# pipeline buckling

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Pipeline arrestorTRANSCRIPT

Proceedings of OMAE0322nd International Conference on Offshore Mechanics and Arctic Engineering

June 8-13, 2003, Cancun, Mexico

OMAE2003-37220

BUCKLE PROPAGATION AND ITS ARREST: BUCKLE ARRESTOR DESIGNVERSUS NUMERICAL ANALYSES AND EXPERIMENTS

Enrico TorsellettiSnamprogetti

Via Toniolo 1, 61032 Fano, Italye-mail: [email protected]

Roberto BruschiSnamprogetti

Via Toniolo 1, 61032 Fano, Italye-mail: [email protected]

Furio MarchesaniSnamprogetti

Via Toniolo 1, 61032 Fano, Italye-mail: [email protected]

Luigino VitaliSnamprogetti

Via Toniolo 1, 61032 Fano, Italye-mail: [email protected]

ABSTRACTBuckle propagation under external pressure is a potential

hazard during offshore pipeline laying in deep waters. It isnormal design practice to install thicker pipe sections which, incase of buckle initiation and consequent propagation, can stopit so avoiding the lost of long pipe sections as well as threats tothe installation equipment and dedicated personnel.

There is still a series of questions the designer needs toanswer when a new trunkline for very deep water applicationsis conceived:- What are the implications of the actual production

technology (U-ing, O-ing and Expansion or Compressione.g. UO, UOE and UOC) on the propagation and arrestcapacity of the line pipe,

- How formulations for buckle arrestors design can be linkedto a safety objective as required in modern submarinepipeline applications.

The answers influence any decision on thickness, length,material and spacing of buckle arrestors.

This paper gives an overview of buckle propagation andarrest phenomena and proposes a new design equation,applicable for both short and long buckle arrestors, based onavailable literature information and independent numericalanalyses.

Partial safety factors are recommended, based on acalibration process performed using structural reliabilitymethods. Calibration aimed at fulfilling the safety objectivesdefined in DNV Offshore Standards OS-F101 and OS-F201.

INTRODUCTIONAn offshore pipeline installed in deep waters is often

collapse-critical due to the ambient external pressure.Designing against collapse involves selecting the appropriatewall thickness for a given pipe diameter and line pipe material,as well as specifying appropriate geometric fabricationtolerances. Unfortunately incidental dents induced by impactingobjects, ovalisation induced by excessive bending duringinstallation, wall thickness reduction due incidental corrosionetc., may locally reduce the collapse strength of the pipeline.

If the pipe is not sized against propagation when collapseor sectional ovalisation buckling occurs in the depths, thebuckle propagates and stops at a depth the required work forsectional plastification is larger than the one the externalpressure can do.

The buckle propagation phenomenon can be considered tooccur in three phases (see Figure 1):- Buckle initiation,- Buckle propagation,- Buckle arrest at the arrestor or crossover of the arrestor.

The buckle propagation pressure has been extensivelystudied in the last decades and design approaches have beendeveloped and experienced in a number of projects. Researchactivities, both experimental and analytical, have beendedicated to the development of the most suitable bucklearrestors shape for deep water applications: integral, external orinternal rings, spiral, etc. In this paper integral buckle arrestors(BA) are considered and analysed, as classified into two maincategories:- “long” arrestors are those for which the buckle crossover

the arrestor after it has collapsed for its whole length, e.g.

1 Copyright © 2003 by ASME

the capacity to arrest propagation is ensured by suitablysized wall thickness, in accordance with the propagationpressure formula.

- “short” arrestors, where the buckle crossover the arrestorthat remains integer in shape i.e. the arrestor capacity isensured by wall thickness far thicker than for “long”arrestors.

As far as the transition between long and short bucklearrestor behaviour is considered, it can be affirmed that longarrestors are longer than about 4 to 6 pipe diameters. In designguidelines for offshore pipelines [1], there is no indication onhow to size short buckle arrestors while long arrestors arecovered. For both cases, it does not appear that a rationalcalibration of partial safety factors has been carried out.

Figure 1 How Kyriakides describes the different load phasesto which a pipeline is subjected during a buckleinitiation, propagation and crossover [18].

According to the limit state based approach drawn in [1]the buckle arrestor must be sized in order to fulfill the specifiedsafety targets. In particular, the failure probability of a bucklearrestor can be expressed as:

(1) StopFopagationFInitiationFF PPPP ,Pr,, ⋅⋅=PF is the total failure probability that has to be compared

with the specified target (see [1] for reference values to be usedfor offshore pipeline systems), PF,Initiation is the probability tohave a buckle, PF,Propagation is the probability that a given bucklewill propagate, PF,Stop is the probability that a given propagatingbuckle will crossover the buckle arrestor length, so continuingpropagation (the capacity of the buckle arrestor is exceeded).

Undeformed pipe

Buckle initiation

Buckle propagation

Buckle arrestorengagement

Buckle arrestorcrossover

When pipes are sized to avoid propagation, the product ofthe probability of initiation by the probability of propagationgives the total failure probability (PF). For a pipeline systemwith buckle arrestors PF is given by the product of PF,initiation byPF,Stop, and PF,propagation is equal to 1.

Scope of this paper is to introduce a new design formulaincluding partial safety factors that meet the safety objective ofDNV-OS-F101.

PROPAGATION PRESSUREThe problem of propagating buckles was recognized in the

early 1970s [2]. Palmer and Martin made the first theoreticalanalysis in 1975 [3]. They recognized that the work done by theexternal pressure, as the buckle moves forward by unit distanceis mainly absorbed by plastic deformation associated to thechange in shape of unit length of pipe, from its original circularform to final "dog bone" conformation. Assuming a simplemechanism of plane strain collapse for the ring, involving fourconcentrated "plastic hinges" (Figure 2), the following energybalance equation for unit length of pipe, was defined:

(2) M2=A p pe π∆Here pe is the external pressure, ∆A is the change in

cross-sectional area and Mp is the full plastic moment per unitlength of the pipe wall.

Figure 2 Sequence of collapse configurations of a long tubeunder external pressure.

Being the above formulas considered as lower bound,researchers tried to introduce new buckle propagation equationsthat give a better prediction of the critical propagation pressurethan the formula from Palmer, see Kamalarasa and Calladine in1987 [4].

While it has never been contested that the shortcomings ofequation (2) lies in its neglect of both surface stretching andstrain hardening, most researchers have chosen to overlook thestretching effects and concentrate entirely on "ring-bending"investigations.The concentrated plastic hinges, which are animportant feature of the analysis of Palmer and Martin, are onlylegitimate in the context of a perfectly plastic, non-hardeningmaterial. In the presence of strain hardening, we must expect tofind hinges of finite length which can travel around the

2 Copyright © 2003 by ASME

circumference of the ring. Several attempts to improve theanalysis of Palmer and Martin, by including strain hardening inthe study of the irreversible circumferential bending of rings,have been made. Wierzbicki and Bhat [5], Steel and Spence [6],Croll [7] and Kyriakides et al. [8] have analysed the bending ofstrain-hardening rings using different schemes, and proposeddifferent expressions for the critical pressure.

In recent years, several tests were performed to evaluatethe formulation of the propagation pressure design format, andare reported in literature (Kyriakides et al. [2], Langner et al.[9] and Estefen et al. [10]).

In 1996 a tentative reliability based calibration of designequations available in literature, for the evaluation of thepropagation pressure, was performed in the framework of theSUPERB project [11]. The equation reported in DNV ’96 [12]reads:

(3)

⋅

D

t SMYS 26 = Pest

nom

2.5

cp,

This equation is based on a conditional target failureprobability PF,Stop of 10-2 per pipe joint.

0

20

40

60

80

100

120

10 15 20 25 30 35

D/t

Pp

* 1

000

/ SM

YS

Experiments X65

Experiments X42

Experiments Estefen [10]

DNV’96 [12], SUPERB [11]

BS80110 [13]

Langner [9]

Battelle [14]

Palmer [3]

Kyriakides [15]

Kyriakides [16]

Kyriakides [16]

AGA Fowler

Figure 3 Propagation pressure formulas versus D/t andexperimental values [11].

Figure 3 compares the propagation pressure calculated withequation (3) with the experiments by Kyriakides [2] and byEstefen et al. [10], respectively. Both BS8010 [13] and Langnerapproach [9] are considered conservative, while Battelle [14]and Kyriakides [2, 15, 16] are considered good mean valuepredictors. The formulation from DNV’96 was a step forwardin terms of reducing excessive conservatism, fulfilling in a waypre-defined safety requirements.

DNV-OS-F101 modified the above approach, in order tobetter introduce a flexible safety target, through the so-calledSafety Classes:

(4) 5.2;35;, ==

⋅⋅⋅⋅= ααα

α

kD

tSMYSkP

est

nomUfabCP

Where SMYS is the minimum yield strength of the steelmaterial, αfab is the fabrication factor, tnom is the nominal steel

wall thickness (less the corrosion allowance if present), Dest isthe nominal outer diameter of the pipe.

The design criterion reads:

(5)SCm

CPce,

PP γγ ⋅

≤ ,

where Pe,c is the external pressure, γm is the materialresistance factor (1.15), γSC is the safety class resistance factor(1.04 for safety class LOW, 1.14 for safety class NORMAL and1.26 for safety class HIGH, corresponding to a target failurerate of 10-2, 10-3 and 10-4, respectively). This design equation,when a safety class NORMAL is adopted, is almost coincidentwith the design equation of DNV ’96 [12], see Figure 4.

5

10

15

20

25

30

35

15 17 19 21 23 25

Diameter to thickness ratio, D/t

PP*1

000/

σ Y

Superb DNV’96

Safety Class LOW

Safety Class NORMAL

Safety Class HIGH

Figure 4 Comparison between DNV OS-F101 [1], DNV ’96[12] and SUPERB [11] formulations.

MORE ON CROSSOVER PRESSUREWhile the propagation front is far from the buckle arrestor

section, the relevant propagation pressure is the one of thepipeline cross section. As soon as the propagation frontapproaches the buckle arrestor, the propagation pressure risesup to a maximum value (the crossover pressure PX), seeFigure 5. The crossover pressure is a function of:- Geometrical characteristics of the pipeline (thickness and

diameter),- Geometrical characteristics of the buckle arrestor

(thickness, length and diameter),- Mechanical characteristics of both pipeline and buckle

arrestor (yield strength, ultimate strength).

In relation to crossover, buckle arrestors can be classifiedaccording to length, namely short versus long buckle arrestors.The simplest design formula is for long buckle arrestor, i.e.when arrestor length LBA long compared with the propagatingbuckle wavelength.

In order to define the transition between short and longbuckle arrestors, the crossover pressure has been measured inexperiments and has been calculated with FE analyses:

3 Copyright © 2003 by ASME

- For buckle arrestor length longer than a limiting value(LBA,T), the crossover pressure PX is, at least, thepropagation pressure of the buckle arrestor, independentlyof how long is the arrestor.

- For buckle arrestor lower than the same limiting value(LBA,T), the crossover pressure PX is lower than thepropagation pressure of the long buckle arrestor.

The designer has to select the limiting length LBA,T for agiven thickness, such that the crossover pressure is at leastequal to the propagation pressure including a certain margin ofsafety (Figure 5).

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25TIME

PR

ES

SU

RE

Long ArrestorShort Arrestor

LBA,T

Figure 5 Definition of the buckle arrestor length at thetransition between long and short arrestor types.

The definition of the limiting value of the buckle arrestorlength, LBA,T, has been the subject of several investigations overthe last 20 years. Being the use of short buckle arrestor verylimited, a conclusive approach on the matter is still pending.

In the following the design approaches developed over thelast years by some authors are reviewed ([9, 17, 20]). All theapproaches presented are based on the crossover pressure PX.

Langner Approach 1975 [9]An early study from Langner [9] provided the first insight

on the subject. In particular Langner proposed an analyticalexpression for the crossover pressure, PX,L75 (L76 stands forLangner 1975), that includes also the buckle arrestor effectivelength:

(6) ( ) 60;1275,,75,,75,,75, =

⋅−−⋅−+= ααest

BATLTPLBAPLTPLX D

LtEXPPPPP

Where PP stands for the propagation pressure, suffices BAand T stand for buckle arrestor and nominal pipe, t is thepipeline steel wall thickness, Dest is the outer diameter of thepipe, LBA is the effective length of the buckle arrestor, e.g. thelength of the buckle arrestor section with constant thickness.

The above equation refers to the following definitions forthe propagation pressures of both pipe and buckle arrestor:

(7)2

,75,, 4

⋅⋅=

est

TTYLTP D

tP σ

(8)2

,75,, 4

⋅⋅=

est

BABAYLBAP D

tP σ

Where σY,T and σY,BA are the yield strength of the pipe andbuckle arrestor steel materials, tT and tBA are the pipeline andbuckle arrestor steel wall thickness, Dest is the outer diameter ofthe pipe. To be noticed the use of the pipe external diameteralso for equation (8).

The crossover pressure PX,L75 has to be compared with theexternal pressure to be applied on the buckle arrestor Pest,

according to the following design criterion:

(9)75,

75,

LX

LXest

PP

γ≤

γX,L75 is the safety factor accounted for in design.Equations (6) to (8) are quite conservative, compared with

recent experimental data and relevant design approaches.Nevertheless, it is very attractive for a design approach, as it issimple and gets some important aspects:- the crossover pressure approaches the propagation pressure

formula of a long buckle arrestor,- for short buckle arrestors, the steel wall thickness is higher

than the one defined for long buckle arrestors, where thethickness is defined using the propagation pressureformula.

Langner 1975

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Buckle Arrestor Length / Pipe Diameter

Bu

ckle

Arr

esto

r T

hic

knes

s [m

]

Water depth 2150mPX = Pest

D/t = 19

Figure 6 Buckle arrestor thickness versus buckle arrestorlength to pipe diameter ratio according to Langner1975 [9].

Figure 6 shows the relation between the buckle arrestorthickness and length for a safety factor γX,L75 equal to 1 and apipe Dest/tT ratio equal to 19.

Langner approach [9] gives the static crossover pressurefor an integral buckle arrestor. In addition to the net hydrostaticpressure at the design depth, a pipeline can be exposed topressure surges due to storm conditions and to a dynamic over-pressure generated when a propagating buckle is suddenlystopped at the buckle arrestor. Langner [9] recommends a value

4 Copyright © 2003 by ASME

for γX ranging from 1.3 to 1.5 to include dynamic effects.Langner [9] also recommends a safety target related to theavoidance of buckle arrestor crossover that should not be higherthan the one related to the avoidance of collapse of the pipelinesections.

Kyriakides Approach 1998 [18]Kyriakides et al. developed an approach [18] based on both

experimental and numerical results. They use a measure of theeffectiveness of the buckle arrestor: the so-called “arrestingefficiency”, η, defined as:

(10) 10;,

, ≤≤−−

≤ ηηTPCO

TPX

PP

PP

PCO is the collapse pressure of the pipe. The higher is theeffectiveness (η > 1) the higher is the crossover pressure (η = 1implies PX = PCO). Value of effectiveness greater than 1 is notconsidered. The authors suggest that the crossover pressure willdepend on the following variables:

(11) ),,,,,,,( ,,98,,98, BABATestBAYTYKTPKX tLtDEPfP σσ=The experimental data were found to exhibit a bimodal

trend with η = 0.7 as the boundary. In order to produce the bestcorrelation between the available data the following efficiencyis to be used, with equation (11) to size the buckle arrestor:

(12)

−

=1

98,,

2/58.04/52/1

,

2/1

,

1

KTP

CO

T

BA

T

BA

est

TBAYTY

P

P

t

t

t

L

D

t

EEA

σσ

η

All the data used by the authors are plotted together withequation (12) in Figure 7.

Kyriakides Chart [18, 19]

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Empirical Function

η=(P

x-P

p)/

(Pco

-Pp

)

Kyrialides Experimental Tests Ref./19/

Shell Small Scale Tests [17]

Shell Full Scale Tests Ref./17/

Shell-Kyriakides Small Scale Tests Ref./17/

Beptico Numerical Tests Ref./19/

Kyriakides Mean

Kyriakides Design Ref./18/

Figure 7 Comparison between design approach fromKyriakides et al. [18] and experimental data.

The data for η < 0.7 has coalesced to produce a nearlylinear relationship between η and equation (12). The numeratorin equation (12) is called empirical function in the followingsections. The choice of A1 = 667.6 made by the authors, drawn

in the figure, produces a best fit for η < 0.7. For higher valuesof tBA, where a different behaviour is experienced (flatteningversus flipping mode, [18]), this expression is not as effectiveand a lower bound envelope is proposed (curve labelled“Kyriakides Design” in Figure 7). Nevertheless, to comparethis approach with other approaches also a less conservativeassumption is made (curve labelled “Kyriakides Mean” inFigure 7).

Authors define a minimum steel thickness for the arrestor,tBA,M, as the one that yields efficiency of 1.0, and the followingrelations apply:

(13) COMBAKBAP PtP ≥)( ,98,,

where

(14)β

σσ

+⋅=

BAest

BA

BAYBAYKBAP D

tEBAP

,,

’

,98,,

The propagation pressure of the pipe is:

(15)β

σσ

+⋅=

Test

TA

TYTYKTP D

tEBAP

,,

’

,98,,

The coefficient A, B and b are constants determinedempirically, E’ is the post-yield modulus in a bilinearstress-strain relationship. Because of lack of information, bothequations (14) and (15) are substituted with equation (4) withαfab=αU=1.0.

Kyriakides showed also that arrestors shorter than 0.25 Dest

could not achieve the efficiency of 1.0, irrespective of thearrestor thickness. For this reason the minimum arrestor lengthis LBA,M = 0.25 �est. In summary, the following procedure isrecommended [18]:- Calculate the collapse pressure and propagation pressure of

the pipeline;- Select a steel grade of the arrestor;- Calculate the value of the arrestor minimum thickness

using equation (13);- Select either the length of the arrestor such that

LBA > 0.25 �est, or an arrestor thickness such thattBA > tBA,M;

- Use the problem variables in equation (12) to evaluateeither the arrestor thickness or its length for the desiredefficiency.

An appropriate safety factor should be applied in thechoice of either PX or arrestor thickness (or length). FromFigure 7, the design equation adopted by Kyriakides is a lowerbound for arrestor efficiency higher than 0.7. Consequently, therelated design thickness of the arrestor is expected to be higherthan the experimental findings. A value η > 0.7 is often the caseif an extra safety factor γX according to equation (9) on thepropagation pressure PX is considered. An application of thisapproach for a 24”, pipe with an outer diameter to thicknessratio of 19, is shown in Figure 8.

5 Copyright © 2003 by ASME

Kyriakides 1998

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Buckle Arrestor Length / Pipe Diameter

Bu

ckle

Arr

esto

r T

hic

knes

s [m

]

Water depth 2150mPX = Pest

D/t = 19

Figure 8 Buckle arrestor thickness versus buckle arrestorlength to pipe diameter ratio according toKyriakides et al. 1998 [18].

Langner Approach 1999 [17]Langner in 1999 [17] presented an approach based on old

experimental data from Kyriakides as well as new data. Theapproach is very similar to the one presented by Kyriakides in[18]. The same definition of arrestor efficiency as given inequation (10), is here used together with the followingparameters:

(16)4.2

,99,, 24

⋅⋅=

est

TTYLTP D

tP σ

(17)4.2

,99,, 24

⋅⋅=

est

BABAYLBAP D

tP σ

(18)2299,

EY

EYLCO

PP

PPP

+⋅=

(19)3

, 1

2;2

−⋅=⋅⋅=

est

TE

est

TYYY D

tEP

D

tP

νσ

Where ν is the coefficient of Poisson. All the othervariables are defined previously. Langner proposes thefollowing formulas for the design of the buckle arrestorthickness versus length:

(20)

>≤≤≥

kif

kifkλ

λλη

1

0

where

(21)

>

≤≤=

)(28

)(25.05

arrestorwidet

Lfor

arrestornarrowt

Lfor

k

BA

BA

BA

BA

and

(22)99,,

99,,

LTP

LBAP

est

BA

P

P

D

L ⋅=λ

λ is the arrestor strength factor, which depends on thearrestor length LBA, thickness tBA, yield strength σY,BA andcharacteristics propagation pressure PP,BA. The distinctionbetween narrow and wide arrestors refers to short arrestortypes, as defined in the beginning i.e. do not affect the longarrestors sized with the propagation formula. The design factork = 5 is recommended for a narrow arrestor, and k = 8 isrecommended for a wide arrestor. This because the experimentsin [17] showed that narrow arrestors are more efficient thatwide arrestors. According to our classification of bucklearrestor given above (short versus long), both narrow and widearrestors are relevant for short buckle arrestors. For designapplications, Langner assumes that the formula of the arrestorefficiency can be used to size the arrestor thickness consideringthe crossover pressure, PX,L99, defined according the followingdesign formula:

(23)99,

99,

LX

LXest

PP

γ≤

The safety factor γX,L99 is proposed as 1.35 by the author.All the data used by the authors are plotted againstequations (16) to (22) in Figure 9.

Langner Chart [17]

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0

Strength factor

η=(P

x-P

p)/

(Pco

-Pp

)

Kyrialides Small Scale Experimental Tests Ref./19/

Shell Small Scale Tests Ref./17/

Shell Full Scale Tests Ref./17/

Shell-Kyriakides Small Scale Tests Ref./17/Beptico Numerical Tests Ref./19/

Langner design k=5 Ref./17/

Langner design k=8 Ref./17/

Figure 9 Comparison between design approach fromLangner [17] and experimental data.

The following procedure is recommended in [17]:- Calculate the collapse, equation (18), and the propagation

pressure, equation (16), of the pipeline, as well as theminimum crossover pressure with equation (23).

- Calculate the arrestor thickness and length according toequations (10), (20), (21) and (22).

- The adopted thickness should not be less than the thicknessof a long arrestor sized according to equation (23) wherePX,L99 = PP,BA,L99 is used.

An application of this approach for a pipe D/t of 19,nominal diameter equal to 24” and water depth of 2150 m isshown in Figure 10. In the figure three curves are plotted. Thehorizontal line is the minimum buckle arrestor thickness to beused independently of the buckle arrestor length. The designcurve for k = 8 is representative for buckle arrestor length over

6 Copyright © 2003 by ASME

thickness ratio greater than 2. For the subject case the safetyfactor γX,L99 is set equal to 1.0.

Langner 1999

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 1 2 3 4 5 6

Buckle Arrestor Length / Pipe Diameter

Bu

ckle

Arr

esto

r T

hic

knes

s [m

] Water depth 2150mPX = Pest

D/t = 19

k=5

k=8

Figure 10 Buckle arrestor thickness versus buckle arrestorlength to pipe diameter ratio according to Langner1999 [17].

RECOMMENDED DESIGN APPROACHThe available design approaches from literature are

compared with experimental data ([17,18,19,20]) as well asbetween them. The objective is twofold:- To evaluate the robustness of the proposed approach with

respect to a design application,- To estimate the uncertainty of the different models with

respect to the experimental data set.

In addition finite element modeling has been performed onavailable experimental data to better understand theexperimental findings and to qualify in details the effects ofdifferent parameters.

Figure 7 and Figure 9 show the experimental data reportedin [19] together with the design approaches proposed byKyriakides [18] and Langner [17], respectively. The two figureshave the same y-axis (the arresting efficiency η) but differentx-axis. In fact, Figure 7 uses the empirical function defined byKyriakides in the numerator of equation (12) while Figure 9uses the strength factor λ defined by Langner in equation (22).The horizontal line, for η = 1.0, represents the upper bound forthe definition of the arrestor efficiency of both designapproaches.

The continuous line drawn in the figures represent thedesign approaches of both authors (see previous section). Allthe data from Kyriakides [19] are lower bounded by the linesdrawn in Figure 7. In particular, the data having η < 0.7 liesover the relevant line, so allowing to conclude that thedispersion of the data is negligible for that region. On the otherhand, a few small-scale test data from Langner [17] lie underthe design lines, meaning that the previous conclusions drawnby Kyriakides are not always applicable.

The same dispersion of the experimental data with respectto the design lines of Langner, is evidenced in Figure 9.

The analytical approaches from both Kyriakides andLangner are directly compared in Figure 11 and Figure 12, forD/t ratio of the pipeline equal to 20 and 30, respectively. Thesefigures show that both approaches are equivalent, while theformer approach from Langner-1975 [9] is conservative.Kyriakides is more conservative than Langner for pipelineswith High D/t ratio.

Due to the dispersion of the data set, two approaches canbe followed to calibrate a design equation:- Assume an absolute lower bound. This can result in a

different safety margin for different design cases and canbe conservative for some applications. This is also whathas been done by Kyriakides for η > 0.7 [20].

- Fit an analytical equation to the mean value of theexperimental data (RMS or other similar methods can beused) and then calibrate a safety factor using reliabilitymethods to fulfill a given safety target.

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 1 2 3 4 5 6

Buckle Arrestor Length / Pipe Diameter

Bu

ckle

Arr

esto

r T

hic

knes

s [m

]

Langner 1975Kyriakides 1998Langner 1999 k=8Langner 1999 k=5

Water depth 2000mPX = 1.0*Pest

D/t = 20

Figure 11 Comparison between design approaches proposedby Langner, [17] and [9], and Kyriakides, [18].Water depth 2000 m, pipe D/t = 20.

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 1 2 3 4 5 6

Buckle Arrestor Length / Pipe Diameter

Bu

ckle

Arr

esto

r T

hic

knes

s [m

]

Langner 1975Kyriakides 1998Langner 1999 k=8Langner 1999 k=5

Water depth 2000mPX = 1.0*Pest

D/t = 30

Figure 12 Comparison between design approaches proposedby Langner, [17] and [9], and Kyriakides, [18].Water depth 2000 m, pipe D/t = 30.

7 Copyright © 2003 by ASME

Proposed Design EquationsIn this paper the second approach is followed and a new

design equation for the crossover pressure is fitted to theexperimental data set reported in [19], namely:

(24) ( ) 20;12

,,,, =

⋅−−⋅−+= ααTest

BATTPBAPTPX D

LtEXPPPPP

where PP,T and PP,BA are the propagation pressures of a pipewith the wall thickness of the pipeline and of the bucklearrestor, respectively. LBA is the length of the arrestor (taperingterminations not included).

The propagation pressure formula for the pipe and for thebuckle arrestor is taken from DNV OS-F101, to maintain thecompliance with the mentioned international standard:

(25)5.2

,, 35

⋅=

Test

TYTP D

tP σ

(26)5.2

,,, 35

⋅=

BAes

BABAYBAP D

tP σ

where σY,P and σY,BA are the actual yield strength of thesteel materials. The above formulations are to be appliedthrough the following design equation:

(27)X

Xest

PP

γ≤

where γX is a safety factor that has to be calibrated againsta predefined safety target.

The coefficient α = 20 has been chosen as an optimalsolution for:- Reducing as much as possible the standard deviation of the

ratio between the experimental data and the calculatedcrossover pressure. In particular, for the measuredcrossover pressures normalised with equation (24), XPx, amean value of 1.20 and Coefficient of Variation, CoV, of16% was obtained.

- The propagation wavelength obtained from dedicatedABAQUS FE simulations with the one obtained fromequation (24). In particular, as explained in the following,the analytical value is about two times the values from theFE simulation.

A series of FE static analyses have been performedmodeling both pipe and buckle arrestors using the commercialFE package ABAQUS [22]. The simulations were made toevaluate the propagation wave length (both in the pipe and inthe buckle arrestor) and the propagation and crossoverpressures. In the simulations, different material characteristics(pipe and arrestor, tensile and compressive) were considered.

Figure 13a show an example of the FE results where theovality along the pipe axis, f0,d, is plotted as a function of theapplied external pressure. The figure shows also the position ofthe buckle arrestor. Figure 13b shows the applied externalpressure. The figures show how the pipe deformation patterns

are related to the applied external pressure at equilibrium. Inthis case the B.A. is 4m long and the maximum externalpressure is attained for a deformed shape which involves halfbuckle length. In addition, at the maximum pressure, the pipesection following the arrestor is not deformed, i.e. the pipecross section ovality is not affected by the arrestordeformations.

Long buckle arrestor, i.e. sized using the propagationpressure formulas, usually has an actual crossover pressurehigher than the propagation pressure (see Figure 13b whichgives PX=36 MPa and PP,BA=28 MPa). This is also evidenced(but conservatively neglected) by the approaches fromKyriakides (Figure 8) and Langner (Figure 10). The approachproposed in this paper neglect this effect too.

Ovality Distribution During PropagationPipe: ID 21.5", D/T=19

Arrestor: ID=21.5", D/t=12

0

50

100

150

200

0 1 2 3 4 5 6 7 8 9 10 11 12 13Pipe length (m)

Ova

lity

(%)

Inc= 200 ; 27.9 MPa

Inc= 180 ; 25.4 MPa

Inc= 140 ; 35.4 MPa

Inc= 120 ; 32.2 MPa

Inc= 100 ; 22.0 MPa

Inc= 50 ; 10.6 MPa

Inc= 30 ; 9.7 MPa

Figure 13a FE results: ovality along the pipe axis, f0,d, isplotted as a function of the applied externalpressure.

Pressure Distribution During PropagationPipe: ID 21.5", D/T=19

Arrestor: ID=21.5", D/t=12

0

5

10

15

20

25

30

35

0 50 100 150 200 250

Increment Number

Pre

ssu

re (

MP

a)

Figure 13b FE results: applied external pressure as a functionof the increment number in the FE analysis.

Equation (24) is quite simple and gives a unique designapproach for both short and long buckle arrestors. Thetransition between them is conservatively represented by thepoint of tangency between the horizontal line and theexponential curve (see Figure 14 where the transition of theanalysed case is ca 3-4 pipe diameters).

8 Copyright © 2003 by ASME

PROPOSED APPROACH

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0 1 2 3 4 5 6

Buckle Arrestor Length / Pipe Diameter

Bu

ckle

Arr

esto

r T

hic

knes

s [m

] Water depth 2000mPX = 1.0*Pest

D/t = 19Dest = 24"

Figure 14 Buckle arrestor thickness versus length using theequation calibrated in this note, equation (27).

Proposed Equation vs. ExperimentsTo better quantify the ability of the analytical equations to

fit experiments the following bias for the crossover pressure isdefined:

(28)valueAnalytical

valueMeasuredBIAS =

Figure 15 shows the bias as a function of the arrestorlength to pipe diameter ratio. This bias is statistically analyzedto calculate mean, standard deviation and coefficient ofvariation (ratio between standard deviation and mean) values.The goodness of the analytical formulation is a function of:- The mean value, the nearer to 1.0 the better;- The standard deviation, the lower the better.

0.5

1

1.5

2

2.5

3

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

B.A. Length / Pipe OD ratio

BIA

S =

mea

sure

d /

pre

dic

ted

Langner 1975

Langner 1999

Proposed Approach

Kyryakides_mean - Pp_DNV

Beptico

Figure 15 Bias of the crossover pressure versus bucklearrestor length to pipe diameter ratio.

In particular, the following mean and standard deviation(std) values are found:- Langner 1975: mean equal to 2.04 and std equal to 18.1%;- Langner 1999: mean equal to 1.08 and std equal to 18.2%;- Kyriakides_Mean: mean equal to 1.13 and std equal to

29.9%;- Kyriakides_Design: mean equal to 1.20 and std equal to

26.5%;

- Proposed approach, equations (24)-(27): mean equal to1.19 and std equal to 16.6%;

- BEPTICO [19]: mean equal to 1.0 and std equal to 2.0%;

The calculations with BEPTICO [19] give the bestprediction of the experimental tests. The recommendedequation gives reasonable mean and standard deviation values.

Moreover, from Figure 16 and Figure 17, it is evident thatthe approach developed here is in line with the approaches fromKyriakides [18] and Langner [17]. In addition, when varyingthe safety factor γX from 1.0 to 1.5 the approach fromKyriakides becomes quite conservative (this because forγX = 1.0 being η<0.7, the relevant design curve is a lowerbound, not a best fit of the experiments as it is for γX = 1.5where η>0.7).

For γX = 1.0, the approach from Kyriakides (named “design” inthe figures) and the modified one (named “mean” because fitsbetter the mean value of the experiments, see Figure 7) arecoincident (see Figure 17), because η < 0.7 and the same designcurve applies for both.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 1 2 3 4 5 6

Buckle Arrestor Length / Pipe Diameter

Bu

ckle

Arr

esto

r T

hic

knes

s [m

]

Langner 1975Kyriakides Design 1998Kyriakides Mean 1998Langner 1999 k=8Langner 1999 k=5Proposed Approach

Water depth = 2000mPX = 1.5*Pest

D/t = 20

Figure 16 Comparison between developed design equationand design approaches proposed by Langner, [17]and [9], and Kyriakides, [18]. Water depth 2000 m,pipe D/t = 20, safety factor of γX = 1.5.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 1 2 3 4 5 6

Buckle Arrestor Length / Pipe Diameter

Bu

ckle

Arr

esto

r T

hic

knes

s [m

]

Langner 1975Kyriakides Design 1998Kyriakides Mean 1998Langner 1999 k=8Langner 1999 k=5Proposed Approach

Water depth = 2000mPX = 1.0*Pest

D/t = 20

Figure 17 Comparison between developed design equationand design approaches proposed by Langner, [17]and [9], and Kyriakides, [18]. Water depth 2000 m,pipe D/t = 20, safety factor of γX = 1.0.

9 Copyright © 2003 by ASME

Safety Factor CalibrationThe conditional (given the propagation) probability to have

a buckle arrestor that does not stop a propagating buckle isevaluated as the probability that the actual crossover pressure isless than the applied external hydrostatic pressure. Thisprocedure is in line with the one used in SUPERB [11] andDNV’96 [12].

The limit state function for the calibration is:

(29) XestBABATBAYTYCX

estBABATTBAYTYYXP DLttp

DLttXXpXxg

X γσσσσ 1

),,,,,(

),,,,,,,()(

,,,

,, −⋅=

Where XPx is the crossover pressure model uncertainty(normal distribution with a mean value of 1.20 and Coefficientof Variation, CoV, of 16%), XT is the steel wall thicknessuncertainty (normal distribution [21] with a mean value of 1.0and Coefficient of Variation, CoV, of 2%), XY is the yield stressuncertainty (normal distribution [21] with a mean value of 1.08and Coefficient of Variation, CoV, of 4%).

Failure probability vs. Safety factor

0.0001

0.001

0.01

0.1

1

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

Safety Factor γX

DNV OS-F101Safety Class

NORMAL

Figure 18 Unconditional failure probability PF,STOP versus thesafety factor γX. LBA/Dest = 6.

For the evaluation of the failure probability, a SecondOrder Reliability Method has been used (SORM). Figure 18shows the the unconditional failure probability PF,Stop for thegiven limit state function versus the safety factor γX. For thecalculations, a buckle arrestor length over pipe diameter ratio of6 has been used.

A sensitivity analysis has been performed on the relevantvariables: diameter, thickness, yield strength, buckle arrestorlength and water depth. The main variables affecting the resultsare the model uncertainty and the yield stress uncertainty. Allthe other variables do not change significantly the failureprobability.

Figure 19 shows a sensitivity on the buckle arrestor lengthfor a fixed γX = 1.311. This value is taken from DNV rule [1]and is relevant to the propagation pressure design criteria,where the safety class NORMAL is applied. The failureprobability does not change with the buckle arrestor length.

Failure probability vs. Buckle arrestor length

0.001

0.01

0.1

1

0 1 2 3 4 5 6

LBA/Dest

Figure 19 Failure probability versus buckle arrestor length. γX

= 1.14*1.15 = 1.311.

In section 12-F1000 of OS-F101 [1], it is said that thefailure probability for propagation i.e. the probability to have apropagating buckle, is 1-2 decades higher than the probabilityof other ULS limit states. Comparing DNV '96 [12] approachwith the new approach of OS-F101, the former is equivalent tothe latter, when a safety class NORMAL is adopted (actually inthe former there is no mention of any safety class), seeFigure 4. Therefore, a pipeline can be sized against propagationusing a safety class NORMAL in [1] or the approach ofDNV’96.

Relating to the calibration results for the crossover pressureformula (see Figure 18, where the vertical line indicates thesafety factor correspondent to a safety class Normal), theadopted design equation is in line with OS-F101 safety classapproach (i.e. γSC = 1.04, 1.14 and 1.26 for safety class Low,Normal and High, respectively).

Design FormatThe design criterion is:

(30)DynSCm

X

X

Xext

PPP γγγγ ⋅⋅

=≤

where Pext is the external pressure, γDyn is the dynamic loadeffect factor (1.1), γm is the material resistance factor (1.15), γSC

is the safety class resistance factor (1.04 for safety class LOW,1.14 for safety class NORMAL and 1.26 for safety classHIGH). Equation (24) is used for evaluating the crossoverpressure, PX. The propagation pressure formula for the pipe andfor the buckle arrestor is taken from DNV OS-F101, tomaintain the compliance with the mentioned internationalstandard:

(31) 5.2;35; ==

⋅⋅⋅⋅ ααα

α

kD

tSMYS k = P

est

nomUfabp

Where SMYS is the minimum yield strength of the steelmaterial, αfab fabrication factor (1.0 for seamless pipes, 0.93 forUO&TRB pipes, 0.85 for UOE pipes), αU is the materialstrength factor (1.0 for steel material that satisfies the additional

10 Copyright © 2003 by ASME

requirements of [1], 0.96 the other cases), tnom is the nominalsteel wall thickness (less the corrosion allowance, if any), D0 isthe nominal outer diameter.

In section 12-F1000 of OS-F101 [1], relevant for theevaluation of the propagation pressure, static versus dynamiceffects at the propagation front are discussed. In principle, thedynamic overpressure is relevant for a running buckle suddenlystopped at a thicker pipe section (buckle arrestor). This aspect,being studied by Langner (Ref./10/), was evaluated as 5 to 15%the external hydrostatic pressure, and described by introducinga dynamic overpressure coefficient γDyn as follows:

(32)⋅⋅

+=BA

SDyn tA

L1γ

where LS is the propagation wave length, tBA is the bucklearrestor thickness, A is a constant that depends on geometry,material, etc. (quoted by Langner equal to 36).

Netto and Kyriakides [20] showed through experimentsthat, during propagation, the material is subject to high strainrates, meaning that, at the propagation front, the steel materialbehaves as mechanically stronger than it is statically. Thereforethe dynamic crossover pressure is resulting higher than thestatic one (experiments).

On the basis of this discussion, it is suggested that, only forshort buckle arrestors e.g. when equation (24) gives rise to abuckle arrestor thickness higher than the one coming fromequation (26), a safety factor γDyn equal to 1.1 should be addedto the standard safety factors applied in DNV OS-F101 for thepropagation pressure design formula.

MATERIAL AND FABRICATION IMPLICATIONSThe manufacturing process (cold bending applied in the

Uing-Oing and Three Roll Bending processes) can give rise toa degradation of the material capacity to resist collapse andpropagation. DNV [1] and equation (31) addressed this effectintroducing a fabrication factor αfab. This factor is specific forthe collapse resistance of the pipeline and its applicability to thebuckle arrestor design has to be addressed, particularly:- When dealing with the propagation buckle and its arrest by

a buckle arrestor, is the mentioned safety factor αfab still tobe considered?

- Which is the most relevant yield stress to be considered forthe material strength qualification, the minimum measuredyield stress on the wall thickness or the yield stressaveraged on the wall thickness?

In the following we refer only to long buckle arrestor typebecause the short ones are generally produced by forging whichgives αfab=1.

The use of the minimum yield stress on the wall thicknessensures a larger capacity to the B.A. than the use of the averageyield stress (if the minimum value is larger than SMYS, theaveraged value is larger than minimum and quite larger thanSMYS). Therefore analyses were addressed to investigate the

differences in the B.A. capacity considering two differentmaterials:- the first with yield stresses decreasing moving on the wall

thickness from the inner to the outer surface, as a result ofthe UO and TRB forming processes,

- the second made by a homogeneous material with yieldstress equal to the average on the wall thickness of theyield stress of the first one.

The first step of the analyses consisted in the simulation ofthe UO forming process using an analytical-numerical model,starting from a straight plate with homogeneous material (yieldstress equal to SMYS and tensile stress equal to SMTS) andbending it up to reach the nominal B.A. circular cross section.

The simulation of the UO process has been performedconsidering a material characterized by bilinear kinematichardening. Sensitivity has been carried out on the non-linearmaterial characteristics considering a steeper second linearregion (see Figure 20). The yield stress value averaged on thewall thickness has been calculated, resulting equal to that of thestarting plate (see Figure 21).

0

100

200

300

400

500

600

0.0% 2.5% 5.0% 7.5% 10.0% 12.5% 15.0%

strain

stre

ss (

MP

a)

Base Case

Material Type 2

Figure 20 Bi-linear stress-strain relationship for base casematerial and material type 2.

-0.16 -0.14 -0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0-600

-500

-400

-300

-200

-100

0

Figure 21 Non linear material behavior in compression forthe plate material and for the inner and outer fiberson the wall thickness after the forming process(base case material). The outer and inner fibers of

Strain (-)

Stress(MPa)

11 Copyright © 2003 by ASME

the wall thickness are given by the lowest andhighest yield stress, respectively.

Then the pressure-ovalisation and the collapse pressurerelationships of a ring (i.e. a cross section) of the B.A have beenevaluated using a four-hinge model (see Figure 2). A materialthat has previously experienced the UO process and an“averaged” homogeneous (plate) material have been used. Inthe four-hinge model, the deformation of the cross section isconcentrated on the hinges, where a bending is developedfollowing a rotation. Therefore, bending moment-curvaturesrelationships have been calculated for plate and UOexperienced materials (see Figure 22a and Figure 22b,respectively.

0 0.5 1 1.5 2 2.5 30

0.05

0.1

0.15

0.2

0.25

Figure 22a Bending moment curvature relationships for platematerial. Dashed line for increasing curvature.

The pressure-ovalisation curves calculated with this approachresulted in an overall decrease in the collapsecapacity of the B.A. cross section. In particular, thereduction depends on both initial ovality andmaterial strain hardening behaviour (see

Table 1), and ranges from 12% to 17%.

0 0.5 1 1.5 2 2.5 30

0.05

0.1

0.15

0.2

0.25

M decExternalPressure

M inc

M decExternalPressure

M inc

Curvature (1/m)

Curvature (1/m)

Moment(MNm)

Moment(MNm)

Figure 22b Bending moment curvature relationships formaterial after UO process. Dashed line for increasingcurvature.

Table 1 Calculated reduction in the B.A. collapse pressure.

Initial Ovality Base case material Material type 20.5% 14.0% 17.6%1% 9.6% 13.2%2% 8.6% 12.1%

A finite element analysis using a model developed inABAQUS [22] has been performed to qualify the abovemodels. The UO forming process has been simulated on a stripof plate (using shell S4R elements [23, 24]), followed by theapplication of the external pressure up to the collapse. On thesame geometry arising from the UO process simulation, butconsidering the plate material i.e. the base case material, theexternal pressure has been applied up to collapse. The collapsepressure has shown a reduction of about 10%.

To analyse the propagation pressure of the B.A., a modelbased on the allowable pressure at equilibrium is used i.e. thecollapse pressure for a given cross-section ovality. The ovalityhas been distributed along the propagating buckle wavelengthtaking as a reference the buckle shape calculated through thefinite element analysis simulating the propagatimgphenomenon (Figure 23). The performed analyses have shownthat considering the UO forming process the propagationpressure is about 7-10% lower than the one calculatedconsidering a circular B.A. with homogeneous (plate) material(Table 2). This is in line with the decreased collapse capacityshowed by UO pipes (Table 1). Nevertheless, this simulationdid not consider the fact that the cold forming does not affectthe stress-strain curve when high strains are considered (asthose experienced during propagation in the pipe hoopdirection).

Table 2 Estimation of the effects due to B.A. formationprocess.

Calculated propagation pressure (MPa) and reduction due toUO processPlate Base case material

25.85lMaterial type 2

26.02UO Formed 24.30 23.41Reduction 6% 10%

Therefore, finite element analyses [22], simulating theforming process and the propagation over a long section of thepipe, have been performed. Results showed a lower reductionin the propagation pressure (about 2% with respect to thepropagation pressure of a pipe not subject to cold formingprocess). This can be explained considering that part of the

12 Copyright © 2003 by ASME

external work is absorbed in plastic deformations, that are wellabove the ones modified by the UO process.

The collapse pressure resistance gives a clear indication ofthe capacity of the B.A. to sustain the external pressure and,then, of the B.A. capacity to stop a propagating buckle.However, in arresting a propagating buckle, a long arrestor hasmany sections working in the post-buckle region and whichcould affect the differences between plate and UO formedmaterials.

0

20

40

60

80

100

120

140

160

180

200

0.00 0.50 1.00 1.50 2.00 2.50 3.00

Distance from Collapsed Sections (m)

Ova

lisat

ion

(%)

Figure 23 Ovalisation vs. distance from the collapsed B.A.sections (FE results).

On this basis, the propagation pressure of the UO formedbuckle arrestors may be up to10% lower than the one calculatedusing the yield stress averaged on the wall thickness. A lowerreduction may be considered for long arrestors i.e. arrestors thatwill experience applied high strains.

CONCLUSIONSThis paper gives an overview of the technical issues related

to the buckle propagation and arrest, and proposes a new designequation, applicable for both short and long buckle arrestors,based on available literature information and numericalanalyses.

Partial safety factors applicable to the new design equationare calibrated using structural reliability techniques, in order tofulfil the safety objectives in compliance with DNV OffshoreStandards OS-F101 and OS-F201.

The implications of the technology used for buckle arrestorfabrication (UO/UOE) on its capacity to arrest a propagatingbuckle have been analysed using numerical models.

FE simulation of the forming process and of the bucklepropagation following the collapse due to external pressure,showed a reduction of about 2% in the propagation pressuredue to cold forming during the manufacturing process.

ACKNOWLEDGMENTSThe authors wish to thank Snamprogetti for the permission

to publish this paper.

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Norske Veritas, Høvik, January 2000.

2. Kyriakides, S. and Yeh, M. K.: "Propagating Buckle andthe Propagating Pressure", Factors Affecting PipeCollapse - Phase I, 1985.

3. Palmer A. C. and Martin J. H.: "Buckling Propagation inSubmarine Pipelines", Nature, 254, 46-48, 1975.

4. Kalamarasa S. and Calladine C. R.: "Buckle Propagationin Submarine Pipelines", CRC/Pipeline/4, 1987.

5. Wierzbicki T. and Bhat S. U.: "On the Transition Zone inUnconfined Buckle Propagation", J. Energy ResourcesTechnology, 1986.

6. Steel W. J. M. and Spence J.: "On Propagating Bucklesand their Arrest in Subsea Pipelines", Proc. of theInstitution of the Mechanical Engineers, 187A, 139-147,1983.

7. Croll J. G. A. : "Analysis of Buckle Propagation in MarinePipelines", J. of Construction Steel Research, 5, 103-122,1985

8. Kyriakides, S., Babcock, C.D. and Elyada, D.: "Initiationof Propagating Buckles from Local Pipeline Damage",Proceedings of the Energy Resources TechnologyConference, ASME, 1983.

9. Langner, C. G.: "Arrest of Propagating Collapse Failuresin Offshore Pipelines", in Deepwater Pipeline FeasibilityStudy, October 1975.

10. Estefen S. F., Aguiar L. A. D. and Alves T. M. J.:"Correlation Between Analytical and ExperimentalResults for Propagating Buckling", OMAE, Florence-Italy, 1996.

11. SUPERB Project: “Propagating Buckle: State of the Artand Design Criteria Calibration”, Doc. No. STF22F96750, Snamprogetti, Sintef and DNV, 1996.

12. DNV ‘96: “Submarine Pipelines Rules” by Det NorskeVeritas, Høvik, December 1996.

13. BS8010 Part 3 (1993):"Pipelines Subsea: Design,Construction and Installation", British StandardsInstitution.

14. Johns, T. G., Melosh, R. E. and Sorensen, J. E.:"Propagation Buckle Arrestors for Offshore Pipelines",OTC 2680, Offshore Technology Conference, 1976.

15. Kyriakides, S. and Babcock, C.D.: "ExperimentalDetermination of the Propagation Pressure of CircularPipes", Journal of Pressure Vessel Technology,Transactions of ASME, Vol. 103, 1981.

16. Kyriakides, S, Yeh, M. K. and Roach, D.: "On theDetermination of the Propagation Pressure of LongCircular Tubes", Journal of Pressure Technology,Transactions of ASME, Vol. 106., 1984.

17. Langner C. G.: “Buckle Arrestors for DeepwaterPipelines”, Proceedings of the Offshore TechnologyConference, OTC 10711, Houston, TX, 1999.

18. Kyriakides S., Park T. D. and Netto T. A.: “On the Designof Integral Buckle Arrestors for Offshore Pipelines”, Int.J. of Applied Ocean Research, Vol.20 pp.95-104, 1998.

19. Park T. D. and Kyriakides S.: “On the Performance ofIntegral Buckle Arrestors for Offshore Pipelines”, Int. J.Mech. Sc., Vol.39 pp.643-669, 1997

13 Copyright © 2003 by ASME

20. Netto T. A. and Kyriakides S.: “Dynamic Performance ofIntegral Buckle Arrestors for Offshore Pipelines”, 17thInt. Conf. on Offshore Mechanics and Arctic Engineering,1998.

21. SUPERB Project: “Statistical Data: Basic UncertaintyMeasures for Reliability Analysis of Offshore Pipelines”,Doc. No. STF70 F95212, Snamprogetti, Sintef and DNV,1995.

22. Hibbit H. D., Karlson B. I. and Sorensen P. (2000):“ABAQUS - User Manual - version 6.1”, Hibbit, Karlsonand Sorensen Inc., Pawtucket, RI 02860-4847.

23. Vitali L., Bruschi R., Mork K.J., Levold E. and Verley R.(1999): “HOTPIPE Project: Capacity of Pipes Subject toInternal pressure, Axial Force and Bending Moment”,Proc. 9th Int. Offshore and Polar Engineering Conference,Brest, France.

24. Torselletti E., Vitali L., Bruschi R and Collberg L. (2003):“Minimum Wall Thickness Requirements for Ultra Deep-Water Pipelines”, OMAE2003, Cancun, Mexico.

14 Copyright © 2003 by ASME