2012_9_12_3315_3324

Journal of Information & Computational Science 9: 12 (2012) 3315–3324Available at http://www.joics.com

Post-buckling Studies on Snaked-lay Pipeline with

New Shape ⋆

Yuxiao Liu a,∗, Xin Li b, Jing Zhou b

aDept. of Management Science and Engineering, Shandong Institute of Business and TechnologyYantai 264005, China

bState Key Laboratory of Coastal and Offshore Engineering, Dalian University of TechnologyDalian 116023, China

Abstract

Snaked-lay method is an effective lateral buckling control method, for design of snaked-lay pipeline thekey is to control lateral buckling of pipeline. Namely, the lateral buckling is triggered at the designedlocation, the moment and strain of post-buckling are acceptable. A new shape of snaked-lay pipeline ispresented, based on ANSYS, nonlinear finite element model of exposed pipelines laid on even seabed isbuilt. Post-buckling of pipeline is studied, effect of sine length, snaked-lay radii and offset angle are allincluded. Based on analysis, a control criterion of offset angle is also presented.

Keywords: Submarine Pipeline; Global Buckling; Snaked-lay Method; Sleeper Method; Snaked-layRadii

1 Introduction

In recent years, there has been a rapid increase in the number of subsea pipelines transportinghigh pressure and high temperature hydrocarbons. Pipelines operating at temperatures andpressures above ambient will tend to expand, due to thermal and pressure loading. If the pipelineresting on the seabed is restrained, axial compressive load develops due to increasing temperatureand, at some critical value, the pipe may experience lateral deformation activated by initialmisalignments. Any perturbation from the rectilinear configuration may cause the pipeline tobuckle laterally and to form a new shape on the horizontal plane. In these cases, pipeline failurehas occurred in operation. These include three catastrophic failures in the North Sea, West Africaand Brazil, each leading to full-bore pipeline rupture [1]. Thus, the industry has generally soughtto control buckling by snaked-lay method, rock dumps, distributed buoyancy and sleeper.

⋆Project supported by the National Nature Science Foundation of China (No. 50439010). Project supportedby the natural science foundation of Shandong Province (No. ZR2011DL004). Project supported by the Openingfoundation of State Key Laboratory (No. LP1115).

∗Corresponding author.Email address: [email protected] (Yuxiao Liu).

1548–7741 / Copyright © 2012 Binary Information PressOctober 15, 2012

3316 Y. Liu et al. / Journal of Information & Computational Science 9: 12 (2012) 3315–3324

The traditional method of controlling thermal buckling of subsea pipelines has been by trenchingand burying, then critical buckling forces of pipeline is very important in pipeline design. Hobbs [2]presented both vertical (upheaval) and lateral (snaking) critical buckling forces of perfect pipeline.But the effect of initial imperfection was not quantitatively studied. Neil Taylor [3] studied criticalbuckling forces of both isolated prop and contact undulation imperfection topologies theoreticallyand experimentally, but the study assumed that the initial imperfect pipeline under no axial load,i.e. is stress free. James G. A. Croll [4] studied upheaval thermal buckling of subsea pipelinebased on a simplified mode which considered the initial imperfect pipeline under axial load.

By safely triggering controlled buckles at predetermined locations, snaked lay design is oftenthe preferred method to manage lateral buckling. For snaked lay and sleeper methods, there aremany studies, for example, Jiong Guan et al. [5] discussed optimized snaked lay solution based onFE analysis of snaked lay pipeline. Rundsag et al. [6] presented guidance of how to optimize thesnake geometry based on how the lay geometry of a snake lay configuration governs the criticalbuckling force as well as the resulting loads. A. D. Rathbone et al. [7] studied effect of lateralpipelay imperfections on global buckling designs and presented the proposed methodology todefine and assess potential as laid variations of the idealized lay rote during detailed design. Kienet al. [8] proposed a mitigation scheme using the combination of vertical triggers and lateral pullwhich provided a solution to manage the thermal expansions. NystrΦm PR et al. [9] used newmethods (low density concrete coating, trigger berms, rock carpets) to reduce critical bucklingload and hence also reduce the requirement for seabed intervention. The King project has madea number of significant innovations in subsea pipeline design including the heated pipe-in-pipesystem and the sleeper scheme et al. novel methods to control thermal buckling [10]. DavidBruton et al. [11] evaluated how buckles form and outlined the key parameters that contribute tobuckling process. Snaked-laying and sleeper have been used on a number of projects over recentyears. For example, snaked-laying was adopted in the 16/22 Penguin PIP [12] and the Echo Yodelproject [13], sleepers were used in the 42 Asgard Transport [9] and 8/12 King PIP [10]. But forthe above studies, shapes of snaked-lay pipelines are all arc line. Besides, snaked-lay method andsleeper method are used independently.

The method of triggering buckling at pre-determined location along pipeline is an effectivemethod to control global buckling of pipelines. The key of snaked-lay method is to trigger buckleat pre-determined locations along the pipeline, and control post-buckling of pipeline. Then itis very important to reduce critical buckling force effectively. Based on studies of snaked-laypipeline, a new shape of snaked-lay pipeline is presented, control criteria of offset angle is alsopresented.

2 Snaked-lay Method

2.1 Snaked-lay Shape

The main purpose of installing deliberate horizontal lay imperfections is to trigger a sufficientnumber of thermal buckles at pre-determined locations along the pipeline so that the thermalexpansion is distributed among a number of buckles rather than being concentrated at a fewbuckle sites. Compared to other means of controlling buckling, i.e. such as installation of triggerstructures, the main benefit of snake lay is that it is inexpensive.

Y. Liu et al. / Journal of Information & Computational Science 9: 12 (2012) 3315–3324 3317

Fig. 1 presents a typical lateral snaked-lay configuration. It can be seen that straight andcurved pipeline are included in snaked-lay pipeline.

2.1.1 Arc Shape of Snaked-lay Pipeline

In engineering the cured section of snaked-lay pipeline is arc curve [6, 7], the relationship betweenthe arc length, pipelay offset angle and radius is shown in Fig. 2 and is expressed by Equation(1) below.

Larc = Rθ, (1)

where Larc is Arc Length, R is Bend Radius, θ is Offset Angle.

Curved section

Straight section

Fig. 1: Shape of snaked-lay pipeline

RR

y

x

Offset angleθ

θ

2

θ

θ

2

Fig. 2: Arc shape of snaked-lay pipeline

2.1.2 Sine Shape of Snaked-lay Pipeline

The new shape of snaked-lay pipeline is applied in the shape of sine curve as shown in Fig. 3. Therelationship between the sine length, pipelay offset angle and radius is expressed by Equation (2)below:

y0 = w0sin(π/2− πx/L0), (2)

where y0 is the initial y coordinated of arbitrary point located at coordinate x along snaked-laypipeline, w0 is amplitude of y coordinated located at coordinate x along snaked-lay pipeline, L0

is the sine length.

In Fig. 3, lay radius, sine length and offset angle of snaked-lay pipeline satisfy the followingrelationship:

sin(θ/2) = L0/(2R). (3)

From Equation (2), the following expression can be obtained:

tan(θ/2) = πw0/L0. (4)


y

x

RR

L0

w0

Offset angle

θ

θ

θ

2θ

2

Fig. 3: The new shape of snaked-lay pipeline

Sine 200/1000

Arc 200/1000

Am

plitu

de

alon

g pip

elin

e/m

8

4

0

−4

−8

−12

−160 50 100

Length along pipoeline/m150 200 250

Fig. 4: Shape of snaked-lay pipeline

2.2 Finite Element Analysis

2.2.1 Constitutive Relationship of Material

The material behavior of pipe steel is defined by Ramberg-Osgood model [14]. The stress-strainconstitutional relationship is shown in Fig. 5. The expression of the Ramberg-Osgood model isexpressed by Equation (5).

εx =σx

E0

[1 +

n

1 + r

(σx

σy

)r], (5)

where εx and σx are the engineering strain and stress, E0 is the initial Youngs modulus, σy is theyield stress of pipe material, n and r is the yield stress of pipe material.

6.00E+08

5.00E+08

4.00E+08

3.00E+08

2.00E+08

1.00E+08

0.00E+00

σx

εx

0 0.025 0.050 0.075 0.010

Fig. 5: Stress-strain relationship for X65 pipeline steel

Non-linear ideal elasto-plastic soil axial and lateral friction behavior was modeled using theCOMBIN39 spring element [15-17], as Fig. 6 shows. As only lateral buckling is of interest inthis paper, the seabed was modeled as a flat seabed ignoring spanning parts of the pipeline.The pipeline was pinned in the vertical direction at each pipe node. The force-displacementrelationship is illustrated in Fig. 7. The relationship between yield force, friction coefficient andsubmerged weight along pipeline per unit can be expressed as:

F = µW, (6)


where F is yield force, µ is friction coefficient between seabed and pipeline, W is submergedweight along pipeline per unit.

z

x

y

Fig. 6: Pipeline-soil interaction model

Force

Loading

Loading

Unloading

Unloading Deformation

FLy

−FLy

−∆Ly

∆Ly

Fig. 7: Force-displacement relationship

2.2.2 Finite Element Model of Pipeline

Based on ANSYS, nonlinear finite element model of pipeline was built in this paper. The pipelinewas modeled with Pipe20 element, which are able to capture nonlinear elasto-plastic materialbehavior. Interaction between seabed and pipeline was modeled using COMBIN39 spring element[15-18]. FEM of pipeline is shown in Fig. 8.

x

y

z

Fig. 8: Pipeline finite element model

Computation example of Ref. [7] is simulated in this section. lay radius R=900 m, L0=8 m,16 m, 31.4 m, 62.8 m, other parameters are shown in Table 1, and pipeline finite element modelis shown in Fig. 7. Comparison of critical buckling forces are shown in Table 2, As Table 2 shows,the discrepancy is within 4%, then pipeline finite element model is verified.

2.3 Sensitive Factors Study

2.3.1 Comparison Between Two Snaked-pipeline Shapes

Comparison between arc shape and sine shape of pipeline is studied. Out diameter of pipeline is0.814 m, pipe thickness is 0.0254 m, lateral friction coefficient between seabed and pipeline is 0.87,lateral friction coefficient is 0.5, pipe length is 1000 m, lay radius R=1000 m, sine length=400 m.

Comparison between two snaked-lay shapes is shown in Table 3. As Table 3 shows, comparedwith arc shape, for maximum moment of sine shape, 21.7% is reduced; and for total axial strain,19.9% is reduced; for critical buckling force 28.81% is reduced too. Namely, compared with arc


Table 1: Parameters of pipeline

Parameter Units V alue

Outside diameter mm 508

Submerged weight kN/m 2.1

Peak axial friction mobilization distance mm 10

Peak axial friction factor - 0.6

Residual axial friction mobilization distance mm 2000

Residual axial friction factor - 0.6

Peak lateral friction mobilization distance mm 140

Peak lateral friction factor - 1.1

Residual lateral friction mobilization distance mm 990

Residual lateral friction factor - 0.6

Table 2: Comparison of critical buckling force

Offset angle/◦ Results of paper/KN Results of FEA/KN Reduced/%

0.5 3250 3201 1.53

1.0 2650 2558 3.60

2.0 2050 1966 2.71

4.0 1750 1738 0.69

Table 3: Comparison between two snaked-lay shapes

Sine curve Arc curve Reduced/%

Maximum moment 3.69MN.m 5.06MN.m 21.7

Total axial strain 1.6110−3 2.0110−3 19.9

Critical buckling force/N 2.1MN 2.95MN 28.81

shape, critical buckling force of sine shape is lower, and buckle is triggered more easily. On theother hand, post-buckling of pipeline is controlled well. When lay radius is fixed, effect of arclength on maximum moment is illustrated in Fig. 9. As Fig. 9 shows, for arc length exceeding 200m, there is no further reduction in the resulting bending moment. But for sine shape, moment andstrain of post-buckling are all reduced evidently compared with arc shape. On the other hand,critical buckling force is also reduced obviously. So for sine shape, buckle at pre-determinedlocation along pipeline is triggered easily rather than un-determined location.

2.3.2 Effect of Sine Length on Critical Buckling Force

Fig. 10 is effect of sine length on critical buckling force. As Fig. 10 shows, when lay radius isfixed, critical buckling force of pipeline is reduced with sine length increasing. But for sine lengthexceeding 100 m, there is no further reduction in the resulting bending moment. But for a fixedsine length, critical buckling is increased with lay radius increasing.

When offset angle is fixed, effect of sine length on critical buckling is illustrated in Fig. 11. Itcan be seen that, when offset angle is fixed, critical buckling force is increased with sine length


increasing.

50100150200250300350400450500

0

7.E+6

6.E+6

5.E+6

4.E+6

3.E+6

2.E+6

1.E+6

0.E+630 60 90 120 150

Temperature (°C)

Max

imum

mom

ent

(Nm

)50100150200250300350400450500

Fig. 9: Temperature-maximum moment curve

7E+6

6E+6

5E+6

4E+6

3E+6

2E+6

1E+6

0E+0Cri

tica

l buck

ling

forc

e/N R=700m

R=1000mR=1300m

0 100 200 300 400 500 600 700 800 900Length along pipeline/m

Fig. 10: Critical buckling force changing with L0

5E+6

4E+6

3E+6

2E+6

2E+5

8E+5

0E+0Cri

tica

l buck

ling

forc

e/N

0 100 200L0/m

300 400

Fig. 11: Critical buckling force (θ=11.5◦)

2.3.3 Effect of Offset Angle on Maximum Moment

Increasing offset angle has beneficial on reducing moment and plastic strain of post-buckling.Offset angle is studied in this section. The main pipe and soil parameters used in the finiteelement analyses are given in Table 4.

Table 4: Parameters

Outside Diameter/m Inner Diameter/m D/t Submerged Weight/N/m Design Temperature/◦C

0.3 0.272 21 900 120

0.814 0.7632 32 3386 120

0.55 0.524 42 1500 120

The effect of offset angle on maximum moment is illustrated in Fig. 12-Fig. 14, where themaximum moment as a function of sine length. As Fig. 12-Fig. 14 show, maximum moment of


6.00E+05

5.00E+05

4.00E+05

3.00E+05

2.00E+05

1.00E+05

0.00E+00Max

imum

mom

ent/

Nm

0 100 200 300 400 500 600 700 800

Since length/m

29°

19.2°

14.4°

11.5°

9.6°

8.2°

5.7°

3.8°

Allowablemoment

29°

19.2°

14.4°

11.5°

9.6°

8.2°

5.7°

3.8°

Allowable

Fig. 12: Maximum moment (D/t=21)

7.00E+06

6.00E+06

5.00E+06

4.00E+06

3.00E+06

2.00E+06

1.00E+06

0.00E+00

Max

imum

mom

ent/

kN

m

0 100 200 300 400 500 600 700 800Since length/m

29°

19.2°

14.4°

11.5°

9.6°

8.2°

7.2°

5.7°

3.8°

Allowable moment

29°

19.214.411.59.6°

8.2°

7.2°

5.7°

3.8°

Allo


1.80E+061.60E+061.40E+061.20E+061.00E+068.00E+056.00E+054.00E+052.00E+050.00E+00M

axim

um

mom

ent/

Nm

0 100 200 300 400 500 600 700 800Since length/m

29°

19.2°

14.4°

11.5°

9.6°

8.2°

5.7°

3.8°

Allowable moment


post-buckling is reduced with offset angle increasing. As offset angle is smaller than 11.5◦, fora fixed offset angle, changing sine length and snaked-lay radius have little effect on maximummoment of post-buckling of pipeline. However, as offset angle is not smaller than 11.5◦, maxi-mum moment is reduced obviously with offset angle increasing. Besides, for a fixed offset angle,maximum moment is increasing after falling with sine length increasing. It can be seen fromabove analysis that maximum moment of post-buckling is well controlled when offset angle is notsmaller than 11.5◦. Then offset angle can be selected as following:

11.5◦ ≤ θ. (7)


3 Conclusions

A new shape of snaked-lay pipeline is presented, sensitivity analyses show that critical bucklingis reduced with sine length increasing when lay radius is fixed, but when sine length exceeding acertain value, there is no further reduction in resulting critical buckling force; when offset angle< 11.5◦, no further maximum moment reduction is achieved changing sine length/lay radius;selection criteria of offset angle is: θ≥11.5◦, and the upper limit should be determined accordingto engineering.

References

[1] A. M. Costal, C. A. Cardoso, Soil-structure interation of heated pipeline buried in soft clay,Proceedings of the 4th International Pipeline Conference, 2002, Calgary, Alberta, Canada, IPC02-27193

[2] R. E. Hobbs, In-service buckling of heated pipelines, Journal of Transportation Engineering, ASCE,110, 1984, 175-189

[3] N. Taylor, V. Tran, Experimental and theoretical studies in subsea pipeline buckling, MarineStructures, 9, 1996, 211-257

[4] James G. A. Croll, A simplified model of upheaval thermal buckling of subsea pipelines, Thin-Walled Structures, 29, 1997, 59-78

[5] Jiong Guan, Per R. NystrΦm, Hans F. Hansen, Optimized solutions to control lateral buckling ofpipelines with snaked-lay: Theoretical and numerical studies, Proceedings of the 26th InternationalConference, 2007, San Diego, California, USA, OMAE2007-29256

[6] J. O. Rundsag et al., Optimized snaked lay geometry, Proceedings of the 8th International Offshoreand Polar Engineering Conference, 2008, 27-33, Vancouver, BC, Canada

[7] A. D. Rathbone, K. TΦrnes, G. Cumming et al., Effect of lateral pipelay imperfections on globalbuckling design, Proceedings of the 8th International Offshore and Polar Engineering Conference,2008, 224-232, Vancouver, BC, Canada

[8] L. Kien et al., Design of high temperature/high pressure pipeline against lateral buckling, AsianPipeline Conference Exhibition, 27th-28th September, 2005, 2-14, Kuala Lumpur

[9] P. R. NystrΦm, K. TΦrnes, J. S. Karlsen, G. Endal et al., Design of the asgard transport gas trun-kline for thermal buckling, Proceedings of the 11th International Offshore and Polar EngineeringConference, 2001, 7-17, Stavanger, Norway

[10] G. E. Harrison, M. S. Brunner, D. A. S. Bruton, King flowlines-thermal expansion design andimplementation, Offshore Technology Conference, 2003, Houston, Texas, USA

[11] David Bruton, Malcolm Carr, Michael Crawford et al., The safe design of hot on-bottom pipelineswith lateral buckling using the design guideline developed by the SAFEBUCK joint industryproject, Deep Offshore Technology Conference, 2005, Vitoria, Espirito Santo, Brazil

[12] I. Matheson, M. Carr, R. Peek, P. Saunders, N. George, Penguins flowline lateral buckle formationanalysis and verification, Proceedings 23th International Conference on Offshore Mechanics andArctic Engineering, 2007, Vancouver, OMAE2004-51202

[13] M. Wagstaff, Detailed design and operational performance assessment of pipeline buckle initiatorsto mitigate lateral buckling, Petromin Pipeline Conference, 2003, Singapore

[14] W. Ramberg, W. R. Osgood, Description of Stress-Strain Curvesby Three Parameters, NACATechnical Note, 1943


[15] Enrico Torselleti, Luigino Vitali, Erik Levold, Snaking of submarine pipelines resting on flat seabottom using finite element method, Proceedings of the 9th International Offshore and PolarEngineering Conference, 1999, 34-44, Brest, France

[16] Yong Bai, Qiang Bai, Subsea Pipelines and Risers, Elsevier Science Ltd, 2005, 41-61

[17] Lars Christensen, Displacement control in lateral buckling of “short” pipelines, Proceedings of the15th International Offshore and Polar Engineering Conference, 2005, 84-92, Seoul, Korea

[18] Nader Yoosef-Ghodsi, Analysis of Buried Pipelines with Thermal Applications, Canada: Universityof Alberta, 2002

Documents

2012_9_12_3315_3324