification test case data

Type Data Pipeline diameter/in. 10 Wall thickness/mm 20,25,30 Temperature difference/°C 60,90,120 Pressure difference/MPa 30,50,70

When the structural and environmental characteristics have been defined,two types of exponential function indices(α,β)are then selected based on the developed chart shown in Fig.4.In the previous section,we showed several charts for selecting exponential function indices to verify the proposed method.These obtained charts for the exponential function indices seem sufficient for their application in estimating the expansion of subsea pipelines.However,there are also some limitations regarding the estimation of each index.

To determine the two types of exponential function indices,we use new specific relations between the pressure and temperature differences to obtain the appropriate equations.These two specific relations are expressed as shown in Eqs.(9)and(10):

Finally,Fig.5 shows the relation between the exponential function indices,for which we considered a total of 100 test cases,and the new specific variables.Once we have determined the exponential function indices,we can develop the empirical formula(step 4)using Eq.(8),which contains both the exponential function indices(α,β),and the SDR.

2.3.2 胎儿产前诊断结果及新生儿听力随访 18例胎儿产前诊断结果中，3例胎儿遗传父母双方变异(均为c.235delC复合c.109G>A)，携带者10例，5例未遗传父母双方变异。术后随访，1例患者因胎儿复合杂合变异选择终止妊娠。产后电话随访夫妇双方均为携带者的30例新生儿听力情况，自诉新生儿听力筛查均为正常，其中包含2例 产前诊断为GJB2基因c.235delC复合c.109G>A患者。

Furthermore,the indices and variables,which are composed of the exponential function indices,are directly related to the pipeline OD and this relation is illustrated in Fig.6.

3）立体的投影。该部分设置六个学习任务。其中前五个学习任务以棱柱、棱锥、圆柱、圆锥、球各个不同体进行设计；每一个任务又分别包含三个子任务，分别是体的投影绘制、体表面取点投影绘制和体被平面所截取的投影绘制。后一个学习任务是相贯线投影绘制。

According to the experiential equations derived above,we obtain five variables(aα,bα,aβ,bβ,and cβ)for the power function indices and the polynomial function variables with OD values in Eqs.(11)and(12),and those relationships are shown in Fig.6.Using the diagrams shown in Figs.5 and 6,we can estimate the indices of the virtual anchor length equation.

Briefly,under variable operating conditions and diverse pipeline sizes,we can derive the functions for the virtual anchor length by the expansion analysis shown in Fig.3,which shows the exponential proportional relationship between the SDR and LA.By using the functions in Eqs.(8)to(12)for the outer diameter,wall thickness,and pressure and temperature differences,engineers can easily determine the virtual anchor length,which makes it possible to estimate the pipeline expansion length.

4 Verification o f Simplified Virtual Anchor Length Equation

Fig.7 Test case comparison results.a ΔT=90 °C.b ΔP=50 MPa

We verified the diagrams proposed before the steps and simplified exponential equations for several cases against the conventional calculation results obtained using Eqs.(2)and(3).We determined the expansion length using the proposed method as the exponential function for the virtual anchor length,which we put into Eq.(3).Table 4 shows the selected cases used to verify the proposed method,as compared with the results shown in Fig.7.

According to Fig.7,the proposed method has minor errors in comparison with the analytical solution.To determine there as on for these errors,we fixed or changed the parameters such as pressure and temperature differences with respect to the SDR,the results of which are shown in Tables 5 and 6,respectively.

In Tables 5 and 6,for the specific reliable environmental,structural,and operating conditions described in Tables 1 and 2,the expansion lengths determined using the proposed method are almost the same as those by the analytical method shown in Fig.7.The coefficient of variation(COV)values are also very small,ranging from orders of 10-4 to 10-2,which means that the proposed diagram approaches may be considered reliable.

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5 Concluding Remarks

In this study,we developed useful diagrams for estimating the virtual anchor length,which makes it possible to determine the expansion length of subsea pipelines.We verified the applicability of this approach by using example cases.The purpose of this study was to propose a method for generating easy,accurate,and efficient diagrams for predicting the expansion length of subsea pipelines.To illustrate the expansion length,we adopted four representative cases of outer pipeline diameters and 25 sub-cases.Once we have determined the pipeline diameter and differences in the temperature and pressure,we can directly calculate the exponential function indices(α,β).Once we have determined these two variables,we can easily obtain the expanded length of subsea pipelines using simple exponential equations and the net strain value.

习近平强调:“环境治理是一个系统工程，必须作为重大民生实事紧紧抓在手上。”［7］236环境工程涉及人们生产生活的方方面面，因此要按照系统工程的思路，创新思维，制定政策，严格制度，到位措施，重在行动。习近平绿色发展理论从这五个方面切实发力，力度之大，前所未有。

Despite our consideration in this study of diverse combinations of pressure and temperature under reliable environmental conditions,the applicability of our proposed expansion estimation method is rather limited in that we could not include the length of the pipeline as a factor.However,the development of pipe expansion length estimation methods is worthwhile as it shows that the amount of pipeline expansion can be simply determined as a function of pressure,temperature,and pipe dimensions.In further analyses that include various pipeline lengths as a factor,we will develop a universal diagram for predicting the expansion length of pipelines.

Based on our results,we can conclude that our proposed method will be useful for estimating the expansion length of subsea pipeline structures by changing the dimensional inputs under similar conditions.The proposed method may also be employed to determine the number of spool or bend systems based on the obtained expansion length.In addition,it can be used to develop acceptance criteria for structural buckling behavior of installed subsea pipelines.

Acknowledgements This study was undertaken at Ocean and Ship Technology(OST)under Deepwater Technology Mission Oriented Research at Universiti Teknologi PETRONAS.This research was supported by the Technology Innovation Program(Grant No.:10053121 and 10051279)funded by the Ministry of Trade,Industry,and Energy(M I,Korea)and YUTP Grant(0153AA-E60,Malaysia).The authors would also like to thank for the great support of POSTECH,POSCO,and Daewoo E&C,Republic of Korea.Some part of this paper was presented in The 3rd International Conference on Civil,Offshore and Environmental Engineering(ICCOEE 2016),15-17 August,Kuala Lumpur,Malaysia.

随着全面深化改革不断推进，一系列的“政策套餐”，极大地增强了云南省民营经济和中小企业发展的动力和活力。

Foundation Item Supported by the Technology Innovation Program(Grant No.:10053121 and 10051279)funded by the Ministry of Trade,Industry&Energy(M I,Korea).

References

AGA(1987)Pipeline riser system design and application guide.In:AGA project number 178-622.Washington,Brown and Root

API(2015)Design,construction,operation,and maintenance of offshore hydrocarbon pipelines:APIRP 1111.American Petroleum Institute,Washington

Bai Q,Bai Y(2014)Subsea pipeline design,analysis,and installation—part II:pipeline design,Chapter 9:Thermal Expansion Design.Gulf Professional Publishing,Oxford

Choi HS(1995)Expansion analysis of offshore pipelines close to restraints.The 5th International Offshore and Polar Engineering Conference(ISOPE 1995),Hague,The Netherlands

Choi HS(2002)Expansion analysis of subsea pipe-in-pipe due to high temperature and high pressure product.J Ocean Eng Technol 16(5):56-60

Choi HS,Lee S,Chun E(2008)A review of the expansion behavior of marine pipelines.J Ocean Eng Technol 22(2):13-19

DNV(2011)On-bottom stability design of submarine pipelines:recommended practice F109.Det Norske Veritas,Oslo

DNV(2013)Submarine pipeline systems:offshore standard F101.Det Norske Veritas,Oslo

Harrison GE,Kershenbaum NY,Choi HS(1997)Expansion analysis of subsea pipe-in-pipe flow line.The 7th International Offshore and Polar Engineering Conference(ISOPE 1997),Honolulu,Hawaii,USA

Hobbs RE,Liang F(1989)Thermal buckling of pipe-lines close to restraints.The 8th International Conference on Offshore Mechanics and Arctic Engineering(OMAE 1989),Hague,The Netherlands

Kershenbaum NY,Harison GE,Choi HS(1996)Subsea pipeline lateral deviation due to high temperature product.The 6th International Offshore and Polar Engineering Conference(ISOPE 1996),Los Angeles,USA

Kim DK,Park DK,Kim JH,Kim SJ,Kim BJ,Seo JK,Paik JK(2012a)Effect of corrosion on the ultimate strength of double hull oil tankers—part I:stiffened panels.Struct Eng Mech 42(4):507-530.https://doi.org/10.12989/sem.2012.42.4.507

Kim DK,Park DK,Park DH,Kim HB,Kim BJ,Seo JK,Paik JK(2012b)Effect of corrosion on the ultimate strength of double hull oil tankers—part II:hull girders.Struct Eng Mech 42(4):531-549.https://doi.org/10.12989/sem.2012.42.4.531

Kim DK,Kim HB,Zhang XM,Li CG,Paik JK(2014)Ultimate strength performance of tankers associated with industry corrosion addition practices.Int J Naval Architect Ocean Eng 6(3):507-528.https://doi.org/10.2478/IJNAOE-2013-0196

Kim DK,Kim SJ,Kim HB,Zhang XM,Li CG,Paik JK(2015)Ultimate strength performance of bulk carriers with various corrosion additions.Ships and Offshore Struct 10(1):59-78.https://doi.org/10.1080/17445302.2014.883957

Mohd Hairil M,Kim DK,Kim DW,Paik JK(2014)A time-variant corrosion wastage model for subsea gas pipelines.Ships and Offshore Struct 9(2):161-176.https://doi.org/10.1080/17445302.2014.906922

Nes H,Saevik S,Levold E,Johannsen A(1996)Expansion control design of large diameter pipelines.The 15th International Conference,Offshore Mechanics and Arctic Engineering(OMAE 1995),Florence,Italy

Paik JK,Kim DK(2012)An advanced method for the development of an empirical model to predict time-dependent corrosion wastage.Corros Sci 63:51-58.https://doi.org/10.1016/j.corsci.2012.05.015

Paik JK,Lee JM,Hwang JS,Park YI(2003a)A time-dependent corrosion wastage model for the structures of single/double hull tankers and FSOs/FPSOs.Mar Technol 40(3):201-217

Paik JK,Thayamballi AK,Park YI,Hwang JS(2003b)A time dependent corrosion wastage model for bulk carrier structures.Int J Mar Eng 145(Part A2):61-87

Palmer A,Ling MTS(1981)Movement of submarine pipelines close to platforms.The 13th Offshore Technology Conference(OTC 1981),4-7 May,Houston,TX,USA(OTC4067)