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International Journal of Mechanical Sciences 50 (2008) 1058– 1064

Contents lists available at ScienceDirect

International Journal of Mechanical Sciences

0020-74

doi:10.1

� Corr

E-m

journal homepage: www.elsevier.com/locate/ijmecsci

Integral buckle arrestors for offshore pipelines: Enhanced design criteria

L.-H. Lee a, S. Kyriakides a,�, T.A. Netto b

a Research Center for Mechanics of Solids, Structures & Materials, The University of Texas at Austin, WRW 110, Austin, TX 78712, USAb COPPE-Federal University of Rio de Janeiro, Rio de Janeiro, RJ 91945-970, Brazil

a r t i c l e i n f o

Article history:

Received 19 October 2007

Received in revised form

11 February 2008

Accepted 16 February 2008Available online 29 February 2008

Keywords:

Buckle arrestors

Propagating buckles

Offshore pipelines

03/$ - see front matter & 2008 Elsevier Ltd. A

016/j.ijmecsci.2008.02.008

esponding author. Tel.: +1512 4715963; fax:

ail address: skk@mail.utexas.edu (S. Kyriakide

a b s t r a c t

Integral buckle arrestors are relatively thick wall rings periodically welded in an offshore pipeline at

intervals of several hundred meters in order to safeguard the line in case a propagating buckle initiates.

They provide additional circumferential rigidity and thus impede downstream propagation of collapse,

limiting the damage to the length of pipe separating the two arrestors. The effectiveness of such devices

was studied parametrically through experiments and numerical simulations in Park and Kyriakides [On

the design of integral buckle arrestors for offshore pipelines. International Journal of Mechanical

Sciences 1997;39(6):643–69]. The experiments involved quasi-static propagation of collapse towards an

arrestor, engagement of the arrestor, temporary arrest, and the eventual crossing of collapse to the

downstream pipe at a higher pressure. The same processes were simulated with finite element models

that included finite deformation plasticity and contact. The experimental crossover pressures enriched

with numerically generated values were used to develop an empirical design formula for the arresting

efficiency of such devices. A recent experimental extension of this work revealed that for some

combinations of arrestor and pipe yield stresses, the design formula was overly conservative. Motivated

by this finding, a new broader parametric study of the problem was undertaken, which demonstrated

that the difference between the pipe and the arrestor yield stress affects significantly the arrestor

performance. The original arrestor design formula was then modified to include the new experimental

and numerical results producing an expression with a much wider applicability.

& 2008 Elsevier Ltd. All rights reserved.

1. Introduction

Offshore pipelines are usually protected from a potentialinitiation and propagation of collapse (propagating buckle) bythe installation of buckle arrestors at regular intervals along theline. Buckle arrestors are circumferential stiffeners that aredesigned to stop an incoming propagating buckle and in thismanner limit the extent of damage suffered by the line to thesection between two adjacent arrestors. The integral buckle

arrestor is a device commonly used in deepwater applications. Itconsists of a ring that has the same internal diameter but isthicker than the pipe (see Fig. 1). The rings are welded betweentwo adjacent pipe lengths at intervals of several hundred meters.The effectiveness of integral buckle arrestors was first evaluatedexperimentally by Johns et al. [1]. The concept was furtheranalyzed through a set of 15 full-scale experiments on 4.5-inseamless pipes with D/t of approximately 22 by Park andKyriakides [2] (henceforth referred to as PK). A numerical modelcapable of simulating accurately the buckle propagation, arrest,

ll rights reserved.

+1512 4715500.

s).

and arrestor crossover was developed in the same study.Kyriakides et al. [3] used the experimental results enriched witha set of numerically generated crossover pressures to develop thefollowing empirical design formula for arrestor efficiency (Z) interms of the major geometric and material parameters of the pipeand the arrestor:

Z ¼PX � PP

PCO � PP¼

A1so

E

� �0:5 soa

E

� �0:5 t

D

� �1:25 L

t

� �0:8 h

t

� �2:5

PCO

PP� 1

� � . (1)

Here, PX, known as the crossover pressure, is the pressure at whicha propagating buckle that engages an arrestor quasi-staticallycrosses it; PCO is the collapse pressure of the intact pipe, and PP is itspropagation pressure. D is the diameter of the pipe, t its wallthickness while E and so are the elastic modulus and yield stressof the pipe material. L and h are, respectively, the length andthickness of the arrestor and soa the yield stress of its material.A procedure for using this formula to design integral bucklearrestors is given in [3]. A somewhat different design formulabased on a set of tests on 4.5, 12.75, and 18 in pipes appears in [4].Similar design formulae for other types of arrestors appear in [5](internal ring) and [6] (slip-on). In the present extension of this

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L.-H. Lee et al. / International Journal of Mechanical Sciences 50 (2008) 1058–1064 1059

work new experimental results coupled with results froma broader parametric study conducted numerically are used toenhance the design formula (1).

2. Experiments and motivation

J-lay is a method for installing pipelines to the sea floor in anearly vertical configuration that is preferred for deepwaterapplications. For several of the existing J-lay installation vesselsthe pipe is hung from stiff collars welded at intervals of 160–240 ft(49–73 m). The collars are designed to also serve as bucklearrestors (see [7], Chapter 2) but tend to be shorter than integralbuckle arrestors used on S-lay installed pipelines. This differencemotivated a recent study involving 18 tests on buckle arrestorswith lengths of 0.5D. The tests were performed on 2-in stainlesssteel (SS) 304 seamless tubes with D/ts of approximately 24 and21. The arrestors were machined out of SS-304 solid stock andwelded between sections of tubes 13D (upstream) and 11D

(downstream) long (see Fig. 1). The effectiveness of the arrestorswas measured in the manner described in [2]. A dent was

Fig. 1. Schematic of an integral arrestor welded between two pipe strings.

Table 1Summary of integral arrestor experimental results. Included are tube and arrestor geom

pressures

Exp no. t (in)a D/t Do (%) h/t L/D so (k

1 0.0951 21.01 0.045 2.731 0.5 44.3

2 0.0951 21.01 0.034 2.411 0.5 44.3

3 0.0962 20.76 0.093 2.210 0.5 48.9

4 0.0962 20.75 0.033 2.052 0.5 48.9

5 0.0958 20.83 0.050 1.898 0.5 48.9

6 0.0966 20.02 0.053 1.723 0.5 48.9

7 0.1020 19.60 0.145 1.571 0.5 40.2

8 0.1017 19.65 0.228 1.424 0.5 40.2

9 0.1019 19.66 0.083 1.308 0.5 40.2

10 0.0867 23.10 0.223 1.837 0.5 43.4

11 0.0866 23.09 0.253 1.708 0.5 43.4

12 0.0863 23.19 0.260 1.576 0.5 43.4

13 0.0868 23.03 0.347 1.982 0.5 43.4

14 0.0860 23.24 0.288 1.436 0.5 42.5

15 0.0861 23.25 0.178 2.111 0.5 42.5

16 0.0864 23.13 0.243 1.279 0.5 42.5

17 0.0865 23.11 0.373 2.214 0.5 42.5

18 0.0867 23.06 0.160 2.324 0.5 41.5

a 1 in ¼ 25.4 mm.b 1 ksi ¼ 6.897 MPa.c 14.5 psi ¼ 1 bar.

introduced to the upstream tube in order to initiate collapse.The specimen was pressurized in a stiff pressure vessel undervolume control. Local collapse initiated and subsequently propa-gated quasi-statically towards the arrestor. Collapse was arrested,leading to a gradual increase of the pressure in the system. At apressure PX (crossover pressure), the buckle crossed the arrestorand continued propagating in the downstream tube.

Nine experiments were conducted for each D/t. The pipe andarrestor parameters are listed in Table 1 together with themeasured propagation and crossover pressures. The collapsepressures of the downstream tubes, used to estimate the arrestorefficiencies, were calculated using BEPTICO (PCO). The results spanefficiency values from approximately 0.2 to 1.0. Twelve of thearrestors were crossed by the flattening mode ( , see Fig. 2a) andsix by the flipping mode ( , Fig. 2b).

Fig. 3 shows the PK data plotted against Eq. (1). For Zp0.7 thedata fall along a linear trajectory with a slope (A1) of 6.676. ForZ40.7 the data exhibit significant scatter and so a linear lowerbound was constructed for use in the design as shown in thefigure [3]. Interestingly, the value of Z ¼ 0.7 separated thearrestors that were crossed by the flattening mode (lower than0.7) and those crossed by the flipping mode (larger than 0.7). Thefigure includes 18 new data points. The data with Zp0.7 fall nicelyalong a linear trajectory with a slope of 13.04 (R2

¼ 0.9146); inother words, the new arrestors are ‘‘stiffer’’ than the ones in PK.Furthermore, data with Z40.7 are also in reasonable agreementwith this linear fit albeit with somewhat larger scatter. The sixcases with a flipping mode, marked in the figure with ‘‘ ’’, are allabove Z40.7 but now this efficiency level is no longer theboundary separating the two modes.

Comparing the PK experimental and numerical data with thepresent ones, the following trends can be observed. In the PK data,most of the arrestors had yield stresses that were comparable toor were the same as those of the pipes, while in some cases thearrestor yield stress was significantly lower than that of the pipe.On the contrary, in the present results the arrestor material had ayield stress of 95.5 ksi (659 MPa) while the pipe yield stresses

etric and material parameters, and measured collapse, propagation, and crossover

si)b PP (psi)c PX (psi)c Mode PCO (psi)c Z

3 812 3287 3729 0.8485

3 820 3144 3763 0.7897

2 870 3089 3612 0.8093

2 880 3264 3750 0.8307

2 885 2682 3683 0.6422

2 885 2488 3726 0.5642

7 895 2243 3482 0.5211

7 887 1940 3360 0.4258

7 902 1689 3574 0.2945

7 608 2069 2595 0.7353

7 614 1677 2569 0.5437

7 612 1367 2543 0.3910

7 605 2383 2498 0.9392

5 594 1194 2507 0.3136

5 587 2419 2607 0.9069

5 612 1045 2568 0.2214

5 615 2481 2463 1.0097

6 612 2273 2751 0.7765

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Fig. 2. Photographs of (a) the flattening and (b) the flipping modes of arrestor crossover.

0.2

0.4

0.6

0.8

1

Fit

Lower Bound Envelope

KPN-1997

Present Results (D/t)

Fit

L.-H. Lee et al. / International Journal of Mechanical Sciences 50 (2008) 1058–10641060

ranged between about 40 and 48 ksi (276–331 MPa, see Table 1).Thus, the apparent ‘‘stiffer’’ performance of the new data is at leastpartly due to the arrestors having twice the yield stress of the pipes.Such a large difference between the arrestor and pipe yield stresseswas not considered previously. Kyriakides et al. [3] finished theirrecommended design procedures by pointing out that ‘‘ylike allempirical expressions of results of complex phenomena, Eq. (1)(present number) can be a dependable tool provided that theparameters of the arrestor and pipe being designed do not deviatesignificantly from the range of data used to generate it. If theproblem parameters deviate significantly from those of the presentdatabase, new dependable data must be added to it and a new fitshould be attemptedy’’. Clearly, the new results fall outside therange of applicability of Eq. (1). Motivated by this, a new parametricstudy is undertaken that will be used together with the newexperimental data to extend the design formula.

00 0.1 0.2 0.3 0.4 0.5 0.6

23 20

ht

oaE

1.25 2.5

Lt

tD

PCOPP

- 1

0.5 0.8

oE

0.5

x 100

Fig. 3. Arrestor efficiency plotted against empirical function of pipe and arrestor

parameters from [3]. Included are new experimental results that show a higher

performance.

3. Parametric study of arrestor efficiency

A FE model for simulating the quasi-static buckle propagation,its arrest by an integral arrestor and its eventual crossing of thearrestor at a higher pressure was first developed by Park andKyriakides [2]. This framework as modified in [8] was adopted inthe present study (same symmetries, slightly different mesh, useof hydrostatic fluid elements to pressurize the system). Typicallengths of the upstream and downstream sections of pipe were7.5D and 5D, respectively. Results from two sample simulations oftwo experiments in Table 1 are shown in Figs. 4 and 5. Theycorrespond to Exp. 5 and 2, respectively, and are based on theparameters given in Table 1. Fig. 4a shows the calculated pressure-change in volume (P�du) response for the parameters of Exp. 5while Fig. 4b displays the initial and six deformed configurationscorresponding to the numbered bullets marked on the response.The first pressure maximum corresponds to the initiation ofcollapse caused by a local imperfection in the neighborhoodof the plane of symmetry on the LHS. The collapse is seen in

configuration A to localize, leading to first contact of the walls inconfiguration B. Subsequently, collapse propagates at the pipepropagation pressure as illustrated in configuration C. Eventuallythe arrestor is engaged, collapse is halted (see D) and the pressurein the system increases, reaching a maximum value of 2752 psi(189.8 bar). This represents the crossover pressure of this arrestor.In the corresponding experiment the crossover pressure was2682 psi (185.0 bar) which is 2.6% lower. The arrestor flattened,allowing some ovality to be passed on to the downstream pipecausing it to collapse as illustrated in configuration F.

ARTICLE IN PRESS

0

0.2

0.4

0.6

0.8

0 0.1 0.2 0.3 0.4 0.5

= 20.83D t

PPCO

SS 3040

12 3

4

5

6

/ o

PPExp. 5

= 0.05%

PX

Fig. 4. (a) Calculated pressure-change in volume response for Exp. 5 and (b)

corresponding sequence of deformed configurations that illustrate the flattening

mode of crossover.

0

0.2

0.4

0.6

0.8

0 0.1 0.2 0.3 0.4 0.5

= 21.01Dt

P

PCO

SS 3040

12 3

4

5

6

/ o

PP

= 0.034%

PX

Exp. 2

Fig. 5. (a) Calculated pressure-change in volume response for Exp. 2 and (b)

corresponding sequence of deformed configurations that illustrate the flipping

mode of crossover.

L.-H. Lee et al. / International Journal of Mechanical Sciences 50 (2008) 1058–1064 1061

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L.-H. Lee et al. / International Journal of Mechanical Sciences 50 (2008) 1058–10641062

Figs. 5a and b show corresponding results for a thicker arrestorwith higher crossover pressure (simulation of Exp. 2). The basicevents are very similar but the crossover pressure is now 3214 psi(226.6 bar), which is very close to the experimental value of3144 psi (216.8 bar). The main difference is that, in concert withthe experiment, this arrestor was crossed by the flipping modethat is clearly illustrated in configuration F of Fig. 5b. Thickerarrestors are more difficult to flatten; instead their walls deformin a manner that causes the opposite ends to ovalize at 901 to eachother. In this manner, stretching of the ring generators isminimized [2,9]. Some reverse ovalization is passed on to thedownstream tube, causing the 901 switch in its collapse mode.

This high level of performance by the model was repeated in atotal of nine one-to-one simulations of the experiments in Table 1(as indeed was the case for all simulations of experimentsperformed in [2,8]). The model was then used to extend theparametric study of the problem. The parametric study of PKinvolved X65 pipes with D/ts of 17, 22.5, and 34 (PK, Figs. 12and 19) and arrestors of the same material with various lengthsand thicknesses. In the current extension the pipes analyzed hadD/t ¼ 22.5, the arrestor length was kept at L ¼ 0.5D, while theyield stresses of the pipe and arrestors were varied independently.In the new calculations, the hardening characteristics of thestress–strain responses used were kept the same as those of theX65 material of PK (Ramberg–Osgood hardening exponent (n) of10.7 up to a strain of 8%); the elastic limit was however varied toachieve various values of yield stress (so and soa). In this manner,results for several combinations of pipe and arrestor yield stresseswere generated that are listed in Table 2. For each (so,soa)combination several arrestor thicknesses were considered that arelisted in the same table.

Each calculation provides the pipe propagation [12] and thearrestor crossover pressures, which are listed in Table 2. Thecollapse pressure of the downstream pipe of each model wasevaluated separately using the custom numerical model BEPTICO[10] and an initial ovality (Do) of 0.1% (PCO in Table 2). Using thesethree pressures arrestor efficiencies are evaluated using the firstpart of Eq. (1). The resultant efficiencies are plotted in Fig. 6against the following parameter:

t

D

� �1:25 L

t

� �0:8 h

t

� �2:5,

PCO

PP� 1

� �. (2)

This expression includes the three geometric non-dimensionalvariables of Eq. (1) but excludes the two material ones. For clarity,the results of each material combination are plotted with adifferent symbol and are identified by three numbers thatrepresent the following (s0o : s

0oa � D=t) (yield stresses are in ksi;

s0o is the stress at a strain of 0.5% and consequently is slightlydifferent from so, the stress at a strain offset of 0.2%, in Table 2).Included are all the numerical results of PK identified as(65:65-XX) as well as the new experimental results from Table 1plotted with open circles and squares (J, &). Results for efficiencylevels higher than 0.8 are excluded and consequently the data foreach yield stress combination are seen to fall along a nearly lineartrajectory (a linear fit of each set is included).

The (65:65-XX) data fall along a nearly linear path with anintermediate slope (linear fit drawn in red). Interestingly, the newresults for (52:52–22.5) and (75:75–22.5) fall in line with this setof data. We now let the yield stress of the pipe stay constant at75 ksi and consider arrestors with progressively lower yieldstresses such as (75:65–22.5), (75:52–22.5), and (75:42–22.5).Each set of data falls on a nearly linear trajectory with aprogressively decreasing slope. Next we consider several caseswhere the arrestor yield stress is progressively higher than that ofthe pipe. Thus for (75:95–22.5), the data fall along a linear path

with higher slope than the equal yield stresses results,the (65:95–22.5) data have an even higher slope, and the(52:95–22.5) data have the highest slope exhibited by thenumerical results. Clearly, the results demonstrate that the ratioof the two yield stresses influences significantly the performance ofthe arrestor. Indeed, the performance is seen to increase ifthe arrestor yield stress is higher than that of the pipe, with theincrease being more significant as the difference between thearrestor and pipe yield stresses becomes larger. The experimentaldata of Table 1 had an even larger difference between the two yieldstresses than those of the parametric study and consequently theyfall along a stiffer trajectory than the numerical results.

4. Updated design equation

The new experimental and numerical results are now usedtogether with the ones of PK to update the empirical designformula of Kyriakides et al. [3] for integral arrestors. Theprocedure used is based on dimensional analysis, is similar tothat in [3] and will not be repeated here. The much broadervariation of parameters conducted and the much larger data setdeveloped (145 sets of data) make the approximation of theefficiency with a product of powers of the major non-dimensionalparameters more difficult. Once again, the fitting will be based onresults that produced efficiencies Zp0.7. The expression thatyielded the best fit of the data is as follows:

Z ¼A1

E

so

� �0:65 soa

E

� �0:95 t

D

� �1:25 L

t

� �0:8 h

t

� �2:5

PCO

Pp� 1

� � . (3)

In other words, the powers of the two material parametervariables are different from those of the original formula (Eq. (1)).The efficiency plotted against the function on the RHS of Eq. (3) isshown in Fig. 7. The data for Zp0.7 is seen to fall along a nearlylinear path while for Z40.7 the data exhibit the wide scatter seenin the original fit. The plot includes a best linear fit of the data forZp0.7, which has a slope of 9.541 (A1) with a correlationcoefficient of R2

¼ 0.941. Because the data exhibit some scatter,a conservative design could be based on a lower bound linear fitinstead in which case the slope is reduced to A1 ¼ 7.96. For Z40.7in both cases we recommend that a lower bound of the data inFig. 7 be used such as the one drawn in the figure. Finally, theintegral arrestor data of [4] plotted according to Eq. (3) fallsomewhat above the linear fit for Zp0.7. Because of the age of thisdata, finding a reason for this higher performance is difficult.However, the present fit remains a conservative option withregard to that set of data.

The reader is reminded that the practically relevant issue of theperformance of integral arrestors under dynamic buckle propaga-tion was addressed in [8,11], where it was shown that dynamicsenhances the arresting performance of such devices. Conse-quently, design based on quasi-static results, such as the onepresented here, tends to be conservative. The procedure for usingthis formula to design integral arrestors, including limits onarrestor length and choice of safety factors, remains the same as in[3]. Once again, we reiterate that despite the much widerparametric study on which the updated formula of efficiencyEq. (3) depends, the user should be aware that the formula isdependable provided the parameters of the pipe and arrestor fallwithin the ranges of the parameters of the data used in this study.Finally, as we have always recommend for such complexproblems, once the formula is used to design an arrestor for aparticular pipeline, the design should be proven by a numericalarrestor crossover simulation and/or by a full-scale test.

ARTICLE IN PRESS

Table 2Calculated propagation, crossover, and collapse pressures, and arrestor efficiencies

(D/t ¼ 22.5, L/D ¼ 0.5)

h/t so (ksia) soa (ksia) PX (psib) Mode Z

(a) PP ¼ 1080 psi; PCO ¼ 5060 psi

1.25 74.84 94.45 1472 0.0985

1.50 74.84 94.45 1776 0.1749

1.75 74.84 94.45 2118 0.2608

2.00 74.84 94.45 2501 0.3570

2.25 74.84 94.45 3173 0.5259

2.50 74.84 94.45 3901 0.7088

2.75 74.84 94.45 4121 0.7641

3.00 74.84 94.45 4012 0.7367

2.00 74.84 74.84 2255 0.2952

2.25 74.84 74.84 2705 0.4083

2.50 74.84 74.84 3319 0.5626

2.75 74.84 74.84 3994 0.7322

3.00 74.84 74.84 4117 0.7631

(b) PP ¼ 881 psi; PCO ¼ 5289 psi

1.50 67.06 94.04 1549 0.1515

1.75 67.06 94.04 1892 0.2294

2.00 67.06 94.04 2488 0.3646

2.25 67.06 94.04 3163 0.5177

2.50 67.06 94.04 3811 0.6647

2.75 67.06 94.04 4398 0.7979

3.00 67.06 94.04 4378 0.7933

2.00 67.06 67.06 1868 0.2239

2.25 67.06 67.06 2396 0.3437

2.50 67.06 67.06 2941 0.4673

2.75 67.06 67.06 3459 0.5848

3.00 67.06 67.06 3952 0.6967

(c) PP ¼ 839 psi; PCO ¼ 3257 psi

1.25 49.03 94.45 1332 0.1998

1.50 49.03 94.45 1620 0.3230

1.75 49.03 94.45 2013 0.4855

1.88 49.03 94.45 2295 0.6022

2.00 49.03 94.45 2628 0.7399

2.25 49.03 94.45 3104 0.9367

2.50 49.03 94.45 2870 0.8400

2.75 49.03 94.45 2936 0.8672

3.00 49.03 94.45 3023 0.9032

1.25 49.03 49.03 1077 0.0984

1.50 49.03 49.03 1288 0.1857

1.75 49.03 49.03 1503 0.2746

2.00 49.03 49.03 1734 0.3701

2.25 49.03 49.03 2133 0.5352

2.50 49.03 49.03 2566 0.7142

2.75 49.03 49.03 3070 0.9227

3.00 49.03 49.03 2918 0.8598

(d) PP ¼ 977 psi; PCO ¼ 4314 psi

1.25 62.90 94.45 1407 0.1289

1.50 62.90 94.45 1706 0.2185

1.75 62.90 94.45 2044 0.3197

2.00 62.90 94.45 2559 0.4741

2.25 62.90 94.45 3212 0.6698

2.50 62.90 94.45 3963 0.8948

2.75 62.90 94.45 3488 0.7525

3.00 62.90 94.45 3534 0.7663

2.00 62.90 62.90 2023 0.3135

2.25 62.90 62.90 2449 0.4411

2.50 62.90 62.90 2977 0.5993

2.75 62.90 62.90 3555 0.7726

3.00 62.90 62.90 3656 0.8028

(e) PP ¼ 1080 psi; PCO ¼ 5060 psi

2.00 74.84 62.90 2111 0.2590

2.25 74.84 62.90 2423 0.3374

2.50 74.84 62.90 2960 0.4724

Table 2 (continued )

h/t so (ksia) soa (ksia) PX (psib) Mode Z

2.75 74.84 62.90 3528 0.6151

3.00 74.84 62.90 4173 0.7771

2.00 74.84 49.03 1952 0.2191

2.50 74.84 49.03 2571 0.3746

2.75 74.84 49.03 3059 0.4972

3.00 74.84 49.03 3592 0.6312

3.25 74.84 49.03 4121 0.7641

2.50 74.84 39.18 2272 0.2995

2.75 74.84 39.18 2678 0.4015

3.00 74.84 39.18 3096 0.5065

3.25 74.84 39.18 3575 0.6269

3.50 74.84 39.18 4047 0.7455

a 1 ksi ¼ 6.897 MPa.b 14.5 psi ¼ 1 bar.

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8

h t

1.25 2.5Lt

tD

PCOPP

- 10.8

42:95-2344:95-2052:52-22.552:95-22.565:65-1765:95-22.575:65-22.575:52-22.575:75-22.575:95-22.565:65-22.565:65-3475:42-22.5

'o: 'oa -D/t

Fig. 6. Arrestor efficiency as a function of problem geometric parameters for

various combinations of pipe and arrestor yield stresses.

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5 0.6

42:95-2344:95-20E-PK-2252:52-22.552:95-22.565:65-22.565:95-22.568:68-22.568:94-22.575:75-22.575:95-22.565:65-1765:65-3475:65-22.575:52-22.575:42-22.5

Lower Bound Envelope

Fit

h t

oa E

1.25 2.5

Lt

tD

PCOPP

- 1

0.95 0.8

E0.65

R2 = 0.9409 ( < 0.7)

A1 = 9.5411

o

Fig. 7. Arrestor efficiency vs. empirical function of parameters and fits recom-

mended for design.

L.-H. Lee et al. / International Journal of Mechanical Sciences 50 (2008) 1058–1064 1063

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L.-H. Lee et al. / International Journal of Mechanical Sciences 50 (2008) 1058–10641064

5. Summary and conclusions

The problem of arrest of a propagating buckle in a long pipelineby a relatively short thicker wall ring welded into the line (integralbuckle arrestor) was studied through experiment and analysis byPark and Kyriakides [2]. The experimental crossover pressuresenriched with numerically generated values were used to developa formula for the arresting efficiency of such devices. The presentpaper presents experimental results that show that for somecombinations of arrestor and pipe yield stresses the formulagenerated was overly conservative. Motivated by this finding, anew broader parametric study of the problem was undertakenusing large-scale numerical simulations of the process. The resultsdemonstrated that the difference between the pipe and arrestoryield stress affects significantly the arrestor performance. The newexperimental and numerical results were then combined with theoriginal results to generate a new expression for arrestingefficiency with a much wider applicability.

Acknowledgments

The work reported was conducted with financial support froma consortium of industrial sponsors under the project StructuralIntegrity of Offshore Pipelines, while the work of TAN was alsosponsored by Brazil’s CNPq. The financial support is acknowl-edged with thanks. The authors are also grateful to Petrobras forsponsoring the new experiments.

References

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[2] Park T-D, Kyriakides S. On the design of integral buckle arrestors foroffshore pipelines. International Journal of Mechanical Sciences 1997;39(6):643–69.

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