5/22/2018 Otc 6335 1990 Palmer Upheaval Buckling

1/10

Te6 5Design o Submarine Pipelines Against Upheaval BucklingA.C. Palmer, Andrew Palmer Assocs.; C.P. Ellinas, Advanced Mechanics Engineering;D.M. Richards, Lloyds Register; and J. Guijt, AlS Norske Shell

Copyright 1990, Offshore Technology ConferenceThis paper was presented at the 22nd Annual OTC in Houston, Texas, May 7-10, 1990.This paper was selected for presentation by the OTC Program Committee following review o information contained in n abstract submitted by the author(s). Contents of the paper,as presented, have not been reviewed by the Offshore Technology Conference and are subject to correction by the author(s). The material, s presented, does not necessaril'y reflectany position of the Offshore Technology Conference or its officers. Permission to copy is restricted to n abstract of not more than 300 words. Illustrations may not be copied. Theabstract should contain conspicuous acknowledgment of where and by whom the paper is presented.

BSTR CTThis paper describes par t of acomprehensive jo in t - indus t ry p ro jec t onupheaval buckling. I t develops a semi-empirical s impli f ied design method andde ta i l ed design methods based on a newnumerical analys is , and i l l u s t r a t e s the i rappl icat ion by examples. I t assessesa l t e rna t ive design s t ra teg ies , and theimplicat ions of s t ra in-based design.INTRODUCTION

When a pipel ine i s operated a t atemperature and pressure higher thanambient t wi l l t ry to expand. I f thel i ne is not f ree to expand the pipe wil ldevelop an ax ia l compressive force . I theforce exerted by the pipe on the so i lexceeds the ver t ica l r es t r a in t agains tupl i f t movement created by the p i p e ssubmerged weight i t s bending s t i f fness ,and the res is tance of the so i l cover thepipe wil l tend to move upward andconsiderable ver t ica l displacements mayoccur . The pipel ine response might then beunacceptable because of excessive ver t ica ldisplacement or excessive p las t ic y ie lddeformation. Upheaval buckling i s hence afa i lu re mode tha t has to be taken in toaccount in the design of trenched andburied p ipe l ines .The poss ib i l i ty of upheaval buckling i s ofinc reas ing concern to the opera tors off lowlines in the North Sea and elsewhere.Their concern has been heightened by

References and f igures a t end of paper55

upheaval buckling incidents in the Danishand Norwegian sectors , and by the cos t ofpro tec t ive measures such as rock dumping.Shel l In ternat ional Petroleum MaatschappijSIPM) in i t i a t ed a comprehensive upheavalbuckling research program in 1987. In i t sf ina l form the research program includeds ix phases:1 review of avai lable models;2 comparative analys is ;3 cover response t e s t ing and modell ing;4 numerical upheaval buckling model;5 analys is of a l t e rna t ive concepts;6 development of an upheaval bucklingguideline.The present paper Ls one of a se r i esdescr ib ing the r esu l t s of the programme.I t concentra tes on phases 5 and 6 whichwere subcontracted by SIPM to a j o in tventure of three UK engineering companiesAndrew Palmer and Associates AdvancedMechanics and Engineer ing and LloydsRegister .The paper i s pr imar i ly concerned with thedesign aspects of upward buckling of buriedpipel ines . Unburied pipel ines can bucklein a re la ted but d i f f e r en t mode in whichthey snake sideways across the seabed.This mode too i s important in pract ice , andcan play a major par t in r e l i ev ing thee f fec t s of ax ia l force but t i s outs idethe scope of the present paper.The paper f i r s t br ie f ly describes thephenomenon and puts forward a s impl i f iedmethod for prel iminary design. I t goes onto descr ibe a conceptual design methodbased on the appl icat ion of the UPBUCK

5/22/2018 Otc 6335 1990 Palmer Upheaval Buckling

2/10

2 DESIGN OF SUBM RINE PIPELINES G INST UPHE V L BUCKLING OTC 6program, and appl ies the methodS to adesign example. The paper then considersa l te rna t ive s t r a teg ies to resolve upheavalproblems, and examines in more de ta i l oneof these s t r a teg ies , a reduct ion in wallthickness made possible by the replacementof s t r es s c r i t e r i a on longi tudinal s t r es swith s t ra in -based design c r i t e r i a .UPHE V L BUCKLING

The source of upheaval buckling i s anin te rac t ion between the axia l compressiveforce and overbend hi l l imperfect ions inthe p ipe l ine prof i l e .Figure 1 i l lu s t ra te s a sequence of eventswhich i n i t i a t e s buckling in a buriedpipe l ine . The pipe l ine i s l a id across anuneven seabed Figure l a ) , and l a te rt renched and buried ( lb) . The t renchingand bur i a l operations modify the prof i l e ofthe foundation on which the pipe i sr e s t ing , so tha t it i s not prec ise ly thesame as the or igina l prof i l e . Trenchingmay smooth the prof i l e overbends, but maya l so in troduce add i t iona l imperfect ions ,i f , for ins tance, a lump of bottom so i lf a l l s under the pipe.When the pipe goes in to operation, i t sin te rna l pressure and tempera ture arehigher than when it was in s ta l l ed andt renched, and the axia l force becomescompressive. The ef fec t ive axia l force ina constrained pipe l ine has two components,both of which con t r ibu te towards buckl ingPalmer 1). The axia l force in the wall i sthe r esu l tan t of a compressive constrainedthermal expansion component and a t ens i l ePoisson component, while in addi t ion therei s a compressive force component in thecontained f lu id .On an overbend, the axia l compressive forcereduces the upward react ion between thefoundation and the pipe l ine Figure l c ) .A fur ther increase of operat ing temperatureand pressure may reduce the react ion tozero. The pipe then l i f t s on the overbend,moves towards the surface of the cover , andmay break out through the surfaceFigure ld) .SIMPLIFIED N LYTIC L MODELThe s t a b i l i t y of the pipe l ine in i t si n i t i a l pos i t ion turns out to depend on theloca l prof i l e of the pipe in contact withi t s foundat ion, and on whether or notenough downward force i s present to holdthe pipe in posi t ion. I f the pipe does notmove, the governing fac to rs a re theconstrained axia l force and the pipef l exura l r ig id i ty , and other parametershave no ef fec t .

55

n arb i t r a ry pipel ine prof i l e can bedefined by a height y and a horizontald i s t ance x. The pipel ine i s idea l i sed asan e l a s t i c beam which car r ies an axia lcompressive force P and has f lexura lr ig id i ty EI. I t follows from elementarybeam-column theory tha t the downward forcew x) per uni t length required to maintainthe pipe l ine in equi l ibrium in t h i sposi t ion i s

and therefore depends on the prof i l e shapethrough the fourth and second der iva t ives .Consider f i r s t a simple s inusoidal prof i l eimperfect ion of height S and length Ldefined by

y 5 cos 2 rrx/L) in ~ L < x < ~ L 2)

The downward force required to maintaint h i s prof i l e i s thereforew X) -8SEI rr/L)4 + 2SP rr/L)2)cos 2rrx/L)

.. 3)and has i t s l a r ge s t numerical value a t thecres t of the imperfect ion, where

w 25P rr/L)2- 8SEI rr/L)4 4)the downward force per uni t length requiredto s t a b i l i s e the pipe l ine a t the cres t ofthe prof i l e imperfect ion.Equation 4) appl ies to a par t i cu la rp ro f i l e shape, but the spec i f ic shape onlyaf fec ts the coef f ic ients and not thegeneral form of the equat ion. I t can berewr i t t en

a re la t ionship between a dimensionlessmaximum download parameter ~ w defined by

~ w wEI/SP2 6)and a dimensionless imperfect ion lengthdefined by

L P / E I ) 7 )

This suggests tha t a useful way ofrepresent ing the resul ts of upheavalbuckl ing ca lcu la t ions i s to plo t ~ w against

5/22/2018 Otc 6335 1990 Palmer Upheaval Buckling

3/10

OTC 6335 PALMER ELLINAS, RICHARDS, GUIJT~ L The resu l t ing p lo t i s universa l , andforms a valuab le summary, which can includeboth the r e su l t s of numerical ca lcu la t ionsand then obse rva t ions from fu l l - s ca le f i e ldexper ience and t e s t s .All poin ts t ha t r epresen t a s ing leimper fec t ion shape wi l l l i e on a s ing lecurve on a ~ w agains t ~ L p lo t . Poin t s t ha tr epresen t d i f f e r en t imperfect ion shapeswi l l l i e on d i f f e r en t curves, and thevar i ab i l i t y between curves wi l l r e f l ec t theef fec t of imperfect ion shape ( the hardes tparameter to determine r e l i ab ly inpr ac t i c e ) . The form of equat ion 5 sugges t st h a t the funct ional r e l a t i o n s h i p between ~ wand ~ L i s

~ w C ~ L - 4 + d ~ L - 2 8 )where c and d are constants to bedetermined numerica l ly . This i s done byp lo t t i ng ~ w ~ L 2 agains t ~ L - 2 , in Figure 2, onwhich the po in ts r epresen t the r esu l t s ofnumer ical ca lcu la t ions with the UP BUCKprogram desc r ibed below. The r ightmostgroup of poin ts r epresen ts imper fec t ionpr of i l e s whose shape i s an upheavalfoundat ion, t h a t i s , a foundat ion in theshape of a pipe l ine suppor ted by a x i a lforce in a post -upheaval mode. Theremaining poin ts correspond to propimper fec t ion prof i l es , whose shape i s t h a ttaken up by a pipe l ine l a id across a s ing lei so l a t ed h i l l in a hor izon ta l pr of i l e . Thef ina l r e l a t i o n s h i p tu rns out to beb i l inear , with one pa i r of va lues c and dcorresponding to small values of ~ L and asecond pa i r to l a rge values .An add i t iona l condit ion occurs when theprof i l e includes a very shor t imperfect ion,so t ha t the pipe l ine i s only in contac twith the cres t of the imper fec t ion . Thel eng th ~ L i s then immater ia l , and t h i scondit ion forms a cut -of f fo r shor timperfect ions.The r e su l t s are combined in Figure 3, auniver sa l curve which can be used d i r e c t l yfo r design. The th ree condit ions t h a ttogether give the design download r equ i redfo r s t a b i l i t y are :

~ L

5/22/2018 Otc 6335 1990 Palmer Upheaval Buckling

4/10

4 DESIGN OF SUBMARINE PIPELINES AGAINST UPHEAVAL BUCKLING OTCCONCEPTUAL AND DETAILED DESIGN

Conceptual and de ta i l ed design are based on~ h e UP BUCK f in i e - e l ~ m e n t program descr ibedIn a separate paper . The program takesaccount of a number of fac tors not includedin the s impl i f ied ana ly t i ca l procedure.These fac tors have a s igni f icant e f f e c t onthe response of the p ipe l ine a f t e r it hasbegun to move in response to axia l forceand thence on i t s post buckl ing behaviou;and the amplitude of the f i na ldisplacement. Among the fac tors are :

2

3

4

the f i n i t e ax ia l s t i f fness of thel i ~ e which determines how rapid ly theaXlal force diminishes as the l i nemoves upwardsithe p ipe l ine s longi tudina l r es i s t anceto movement through the so i l whichd e ~ e r m i n e s how far the pipel. ine cans l l de towards a developing uck le ithe incremental f lexura l r i g i d i t y forla rge def lec t ions , which determineswhether the p ipe l ine s res is tance to

b ~ n d i n g decreases as l a rged l s p ~ c e m e n t s occur: the r i g i d i t y maybe lnf luenced by p las t i c bendingdeformation.the f i n i t e s t i f fness of thefoundat ion, which allows thefoundation to deflec t under forcesappl ied by the pipe, and s l igh t lymodifies the def lec ted form of thepipe.

UP BUCK makes it poss ib le fo r the use r toca lcu la te the response of the pipel ine toincreas ing operat ing pressure andtemperature , and to fo l low the deformationin to the post -buckl ing range.DESIGN EXAMPLE

The example i s a 10-inch o i l pipel ine , witha maximum operat ing pressure of 15 MPa2175 ps i ) and a maximum operat ingtemperature of 80 deg C. The chosen s tee lgrade i s API 5LiX60 which corresponds toa speci f ied minimum yie ld s t re ss SMYS) of413.7 N/rnrn2. The exte rna l ant i -cor ros ioncoa t ing i s 2 r r of polyethylene. The l inei s to be designed to DnV 1981 ru les .The l ine wil l be t renched, in order toprotect it aga ins t f i sh ing gear . A reviewof ex i s t ing survey da ta along a nearbypipel ine route has es tabl i shed t ha t theseabed i s re l a t i ve ly smooth, and tha t themaximum expected he ight of overbends wil lbe 0.2 m. However, it i s thought tha tt r enching might induce addi t ionalimperfections in the bottom pro f i l e , andthe design imperfection he ight i s the re fore

55

taken as 0.3 m. The t rench wil l bbackf i l led with rock, which has a minimui n - s i t u submerged un i t weight of 8 .5 kN/mand an up l i f t coef f i c ien t of 0.5. Thassumed i n - s i t u submerged uni t weight i slow conserva t ive va lue , and corresponds ta voids r a t i o of 0.87 and a rock fragmedens i ty of 2650 kg/m3 The opt ion ot renching and rock-dumping, ra the r tharock-dumping alone, i s se lec ted becausana lys i s has shown t ha t the saving in roccos t more than outweighs the cos t ot renching.The wall th ickness design ar r ives a tnominal wall th ickness of 11.1 rnrn Thins ta l l a t ion submerged weight i s 591.3 N60.2 kg/m, 40.5 l b / f t ) , and the operat insubmerged weight i s 984.2 N/m.The f i r s t s tep i s pre l iminary des ign . Icalcula tes the fac tor of safe ty on pipel inweight and cover up l i f t res is tance taketoge ther . This i s the r a t io between threquired va lue , ca lcula ted from equatio

12), and the ac tua l value, the sum of thoperat ing submerged weight and the covup l i f t r es i s t ance taken from equat ion 13Figure 4 plo ts the ca lcula ted fac tor osafe ty aga ins t the depth of cover. I t cabe seen t ha t i f the cover i s 0.6 m or l e s sthe fac tor of safe ty i s less than 1 t hathe cover i s 0.7 m the fac tor of ~ f e tlS 1.11, and tha t i f the cover i s 0.8 m th

f c : c ~ o r i s 1.32. This suggests t ha t thffilnlmum cover should be a t l ea s t 0.8 ms i n c ~ a 0.7 m cover leaves only a narromargln. Accordingly, a minimum cover o0.8 m i s taken as the s t a r t i ng point foUPBUCK calcula t ions .A separate calcula t ion determines thextreme s t r es ses in operat ion, a t thimperfection and under the axia l loadinduced by the operat ing temperature anpressure . Although the hoop s t re ss i

r ~ l t i v e l y low 183 N/rnrn2, 44 per cent oYle ld) , the longi tudina l s t re ss i s highand the von Mises equivalent s t r e s s i s avyie ld . This condi t ion i s allowed by macodes, since the pipe l ine i s continuoussupported , but the high l eve l of equivalens ~ r e s ~ i s an important warning tha t th

~ l p e l l n e response to ax ia l loading may blnf luenced by p l a s t i c i t y , and t ha t it wibe prudent to carry out de ta i l ed UP BUCcalcula t ions using the p l a s t i c i t y option.Moving now to conceptual design, a se r i eof UP BUCK calcula t ions are car r ied out . Ith i s phase of the analys is , the pipe l ine it r ea ted as e la s t i c .The re su l t s of th ree UP BUCK calcula t ionare summarised in Figure 5, which p lomovement aga ins t temperature increase focover depths of 0.7, 0.8 and 0.9 m abovthe peak of the 0.3 m imperfection. I f thc,?ver. i s 1 . m from the basel ine) , th~ l p e l l n e ~ e g l n s to li t ( a t the top of thlmperfectlon) a t a temperature of about 7

5/22/2018 Otc 6335 1990 Palmer Upheaval Buckling

5/10

OTC 6335 PALMER ELL INAS RI CHARDS GUIJ ldeg C, some 10 deg C shor t of the opera t ingtempera ture . I t becomes uns tab le and jumpsin to a buckled conf igura t ion a t 88.5 deg C.This opt ion leaves too little marginbetween the opera t ing temperature and thetemperature a t which l a rge movements mightoccur , and i s therefore re jec ted .I f the cover i s 1 .1 m movements begin a tabout 80 deg C, and an unstable jump occursa t 95 deg C. At the design maximumopera t ing tempera ture , the von Misesequivalen t s t r es s i s 83 per cen t o f y i e l d ,which i s wi th in the maximum s t r es s allowedby the code.I f the cover i s 1.2 m movement does notbegin u n t i l the design temperature i sreached. The conclus ion o f the conceptualdesign phase i s therefore t ha t a cover of1.1 m from the base l ine i s adequate , andt h i s value i s chosen as the s ta r t ing poin tfo r d e t a i l ed design.Continuing to de ta i l ed design, it has beenshown e a r l i e r t ha t the pipe i s close top las t i c yie ld , and tha t UP UCK ca lcu la t ionsusing the p l a s t i c i t y opt ion are r equ i red .The r e su l t s show t ha t movements i n i t i a t e a talmost exact ly the 80 deg C designtempera ture , but do not exceed 10 mm un t i lthe tempera ture has r i s n to 88 deg C. Thei n s t a b i l i t y temperature i s 97.3 deg C.Figure 6 plo t s the movement of the pipe a tthe peak of the imperfect ion agains t thetempera ture , and shows t ha t i n s t a b i l i t ywi l l be accompanied by very l a rgemovements, in which the pipe l ine wil l breakabove the sur face of the cover . However,there i s an adequate tempera ture increasemarg in between the operat ing tempera tureand the i n s t a b i l i t y tempera ture .A cover of 1 .1 f i , measured from thebase l ine , i s therefore se lec ted . Itcorresponds to 0.8 m cover a t the peak ofthe 0.3 m imperfect ion. I t happens toco inc ide with the value reached by thes imp l i f i ed method, though th i s i s notalways the case .This cover i s only required on theoverbends. I f the c r i t i c a l overbends canbe conf iden t ly i den t i f i ed from a survey,rock need only be dumped on thoseoverbends. I t wil l usual ly be cheaper todevote resources to survey r a the r than tocont inuous dumping. This design opt ion wasrecen t ly appl i ed to the s t a b i l i s a t i o n ofthe Tern and Eider pipe l ines 4 I f on theo ther hand the s.urvey accuracy i s notsuf f i c i en t to loca te the c r i t i c a loverbends the whole l eng th must becovered.

ALTERNATIVE DESIGN STRATEGIES

The s imples t and most s t r a igh t fo rward wayof s tab i l i s ing a pipe l ine ag a in s t upheavali s to bury it. This opt ion i s of tend i f f i c u l t and expensive, and prompted asearch fo r a l t e r na t ive s . Phase 5 o f theresearch programme examined some fo r t ya l t e r na t ive des ign s t r a t eg ie s , eva lua tedeach one, and i den t i f i ed the most genera l lya t t r a c t i v e and appl icab le .Two obvious s t r a t eg ie s are to reduce thedesign opera t ing temperature and pressure ,and to increase the submerged weight of thepipe l ine . A reduc t ion in opera t ingtempera ture i s genera l ly impract icab le , butcould be accomplished by adding a heatexchanger to the system. I t i s not u su a l lyprac t i cab le to resolve the problem by anincrease in submerged weight , because toomuch weight i s required.The remaining s t r a t eg ie s can be c las s i f i edin to groups . The most promising techniquesare l i s t e d in t able 1.The f i r s t group i s based on reducing thedr iv ing fo rce , the ax ia l compressive forcein the pipe l ine . The most di r ec t method i sto reduce the wall thickness of the l i ne .This reduces the temperature component o fthe e f f ec t ive ax i a l force, which i spropor t ional to the wall th ickness and i susual ly the l a r ge s t component) , and leavesthe pressure component almost unchanged.A reduc t ion in wall t h i ckness can beachieved by increas ing the design fac to r tothe h ighes t al lowable l eve l , o r byincreas ing the grade of s t e e l , o r byadopting s t r a in -based design c r i t e r i a , aposs ib i l i ty examined below in sec t ion 7.A second method i s to increase lay tens ion .Residual l ay t ens ion balances p a r t of thecompressive force induced by opera t ing , andtherefore reduces the r e su l t an t force. Ad i f f i c u l t y i s t ha t res idua l tension cannotbe measured di r ec t ly , but must beca lcu la ted from the lay condi t ions , andt ha t i t s cont inued presence in the l i nedepends on t h e r e being no l a t e r a lmovements. A t h i r d a l t e r na t ive i s toprehea t the l ine , and to al low it to moveto re lax compressive forces induced bypreheat : the app l ica t ion of t h i s techniqueto the Sun Oil Glamis f lowl ines i sdesc r ibed in a separa te paper5 A second group o f methods depends on makinga radica l change in the s t r uc tu r e of thepipe l ine . One a l t e r na t ive i s to r ep laceone o r more s ing le l ines by a c losed bundlesuppor ted on spacers in a c a r r i e rPalmer6 , or equ ivalen t ly by a pipe- in pipe system in which an i n t e r na l f lowl inei s suppor ted in an outer pipe . Thei n t e r na l l ines in the bundle then developaxial compressive forces in opera t ion , butt hose forces can be balanced by t e n s i l efo rces in the ou ter car r ie r , through end

5

5/22/2018 Otc 6335 1990 Palmer Upheaval Buckling

6/10

6 DESIGN OF SUBM RINE PIPELINES G INST UPHE V L BUCKLING OTCbulkheads and possibly in termediatebulkheads. The in te rna l l ines may bowl a te ra l ly on the spacers , but the movementsare cont rol led and the bending s t ressesinduced may remain a t an acceptable l eve l .This e f f e c t can be fur ther enhanced bymaking the in te rna l bundle he l ica l(Duxburi) : t h i s geometry increases thereduction i n ax i a l compressive force tha taccompanies outward movements of thein te rna l l ines . A decis ion to opt fo r abundle concept na tu r a l ly has broaderimpl icat ions tha t extend f a r beyondupheaval buckl ing, which i s only one of thefac tors involved.A second radica l a l te rna t ive i s to rep lacea r i g i d s t ee l pipe l ine with a f l ex ib le .Flex ib les a re sub iec t to upheaval buckl ing(Bournaze18, Putot ,10), pr imar i ly because ofthe pressure ef f ec t . The tendency tobuckle in serv ice can be reduced by layingo r t r enching under in te rna l pressure , o r bymodifying the in ternal s t ructure away froma balanced design, so as to produce apipe which tends to con t rac t ax ia l ly whenloaded by in te rna l pressure.A t h i rd group of methods i s based ons t ab i l i s ing the pipe l ine with rock, butusing the rock in a more ef f i c i en t way, soto gain an equal ly ef fec t ive s t ab i l i s ingef f ec t with less rock. The most ef fec t iveof these methods i s only to place rock onc r i t i ca l overbends (Locke4 , but t h i s doesof course make it es sen t ia l to be able toiden t i fy the overbends confident ly , ademanding survey t ask in deep water , orwhen the c r i t i ca l imperfect ion he ight i ssmall . A second method i s to place ageo tex t i l e over the p ipe befo re the rock i splaced. When the pipe l ine begins to lift,the weight of the rock on the geo tex t i l e one i the r s ide of the pipe holds thegeo tex t i l e down, and generates a tensionwhose downward component adds to the up l i f tres i s tance of the rock above the pipe l ine .At the same t ime, the geo tex t i l e pu l l s therock inward, and increases the horizontalcompressive s t r es s in the rock above thepipe l ine , and t h a t in turn increases theshear res i s tance across po ten t ia l shearsurfaces above the pipe, fur ther increas ingthe u p l i f t res i s tance . Against th i s , onthe other hand, the use of a geo tex t i l e i na subsea environment wil l requ i re acomprehensive inves t iga t ion of i t s longterm s t a b i l i t y agains t creep and s t ruc tu ra lde te r io ra t ion .A f ina l a l t e rna t ive i s to not to place therock cont inuously along the whole length ofthe pipe l ine , but to place the rock inin te rmi t ten t dumps. This poss ib i l i t y i sdiscussed in an accompanying paperl l .The offshore pipe l ine indus t ry i s only nowbeginning to explore the many d i f fe ren tconcepts t h a t can be used to secureef fec t ive and economical s t ab i l i sa t ion , andmuch more remains to be learned.

6

STRAIN-BASED DESIGN CRITERIAIn the past , the conventional approach twall th ickness design was genera l lgoverned by two s t r es s requirements . Thf i r s t requirement i s tha t the hoo

c i rcumferen t i a l ) s t r es s n ~ t e x c ~ e ~defined f rac t ion of the spec1f1ed m1n1muyie ld s t r es s SMYS). A second requiremena l so has to be sa t i s f i ed , and takes accounof long i tud ina l s t r ess ; the maximum valuof an equivalent s t r es s must not exceedspec i f ied f rac t ion of the SMYS.. Thspec i f ied f rac t ion for the equ1vales t r ess i s genera l ly higher than thspec i f ied f rac t ion fo r the hoop s t r essThe equivalent s t r es s i s defined e i t h ~ r aa von Mises equiva lent s t r es s (proport1onto the square roo t of the second invar ianof the devia tor ic s t r ess t ensor ) , or as thdi f fe rence between the l a rges t and smal lepr inc ipa l s t r es ses .I f t h i s approach i s adopted for pipe l inetha t operate a t a high temperature, thsecond requirement often determines thwall th ickness . This happens because thlong i tud ina l s t r es s in operation i s l a rgand compressive, and because thtemperature component of s t r essindependent of the wall th ickness . Tneed to reduce the equiva lent s t r es s belothe al lowable l imit then forces down tal lowable hoop s t r ess , and t h i s in tuleads to a high wall th ickness .

n a l te rna t ive approach i s be t te r . In ~case of a cont inuously-supportconst ra ined pipe l ine on o r in the seabeexceedance of an al lowable combined s t r edoes not in i t s e l f correspond to a l ims t a t e which in any way th rea tens the safeof the l ine . I f the combined s t r es s shoureach yie ld , a l imi ted amount of p las tdeformation wil l occur, but it can be shot h a t the p las t i c components of long i tud inand hoop s t r a in are small by comparis

5/22/2018 Otc 6335 1990 Palmer Upheaval Buckling

7/10

OTC 6335 PALMER ELLINAS, RICHARDS, GUIJTthe wall th ickness . I f the equivalents t r es s requirement i s adopted, and theequivalent s t r es s i s l imi ted to 0.96 ofSMYS (as in the DnV ru les , and the s t ee lhas an SMYS of 413.7 N/mm2 (correspondingto API X60), the minimum wall th ickness i s12.8 mm. I f on the other hand theequ iva len t s t r ess requirement onlongi tudinal s t r es s i s dropped, and thehoop s t r es s i s l imi ted to 0.72 of SMYS (asin many codes) , the minimum wall th icknesscan be reduced to 9.6 mm.This reduct ion in wall th ickness leads toa substant ia l reduct ion in axia l force inoperation, and to a corresponding reduct ionin minimum cover required for s t a b i l i t y .Adoption of s t rain-based c r i t e r i a doeshowever r a i s e a number of wider quest ions ,which tend to reduce the advantages.Figure 8 plo t s the s t r es s path followed ina sequence of laying, increase intempera ture , and increase in operat ingtempera ture , in a diagram whose axes arelongi tudinal s t ress and hoop s t r es s . Thee l l ipses represent success ive yie ld l oc ifor a von Mises material with an i sot ropichardening rule . The heavy e l l i p s erepresents the nominal yie ld locus ,corresponding to the 0.5 per cent yie ldlocus , but yie ld begins before th i s locusi s reached, and i s representedschematical ly by the inner loci .I f a s t r a i n cr i t e r ion i s adopted, thes t r es s poin t S tha t represents the meanlongi tudinal and hoop s t r e s se s duringoperat ion l i e s beyond the yie ld locus , eveni f the hoop s t ress i s l ess than 0.72 ofnominal yie ld . I f the pipe then begins tobend, the points representing the s t r e s se sin the pipe in the ins ide and outsideof the curve follow the paths shown inFigure 9b. On the ins ide of the curve , thelongi tudina l s t r ess becomes morecompressive, and the s t r es s pOint moves tothe l e f t . This takes t across add i t iona ly ie ld loci , and more yie ld occurs . On theouts ide, the longi tudinal s t r es s becomesmore t ens i l e , and the s t r es s poin t movesinward, so tha t the incremental response i se l a s t i c .I t follows tha t the incremental bending ofa pipe l ine designed according_to s t r a inc r i t e r i a wil l always be accompanied byp las t i c deformation, however small thebending i s . The ef fec t i s to generate bothcircumferent ial and longi tudinal p l a s t i cs t r a in . The incremental increase inbending moment i s much smaller than twould be i f the pipe were e l a s t i c , becauseonly pa r t of the pipe i s respondinge las t i ca l ly : the ef fec t i s to reduce theincremental f l exura l r ig id i ty , which i s oneof the parameters tha t enable the p ipe tor e s i s t upheaval buckl ing. At the samet ime, p las t i c deformations re l ieve some ofthe axia l compressive force in the pipewall , and therefore reduce the drivingfo rce .

7

Plas t i c i ty e f f ec t s w i l l therefore have as ign i f i c an t influence on upheaval bucklingof pipel ines designed according to s t r a inc r i te r ia . The solut ion wil l be sens i t iveto the de ta i l s of the s t r ess - s t r a inr e l a t ion for the s tee l , pa r t i cu la r ly tos t rain-hardening. These ef fec ts are takenin to account in analysis by the UPBUCKprogram.CONCLUSION

This paper summarises design methods basedon the r esu l t s of an extensive program ofresearch in to upheaval buckl ing.

ACKNOWLEDGEMENT

The research described here was car r ied outas pa r t of a j o in t indust ry program led byShell In te rna t iona l Petroleum Maatschappijand supported by the following companies:Shell In te rna t iona le Petroleum MaatschappijMaersk Olie og Gas A/SNederlandse Aardol ie Maatschappij BVShell UK Explora t ion and ProductionA/S Norske Shel lB r i t o i l Plc BP Explora t ion)UK Department of EnergyMarathon Oil UK LimitedElf Petroland BVOccidenta l Petroleum (Caledonia)Saga Petroleum A/SSun Oil Bri ta in LimitedTotal Oil Marine plcThe authors wish to record t he i r gra t i tudefor permission to publish th i s paper .REFERENCES

Palmer, A.C.buckl ingpipe l ines .Technology,

and Baldry, J.A.S. Lateralo f ax ia l ly - compr essedJournal of Petroleum~ 1284-1284 (1974).2 Schaminee, P.E.L. , Zorn, N.F. , Schotman,G.J.M. Soi l response for p ipe l ineupheaval buckling analys i s : fu l l - s ca lelaboratory t e s t s and modell ing.Proceedings, Twenty-second AnnualOffshore Technology Conference, Houston

(1990).3 Klever, F.J . , van Helvoi r t , L.C., andSluyterman, A.C. A dedicated f in i te element model for analysing upheavalbuckling response of submarinepipe l ines . Proceedings, Twenty-secondAnnual Offshore Technology Conference,Houston (1990).4 Locke, R.B. and Sheen, R. The Tern andEider pipelines. Proceedings, 1989European Seminar on Offshore Pipel ineTechnology, Amsterdam (1989).

7

5/22/2018 Otc 6335 1990 Palmer Upheaval Buckling

8/10

8

IIIIII,I

DESIGN OF SUBM RINE PIPELINES G INST UPHE V L BUCKLING OTC5 Craig, loG. and Nash, N W Upheavalbuckling: a pract ica l solut ion using hotwater f lushing technique. Proceedings,Twenty-second Annual Offshore TechnologyConference, Houston 1990).6 Palmer, A.C. Are bundles expens ive?Proceedings, Pipel ines for MarginalFields Conference, Aberdeen 1988).7 Duxbury, P.G. and Hobbs, R.E.Hel ica l ly - l a id p ipe l ine bundles .Proceedings, Eighth In ternat ionalConference on Offshore Mechanics andArct ic Engineering, 2, 9-16 1989).8 Bournazel, C. Flambage ver t ica l desconduites ensoui l lees . Revue del I n s t i t u t Francais du Petrole , ~ 212-230 1982).

a as laid

. .. .

b trenched and buried

c start-up

~ ~. ... ,pipeline pUShes upwara.

against cover

d ' h . ~ ... - : - : ......... ...._ '_'.___Figure 1 Sequence of laying. trenching and upheaval

8

9 Putot , C.J M Localised buckling buried f l ex ib le pipel ines . ProceedinTwenty-f i rs t Annual Offshore TechnoloConference, Houston, OTC6155 1989).10 Putot , C.J M and Rigaud, J . Upheabuckling of bur ied pressur ispipel ines . Proceedings , EuropSeminar on Offshore Pipe l ine TechnologPar is 1990).11 Ell inas , C.P., Supple, W.J. aVastenholt , H Prevention of upheabuckling of hot submarine pipel inesmeans of in te rmi t ten t rock-dumpinProceedings, Twenty-second AnnOffshore Technology Conference, Hous1990).

8 [J,2 r

~ 1 ____ ____ , ______ ____ ___o .81 .82 .83Figure 2 Numerical correlation of UPBUCK results

5/22/2018 Otc 6335 1990 Palmer Upheaval Buckling

9/10

enen=

(]i j'. 06

. 0..l

.0:I0

temperature100

deg C80

60

40

Figure S

5

Figure 3

.0.02