1995 OMAE -Volume V, Pipeline Technology ASME 1995

BEHAVIOUR OF OFFSHORE PIPELINES SUBJECTED TO RESIDUAL CURVATURE DURING LAYING

Geir Endal, Odd B. Ness and Richard Verley Statoil

Norway

Kjell Holthe and Svein Remseth The Norwegian Institute of Technology

Trondheim, Norway

ABSTRACT During S-lay installation of offshore pipelines, the pipe is

exposed to plastic strains when the pipe passes over a stinger exceeding a certain curvature. This means that the pipe leaves the stinger with a residual curvature. When passing the inflection point, the bending of the pipe is reversed, i.e. the residual curvature has to be overcome. This occurs partially through bending and partially through twisting. The twisting is here referred to as roll.

Three different models are established to investigate the roll phenomenon. Firstly, a simplified analytical energy approach is presented. Secondly, 3D pipeline installation is simulated in a nonlinear FE-program. Finally, a solution of a governing differential equation for the roll based on a 2D pipeline configuration is found. The purpose is to quantify the roll angle and the as-laid state of strain and geometry for specified laying conditions. Furthermore, dimensionless graphs predicting roll initiation and roll angle magnitude are presented.

The results show that if plastic deformations occur on the stinger, roll is likely to occur due to the reversed bending in the Wlderbend. Within the ranges of stinger radii, pipe diameters, water depths and underbend strains considered, roll approaching 180 degrees has been predicted. Only negligible out-of-plane translations have been foWld. For all pipes analysed, the plastic deformations do not affect the configuration of the pipe on the sea-bottom; it attains its planned straight configuration and experiences no on-bottom instabilities, even when abandoned. Thus, the primary consequences of the plastic deformation over the stinger and subsequent pipeline roll in the underbend are additional strains and stresses in the as-laid pipe.

INTRODUCTION The S-lay method is frequently used for installation of offshore

pipelines, see Fig. 1. As the pipe is played out it is first bent in

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one direction at the overbend (stinger), moves through the suspended section and the underbend (sagbend) where it is bent in the reverse direction. If plastic strains are allowed in the pipe when passing over the stinger, the pipe will have a residual curvature and may twist (roll) as it passes through the Wlderbend.

Normal practice for installation of offshore pipelines allows only small plastic deformations in a pipeline over the stinger. However, the specifications may be unnecessarily conservative, and allowance of larger strains on the stinger may give cost savings, especially for large diameter pipes in deep water (Sriskandarajah and Mahendran, 1992): • Larger stinger curvature will permit reduced tension in the

pipe and, on an uneven sea-bottom, less rectification of free spans.

• For large diameter pipes in deep water the total suspended submerged weight can be so large that the pipe cannot be installed due to the limited tension capacity of the laybarge. In such cases the weight must be reduced and the pipe stabilised by trenching. Larger· stinger curvature, however, may allow installation of heavier large diameter pipes.

• Larger curvature of the stinger will result in further cost-reductions being expected since the frequency of laybarge modifications when installing a new pipe will be reduced (the same laybarge becomes more flexible in use). However, allowing plastic deformations over the stinger may

lead to pipeline roll due to the reversed bending in the underbend. Significant pipe roll is not permissible if valves or connections are installed with the pipeline. It is therefore important to quantify the safety against roll for a given residual strain in the pipe due to plastic deformations over the stinger. Furthermore, residual strain in the pipeline may lead to instabilities on the seabed, for example during abandonment.

Fig. 1. S-lay of offshore pipelines.

fu. the literature, only one paper (to the authors' knowledge), Bynum and Havik ( 1981 ), deals with the roll problem, employing an internal and external work balance approach. The compu­tational procedure is, however, not reported.

TI1e present study deals with the effect of residual strains due to' unifonn bending over the stinger, and approaches the roll prediction in three different ways:

1. Firstly, a simplified analytical approach is presented.

2. Secondly, the pipe, stinger and sea bed are modelled with contact friction in 3D, by using the ABAQUS computer program, Hibbit et al. (1992), with required user supplied subroutines.

3. The third approach represents a solution of a governing differential equation for the roll based on 2D pipeline configuration.

The main purpose of this study is to investigate the effect of plastic strain s from the overbend in tenns of geometric instabilities both in the underbend and on the sea bottom. Prediction of roll initiation is developed and presented in terms of approximate dimensionless graphs.

The effect of the residual curvature on instabilities for the as-laid pipe is briefly investigated.

SIMPLIFIED ANALYTICAL APPROACH TI1e simplified analytical energy approach is based on

minimising the work conducted in the underbend due to the reversed bending of the pipeline. The approach complies with the following assumptions:

• The pipeline roll is assumed to happen between the inflection point and the touch down point. The pipeline length between the inflection point and touch down is L, see Fig. 2.

• The pipeline has a residual curvature JC, from the on-stinger bending. The residual curvature JC, is related to the residual strain E, by ~ = E/r, where r is the outer pipeline radius.

• TI1e underbend pipeline curvature x:(x) is assumed to be a sum of the following two contributions:

x:(x) = JC0(x) + ~ cos$(x)

where $(x) is the roll angle and K0(x) is referred to as the nominal pipeline curvature, which is represented by a 2"' order polyuoinial (see Fig. 2);

K0(x) = OX: + ~x + y

514

Overbend E -........

Kr=.!:::L~ r )..'\.

__ ,,' "' _L,,··

, ' Inflection point

x

Nomin1I ,._. -----..,---- ......-"? curvature: .:."- r ~ _______ ... D _ ___...-'I. Ko (x) = ax' + flx + y = 4 K ..... (x1 • xl)

' CK ..... = .f.. L' r

' Roll i 2cpo 3!po angl:•---ji-----~x)=ax'+ bx'+cx+ d=7 x'+ 7•'

Fig. 2. Simplified Analytical Approach.

The coefficients are found from the boundary conditions JC0(0) = Ko(L) = 0 and the maximum nominal uuderbend curvature

K0max = E0imx I r. Maximum nominal curvature K0nm is calculated in traditional laying analyses.

• The roll angle $(x) along the pipeline in the underbend is represented by a 3111 order polynomial, see Fig. 2:

$(x) = ax3 + bx2 + ex + d

The coefficients are found from the boundary conditions as functions of the maximum roll angle $ 0 in Fig. 2.

• The total work W tot in the underbend is assumed to consist of a roll contribution WR and a bending contribution W B:

[, l

wtot = WR+ WB = J MR(x) . $(x)dx + J MB(X). K(x)dx 0 0

where - MR(x) is the roll-momentum given as

M (x)= GI d$ R T dx

- Mix) is the bending moment given as

MB (x) =EI· K(x)

Substitution into W tot gives:

- 6 Gip 2 wtot - 5T$o +

EI H 4Komax (t- ~:) + JC,COS (3$0 ~: - 2$o ~:) r dx

The expression for W tot can be solved when assuming a roll angle $0. The value of $0 which gives the lowest value of W tot is

the solution of $0. Pipeline roll calculated by this simplified method is shown together with results from the two other approaches in Fig. 17 at the end of the paper.

It is seen from the above equation for W wt that the roll angle is only dependent on the following three parameters:

L = pipeline length from the inflection point to touch down. K, = residual curvature from the overbend. K0( x) = nominal curvature in the underbend.

ABAQUS COMPUTATIONS The 3D numerical approach is obtained using the general

nonlinear FE-program ABAQUS. 3D S-lay installation simulations (static) are perfonned to investigate the influence of plastic strain and pipe tension on the roll angle.

Numerical Modelling The numerical analyses using ABAQUS are based on a 3D

beam model of the pipeline. The laybarge/stinger and the seabed are modelled as rigid surfaces with specified relative motion. For the system shown in Fig. 3, the surface representing the laybarge/stinger is moved towards the right. A pipeline cross section will then move from the barge, over the stinger and through the underbend to the sea bed.

The beam element used in ABAQUS is a hybrid two node element which accounts for hoop strains and stresses due to internal and external pressure in the elastoplastic constitutive equations. Associated with the pipe element are two sets of different contact or interface elements, defined to model the contact between the pipe and the stinger and t11e pipe and the seabed.

1l1e stinger is modelled as a smooth cylindrical surface without any discrete roll supports or tip, see Fig. 3. The sea-bottom is defined as a horizontal, rigid plane.

The rigid surfaces are defined wit11 anisotropic Coulomb friction in contact witli the pipeline. Tiie friction is very small in t11e axial direction of tl1e pipe (µ. = 0.001 to avoid influencing the pipe tension), but has realistic values in the transverse direction (µ, = 0.8).

An evenly distributed small lateral force of lON/m is introduced along tlie pipe to initiate tlie pipeline roll.

Boundary Conditions Point A, see Fig. 3, is fixed, while point B is fixed against

translation in the y- and z-directions and against rotation about the x- and tlie y-axes. This means U1at the on-bottom end of ilie pipe is fixed against roll. However, after simulating installation of a 'sufficiently long' pipeline, the effect of this boundary condition will die out (see discussion below).

At the top of the stinger the pipe is assumed to be fixed against roll. The change of boundary conditions as a cross section passes the pipe tensioner at t11e stem of the laybarge, is achieved through conditional linear coupling of twisting degrees of freedom for tl1e pipe sections on tlie stinger. TI1is is performed by user-specified subroutines.

5~5

Initial z 19m Point A

-~-- y

,,.

Point B

Fig. 3. Modelling in ABAQUS

Steel Materjal Model The Ramberg-Osgood hardening model is used for tlie

pipeline material (API steel). Furthermore, the steel is defined with pure isotropic hardening in t11e ABAQUS computations. This means that the elastic energy of flexure reversal in the underbend is too large, which in turn means that tlie elastic energy of torsion becomes too large. Isotropic hardening thus gives a conservative (too large) prediction of the pipeline roll, especially if t11e underbend curvature is large.

The hybrid beam elements, which are used for modelling of the pipe, do not account for ovalization of a cross section in bending. However, the most slender pipe in this study has a D/t-ratio tllat equals 34.2 (pipe B). and defonned to a bending strain of 0.3 percent, Uie ovalization is only 0.12% (Murphey and Langner, 1985). Tims, the error assuming a circular pipe is negligible.

Base Case Pipes It is difficult to define a particular base case pipe and perfonn

a parametric study where one parameter is varied, keeping tlie others at base case values. The reason is that tlle parameters are dependent (a larger stinger curvature, for example, will usually lead to a reduced pipe tension).

Two different pipes are taken as a starting point: Pipe A is a 16" pipe, and pipe Ba 20" pipe. Data for pipe A and Bare given in Tables 1 and 2, respectively.

TABLE I Data for pipe A (16" pipe).

Steel

Anti-corrosion coating

Weight, in air Weight, submerged

Outer diameter Wall thickness Grade

Thickness

w<rJ w.,,bmc:!J;cd

TABLE2 Data for pipe B (20" pipe).

Steel

Concrete

Anti-corrosion coating

Weight, in air Weight, submerged

Outer diameter Wall thickness Grade

Thickness

Thickness

422mm 20.5mm API X65

3.5mm

2037.2 Nim 583.7 Nim

509.2mm 14.9mm API X60

40mm

6mm

3566 Nim 753.4 Nim

i· I'

I I I

'I

.. ''

ABAQUS Results

Roll Angles. Pjpe A and B. Tables 3 and 4 below present results obtained from simulations performed for different depths and different combinations of stinger radius and pipe tension. It is seen that large stinger curvature causes the pipeline to roll. Furthermore, it can be seen that 90 degrees roll is obtained for a stinger radius which is only 4%-7% smaller than the radius which initiates roll. This reflects the fact that the roll phenomenon is a typical stability problem; once roll is initiated, the roll increases rapidly.

TABLE3 Results for pipe A ( 16" pipe).

ANA- INPUT OUTPUT LY-SIS Depth R Enom=r/R Tb, tn>e Tb,df. Tb ...... 9

I 300m 69.0m 0.306% -333kN 103kN 294kN 116° 2 72.0m 0.293% -333kN 103kN 295kN 95•

3 75.0m 0.281% -333kN !03kN 295kN 48° 4 76.0m 0.278% -333kN !03kN 296kN 11.5° 5 78.!m 0.270% -333kN 103kN 296kN 2.2°

6 400m 70.3m 0.300% -483kN 98kN 346kN 137° 7 74.0m 0.285% -460kN 121kN 372kN 110° 8 78.lm 0.270% -437kN 144kN 396kN 52° 9 82.0m 0.257% -425kN J56kN 410kN 1.2·

TABLE4 Results for pipe B (20" pipe).

ANA- INPUT OUTPUT LY-SIS Depth R E.nom= r/R Tb, 1n1e Tb,dl Tb,,_ 9

I 287m 84.7m 0.300% -698kN 109kN 353kN 127° 2 88.0m 0.289% -670kN J37kN 385kN 103° 3 90.0m 0.283% -660kN 147kN 397kN 81° 4 92.0m 0.277% -650kN 157kN 407kN 10· 5 94.lm 0.271% -64!kN !66kN 418kN 0.3°

6 400m 84.7m 0.300% -986kN 139kN 47lkN 142° 7 90.0m 0.283% -962kN 163kN 496kN 120° 8 94.lm 0.271% -950kN 175kN 510kN 91° 9 98.0m 0.260% -940kN !85kN 519kN 41° JO 101.6m 0.251% -930kN !95kN 531kN 2.3·

The underbend strain for pipe A is 0 .1 1 % at 300m depth. At 400m depth the underbend strains are in the range 0.08% -0.11 %. The underbend strains for pipe B are in the range 0. 1 % -0.15%.

The results in tables 3 and 4 above are used for comparison with 2D simulation results in a comparison section below.

As mentioned above, U1e boundary condition (b.c.) at the on-bottom end of fue pipeline is rotationally fixed. Even with this b.c. the numerical solution converges towards a stable value, independent of the b.c. after installation simulation of 'sufficiently long' pipe length. 'Sufficiently long' is hard to define, but is set equal to 1300-1 SOOm due to computational cost reasons.

To verify that installation of 1300-1 SOOm of pipe give results that have converged as far as the magnitude of the roll angle is

'i " !iii " ~ " 1ib ::ii

:::; 0

ex:

160

140

120

100

80

60

40

20

0 0 21XI 400 6CKI 800 llKXI 12IKI

Metres of installed pipe (simulated)

Fig. 4. Development of Max. Roll Angle During Installation (Pipe A, Analysis No. 6).

141XI

concerned, the development of the maximum roll angle is presented as a function of installed pipe length for pipe A, analysis no. 6, see Fig. 4. The figure shows two general characteristics which apply to all the numerical simulations:

516

• Maximum roll angle is approximately equal to zero until nearly 4 70m of pipe is installed. After installation of 4 70m of pipeline, a cross section initially placed on U1e stinger has now passed Uie inflection point and is presently in the underbend (approximately 80m from touch down). At this poiut the roll is suddenly initiated. This confirms the roll mechanism: Plastic strains during U1e on-stinger bending in combination with subsequent reversed bending in the underbend.

• The slope of the maximwn roll angle curve is asymptotically decreasing, indicating that the magnitude of the roll allgle is converging. Despite the decreasing slope of the curve, however, the slope never equals zero, and thus the roll angle results presented should not be considered exact maximwn values.

Detailed Results for Pjpe B. Ana!ysjs No, 8, In order to better understand the physical behaviour of a pipe subjected to residual curvature during laying, detailed results for analysis no. 8 in Table 4 are presented il.1 this section. The figures show the instantaneous situation after simulatil.1g 1400m of pipeline installation

Fig. S shows the true axial tension along the pipe. It is seen from the figure that the pipe reaches the sea bottom about 470m behind the laybarge.

Fig. 6 shows the roll angle along the pipe after installation of 1400m of pipe (snapshot). The roll angle equals zero at the stem of the laybarge and at U1e on-bottom end of the pipeline, in accordance wiU1 the given bow1dary condition. From touch down to U1e on-bottom end, U1e roll angle decreases linearly. This is due to zero rotational resistance along the pipe on U1e bottom. Thus, U1e numerical model will always give a roll angle distribution as shown il.1 Fig. 6. When the roll angle approaches its stable value (Fig. 4), maximmn roll allgle will no longer change, but roll angle per installed meter of pipe will decrease (and so also the torsional moment).

C.IXKXXl

400000

Axial force -21Xl000

~ 0 ., 0 ... .g .21xxxx1

O!

~ -400000

· 6()()()()()

-800000

· le+06 0 50 I 00 150 200 250 300 350 400 450 500

X-coordinate [m]

Fig. 5. True Tensile Force Along the Pipe.

()

- Ill Rotation -

·20 ~

"' .]()

" ti, .40 " ~

u .511 Oil ~ -oil 0 I>: -70

·Rll

.90

. l()Q

0 200 400 600 800 1000 1200 1400 1600 1800 2000 X-coordinate [m]

Fig. 6. Roll Angle Along the Pipe.

Fig. 7 shows the distribution of the torsional moment along the pipe during installation. 111e torsional moment reaches its minimum value for X = lOOm, i.e. just after the stinger tip. On the sea-bottom, the torsional moment is constant along the pipe, which corresponds to tl1e linear change of tl1e roll angle seen in Fig. 6.

Fig. 8 shows the bending moment along the pipe during installation. For X < ca.60m (during bending over the stinger), M "'1.2 - l .3MNm. For X "' Orn, however, M = l .4MNm. This is an end effect: Usually, the pipeline will separate 5-!0cm from the laybarge surface as fue pipe leaves the horizontal barge and starts to curve over the stinger. However, fue end of the pipeline (point A in Fig. 3) is fixed, and an extra constraint is introduced when fuis point reaches the end of the horizontal plane and simultaneously is not allowed to separate.

The pipe reaches fue inflection point when M is equal to zero, and in the w1derbend M "' -0.56MNm. On fue sea bottom, fue pipe experiences a pennanent bending moment of -0.4MNm (X <ea. I 300m) due to tl1e residual strain of approximately 0.08%.

For X > I 300m, M equals zero since this part of the pipeline initially was in tl1e suspended section and w1derbend and has not experienced plastic bending over tl1e stinger. Tius part of fue pipe is thus without residual curvature.

517

150000

llKX)(lll

SOO!Xl

0

e .50000 b

E · 100000

" E 0 ·150000 ~

·200000

-250000

·300000

.35()()()()

1.2e+06

1<+06

800000 e b 6()()(J(XJ

E 41XXXXI ., E 0 200000 ~

0

-200000

0

Torsional moment -

200 400 600 800 1000 1200 1400 1600 1800 2000 X-coordinate [m]

Fig. 7. Torsional Moment Along the Pipe.

Bending moment -

This part (M-ONm) hu not been

bent over the stinger.

-400000

·600000 L-.=J~--1.--'---'---'--.L--L-.--L---L--' 0 200 400 600 800 1000 1200 1400 1600 1800 2000

X-coordinate (m] Fig. 8. Moment About Global Y-axis (the Horisontal).

Fig. 9 shows the bending moment about the vertical axis during laying (out-of-plane bending). Tilis bending moment value is primarily due to fue lateral force of I 0 Nim. The moment has a local minimum immediately before the pipe leaves the stinger (M "' -0.46MNm). This negative peak value is caused by prevented lateral motion on the stinger due to the contact friction on the stinger.

The bending moment about fue vertical axis equals zero at the inflection point, and reaches its maximum value of 0.6S:MNm in the underbend.

Configuration. All fue analyses show iliat the pipeline lies along a straight line on fue sea bottom, and no instabilities are experienced as a consequence of fue residual curvature for tl1e pipe tensions and the submerged weights considered. Furfuerrnore, tl1e pipeline roll is found to occur with uegleglible out-of-plane displacements.

The consequences of plastic strains over fue stinger and subsequent pipeline roll in fue underbend primarily manifest themselves as additional strains and stresses in the as-laid pipe (Fig. 7 and 8). However, it is important to keep in mind that the residual curvature of the pipe decreases tl1e safety against

e 2=., ;: ., e 0 ~

800000

600000

moment about the Z-axis -4()(X)()(J

200000

()

· 200000

-400000

-600000 .___, _ __._ _ _,_ _ _._ _ _._ _ _,___..____,.____,_~

0D~~~ l~~IGl~1~2~

X-coordinate [m]

Fig. 9. Moment About the Global Z-axis (the Vertical).

on-bottom instabilities of the pipeline (see abandonment section below).

Effect of Pipe Tensjon. The results have shown that plastic strains over the stinger combined with subsequent reversed bending in the lower bend is necessary to initiate pipeline roll. The lower bend curvature is controlled by the tensile force. Thus, an important parameter for pipeline roll is the pipe tension.

The effect of pipe tension is studied for two pipes, data for which are given in Table 5.

TABLES Data for pipe I and 2.

Pipe D D/t Steel R Enom Depth wsubm

16" 20.6 X65 78.lm 0.27% 400m 584N/m 2 25" 35 X60 105.8m 0.30% 400m 800N/m

Fig. I 0 shows how the roll angles for pipes I and 2 are dependent on the tension. For pipe I the roll angle reaches its maximum value when the effective tension on the bottom Tb ell'"'

0.04tv1N. For Tb elf> 0.04tv1N, the roll angle decreases aS the tension is increased. For Tb, elf E (0.02.MN,0.04MN'}, however, the roll angle increases suddenly from approximately zero to 96 degrees with increasing tension.

Qualitatively, pipe 2 shows the same dependency on the tension as pipe I. Fig. 10 shows, however, that the roll angle for pipe 2 (after the maximum value) does not decrease as much as for pipe 1 with increasing pipe tension. This is due to larger submerged weight and larger strains over the stinger for pipe 2.

Two opposing effects of the tensile force can explain why the roll angle's dependency is as shown in Fig. 10:

• Increased pipe tension results in a decreased underbend curvature. Thus, the roll decreases as the tension is increased.

• Increased tension results in a lower torsional resistance due to a longer suspended span (the touch down point moves away from the laybarge stem). Thus, the roll increases as the tension is increased.

518

0

r

140 ~--.----,.----.----,.----.----,--.----,

120

Pipe2 -+­I ·+···

a: 40

20

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Effective bottom tension [MN]

Fig. 10. Roll Angle as Function of the Tensile Force.

6<Xl()(J(l ~-~--~------,--~--~-~

41!0000

·· .. .

T=0.2JMN -T=O.I SMN ..... T=ll.ltMN T=<J.OSMN T-0.0lMN -- · T=O.OlMN • • •

·WIHKIO '----'----'----'------''-----'----'----' Cl 100 wn 3<X> 400 ~nu "'" ?1)1)

Fig. 11. X-coordinate and True Tension for Pipe 1 at Different Values of the Bottom Tension (the 6 Levels of Effective Tension are (in MN): 0.02, 0.05, 0.08, 0.11 , 0.15, 0.23).

When the pipe tension is very small, the suspended length is very short, see Fig. 11. The configuration suddenly changes from an almost vertical suspension to the horizontal sea bottom. In this case, the lower bend curvature will not result in an instability (roll). Possible defonnation controlled restrained forces that correspond to instability conditions, will not arise at this geometric configuration, and reversed bending occurs as a stable bending process without any roll.

For Tb di'> 0.04tv1N, the roll angle decreases as the tensile force is increased. At these tensile forces, it is the value of the underbend curvature that forces the pipeline to roll . For increasing pipe tension the curvature decreases, and the pipeline roll decreases.

Abandonment. In bad weather situations it may be necessary to temporarily abandon the pipe on the sea bed until the weather improves.

In such an abandonment situation, where the laying stops and the pipe is laid down, the pipe tension is reduced drastically; the effective tension is reduced to zero at the end of the pipe. Thi~ may cause on-bottom instabilities, and a pipe with a pennanent

curvature will be particularly exposed to on-bottom instabilities when the tensile force is decreased.

Generally, an on-bottom instability is governed by (for a given residual tension):

• Residual bending moment due to plastic effects.

• Pipeline roll (rotation of plane in which the residual bending moment occurs).

• Lateral resistance (pipeline submerged weight and bottom friction µ ).

• Bottom topography (in the numerical model, the bottom is flat, and the pipe is everywhere in contact with the bottom).

Given the residual bending moment due to plastic effects and the pipeline roll (from numerical lay simulation), instability can be investigated separately by gradually reducing the tension until ,instability occurs.

As an example, simulations of an abandonment situation are perfonned for a chosen pipe, data for which are given in Table 6. 111e results are shown in Fig. 12.

TABLE6 Data for pipe A, analysis no. 6.

D D/t Steel R Enom Depth w,.,bm 16" 20.6 AP!-X65 70.3m 0.30% 400m 584N/m

From Fig. 12 it is seen that the instability situation is reached for a real negative effective pipe tension, and therefore no on-bottom instability will occur during abandomnent for this pipe.

0.2 ~-~-~--~-~--~-~--~-~

z ~ 0 c: 0

·~ -0.2

~ E -0.4 0

~ -0.6

" . ?: ti ~ LlJ

-0.R

E - 1 => E s :5'

- 1.2

- 1.4 [) 0.1

E..,,m = 0.30% -<>-­

Ennm = 0.35% +

+

n.2 n.3 0.4 n.5 o.6 Lateral Friction Coertisient l-l

0.7 O.R

Fig. 12. Minimum Effective Tension for Stability as a Function of the Bottom Friction.

PIPELAY COMPUTATIONS In this section a simple procedure for estimating the pipe roll

is presented. By neglecting possible out-of-plane displacements, the equilibrium equation in the pipe axis direction for the moments yields a nonli.near differential relation between tl1e torque and the corresponding twist (roll). A solution of this differential equation gives the roll angle. Necessary input to the

519

problem is tl1e 2D as-laid pipe configuration and tl1e maximum plastic strain over the stinger. The 2D configuration and tl1e roll angle are found by a special purpose computer program called PIPELAY.

The 20 Pipe Configuration The formulation contained in the PIPELA Y program for

finding the as-laid 2D configuration of tl1e pipe contains tl1e following characteristics:

• The pipe is divided into 2D beam elements. Each beam element has two nodes witl1 tl1e vertical displacement and the rotation (bending) as nodal degrees of freedom. Geometric stiffness is included by tl1e effective horizontal axial force (which is constant along the suspended part). Large rotations are considered by employing the exact expression for the curvature.

• 111e stinger is described as rigid with a circular shape. At certain locations along the stinger the pipe is resting on rollers which transfer contact forces (unidirectional) nonnal to the pipe axis.

• The steel material is described by a non-linear hardening curve for tl1e bending moment vs. tl1e curvature. Elastic unloading and the Bauschinger effect are included based on a sublayer teclmique. When a u.niaxial elastoplastic stress-strain curve is specified, tl1e corresponding moment-curvature relation is found from stress integration over the cross-section. 111at is, any influence from outer pressure, steel axial force, shear force, ovalization and possible torque is neglected.

Further, when concrete coating is present, its stiffuess contribution is neglected and possible strain concentrations in the field joints are not considered.

• The solution procedure for finding the 2D pipe configuration during steady-state laying conditions may be summarized as follows:

lni tially, botl1 tl1e pipe and tl1e stinger are resting horizontally on the bottom and tension is applied.

- The stinger is displaced vertically and gradually curved to its final geometry .

- An approximate pipe configuration is obtained using linear elastic material behaviour.

- The non-linear moment-curvature relation is employed to include history effects. That is, the bending moment at a cross-section along the pipe is found by integrating the moment-curvature relation from the laybarge to tl1e considered cross-section. The final configuration reflects tl1e material integration.

- The roller contact forces along tl1e stinger are in accordance witl1 tl1e obtained pipe configuration at all stages (through iterations)

Roll Angle Computations Fig. 13 shows a pipe element in the vertical plane with the

torque and the bending moments (forces are not shown). Moment equilibrium in tl1e s-direction gives (neglecting higher order terms):

Roll: 9 YL x

Bending stiffnes: El Torsional stiffness: GI,

El - =1+v GI,

Fig. 13. A Pipe Element with Moments (no Forces Shown).

{IT =Mo 1C as Since out-of-plane displacements are neglected, both the

torque, T, and the bending moment component, M0, due to the initial curvature may be expressed by the roll angle as follows:

ae T = GJ, as and Mo =El JCo ·sine

which yield the governing non-linear differential equation:

0282 + o + v)IJColJCsin e = o

dS

The initial curvature, JC0, is taken as the largest plastic curvature over the stinger (1C0 is negative). The curvatures in the vertical plane, JC(s), are taken from the preceding 2D analysis.

An analytical solution is possible when JC is constant along the suspended pipe. The equation (for constant IC) describes a typical stability problem.

TI1e in-plane bending moment, M, is given by

M =E/(JC - JC0 cos 0)

It should be noted that the above expressions for the moments (T, Mand M0) are based on a linear elastic material behaviour u1 unloading once the pipe has obtained its maximum plastic curvature ( 1C0) .

TI1e non-linear differential equation is solved by a standard Galerkin procedure. The equation is multiplied by a virtual rotation 80 and integrated along an element employing the same element discretization as in the 2D case. The integrated element equation is written in matrix fonn and all elements are merged together to fonn the fu1al uon-lll1ear matrix equation for the system. Filially, the system equation is solved employing a Newton-Raphson tec!mique to iterate for the nodal roll angles. At the top of the stinger the pipe is assumed to be fixed against roll and at the bottom the torque is set to zero.

Pipe Diameter Dependence A parameter study is performed to study the influence of the

pipe diameter upon the roll angle. The pipe diameter is varied between 20" and 40" and the value of other important parameters is given in Table 7.

Fig. 14 shows the roll angle at the bottom for different pipe diameters. It is seen that the roll angle decreases almost linearly with increasing pipe diameter (the D/t-ratio is constant).

520

160

140

120

I 100

~ 80

.~ 'R. 60 ....

40

20

0 20 JU JS 40

Steel di:1mclcr fin}

Fig. 14. Roll Angle as Function of the Pipe Dimension.

TABLE 7 Value of parameters kept constant.

Depth D/t Steel Enom =r/R W subm T.fT. bottom

400m 35 APl-X60 0.30% 800N/m 140kN

When the steel diameter u1creases with a factor of two, the bending stiffuess increases with a factor of 16. Increased stiffuess has two opposite effects: Firstly, decreased curvature along the suspended pipe causing the roll angle to decrease; and secondly, increased length of the suspended pipe causu1g tl1e roll angle to increase. In Fig. 14 the roll angle decreases as the steel diameter increases. Thus, in this case the effect of decreased curvature is dominating.

COMPARISON OF THE DIFFERENT APPROACHES

The Different Assumptions. ABAQUS vs. PIPELAY The main differences between the models in ABAQUS and

PIPELA Y are summarised qualitatively in tlie followu1g.

I . Bolllldary conditions at the on-bottom end of tl1e pipe.

- ABAQUS: Zero roll. This is a too strict adherence, but for 16" and 20" pipes, this end effect dies out after installation of approximately 1400m of pipe, see Fig. 13. However, for larger diameter pipes witli larger torsional stiffiless, tile bolUldary condition uilluences and reduces the roll magnitude.

- PIPELA Y: Zero torsional moment. This is a conservative bolUldary condition.

2. Material model.

- ABAQUS: Isotropic hardening. This probably gives a conservative prediction of the pipelll1e roll, as explained in the ABAQUS section above.

- PIPELA Y: Hardening and Baushinger effects included when establishing the 2D pipe configuration.

3. History effects.

- ABAQUS: All included.

- PIPELAY: Several effects, such as external pressure, steel axial force, shear force and possible torque, are not considered. Besides, the expressions in the PIPELA Y section for the moments (T, M and M0) are based on a linear elastic material behaviour in unloading once the pipe has obtained its maximum plastic curvature (K0).

Case Studies All cases defined in Tables 3 and 4 have been run with the

PIPELA Y program and the roll angles compared with corresponding ABAQUS-values. Fig. 15 shows the roll angles (at the bottom) for the 16" pipe (Table 3) and Fig. 16 shows the roll angles for the 20" pipe (Table 4). It is seen that the results from the two programs are quite similar: Maximum 3 percent deviation in stinger radius at which roll starts to develop and maximum 30 degrees deviation for the highest roll angles. Fig. 15 and 16 show that the pipeline roll increases for increasing water depth when the nominal strain on the stinger is equal.

u ~ :!! = e ~ .s

l

I :!! 'e .~

I

160

140

120

100

80

60

40

2ll

u

Pipelay, depth=400m -Pipelay, deplh=300m -

Abaqus, depth=400m -•-­Abaqus , deplh• 300m -- --

ll.24 0.25 0.26 0 .27 0 .2R ll.29 O.J

160

140

120

llXl

80

60

40

20

II

nominnl ~lrnin. l(pip1.·/1brlnJ!l"r lpt'fft•nll

Fig. 15. Roll Angles for the 16' Pipe (Table 3).

Pipclay, depth=400m -+­Pipelay, deplh=287m -

Abaqus , dcpth=40Um -•--· Abaqus. dcpth=287m -+---

ll.24 U.2S 0.26 0.27 0.2R 0.29 Nomin:\I ~1rain, Rpipc'/R~linj!cr I percent I

O.J

Fig. 16. Roll Angles for the 20' Pipe (Table 4).

ll.JI

11 .. 11

521

u ~ :!! e -~ l

IMI

140

120

100

80

60

40

211

II 11.24

Plpclay -Abaqus · • ··· --~---·

Simplified energy method ·+ ··· •......•..... --·

,,,.. .......... ··

ll.2S

... • ...• ............. ---··· ....

..•.

0.26 0.27 0.2R 11.29 1iomin:"ll ~t rain, Rpipc/l(sl lngcr fpcrc:c11tl

ll.J

Fig. 17. Roll Angle as Function of the Nominal Strain.

ll.JI

Fig. 17 shows the pipeline roll calculated with the three different approaches. The PIPELA Y and the ABAQUS curves are the same as the ones in Fig. 16 at 400 metres depth. The length L, residual curvature K, and maximum sagbend curvature IC-. (which are needed as input to the simplified approach) are found from PIPELA Y. It is seen from Fig. 17 that the results are quite similar. The simplified method, however, predicts a somewhat smaller roll angle than PIPELA Y. This is mainly due to the analytical simplification of assuming the roll to occur between touch down and the inflection point, while PIPELA Y assumes roll to occur all the way to the top of the stinger. Furthermore, the 2D computations may be eyed as a discretization of the simplified method, thus PIPELA Y is generally more accurate.

DIMENSIONLESS GRAPHS The simplified analytical approach based on minimising the

total work W fJJ'. in the underbend showed that the roll angle $ is governed by

L = pipeline length from the inflection point to touch down. K, = residual curvature from the overbend. Ko(x)= nominal curvature in the underbend.

Further development of the expression for WI/;/. can show that the three governing parameters above correspond to the three dimensionless groups L/D, E, and £_,., where D is the nominal pipe diameter and e, and E1mz1c are the residual strain and maximum underbend strain, respectively.

Underbend strain (e0) and LID can be shown (Langner, 1984) to be functions of T/WC, dlD and CID, where CID is only important at low values of T/WC. T0 is the effective pipe tension on the sea bottom, W is the submerged weight, C is characteristic length = (B!Wyn, where B is the pipe bending stiffness, and d is the water depth.

Thus, the following dimensionless groups are expected to be primarily involved:

{ To d c}

$,£,, WC' D' D

1~00

1600

- 1400 , . · .... \.

0 IZOO

k 1000

i :J 800

· .. · ... .. \ \ .

<t \

1/··>:< . ... · ..

le. · •. : · ...

D .• : ·· . ..

!

Boctom tcp<ion T/WC:= 10 -i ' ~ ..... ; : 2 0 ···

: o. ~ •

~mL----'-----'-----'----'----'----'----1 0 .112 0 .(\4 0.06 0.llll U.I 0.12 ll 14

Rc~itlu~I 'ilr-1in ( '1 I

X65 . 0 242 ,}.274 0 30 1 0 327 0 350 0.374 0.397

Total Slroin l'•I

Fig. 18. Curves whicti Deline Roll Initiation.

Boll Initiation Approximate dimensionless graphs predicting roll initiation,

defined as 10 degrees roll, is presented. The developed graphs are based on PIPELA Y analyses, and are shown in Fig. 18. From Fig. l 8, the roll initiation can be found from the three dimensionless groups e,.. d/D and T ;we (the group CID is

neglected). From the figure, the residual strain needed to initiate roll can

be found for a specified pipe which is to be installed at a given depth and with a given residual tension. However, due to the approximate PIPELA Y analyses and the reduction of dimension­less groups, an error of up to 10 per cent may occur and should be accounted for.

The following equation fits the curves in Fig. 18 with a maximwn deviation (in d/D) of approximately 8% and standard deviation - 3.5%:

(A) = 0.45 E~.rn (~)o.os D init we

Boll Angle Fig. 19 shows the roll angle as a function of the dimensionless

group £.-d!D for T ;we = 5.5. The figure shows sample points for a large number of design cases (varying pipe parameters, water depth, stinger geometry, etc.). The small spread in the data points is due to the group CID which has not been included.

It is seen from Fig. 19 that the slope of the curve decreases rapidly as the E.-d!D-value increases once roll is inititated. This reflects the stability-problem behaviour of the roll phenomenon.

Fig. 20 shows the roll angle as function of the dimensionless groups Er ·d!D and T ,jWC. The curves represent best fits to the sample points in Fig. 19 and other similar figures.

522

IS)

tee>

IC>

11zi

f 100

I :

/···· I • I .

I

. . . .

.!!... • 5.5 we

o,__-+-~1----<--+--+--+~-+-~-+---+--~

O.CXXl O.SOO 1.CXXl I.SOO 2.alO 2.SOO 3.CXXl 3.Sll '·CXXl , ,SOO 5.CDl

Er·t

Fig. 19. Roll AA<;j.e for a Large Number of Design Cases.

14)

lZl

o ~~+---1----<--+--+~-+---+---+---+--~

O.CXXl 0.100 Cl.2ll O..Jll O.CD O.SOO O.llOO 0.100 0.8Cll 0.900 1.CDl

Er · .! D

Fig. 20. Roll Angle.

CONCLUSIONS This paper has tried to provide a basic understanding of the

behaviour of offshore pipelines subjected to residual curvature during laying. Three different models have been established to investigate the physical phenomenon. The results show, considering the distinct asswnptions for the different models, good agreement.

It is demonstrated that plastic strains from the bending over the stinger are likely to cause pipeline roll in the underbend. In addition to the plastic strains, however, the pipeline roll is dependent on the water depth, the pipe tension, the pipe diameter, the submerged weight and the bending stiffuess of the pipeline. Prediction of roll initiation and roll angle magnitude is developed and presented in terms of approximate d.imensionless graphs. The pipeline roll is found to occur with minimal out-of-plane displacements.

The plastic deformations over the stinger and subsequent pipeline roll in the underbend are not found to give any on-bottom instabilities of the as-laid pipe; for all the pipes analysed, the pipe attains its planned straight configuration on the sea-bottom, also when abandoned. Thus, the primary consequences of the plastic deformation over the stinger and subsequent pipeline roll in the underbend are additional strains and stresses in the as-laid pipe.

ACKNOWLEDGEMENT The authors would like to thank the management of Statoil for

permission to publish this paper.

REFERENCES Bynum, D. jr. and Ravi.le, K.P. (1981): "Marine Pipeline Roll

Parameters Study", Oil & Gas Journal, Aug. 1981.

Hibbit, Karlson and Soerensen (1992): "ABAQUS Manual, Version 5.2".

Langner, C.G. (1984): "Relationships for Deepwater Suspended Pipe Spans", ASlvfE, 3'° OMAE Symposium, pp. 552-558.

Murphey, C.E. and Langner, C.G. (1985): "Ultimate Pipe Strenght under Bending, Collapse and Fatigue", lnt. Conference on Offshore Mechanics and Arctic Engineering, Vol. 1, pp. 467-477.

Sriskandarajah, T. and Mahendran, I.K. ( 1992 ): "Critique of Offshore Pipelay Criteria and Its Effect on Pipeline Design", Proc. Offshore Technology Conference, OTC 6847, pp. 533-542.

523