Buckling of pipelines

FOliMTEENTH WEGEMT-SCHOOLt S L E N D E R MARINE STRUCTÜS,¥;S

Pay 1 - Möaday 21 laimary

11.00" 11.45 Introduction Motivation

Carl M LarsöE, N T H

Ï2.00 ' 12.45 Tensioned beam, the basic differential equation

Mariaus Van. Hoist, Delft

™ IJ

14,00 - 14,45 E ö e c t f r o m pressme and internal

tlow

15.00 - 15.45 Hydrodynamic force models

Van Holst/Erling Hnse

16,00 - 16.45 Fmite element models

C M Larsen

09.00 - 09,45 Introduction to marine riser systems

D G Owen, Heriot^Watt

10,00 - 10,45 Methods f o r stochastic dynamic analysis

11.00 - 11.45 Linearization techniques

C M Larsen

14.00 •• 14,45 Modelling strategy, global riser analysis

B O Owen

15.00 - 18,00 Exercise: Use of R I S A N A , riser analysis

Day 3 • Wednesday 33 January

09.00 - 09.45 Stress analysis, banded flexible-pipes

D G Owen

10,00 - 10.45 Stress analysis, unbonded pipes

y\rild Bech, SINTEF

ll.ÜO

11A5

Components i n riser systems

D G O^ven

12,0[) - 12.45 Fatigue analysis, steel risers

C M Larsen

14.00 " 14.45 Extreme respoisse estimation, steel risers

C M Larsen

15.00 - 15,45 Model tests o f tengioEed and flexible risers

D G Owen

16.00 - 18.00 Exercise: Use of EJSANA, riser analysis

IDay 4 = Tfena-sjSay 24 Janmary

09.00 - 09.45 Installation of pipelines and risers

Ivar Fyding, ï i A M i ^ n E K

Uplieaval buckling of pipelines

P T Pedersen, D T H

Towing of long pipeline sectioj

H Boonstra, D«!ft |

Bncklmg of pipelines

4

H Boonstra

4

Exercise; Pipeline analysis, upheaval buckling

10.00 - 10,45

11.00-11.45

12,00 - 12,45

14.00 - 14.45

15.00 - 17.00

Day 5 - Friday 2§ January

09,00 - 09,45 On-bottom stability of pipelines

10.00 - 10.45 Torbj0rn Sotberg, SINTEF

11.00 - 11.45 Free-span problems

12.00 " 12.45 Mads Bryndum, Danish Hydraulic Inst

14.00 - 14.45

15.00 - 15.45

Pipeline stresses and deformation during laying

P T Pedersen

1. C M . Larsen

2. Van Hoist

3. E . Huse

4 . D.G.Owen

5 ,

A. BecliL

6. L J. Fylling

7.

P.T. Pedersen

8. H. Boonstra

» •

9. T= Sotberg

10« Mads Bryndum

WEGEMT S c h o o l , Trondheim, J a n u a r y 1991. BUCKLING OP P I P E L I N E S Hotze B o o n s t r a S e n i o r S c i e n t i f i c O f f i c e r T e c h n i c a l U n i v e r s i t y D e l f t F a c u l t y o f M e c h a n i c a l E n g i n e e r i n g

and Marine Technology

SUMMARY

The b u c k l i n g o f p i p e l i n e s due t o ( m a i n l y ) h y d r o s t a t i c p r e s s u r e I s d i s c u s s e d and a l i m i t e d s u r v e y o f r e s e a r c h on l o c a l b u c k l i n g and b u c k l e p r o p a g a t i o n p r e s e n t e d . H y d r o s t a t i c p r e s s u r e on a p i p e l i n e becomes a n important l o a d i n g i n deep w a t e r , b u t f o r p i p e l i n e s where the D/t r a t i o h a s to be h i g h , t h i s l o a d c a s e may be a l s o i m p o r t a n t i n moderate w a t e r depths. Although t h e h y d r o s t a t i c l o a d i n g on a c i r c u l a r p i p e i s o f s t r i k i n g s i m p l i c i t y , the f a c t t h a t a s p e c t s s u c h a s b u c k l i n g ( e l a s t i c a s w e l l a s p l a s t i c ) , a x i a l s t r e s s e s due t o bending and t e n s i o n , and p i p e i m p e r f e c t i o n s p l a y a r o l e , the a n a l y s i s i s n e v e r t h e l e s s complex.

INTRODUCTION

I n t h e o r y the s t r e n g t h a n a l y s i s o f a p i p e l i n e s h o u l d , J u s t as i n o t h e r s t r u c t u r a l e n g i n e e r i n g problems, be b a s e d on a r e a l i s t i c model and take I n t o a c c o u n t a l l p o s s i b l e l o a d i n g c o m b i n a t i o n s . However a l s o i n c o n f o r m i t y w i t h o t h e r e n g i n e e r i n g i n v e s t i g a t i o n s , f o r p r a c t i c a l r e a s o n s che s t r u c t u r a l model i s o f t e n s i m p l i f i e d and the complex l o a d i n g i s g e n e r a l l y s p l i t up o r s i m p l i f i e d t o the one o r two g o v e r n i n g l o a d i n g c a s e s i n a p a r t i c u l a r s i t u a t i o n , w h i l e f o r a d d i t i o n a l l o a d i n g s and f o r p o s s i b l e i m p e r f e c t i o n s o f t h e s t r u c t u r e a c e r t a i n s a f e t y margin i s i n c l u d e d . Examples a r e the a n a l y s i s o f p i p e l i n e s during l a y i n g , where a combination o f bending and e x t e r n a l p r e s s u r e i s g o v e r n i n g (and where s t r e s s e s may d e v e l o p s i g n i f i c a n t l y above the e l a s t i c l i m i t ) and f r e e span problems where h y d r o s t a t i c p r e s s u r e and bending due t o weight a r e g o v e r n i n g . However i n b o t h c a s e s a number o f o t h e r l o a d i n g s may a c t on the p i p e l i n e , w h i c h a r e not e x p l i c i t l y t a k e n i n t o a c c o u n t i n t h e e n g i n e e r i n g a n a l y s i s .

T h i s paper d e a l s w i t h the phenomenon o f b u c k l i n g o f p i p e l i n e s due to ( m a i n l y ) e x t e r n a l p r e s s u r e , but a l s o a t t e n t i o n w i l l be p a i d to a d d i t i o n a l l o c a l e f f e c t s o f bending and a x i a l f o r c e s which w i l l o c c u r d u r i n g l a y i n g o f p i p e l i n e s . T h i s means t h a t c o n s i d e r a t i o n s and formulas p r e s e n t e d here a r e i n p a r t i c u l a r o f i n t e r e s t f o r p i p e l i n e s i n s t a l l e d o r to be i n s t a l l e d i n deep o r v e r y deep w a t e r , s a y 1000 m o r more, where the h y d r o s t a t i c p r e s s u r e i s e x t r e m e l y h i g h . But. a s we w i l l see i n the next s e c t i o n , i n some c a s e s b u c k l i n g due t o e x t e r n a l p r e s s u r e may a l s o be c r i t i c a l I n much s m a l l e r w a t e r d e p t h s . P l a s t i c d e f o r m a t i o n i s i n t h i s c a s e g e n e r a l l y n o t a l l o w e d a s t h e r e i s no r e s t o r i n g mechanism and t h e d e f o r m a t i o n would r e s u l t i n out o f roundness ( w h i c h may p r e c l u d e p i g g i n g o f the p i p e l i n e ) o r may I n the w o r s t c a s e even c a u s e c o l l a p s e .

2

P I P E L I N E S ONDER EXTERNAL PRESSURE

The c l a s s i c a l c a s e o f a p i p e l i n e under e x t e m a l h y d r o s t a t i c p r e s s u r e i s shown i n F i g u r e 1, w h i c h may r e p r e s e n t i n o f f s h o r e t e c h n o l o g y a gas p i p e l i n e i n de-p r e s s u r l z e d c o n d i t i o n . ( P i de-p e l i n e s f o r o i l t r a n s de-p o r t w i l l under normal c o n d i t i o n s n e v e r be empty and a l w a y s have an i n t e r n a l p r e s s u r e about e q u a l to the e x t e r n a l h y d r o s t a t i c p r e s s u r e , even i f no f l u i d i s pumped through che l i n e ) . I t s h o u l d be noCed Chat che h y d r o s C a t i c p r e s s u r e must be c o n s i d e r a b l e i n o r d e r t o become a c r i t i c a l l o a d i n g : s a y 300 m w a t e r head f o r a p i p e w i t h a d i a m e t e r / t h i c k n e s s r a t i o D/t- 50 and 1500 m w a t e r head i n c a s e o f D/t- 25, Nonnal p i p e l i n e s d e s i g n e d f o r t r a n s p o r t o f h y d r o c a r b o n s w i l l g e n e r a l l y comply w i t h t h e s e D/t r a t i o ' s and o n l y i n water d e p t h s o f 2000 m and beyond the h y d r o s t a t i c p r e s s u r e a l o n e becomes the g o v e r n i n g f a c t o r . However i n o t h e r c a s e s p i p e s w i t h a r e l a t i v e l y s m a l l D/t r a t i o a r e r e q u i r e d . F i g u r e 2 shows a c r o s s s e c t i o n o f a p i p e l i n e bundle c o n s i s t i n g o f two f l o w l l n e s p r o v i d e d w t t h i n s u l a t i o n , i n s i d e a c a r r i e r p i p e . The p i p e l i n e b u n d l e t s t r a n s p o r C e d Co l o c a c i o n by means o f che mid depch tow, w h i c h r e q u i r e s an average c r o s s s e c t i o n a l weight which i s l e s s than i t s buoyancy. T h i s requirement l i m i t s the w a l l t h i c k n e s s o f the c a r r i e r pipe and a l s o the w a l l t h i c k n e s s of che s l e e v e p i p e around che i n s u l a C i o n . So i n t h i s c a s e h y d r o s t a c i c p r e s s u r e may become the g o v e r n i n g l o a d i n g a t a much s m a l l e r water depth, s a y 250 m.

RESEARCH ON COLLAPSE OF HYDROSTATICALLY LOADED P I P E L I N E S ,

With t h e e v e r I n c r e a s i n g w a t e r depth i n w h i c h o f f s h o r e p l a t f o r m s a r e o p e r a t i n g and the need to t r a n s p o r t h y d r o c a r b o n s through deep p a r t s o f the o c e a n , a l o t o f r e s e a r c h , t h e o r e t i c a l , c o m p u t a t i o n a l as w e l l a s e x p e r i m e n t a l work has been

i n i t i a t e d on p i p e l i n e s under e x t e r n a l h y d r o s t a t i c p r e s s u r e . Both e l a s t i c and p l a s t i c d e f o r m a t i o n o f p i p e l i n e s has been looked i n t o i n t h i s r e s e a r c h , o f t e n

i n c o m b i n a t i o n w t t h o t h e r l o a d i n g s s u c h as bending and a x i a l t e n s i o n , because t h e l a y i n g o f p i p e l i n e s i s i n many c a s e s c o n s i d e r e d to be the most c r i t i c a l l o a d i n g c o n d i t i o n . I n p a r t i c u l a r d u r i n g l a y i n g o p e r a t i o n s l o a d i n g s i n the p l a s t i c r e g i o n c a n not always be avoided, r e s u l t i n g I n complex s t r e s s - s t r a i n c a l c u l a t i o n s . A s h p r c r e v i e w o f r e l e v a n t l i t e r a t u r e I s g i v e n below.

L a n g n e r , 11) d e s c r i b e s the r e s u l t s o f a deep water p i p e l i n e f e a s i b i l i t y study p e r f o r m e d by a group o f 39 companies headed by S h e l l t n the raid 1970's. U n g n e r a l s o g i v e s an e x t e n s i v e r e v i e w o f p r e v i o u s f i n d i n g s by o C h e r s . He c o n c l u d e s t h a t I n s p i t e o f t h e complex c o l l a p s e b e h a v i o r o f p i p e l i n e s a s a f e p i p e l i n e d e s i g n c a n be a c h i e v e d by a p p l y i n g a s e t o f r e l a t i v e l y s i m p l e d e s i g n r u l e s . However t h e r e s t i l l e x i s t s u n c e r t a l n c y on Che e f f e c C o f o v a l i c y . e c c e n t r i c i t y , and r e s i d u a l s t r e s s on the u l t i m a t e p i p e l i n e c o l l a p s e p r e s s u r e l o a d i n g and Langner a d v o c a t e s e x p e r i m e n t a l t e s t s to i n v e s t i g a t e the e f f e c t o f t h e s e i n a c c u r a c i e s . P a r t o f h i s work w i l l be d i s c u s s e d i n the next s e c t i o n .

Johns e t a l [2] have determined a m a t h e m a t i c a l l y " e x a c t " p l a s t i c b u c k l i n g behavior o f a p i p e by s o l v i n g d i f f e r e n t i a l e q u a t i o n s d e s c r i b i n g the s t r e s s - s t r a i n r e l a t i o n , t h e c o m p a t i b i l i t y e q u a t i o n , and the e q u i l i b r i u m e q u a t i o n . The method i s v e r y c o m p l i c a t e d and t h e r e f o r e d i f f i c u l t to employ i n p r a c t i c a l e n g i n e e r i n g s i t u a t i o n s . De W i n t e r [ 3 , 4 ] p r e s e n t s an approximate method f o r the p l a s t i c b u c k l i n g b e h a v i o r o f a p i p e l i n e s e c t i o n under v a r i o u s l o a d i n g c o n d i t i o n s , i n c l u d i n g h y d r o s t a t i c p r e s s u r e and b e n d i n g . I n an i n g e n i o u s way t h e v e r y c o m p l i c a t e d b e h a v i o r o f the p i p e i s s i m p l i f i e d by assuming t h a t the p i p e c r o s s s e c t i o n c a n be m o d e l l e d by s p l i t t i n g i t i n t o a bending element and a number o f s t i f f r o c k e r e l e m e n t s w i t h

3

h i n g e s . I n t h i s way s o l u t i o n s c a n be o b t a i n e d w i t h r e l a t i v e l y s i m p l e c o m p u t a t i o n s *rfiich o t h e r w i s e would r e q u i r e advanced non- l i n e a r f i n i t e element computer programs. I n the n e x t s e c t i o n the b a s i c i d e a b e h i n d t h i s method w i l l be e x p l a i n e d . Odland [ 5 ] touches upon the b u c k l i n g o f u n s t l f f e n e d c y l i n d r i c a l s h e l l s ( w h i c h p i p e l i n e s i n f a c t a r e ) as the asymptotic c a s e o f more complex s t r u c t u r e s , I n c l u d i n g s t i f f e n e d c y l i n d e r s , f o r which he i n v e s t i g a t e s problems caused by c o m b i n a t i o n s o f e l a s t i c b u c k l i n g and y i e l d i n g and c o m b i n a t i o n s o f s e v e r a l l o a d components. Cortona e t a l [ 6 ) have performed model t e s t s w i t h r e l a t i v e l y t h i c k w a l l p i p e (D/t - 34.5, r e s p e c t i v e l y 18.2) under combined h y d r o s t a t i c p r e s s u r e and b e n d i n g moment. S e v e r a l d e s i g n f o r m u l a ' s p r e s e n t e d by og Langner, De W i n t e r and J o h n s are compared w i t h the r e s u l t s o f the t e s t s . I t i s found t h a t the l o a d i n g sequence ( f i r s t p r e s s u r e , than bending moment o r r e v e r s e ) has a c o n s i d e r a b l e e f f e c t on the outcome o f the t e s t s . I t appears t h a t the sequence w h i c h o c c u r s d u r i n g l a y i n g ( f i r s t p r e s s u r e , then bending) r e s u l t s i n a s u b s t a n t i a l l y lower c o l l a p s e r e s i s t a n c e t h a n the r e v e r s e d l o a d i n g sequence ( f i r s t bending, then p r e s s u r e ) .

Once a b u c k l e i s i n i t i a t e d i n a p i p e l i n e which i s loaded by h y d r o s t a t i c p r e s s u r e the b u c k l e may propagate a l o n g the p i p e . I t a p p e a r s t h a t t h e h y d r o s t a t i c p r e s s u r e which i s r e q u i r e d f o r t h i s b u c k l e p r o p a g a t i o n phenomenon i s c o n s i d e r a b l y l o w e r than the p r e s s u r e r e q u i r e d t o i n i t i a t e the b u c k l e i n a p i p e l i n e s e c t i o n w i t h o u t s e r i o u s d e f e c t s . T h i s means t h a t i f the r i g h t c i r c u m s t a n c e s a r e t h e r e a l o c a l b u c k l e c a u s e d by f o r i n s t a n c e a s m a l l d e f e c t I n the p i p e or a temporary l o c a l h i g h bending moment may r e s u l t I n f l a t t e n i n g o f s e v e r a l k i l o m e t e r s óf p i p e l i n e I n f a c t the b u c k l e o n l y w i l l stop when I t r e a c h e s s h a l l o w e r water depth To a v o i d t h i s p i p e l i n e s which a r e s e n s i t i v e to b u c k l e p r o p a g a t i o n a r e g e n e r a l l y provided w i t h b u c k l e a r r e s t o r s . The mechanism o f b u c k l e propagation and e n g i n e e r i n g formula's to c a l c u l a t e the p r o p a g a t i n g h y d r o s t a t i c p r e s s u r e a r e i n v e s t i g a t e d by U n g n e r ( I ] , De Winter [ 3 J , K y r i a k i d e s ( 7 ) and T a s s o u l a s [ 8 ] . I n the n e x t s e c t i o n the b u c k l e p r o p a g a t i o n w i l l be d i s c u s s e d f u r t h e r .

BASIC COLLAPSE RELATIONSHIPS

I t i s not s t r a n g e t h a t the s i m p l e s t r u c t u r e and s i m p l e l o a d i n g c a s e a s shown I n F i g . l has a t t r a c t e d the a t t e n t i o n o f s t r u c t u r a l e n g i n e e r s and r e s e a r c h e r s i n the I 9 t h c e n t u r y a l r e a d y and indeed the t h e o r e t i c a l c o l l a p s e p r e s s u r e f o r a c i r c u l a r r i n g and a tube under u n i f o r m e x t e r n a l p r e s s u r e a r e r e p o r t e d to have been f o r m u l a t e d by r e s p e c t i v e l y B r e s s e (1866) and Bryan ( 1 8 8 8 ) . They found t h a t b u c k l i n g o f a r e l a t i v e l y t h i n w a l l e d r i n g shows much s i m i l a r i t y w i t h the c l a s s i c a l c a s e o f b u c k l i n g o f a s l e n d e r b a r under a x i a l c o m p r e s s i o n . The r e l a t i o n s h i p s , v a l i d f o r e l a s t i c a n a l y s i s , a r e g i v e n below I n e q u a t i o n ( I ) for a r i n g and e q u a t i o n (2) f o r a tube. I t appears from t h i s e q u a t i o n s t h a t . J u s t a s i n c a s e o f the b u c k l i n g o f a s l e n d e r bar, the y i e l d s t r e s s does not e f f e c t the b u c k l i n g p r e s s u r e The f o r m u l a f o r r i n g b u c k l i n g r e a d s : P.-2£<-|)' ( 1 ) Where: Pe- e l a s t i c b u c k l i n g p r e s s u r e E - modulus o f e l a s t i c i t y t - w a l l t h i c k n e s s D - d i a m e t e r

The f o r m u l a f o r tube b u c k l i n g r e a d s :

P, ( 2 )

Where: v - P o i s s o n ' s r a t i o

Timoshenko and G e r e i n t h e i r c l a s s i c a l work "Theory o f E l a s t i c S t a b i l i t y " [9] e x p l a i n t h e d e r i v a t i o n f o r t h e c a s e t h e tube i s e x a c t l y c i r c u l a r and a l s o g i v e approximate formula's f o r d e c r e a s e o f t h e e l a s t i c b u c k l i n g p r e s s u r e due to i n i t i a l e l l i p t i c l t y ( o r unroundness) which i n r e a l i t y always w i l l be p r e s e n t i n p i p e l i n e s . The r e s i s t a n c e a g a i n s t b u c k l i n g o f a p i p e l i n e i s e x p r e s s e d i n e q u a t i o n ( 2 ) a s t h e a l l o w a b l e e x t e r n a l p r e s s u r e o r w a t e r head. F o r e n g i n e e r i n g purpose t h i s i s a c o n v e n i e n t y a r d s t i c k , however t h e p h y s i c a l r e l e v a n t u n i t i s o f f c o u r s e t h e a l l o w a b l e s t r e s s i n t h e p i p e l i n e m a t e r i a l . The r e l a t i o n between hoop s t r e s s and e x t e r n a l p r e s s u r e i s g i v e n by:

With e q u a t i o n s ( 2 ) and ( 3 ) t h e e l a s t i c b u c k l i n g s t r e s s c a n e a s i l y be d e r i v e d :

Where: b u c k l i n g s t r e s s

F o r a t h i c k - w a l l p i p e e l a s t i c b u c k l i n g does not p l a y a r o l e and t h e c o l l a p s e p r e s s u r e i s e q u a l to o r g r e a t e r t h a n t h e p r e s s u r e a t w h i c h y i e l d o c c u r s : Where: Py- y i e l d p r e s s u r e cr - y i e l d s t r e s s C" Langner ( 1 ) h a s shown t h a t e q u a t i o n ( 2 ) g i v e s a c o n s e r v a t i v e p r e d i c t i o n f o r t h e c o l l a p s e p r e s s u r e o f a t h i n - w a l l p i p e ( a t l e a s t when s u f f i c i e n t margins f o r t h e o v a l i t y , o t h e r i m p e r f e c t i o n s and a x i a l s t r e s s e s a r e t a k e n i n t o a c c o u n t ) and e q u a t i o n ( 5 ) g i v e s a c o n s e r v a t i v e p r e d i c t i o n f o r t h i c k - w a l l p i p e . However f o r t h e zone i n between b o t h e q u a t i o n s p r e d i c t the c o l l a p s e p r e s s u r e c o n s e r v a t i v e . Langner p r o p o s e s to combine both c a s e s a s f o l l o w s :

un-P^y

( 6 ) Where: P c - c o l l a p s e p r e s s u r e

The i n f l u e n c e o f a x i a l s t r e s s e s i n t h e p i p e on t h e e l a s t i c c o l l a p s e p r e s s u r e ( E q u a t i o n ( 2 ) ) maybe n e g l e c t e d , so the e l a s t i c behavior o f t h e pipe i s p r a c t i c a l l y i n d e p e n d e n t o f e x t e m a l l o a d i n g s on t h e p i p e o t h e r than h y d r o s t a t i c p r e s s u r e C o n t r a r y t o t h i s t h e p l a s t i c ( o r y i e l d ) c o l l a p s e p r e s s u r e ( e l . ( 5 ) ) i s c e r t a i n l y r e d u c e d by a x i a l s t r e s s e s . T h i s I s b e c a u s e the e q u i v a l e n t s t r e s s i n t h e p i p e c a n n o t e x c e e d t h e y i e l d s t r e s s .

•>

Langner (1) proposes a s i m p l e f o r m u l a f o r the r e d u c e d y i e l d p r e s s u r e w h i c h t a k e s i n t o account the a x i a l t e n s i o n and bending moment ( o r v e c t o r i a l moment due to combined bending and t o r q u e ) . :

( 7 )

The s u f f i x T and M i n e q u a t i o n ( 7 ) r e f e r to s t r e s s e s due to t e n s i o n and b e n d i n g moment r e s p e c t i v e l y . I t s h o u l d be n o t e d t h a t the t e n s i o n here i s the " e f f e c t i v e t e n s i o n " , l e the s t r e s s c a u s e d by the r e a l a x i a l f o r c e a c t i n g on the p i p e l i n e not I n c l u d i n g the e f f e c t o f h y d r o s t a t i c p r e s s u r e on the end caps o f che p i p e ' O t h e r s have f o r m u l a t e d much more c o m p l i c a t e d r e l a t i o n s h i p s , see f o r i n s t a n c e De W i n t e r e t a l ( 4 J .

The e q u a t i o n s above a r e v a l i d f o r an i d e a l p i p e l i n e . I n r e a l i t y i n i t i a l I m p e r f e c t i o n s reduce the a l l o w a b l e l o a d s . The most i m p o r t a n t i m p e r f e c t i o n s i n t h i s r e s p e c t a c e :

o v a l i t y o r I n i t i a l unroundness

e c c e n t r i c i t y , the d e v i a t i o n o f w a l l t h i c k n e s s from the a v e r a g e v a l u e r e s i d u a l s t r e s s from f a b r i c a t i o n , eg c o l d bending or s t r a i g h t e n i n g Langner ( l ) g i v e s an e m p i r i c a l r e l a t i o n f o r the d e c r e a s e i n c o l l a p s e p r e s s u r e and the I m p e r f e c t i o n s . As the i m p e r f e c t i o n s a r e g e n e r a l l y not known b e f o r e h a n d f o r e n g i n e e r i n g p u r p o s e s i t i s c o n v e n i e n t to adhere to s a f e t y f a c t o r s i n thé d e s i g n o f p i p e l i n e s w h i c h I n c l u d e " s t a n d a r d " f a b r i c a t i o n i m p e r f e c t i o n s . As a g u i d a n c e the f o l l o w i n g can be used:

P < 0.72 P ( c o l l a p s e )

p r o v i d e d t h a t : o v a l i t y < O.Ol e c c e n t r i c i t y < 0.1

I n some c a s e s , n o t a b l y when the p i p e l i n e I s not p r o v i d e d w i t h b u c k l e a r r e s t o r s or when I t i s i m p o s s i b l e to r e p a i r the p i p e l i n e a f t e r i n s t a l l a t i o n , the propagating p r e s s u r e i n s t e a d o f the c o l l a p s e p r e s s u r e should be used a s the r e f e r e n c e p r e s s u r e R e g u l a t o r y b o d i e s may r e q u i r e a n o t h e r s a f e t y f a c t o r t h a n 0.72.

The g e n e r a l r e l a t i o n between h y d r o s t a t i c p r e s s u r e and o v a l i s a t i o n o f a p i p e l i n e i s shown i n F i g 3, where both the c u r v e f o r e l a s t i c and p l a s t i c b e h a v i o r a r e p l o t t e d . The i n t e r s e c t i o n o f both c u r v e s depends on m a i n l y the D/t r a t i o but a l s o on the y i e l d s t r e s s and the a x i a l l o a d i n g o f the p i p e . For t h i n w a l l ' p i p e ( l a r g e D/t r a t i o ) t h e r e i s no i n t e r s e c t i o n between the two c u r v e s : the c o l l a p s e i s c o m p l e t e l y e l a s C l c . F o r mosC p r a c c l c a l c a s e s i n o f f s h o r e p i p e l i n e s che two c u r v e s do i n t e r s e c t and che I n t e r s e c t i o n p o i n t determines the h y d r o s t a c i c p r e s s u r e a t w h i c h c o l l a p s e o c c u r s .

Because c o l l a p s e o f p i p e l i n e s used i n o f f s h o r e a p p l i c a t i o n s almost always i n c l u d e l a r g e p l a s t i c d e f o r m a t i o n s due to the s m a l l D/t r e l a t i o n a n e x a c t a n a l y s i s c a n o n l y be c a r r i e d out w i t h the a i d o f advanced n o n - l i n e a r f i n i t e element computer programs. I n o r d e r to a v o i d t h i s , an approximate model h a s been d e v e l o p e d by Vrouwenvclder and W l t t e v e e n . a d e t a i l e d d e s c r i p t i o n c a n be found i n two p a p e r s by De Winter e t a l , ( R e f ( 2 . 3 ] ) . Based on the o b s e r v a t i o n s o f che c o l l a p s e sequence o f a p i p e s c c c l o n under e x c e r n a l p r e s s u r e and che shape o f che deformed c r o s s s e c t i o n ( s e e F i g 4.5) I t was c o n c l u d e d t h a t the e n e r g y r e q u i r e d to deform t h e p i p e i s mainly c o n c e n t r a t e d I n f o u r p l a s t i c h i n g e s . I t was then d e c i d e d to model the p i p e c r o s s s e c t i o n by a "bending element", w h i c h r e s i s t s d e f o r m a t i o n s and four r o c k e r elements". connected by h i n g e s , on which the e x t e m a l l o a d i s a p p l i e d (see F i g 6 ) . W h i l e t h i s model I s e a s y to u n d e r s t a n d and because I t c a n i n c l u d e

^~

I n i t i a l i m p e r f e c t i o n s o f the p i p e and g i v e s i n s i g h t I n t h e n a t u r e o f c o l l a p s e , the b a s i c i d e a w i l l be e x p l a i n e d h e r e b r i e f l y . As an i n t r o d u c t i o n the c l a s s i c a l c a s e o f che b u c k l i n g o f a column under a x i a l c o m p r e s s i o n w i l l be c o n s i d e r e d , I n c l u d i n g a s i m i l a r approximate model f o r t h i s c a s e , s e e F i g 7. I n che exacC c a s e che d i f f e r e n c i a l e q u a c l o n can be w r l c c e n down and c a n be s o l v e d , r e s u l C s , f o r Che e l a s c i c c a s e i n : which

EI ( B )

4

V

The column c a n be m o d e l l e d a s a bending elemenC w h i c h c a k e s no a x i a l l o a d s and a h i n g e d r o c k e r olemenC on which che a x i a l l o a d i s a p p l i e d ( s e e F i g 7 ) . T h i s s i m p l i f i e d model c a n be s o l v e d by s i m p l e c a l c u l u s and one a r r i v e s a c :

Of c o u r s e the s i m p l i f i e d s o l u c l o n d i f f e r s from Che e x a c c s o l u C i o n but i t g i v e s i n s i g h t i n the r e l e v a n t p a r a m e t e r s I n the b u c k l i n g b e h a v i o r o f the column. I n a s i m i l a r way the model shown I n F i g 6 can be u s e d to a n a l y z e I n a s i m p l i f i e d way the c o l l a p s e b e h a v i o r o f a r i n g o r a p i p e l i n e s e c t i o n . The f o u r s t i f f r o c k e r elements together form a c i r c l e and a r e connected to each o t h e r and to the c i r c u l a r bending element by means o f h i n g e s . The d i f f e r e n t diameters o f the bending element and the r o c k e r element i n t h i s s k e t c h a r e f o r i l l u s t r a t i v e purpose o n l y ; i n the model f o r the a n a l y s i s t h e two r i n g s c o i n c i d e . I n F i g 8 the e x t e r n a l l o a d s a c t i n g on the r o c k e r element a r e shown. F i g 9 shows the " I n t e r n a l " f o r c e s i n the c o n n e c t i o n s between r o c k e r elemenc and bending elemenc. De Wincer e c a l ( 3 , 4 ) have shown chac wlCh C h l s s i m p l e model can be u s e d co a r r i v e aC approxiraace f o r m u l a s f o r Che c o l l a p s e b e h a v i o r o f p i p e s loaded by e x c e r n a l p r e s s u r e , a x i a l f o r c e and bending moment, b o t h i n the e l a s t i c and p l a s t i c r a n g e . A l s o the model c o r r e c t l y p r e d i c t s r e s u l t s known from a n a l y t i c a l and e x p e r i m e n t a l work, i n c l u d i n g

the f a c t t h a t : * I n i t i a l o u t o f roundness h a r d l y a f f e c t s the e l a s t i c c o l l a p s e p r e s s u r e ,

but g r e a t l y r e d u c e s the p l a s t i c c o l l a p s e p r e s s u r e ; I . e . i t i s o f i m p o r t a n c e f o r p i p e s w i t h low D/t r a t i o .

A x i a l t e n s i o n i n t h e p i p e does not a f f e c t the e l a s t i c c o l l a p s e p r e s s u r e b u t d i r e c t l y d e c r e a s e s the p l a s t i c c o l l a p s e p r e s s u r e .

BUCKLE PROPAGATION

ne I t h a s e x p e r i m e n t a l l y been shown c h a t when a b u c k l e i s i n i C l a C e d i n a p i p e l i . . , w h i c h I s l o a d e d by a h i g h e x c e r n a l p r e s s u r e che b u c k l e w i l l propagaCe a l o n g che p i p e w i c h g r e a c s p e e d (300 m/s has been measured) and w i l l c a u s e f l a t c e n l n g o f che complece p i p e l i n e i f no p r e c a u t i o n s have been caken. s u c h a s che t n s c a l l a c l o n o f buckle a r r e s c o r s a t r e g u l a r I n t e r v a l s o f che p i p e l i n e . Experiraencs a l s o I n d i c a c e chac che h y d r o s t a t i c p r e s s u r e r e q u i r e d f o r the b u c k l e p r o p a g a c l o n i s c o n s i d e r a b l y lower Chan Che c o l l a p s e p r e s s u r e due Co h y d r o s C a C i c p r e s s u r e a l o n e , e s p e c i a l l y f o r c h i n w a l l p i p e ( h i g h D/c r a t i o ) . T h i s i s a p o t e n t i a l l y dangerous s i t u a t i o n : b u c k l i n g I n i t i a t e d due to a n I m p e r f e c t i o n i n the p i p e or due to a temporary h i g h b e n d i n g moment d u r i n g l a y i n g may endanger the complete p i p e l i n e . Even i f b u c k l e a r r e s t o r s a r e I n s t a l l e d and the b u c k l i n g i s l i m i t e d to a r e s t r i c t e d l e n g t h , c o s t s o f r e p a i r o f a p i p e l i n e s e c t i o n on the s e a b e d i s e x t r e m e l y h i g h , and I n some c a s e s v i r t u a l l y i m p o s s i b l e . T h e r e f o r e i t i s o f t e n a d v i s a b l e t o b a s e che p i p e l i n e d e s i g n on the maximum b u c k l e p r o p a g a c i n g p r e s s u r e I n s c e a d o f c o l l a p s e p r e s s u r e , e s p e c i a l l y f o r deepwater p i p e l i n e s . For p i p e l i i wlchouC b u c k l e a r r e s c o r s I t I s even a requirement (DnV ( 1 0 ) , Langner ( 1 ) )

7

I n F i g u r e 10 t h e d e f o r m a t i o n o f t h e p i p e due t o the b u c k l e p r o p a g a t i o n i s s c h e m a t i c a l l y shown. The p h y s i c a l e x p l a n a t i o n f o r t h e f a c t t h a t che b u c k l e p r o p a g a t i o n p r e s s u r e i s l o w e r t h a n t h e c o l l a p s e p r e s s u r e s h o u l d be found i n t h e f a c t t h a t an o r i g i n a l l y c i r c u l a r p i p e s e c t i o n I s deformed by t h e f l a t t e n e d a d j a c e n t s e c t i o n . However a t h e o r e t i c a l t r e a t m e n t o f the phenomenon which i n c l u d e s the work d i s s i p a t i o n by s t r a i n h a r d e n i n g and a x i a l e f f e c t s i s n o t a v a i l a b l e . S e v e r a l e m p i r i c a l f o r m u l a t i o n s , based on both model t e s t s and ( s i m p l i f i e d ) computer a n a l y s e s have been f o r m u l a t e d i n t h e r e c e n t pasC ( s e e eg [ 1 ] , [ 4 ] , [ 7 ] , [ 8 ] , [ 1 0 ] ) . I C i s a g r e e d by most i n v e s c l g a t o r s t h a t che b u c k l e p r o p a g a t i o n p r e s s u r e i s p r o p o r t i o n a l t o t h e y i e l d s t r e s s and t o t h e t/D r a t i o t o t h e power 2.0 o r 2.4. Some o f the more w e l l known f o r m u l a ' s r e a d :

K y r i a k i d e s ( 7 ) : fp» (10.4+0.54 (-|!) 3 ( - ^ ) ' - " a ^ ( 1 0 ) Where: Pp- P r o p a g a t i n g p r e s s u r e E ' - P o s t - y i e l d s l o p e o f E l a s t i c i t y modulus DnV ( 1 0 ) : V l- 1 5 i t ( - ^ ) ^ o ^ ( 1 1 ) Langner ( 1 ) : P p = [ 2 4 { - ^ ) ' \ 4 8 0 0 0 ( - | ) ' ] 0 y ( 1 2 ) Froin t h e s e f o r m u l a ' s I t f o l l o w s t h a t the b u c k l e p r o p a g a t i o n p r e s s u r e i n c r e a s e s s h a r p w i t h i n c r e a s i n g t/D r a t i o ( n o t e i n p a r t i c u l a r the second term i n E q u a t i o n 12) and Indeed f o r t h i c k w a l l pipe ( t / D > O.l) I t approaches the c o l l a p s e p r e s s u r e .

REFERENCES

1. C G Langner: "Design o f Deepwater P i p e l i n e s " , TNO-IWECO Symposium on Underwater Technology, The Hague, 1984.

2- T G J o h n s e t . a l . : " I n e l a s t i c B u c k l i n g o f P i p e l i n e s under Combined Loads", (OTC 2 2 0 9 ) , O f f s h o r e Technology C o n f e r e n c e , Houston, 1975. 3- P E de W i n t e r : "Deformation o f S t e e l Tubes i n Deep Water". O f f s h o r e

T e c h n o l o g y C o n f e r e n c e (OTC 4 0 3 5 ) , Houston, 1981

'^^ P E de W i n t e r . J W B S t a r k and J W l t t e v e e n : " C o l l a p s e B e h a v i o r o f Submarine P i p e l i n e s " , i n S h e l l Strucr.nrB..; • S t a b t l i r v and Strentrch E l s e v i e r P u b l i s h e r s , , 1985.

5- J Odland: "Improvement o f D e s i g n Methodology f o r S t i f f e n e d a n d U n s t l f f e n e d C y l i n d r i c a l S t r u c t u r e s " , BOSS C o n f e r e n c e Trondheim, 1988. 6. E Corona and S K y r i a k i d e s : " C o l l a p s e o f P i p e l i n e s under Combined Bending

S K y r i a k i d e s and C D B a b c o c k : " B u c k l e P r o p a g a t i o n Phenomena i n P i p e l i n e s " , 1 9 8 1

J L T a s s o u l a s e t . a l . : " F i n i t e Element A n a l y s i s o f P r o p a g a t i n g B u c k l e s i n Deepwater P i p e l i n e s " , (OTC 6 4 1 3 ) , O f f s h o r e T e c h n o l o g y C o n f e r e n c e , Houston, 1990.

S Timoshenko and J M G e r e : "Theorv o f e l a s t i c s t a b i l i t y " , HcGraw H i l l Book Co.

S

1 1 1 1 1

p

F I G I . CROSS SECTION OF A P I P E L I N E UNDER HYDROSTATIC PRESSURE.

( C A R R I E R P I P E )

( S L E E V E

PIPE)

O I L P I P E )

( I N S U L A T I O N M A T E R Ï A D

F I G 4. DEFORMED CROSS SECTION OF A BUCKLED P I P E SECTION (From R e f . ( 3 J )

COLLAPSE SEQUENCE OF A P I P E SECTION UNDER EXTERNAL PRESSURE. (From R e f . [ 7 ] )

F I G 6. MODELLING OF A P I P E SECTION BY MEANS OF A BENDING ELEMENT AND A ROCKER ELEMENT. (From R e f . [ 4 ] )

E I

^ 4 ,2

E x a c t buckling load of a column.

E l =00

777rr77777 77777777777

Approximate method for the buckling load of a column.

F I G 7. BUCKLING C F A COLUMN UNDER AXIAL COMPRESSION AND AN APPROXIMATION. (From R e f . ( 4 1 )

rocker element bending element

F I G 9 . "INTERNAL FORCES" IN CONNECTION BETWEEN BENDING ELEMENT AND ROCKER ELEMENT (From R e f . ( 4 ] )

r

)

(

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1 .

i ,\

1 ^