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11 February 2008

Accepted 16 February 2008Available online 29 February 2008

Buckle arrestors

Propagating buckles

Offshore pipelines

re

d m

rcum

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

protecpse (

analyzed through a set of 15 full-scale experiments on 4.5-in

hichically

thickness while E and so are the elastic modulus and yield stress

ARTICLE IN PRESS

Contents lists availab

els

of

International Journal of Mechanical Sciences 50 (2008) 10581064based on a set of tests on 4.5, 12.75, and 18 in pipes appears in [4].seamless 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,

of 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 formula

Similar design formulae for other types of arrestors appear in [5](internal ring) and [6] (slip-on). In the present extension of this

Corresponding author. Tel.: +15124715963; fax: +15124715500.

E-mail address: [email protected] (S. Kyriakides).0020-74

doi:10.1The effectiveness of integral buckle arrestors was rst evaluatedexperimentally by Johns et al. [1]. The concept was further

crosses it; PCO is the collapse pressure of the intact pipe, and PP is itspropagation pressure. D is the diameter of the pipe, t its wallconsists 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.

PP

Here, PX, known as the crossover pressure, is the pressure at wa propagating buckle that engages an arrestor quasi-statthe 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 bucklearrestor is a device commonly used in deepwater applications. It

terms of the major geometric and material parameters of the pipeand the arrestor:

Z PX PPPCO PP

A1

soE

0:5 soaE

0:5 tD

1:25 Lt

0:8 ht

2:5PCO 1 . (1)1. Introduction

Offshore pipelines are usuallyinitiation and propagation of colla03/$ - see front matter & 2008 Elsevier Ltd. A

016/j.ijmecsci.2008.02.008Sciences 1997;39(6):64369]. 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 nite element models

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

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

efciency 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 nding, a new broader parametric study of the problem was undertaken, which demonstrated

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

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

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

& 2008 Elsevier Ltd. All rights reserved.

ted from a potentialpropagating buckle) by

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 efciency (Z) inKeywords:Integral buckle arrestors for offshore pi

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

a Research Center for Mechanics of Solids, Structures & Materials, The University of Texb 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

a b s t r a c t

Integral buckle arrestors a

intervals of several hundre

They provide additional ci

journal homepage: www.

International Journalll rights reserved.lines: Enhanced design criteria

t Austin, WRW 110, Austin, TX 78712, USA

relatively thick wall rings periodically welded in an offshore pipeline at

eters in order to safeguard the line in case a propagating buckle initiates.

ferential rigidity and thus impede downstream propagation of collapse,

le at ScienceDirect

evier.com/locate/ijmecsci

Mechanical Sciences

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 oor in anearly vertical conguration that is preferred for deepwaterapplications. For several of the existing J-lay installation vesselsthe pipe is hung from stiff collars welded at intervals of 160240 ft(4973m). 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

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 arrestorefciencies, were calculated using BEPTICO (P^CO). The results spanefciency values from approximately 0.2 to 1.0. Twelve of thearrestors were crossed by the attening mode ( , see Fig. 2a) andsix by the ipping 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 signicant scatter and so a linear lowerbound was constructed for use in the design as shown in thegure [3]. Interestingly, the value of Z 0.7 separated thearrestors that were crossed by the attening mode (lower than0.7) and those crossed by the ipping mode (larger than 0.7). Thegure includes 18 new data points. The data with Zp0.7 fall nicelyalong a linear trajectory with a slope of 13.04 (R2 0.9146); inother words, the new arrestors are stiffer than the ones in PK.

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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

so (k

44.3

44.3

48.9

48.9

48.9

48.9

40.2

40.2

40.2

43.4

43.4

43.4

43.4

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

42.5

41.5

L.-H. Lee et al. / International Journal of Mechanical Sciences 50 (2008) 10581064 105917 0.0865 23.11 0.373 2.214 0.5

18 0.0867 23.06 0.160 2.324 0.5pressures

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

1 0.0951 21.01 0.045 2.731 0.5

2 0.0951 21.01 0.034 2.411 0.5

3 0.0962 20.76 0.093 2.210 0.5

4 0.0962 20.75 0.033 2.052 0.5

5 0.0958 20.83 0.050 1.898 0.5

6 0.0966 20.02 0.053 1.723 0.5

7 0.1020 19.60 0.145 1.571 0.5

8 0.1017 19.65 0.228 1.424 0.5

9 0.1019 19.66 0.083 1.308 0.5

10 0.0867 23.10 0.223 1.837 0.5

11 0.0866 23.09 0.253 1.708 0.5

12 0.0863 23.19 0.260 1.576 0.5

13 0.0868 23.03 0.347 1.982 0.5

14 0.0860 23.24 0.288 1.436 0.5a 1 in 25.4mm.b 1ksi 6.897MPa.c 14.5 psi 1bar.Furthermore, data with Z40.7 are also in reasonable agreementwith this linear t albeit with somewhat larger scatter. The sixcases with a ipping mode, marked in the gure with , are allabove Z40.7 but now this efciency 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 signicantly lower than that of the pipe.On the contrary, in the prese

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