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1 Copyright 2008 by ASME

RISK DESIGN FOR STABLE THIN-WALLED PIPELINES SUBJECT TO GLOBALBUCKLING AND EXCESSIVE BENDING FROM SEABED AND PIPELAY INDUCED

OUT-OF-STRAIGHTNESS

E. A. MaschnerJ. P. Kenny Ltd. (U.K.)

N. Y. WangJ. P. Kenny Ltd. (U.K.)

ABSTRACTRelatively thin walled moderate water depth pipelines

prone to lateral buckling can have very limited bending capacity

in terms of their through-life load, strain and fatigue limit states.

For such pipelines effective force mitigation schemes are often

impracticable and the use of intermittent rock dump constraint

if available, expensive. An alternative option is to design the

pipeline to be stable along its length under operational and

external loading. However a multitude of uncertainties canimpact on such an assessment among them the concrete weight

coat properties (stiffness and weight), residual lay tension, field

joint SCF, corrosion rate, seabed topography, pipe embedment

with associated non-linear pipe soil interactions and the size and

frequency of external impacts.

This paper reports on a methodology for achieving

quantitatively low risk designs meeting regulatory approval

through in-place 3D finite element sensitivity studies coupled

with structural risk assessments. A current design project

utilizing this approach is described along with analytical

equations governing excessive seabed and pipelay induced out-

of-straightness and lateral buckling initiations. Ultimately this

enabled specification of practical limits on pipelay imposed out-of-straightness to safeguard the heavy weight coated pipeline

and its field joints during operation.

1 INTRODUCTIONThis paper describes a risk based design approach adopted on a

project to prove a pipelines through-life operational integrity

based on a unique combination of field constraints imposed on

any solution methodology. Most significant among these were

the following:

A relatively large 26inch diameter surface lay gas exportpipeline procured prior to detail design with minimal 15mm

wall thickness sizing based largely on hoop stress capacity

limits.

A significant concrete weight coating for hydrodynamicstability in the shallow waters (coastal to 120m depth at

KP40).

Design to withstand fishing gear impact, pullover andsnagging loads.

The first 22km of the pipeline route to be trenched andnominally backfilled in clayey silt soil for stability.

Transitioning to surface at KP22 product temperature is

maintained and constrained thermal expansion forces

significant (Figure 1).

From KP 22 the pipeline transitions to surface with theroute encountering a difficult 14km region of undulating

topography associated with variable sub-cropping and out

cropping sandstone rock among general coarse surficial

sediments. In addition, two relatively flat soft clay pockets

within the general KP22 to KP36 rock outcrop region

between 1 and 2km length (see Figure 2).

At 100m-water depth (KP 36) the soil type along the routereverts to uniform clayey silt. With environmental and

thermal impact less significant a minimum 65mm concrete

weight coat is to be utilized.

Long-term intervention works such as rock dumping werenot available to the project and therefore the displacement

response of the as-laid profile had to be acceptable for the

operational life of the pipeline.

Proceedings of the ASME 27th International Conference on Offshore Mechanics and Arctic EngineeringOMAE2008

June 15-20, 2008, Estoril, Portugal

OMAE2008-57067

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0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70 80 90

Distance, Km

Temperatu

re,C

115 barg operating pressure

100 CWC65 CWC

150 to 80 CWC

120 CWCT & B

Min Ambient Temp

Water depth 0m to max 180m at KP52

Figure 1. Project operating temperature profile

20 22 24 26 28 30 32 34 36 38

60

70

80

90

100

110

120

130

140

150

160

KP (km)

c oa rse sedimen t "co ar se sed

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factor can exist if coinciding with regions of significant pipe

bending. Generally, lateral buckling finite element analyses and

DNV OS F101 unity checks show a low bending strain capacity

with probable associated fatigue concerns and potential onerous

girth weld crack defect size in any operational ECA.

Potential solutions to safeguarding the pipeline from seeinghigh levels of bending at isolated global buckle sites considered

two differing approaches

1. Mitigate high levels of effective force with periodicexpansion relief scheme (snake-lay or sleeper design) or

2. Provide additional restraint to the pipeline preventing itfrom seeing large lateral buckles.

Due to fishing interaction being predicted along the route and

with the inability of the pipe section to endure significant

bending stress a closely spaced sleeper design was considered

impractical and too expensive to mitigate high effective forces.

Likewise for snake lay design expansion relief sites would be

required every 1km or less and there would be a high risk ofbuckle localization and rogue buckles from undulating seabed.

Concrete weight coat controls at and between snake-lay

apices would necessitate numerous design sensitivity studies

(friction ranges, cyclic fatigue, strain concentrations at field

joints, 3D seabed profile etc). Other considerations include an

onerous ECA requirement with difficult pipelay coupled with a

need to start any mitigation scheme well before the KP22 trench

transition to achieve a gradual step down in effective force and

not overstress pipeline (without rock this could mean

intermittent trenching within snake lay scheme). Finally a

detailed pre and post operation survey and in-place analysis

would be required with no certainty that the final as-built

scheme would work without rock intervention or similar.

To achieve a reliable safe design within DNV prescribed safety

margins an in-place constraint approach was undertaken to

safeguard the 26 pipeline by maintaining the design within the

limit state load control limits of DNV OS F101 and limiting any

build up of accumulated plastic strain. This solution could be

provided by fully or partially rock dumping the pipeline (100%

risk free approach). Alternatively the weight of the pipeline can

be increased with additional concrete weight coat up to the

practical coating limit. Although this solution provides

additional restraint the pipeline is not fully constrained and an

element of risk remains which requires quantification to prove

the acceptability of the design

3 CONSTRAINT DESIGN METHODOLOGY

Initial 2D and subsequent advanced 3D finite element studies of

the 26-inch pipeline response along the undulating and variable

stiffness seabed showed a risk of global buckling. In critical

regions the adoption of 150mm thick weight coating was seen

to significantly improve the pipelines robustness. However in

certain circumstances it was possible to show any localized low

soil restraint, excessive in-place out-of-straightness or

unforeseen extreme seabed topography was capable of causing

the operational pipeline to displace and overstrain. With a

borderline global buckling risk to the pipeline it was decided to

undertake a quantitative risk assessment to prove the pipeline

within prescribed limit state reliability limits of DNV OS F101.

3.1 Structural Reliability Analysis (SRA)In assessing the global buckling risk to the purpose heavy

concrete weight coated 26-inch pipeline a three-phase SRA

approach was adopted:

1. Ascertain probability of pipeline buckling2. Ascertain probability of pipeline seeing excessive in-place

out-of-straightness to initiate a global buckle

3. Ascertain probability of the pipeline being overstressed dueto excessive in-place out-of-straightness without buckling.

With previous work identifying a rapid build up in strain should

the pipeline displace and see significant bending during its

operation DNV load control safety margins were adhered to [1].

For the constrained 26 heavy weight coat thin walled pipeline

occurrence of either of the above conditions could be said toresult in excessive bending and ultimate limit state failure.

In addition to the usual pipe material and loading parameters

realistic ranges of equivalent non-linear soil friction coefficient

(break out and residual reaction forces) residual pipelay tension,

composite concrete coated steel pipe properties and seabed and

pipelay imperfection levels were all statistically described for

the SRA. Buckle initiation and pipeline integrity reliability

calculations were performed using a Monte Carlo simulation

process via the Crystal Ball commercial software [2].

3.2 Lateral buckling SRA

The limit state function for lateral buckle formation associated

with excessive lateral displacement and associated overstrainingof the pipeline material was derived from the well-known

Hobbss beam-column expression [3] relating idealized mode 1

displacement profiles without initial imperfection or

concentrated vertical reaction points to system effective force

levels.

7

2

5

210597.1

76.80L

IE

wwAE

L

IEP L

AO

+=

(1)

Where

PO,is applied effective force, kN

EI,is elastic bending stiffness, kNm2

EA,is elastic extensional stiffness, kN

A,is residual axial frictionL,is residual lateral frictionw, is submerged weight, kN/m

L,is buckle wave length, m

The above formulation describes a shape curve of stableand unstable buckle length branches against effective force

meeting at a minimum turning point. In a perfect system without

imperfection the pipeline is considered stable if the system

effective force levels are below the level associated with the

minimum turning point. Formulae for the calculation of the

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axial and lateral soil resistance were developed from simple

linear restraint (Coulomb type friction based on residual values)

to non-linear breakout and residual restraint associated with an

embedded pipeline within a cohesive soil type. Based on linear

axial and lateral pipe-soil interaction the buckle length

associated with minimum turning point on the mode 1 beam-column equilibrium curve is given by:

( )

11

2

2

min

)(478.5

=

wwAE

IEL

LA (2)

Substituting minL for L within equation (1) returns the

minimum effective force value for the onset of lateral buckling

(the rapid movement from a small constrained state to a large

deflected form).

In reliability terms safety margin M = R S where R is the

random resistance and S is the random load equivalent to

effective force (PO) in the Hobbs expression (1) above. Setting

up the resulting limit state function within a Monte-Carlo

simulation procedure with relevant parameters statistically

determined the probability of lateral buckle occurrence.

For the 26 pipeline the variation in minimum effective

force value for lateral buckling onset was found to be negligible

for higher modes of buckling. The above initial formulation was

predominately used to prove the pipelines global buckling

stability in the sand regions. However for clay regions the low

level of axial restraint associated with residual axial friction

gives rise to very long slip lengths of several km. In this regard

the linear friction approach is highly conservative as the axially

displacing pipeline meets significant initial restraint from its

embedded state.

For clay regions the previous Mode 1 Hobbs formula was

extended through the inclusion of non-linear axial friction in the

slipping regions, i.e. soil breakout and residual friction, as

shown in Fig. 4. For computational simplicity lateral friction

was conservatively kept as a linear variable.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Displacement (m)

Eq.AxialFriction

coefficient

Peak axial friction

Residual axial friction

Figure 4. Typical non-linear axial soil restraint in clay [4, 5].

The enhanced mode 1 effective force to buckle length

formulation including non-linear axial friction effects is given

below in equation 3:

2

7

2

57

2

5

210597.1

4

10597.17629.80

+= L

EI

w

a

wAEL

EI

wwAE

L

EIP L

A

ADL

AP

Here, (3)

AP is peak equivalent axial break out coefficient

ARAPAD = the difference between peak and residualequivalent axial coefficients

Aa is residual axial friction mobilization distance.

L conservatively taken as the residual lateral frictioncoefficient value

The above equation reverts to (1) and (2) with residual axial

friction when the non-linear axial restraint is insufficient to

balance the large curvature strain developing from a mode 1

lateral buckle, i.e.

04

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an absolute lower bound normal distribution cut-off was used

for the axial and lateral friction distributions, as shown in Fig.

5. The corresponding minimum value for the non-linear lateral

buckling resistance POin the above formulation was determined

by Newton-Raphson iteration and found to fast and reliable

convergence from equation (2) starting values.

Phase 1 SRA provides a nominal measure of the probability of

lateral buckling occurrence along the potential pipeline

buckling region based upon the limit state probabilistic model

and the statistical data used. Within a random sampling

procedure the pipeline is considered to have failed when driving

force associated with the operational and lay tension data

exceeds the quantitative lateral buckling resistance of the 26

CWC pipeline on the seabed. Over a significantly large number

of trials the accumulative number of failures represents the

overall limit state failure probability - here lateral buckling.

The acceptable failure probability depends on the

consequence and nature of failure. For the heavily weightcoated, thin walled 26 pipeline there is a concern that failure

could be a sudden and catastrophic if the pipeline is allowed to

see significant bending from any lateral buckle development.

Therefore, the annual ultimate limit state (ULS) failure

probability of 10-4

per pipeline for normal safety class was

targeted for the purposes of this study.

The load (driving force) and resistance (pipe stiffness and

soil constraint) are described in terms of the following

parameter probability density functions (Table 3):

Table 3. ParametersParameter Mean STD(1) Remarks

Friction

Peak Axial Friction, Sand 0.95 0.03 Normal Dist.

Residual Axial, Sand 0.65 0.13 Normal Dist.

Peak Axial Friction, Clay 2) 0.65 0.13 Normal Dist.

Residual Axial, Clay (2) 0.22 0.04 Normal Dist.

Lateral Friction, Sand 0.85 0.15 Normal Dist.

Lateral Friction, Clay (2) 0.78 0.27 Normal Dist.

Steel Properties (X65 steel)

Modulus of Elasticity, Pa 2.07E+11 1.03E+10 Normal Dist.

Thermal Expansion Coeff. 0.0000117 5.85E-07 Normal Dist.

Concrete wt. coat

Un-cracked Elastic

Modulus, Pa3.00E+10 1.50E+09 Normal Dist.

Damage Ratio (cracking

and loss of steel bond)N/A N/A

Uniform Dist

0/1.0

CWC Tolerance(3)

0.0025 0.0025Normal Dist.

-5 /+10mmOther

Residual Lay Tension, kN N/A N/AUniform Dist,

300/1900

Model Uncertainty 1 0.05 Normal Dist.

Ambient Temperature, C 17.5 0.8 Normal Dist.

1. In this table 2STD is assumed between minimum and maximum values2. Cut-off at 0.13 and 0.33 for axial and lateral friction, respectively3. Cut-off at 5mm and +10mm, respectively

Other parameters were considered to be reasonably certain and

un-varying in regard to their influence on lateral buckle

initiations. Within the SRA the values of these parameters were

taken as per general deterministic design for the 26 pipeline.

Two parameters were assumed uniformly distributed:

concrete damage ratio and the Residual Lay Tension (RLT).Without detailed information, any value between minimum and

maximum extremes is considered to have equal probability of

occurrence. Sensitivity studies undertaken in the 3D finite

element analysis work included consideration of the effects of

composite concrete weight coat stiffness with RLT. For concrete

damage ratio the design range assumed between 20% and 80%

of the concrete was damaged (partially cracked or offering less

than full shear transfer at the interface between the steel pipe

and outer concrete coating). For residual lay tension, the

minimum and maximum values are based on vessel and project

specific data.

The nominal concrete thickness varies along the pipeline

length and was taken in analyses as the sum of the nominalvalue and the variation with the tolerance (5mm/+10mm based

on mean 3 normal standard deviations).

Monte-Carlo simulation process

Figure 6 presents a typical plot of the probability of the 80mm

CWC pipeline developing a single isolated lateral buckle in

uniform clay region using non-linear axial friction constraint in

the SRA model. The figure indicates very small occurrence of

zero or negative safety margin (M = R S where R and S are

random resistance and load respectively). The cumulative

probability of the occurrence from - to 0 safety margin wascalculated as the failure probability.

Figure 6. Typical safety margin distribution

Solution accuracy and convergences can be improved within a

MC simulation process by use of a sample function to generate

random values from an arbitrary probability density function

around the critical limit function [7]. Here in general terms the

failure probabilityfP is given by:

== )(

)()()(

)(

)()(

xf

xfxFEdxxf

xf

xfxFP

V

LRV

xall V

LRf

(6)

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Where in general risk and reliability terms:

Edenotes statistical expectation

)(xFR is the resistance probability distribution function

)(xfL is the load probability density function

)(xfV is the chosen arbitrary sampling function.

For the embedded clay regions of the route the inclusion of non-

linear equivalent axial friction modeling within the mode 1

beam-column formulation served to reduce length of slipping

regions adjacent to the developing buckle and raise minimum

effective force levels for onset of buckling. For the increased

concrete weight coat regions the risk levels were found to be

low and less than the target reliability levels specified in DNV-

OS F101.

From KP 37 with the design temperature profile dropping

off and the seabed tending to a flat uniform clay surface the

pipeline reverted to a nominal 80mm CWC. At this location

SRA results indicate a lateral buckling probability slightlyhigher than the acceptable DNV Ultimate Limit State value of

10-4

but much less than the DNV 10-2

probability associated

with an Accidental Limit State as a consequence of initial gross

pipe out-of-straightness. To prove a low probability of lateral

buckling from KP 37 it was necessary to specify confident out

of straight limits for the 26 pipeline (SRA Phase 2).

3.3 Pipeline out of straightness studies

The Hobbs based limit state formulation identified a higher

than acceptable risk of lateral buckle formation in certain

critical soft clay regions with relatively light CWC. In regard to

passing DNV risk criteria it was necessary to show that the

likelihood of the pipeline seeing excessive out-of-straightness inthe critical regions was indeed small with regard to the

following individual or combination of possible buckle

initiating events:

Pipelay operations

Undulating seabed profile

External impact (ships anchor or fishing interaction)In addition, the most likely critical level of OOS and its

associated bending moments to avoid overstressing the pipeline

were evaluated both qualitatively and quantitatively. For the

project it was known that the seabed is relatively flat in the

critical soft clay regions and shipping frequency low. As an

initial indication of the likely critical OOS (prior to undertaking

quantitative risk analysis), the following approaches were used:

the maximum OOS based on the Taylor and Ganformulation [8]

the critical bending moments based on DNV loadcontrolled limits and

the OOS used in the previous 3D lateral buckling analysis

Taylor and Gan buckle initiation OOS estimates [8]

As an indication of critical out-of-straight levels for the

initiation of lateral buckling an analytical sensitivity study with

fixed parameters was undertaken. Figure 7 shows typical load-

displacement curves based on the Taylor and Gan formulation.

The top three curves are considered as safe OOS since the

temperature loading required is higher than the operating

temperature and no excessive displacement or snap-through is

likely to occur. The mid-curve (forth from the top, OOS=0.4m,dotted line) indicates a likely snap-though of displacement in

order of 2 meters. Therefore, in this example case, 0.4m of

OOS over a half wavelength of 36.2m (Min Radius of curvature

= 455m) is considered as the critical OOS. It should be noted

that this level of out of straightness is associated with point of

buckling instability as distinct from any solution to a 4th

order

beam-column formulation [10] which gives the effective force

required for the initial onset of movement from a given OOS

geometry.

Figure 7:Sample load-displacement - Taylor and Gan.

Table 4 shows the calculated approximate minimum radius of

curvature associated with lateral buckling instability for each of

the soil and CWC regions. These were used as verification of

subsequent reliability based critical OOS levels.

Tabel 4. Taylor and Gan estimated critical OOS

KP Soil

CWC

(mm)

Axial

Friction

Lateral

Friction

Min. Radius of

Curvature (m)

22.5 Sand 150 0.4 0.5 500

24.4 Clay 150 0.13 0.33 800

25.3 Clay 150 0.13 0.33 800

28.1 Clay 150 0.13 0.33 700

29.9 Clay 150 0.13 0.33 60033 Sand 130 0.4 0.5 400

35.8 Clay 130 0.13 0.33 700

37 Clay 80 0.13 0.33 1300

40 Clay 80 0.13 0.33 1300

OOS Imperfection applied in 3D FE Analysis

Without detail as-installed data, previous 3D analysis work

assumed a certain onerous level of out-of-straightness to test for

lateral buckling propensity. Within the FE modeling it is

common practice to generate an artificial OOS by pulling a

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Generally Equation 10 shows that taking the maximum

unfactored bending moment and limiting out-of-straight level

from analyses based on composite pipe stiffness properties will

already overestimate the critical bending moment in regard to

field joint SCF applied to steel only, i.e. the calculated

composite SCF is always less than one.

3.5 Pipelay-induced OOS risk analysis

Following the general lateral buckling propensity SRA using

modified Hobbs formulation any regions still considered at risk

from global buckling and overstress were subject to a phase 2

and 3 reliability analyses. This sought to evaluate the risk of

global buckle initiation and operational overstress associated

with initial pipelay and seabed induced out of straightness.

Pipelay-induced lateral buckle Formations

For analysis purposes the pipelay geometry in the region of the

touchdown point was idealized to the crest type geometric

feature shown below in Figure 9.

BM

(pipelay deviation)

Lateral seabed restraint

Vertical and lateralTouchdown reaction

Figure 9Simplified crest geometry for pipelay OOS

Assume a crest is formed due to the lay barge deviating fromthe pipeline route by an angle, denoted as . The maximum

allowable at the point of lateral buckling instability can bederived from Timoshenko beam-column theory [10, 11] as

given below in equation 11.

34106.5

cr

LP

IEw= (11)

Where:

Pcris driving force, kN

EI is bending stiffness, kNm2

Lis peak lateral frictionw is submerged weight, kN/m

Note that the driving force Pcr is the full force calculated using

the pressure and temperature loading at the corresponding

location and EI is the composite bending stiffness of both steel

and concrete. The probabilistic parameter of concrete damage

ratio was used to account for the cracking and loss of bonding

of the concrete coating. In addition, probabilistic parameters

and distributions were determined for the calculation of

stiffness EI and submerged weight w.

Prior to lateral buckle developments the pipe is stable and

therefore peak breakout lateral friction ranges listed in Table 7

were used to take account of the onset of the buckling during

following pipelay.

Table 7:Lateral friction used in as-laid imperfection probabilitySoil Min. Max. Mean 2 STD 3 STD

Sand 0.9 1.1 1 0.05 0.03

Clay 0.77 1.4 1.085 0.158 0.105

The results for the limiting heading tolerance for lateral buckle

initiation are presented below in Table 8 and show tighter

tolerances should be applied during pipelay from KP38

onwards with the nominal 80mm concrete weight coating.

Table 8: Risk based limiting heading tolerance for lateral

buckle initiation

Limiting Heading Tolerance, (deg)

KP Friction, 2SD Friction, 3SD

22.5 4.4 4.5

24 4.9 5.0

25 4.1 5.1

26 5.6 5.5

38 3.1 3.6

Figure 10 is a typical result plot as evidence for the values listed

in Table 8. The limiting pipelay heading tolerance associated

with initiating a lateral buckle was identified where the

cumulative distribution was shown to give a probability ofoccurrence less than 10

-4. (DNV ALS event Classification)

Figure 10: Limiting heading tolerance in deg

for LB formation at KP38 (2 STD)

Also from elastic beam-column theory the corresponding half

wavelength at the point of buckle instability is given by:

3289.2w

IEL

L

c

= (12)

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Figure 11 shows at the critical KP38 location the half-wave

length associated with buckle development should be no less

than 20m. In conclusion therefore to satisfy risk based design

criteria with regard to pipelay imperfection capable of initiating

a lateral buckle with a low 10-4probability of occurrence, the

limiting heading tolerance should be 3.1 over a distance of20m.

Frequency Chart

m

.000

.006

.011

.017

.023

0

734.7

2939

209.1 281.4 353.8 426.2 498.6

130,000 Trials 127,909 Displayed

Forecast: Half Wave Length

Figure 11:Half wave length, crest formation, KP38, 2STD

(horizontal axis in m x 10-1

)

Pipelay-induced imperfection with operational overstress

Assuming crest geometry at the pipe touchdown region a beam-

column formulation in terms of maximum allowable lateral

pipelay deviation can be developed using critical DNV load-

control bending moments with due consideration to field joint

SCF (equation 7 with composite pipe stiffness).

wEI

M

L

23

667.0= (13)

Four sets of results were obtained with and without concrete

residual stiffness for upper and lower bound equivalent

pipe/soil friction ranges defined as either 2 or 3 normalstandard deviations - Table 9.

Table 9. Unbuckled integrity OOS limits

Limiting Heading Tolerance,

EI Composite EI steel

KP

lat(2 SD) lat(3 SD) lat(2 SD) lat(3 SD)

22.5 4.0 4.1 2.3 2.324 4.0 4.1 2.3 2.3

25 3.5 3.7 2.0 2.126 4.0 4.1 2.3 2.438 5.5 5.7 4.2 4.3

Table 9 indicates that for a cumulative probability of 10-4

the

safe limiting heading tolerance is 3.5 from KP22 to KP37.Figure 12 is presented as evidence of the derived values listed

in Table 9. The limiting heading tolerance was identified at

which the cumulative probability of occurrence is 10-4

(DNV

ULS classification).

Frequency Chart

.000

.005

.011

.016

.021

0

695

2780

3.7 4.2 4.8 5.4 5.9

130,000 Trials 128,108 Displayed

Forecast: Heading Tolerance

Figure 12: Limiting-heading tolerance, unbuckled KP25 OOS

(horizontal axis in )

3.6 3D operational in-place response analysis procedure

The stable pipeline solution was achieved by use of increased

concrete weight coating in a staged approach to increase design

confidence. Apart from the analytical risk assessment describedabove, numerical FE analysis was performed before and after

the risk assessment to identify the likely buckle initiating events

due to pipelay operations on undulating seabed profile and to

calculate the 3D operational in-place buckling response.

Finite Element Modeling

ABAQUS (version 6.6.1) [12] pipe type element PIPE31H was

used to model section by section of the critical 40km long

region of the pipeline route. The 3D uplift and lateral

translation response [13] of the non-linear X65 steel pipe in

contact with the three-dimensional seabed (linear soil stiffness)

was simulated by rigid body element R3D4 subject to variable

operating submerged weight (ranging from about 2 to 6kN/m),pressure (about 120bar) and temperature (about 60C).The three-dimensional seabed was generated from DTM

(Digital Terrestrial Modeling) survey data along the pipeline

route with a corridor width of several kilometers. From this a

narrow 20m wide band of seabed data either side of the pipeline

route was extracted. The DTM data grid is in Easting, Northing

coordinates while the seabed rigid-body node grid is along the

pipeline in the axial and lateral directions. The DTM grid is

transformed into the node grid by interpolation. A 2m rigid

body node grid was used, as shown in Figure 13.

Figure 13: 3D Seabed and pipeline route profile

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The three-dimensional seabed was divided into a few sub-

surfaces according to reported soil conditions along the route.

Upper and lower bound ranges of pipe/soil reaction forces

(axial and lateral equivalent friction values) and the variable

stiffness properties of the seabed were calculated in the critical

clay, rock and coarse sediment regions. Published empiricalformulation more applicable to partially consolidated soil types

in shallower North Sea waters was utilized for the different

weight coated sections along the 26 pipeline route [4, 5].

In detailed 3D finite element analysis, a subsea pipeline is

first laid on the three-dimensional seabed. This is an initially

stressed pipelay condition with the pipeline conforming to route

bends, lateral OOS, and water depth variations. The major

influencing factors in regard to the stabilization of the pipeline

on a three-dimensional seabed were found to be:

Concrete weight coating and the associated submergedweight a dominating factor for a stable pipeline design.

Axial and lateral friction based on calculated embedment

levels with upper and lower ranges based on mean 2 or 3standard deviations. (Table 3).

Temperature and pressure loading determining the lateralbuckling propensity of the pipeline (Fig. 1)

In the FE modeling:

Route bends were incorporated into the modeling bybending the initially straight and stress-free pipe into the

position. When the pipeline overcomes its own initial

bending stress at any local out of straightness the pipeline

has a propensity to displace either laterally or vertically

under sufficiently high levels of effective compression

(pressure and temperature loading). These effective forces

are higher for an initial realistic stressed configurations on

the seabed compared to simpler modeling options ofassuming pipe profiles to be initially unstressed.

Vertical and lateral seabed slopes along the axial directionand normal to the pipeline were included in the FE model.

The seabed surfaces were modeled 20m either side of thepipelines route design centerline.

Eight seabed sections for rock, sand and clay with differentaxial and lateral friction, mobilization distances, and

foundation stiffness were analyzed as part of the

operational response sensitivity studies.

Residual Lay tension (RLT) was included in the modelingby setting axial friction during simulated pipelay.

The numerical procedures in the FE analysis were as follows:Step 1 Pull the pipeline into as-laid position and establish

contact with a false 2D and a real 3D seabed surfaces

Step 2 Lower the false flat seabed below the real 3D seabedStep 3 Apply external pressure and operational submerged

weight

Step 4 Apply internal pressure and temperature loadingStep 5 Apply arbitrary lateral displacement forces at various

locations to test the pipelines global buckling stability

For the long pipeline in this paper, the 3D in-place analysis was

carried out section by section and additionally used to design

key uplift locations such as the trench transition at KP22.

Pipelay and Seabed-Induced OOS

Pipelay simulation undertaken as part of the 3D in-placeanalysis showed locations where the pipeline would slide

sideways when passing over a depression as a combined result

of the lay process and the 3D seabed topography. Figure 14

shows an example of lateral sliding with a local imposed

pipeline out of straightness at KP25. The 2D plan view where

the directions 1 and 2 in the plot are Easting and Northing, is a

contour plot in vertical coordinates, i.e. water depth. The plot

shows the pipeline sliding laterally by 0.15m imposing a

significant degree of seabed induced out of straightness on the

pipeline. Subsequent operational analysis of the displaced pipe

profile, with seabed induced imperfection at KP25, is shown in

Figure 15. Originally, with lower (hydrodynamic stability)

weight coating the KP25 location was found to be over-straining. Figure 15 however shows that with 150mm concrete

weight coat operational lateral displacements are curtailed to

less than 3m with only moderate 0.2% strains.

Figure 14. 3D seabed and plan view showing 0.15m lateral

sliding of the pipeline at KP25

-3

-2

-1

0

1

2

3

4

5

6

7

8

9

24.8 25 25.2 25.4 25.6 25.8KP

Lateraldisplacement(m

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

AbsLo

ngitudinalstrain(

ax = 0.4, 0.13 and lat = 0.77, 0.33

150mm CWC from KP20-30

0

0.1

0.2

18 23 28 33 38

Figure 15. Operational displacement and strain values from 3D

analysis with 150mm concrete weight coating

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Composite pipe stiffness

In general it is accepted that the concrete weight coat provides

some additional composite bending stiffness to the steel pipe. In

this study different stiffness levels from un-cracked to partially

cracked concrete have been considered. Concrete stiffness

within the FE model was achieved by attaching a concrete beamelement to the main steel pipe element. The concrete beam

element has no axial stiffness but a user defined bending

stiffness depending upon the degree of concrete weight coat

damage. The results indicated that the concrete stiffness has

beneficial effects to the 26 pipeline buckling behavior and

provided qualitative evidence of acceptable constraint and

limited in-place displacements occurring during operation.

3.7 Final constrained pipe design recommendationsThe design recommendation from the global buckling risk and

in-place analysis work was to locally increase concrete weight

in critical undulating seabed regions to ensure global buckling

stability and limited bending during operational life of thepipeline. The described SRA approach satisfied DNV code

requirements with acceptable low failure probability

4. CONCLUSIONS

Predicting the global buckling and displacement response of a

pipeline seated on a 3D seabed may on the face of it seem a

difficult undertaking with a multitude of uncertainties. The work

reported in this paper may be specific to a unique set of design

constraints and a pipeline under modest pressure and

temperature loading which was marginal in regard to its

potential to global buckling. The work is presented as in the

authors experience many such pipelines fail initial Hobbs type

lateral buckling checks due to the necessary selection of worsecase deterministic parameters in design.

Limit state design codes such as DNV OS F101 allow the

engineer some leeway to demonstrate code compliance when

design elements fail LRFD format with characteristic values of

load and resistance. One such example of applied SRA is the

Hotpipe project [14], which seeks to evaluate loading

uncertainty (force and moment) from variable seabed restraint

through a calibrated load control check.

The combined SRA and 3D finite element approach adopted

for this project is felt to adequately demonstrate to DNV

implemented industry agreed safety standards that the pipeline

will remain stable and not overstress under operational pressure

and temperature loading with locally increased concrete weightcoat. It is not claimed however that the described approach will

always be applicable as certain key design parameters may

require far more detailed statistical evaluation in regard to their

impact on general pipeline displacement response.

An example of key parameter impact is the seabed

uncertainty. For this project the seabed profile was available

and considered to be representative of the level of vertical out-

of-straightness the pipeline could see following pipelay and

during operation. Generally due to concerns regarding the

limited bending capacity of the 26 pipe section care was taken

to select conservative soil restraint and stiffness parameters

even within the confines of an overall global buckling SRA

design philosophy. In certain circumstances however it could be

argued that the seabed topography is itself a design variable

requiring statistical evaluation in regard to its impact on

operational pipeline displacement response.

ACKNOWLEDGMENTSThe authors would like to acknowledge their gratitude to the

other members of the JP Kenny project team for their guidance

and input to the analysis work: Mr. Adrian Straughan (project

manager), Dr Chas Spradbery and Mr. Ashley Ruthnum.

REFERENCES[1] DNV, ' Offshore Standard for Submarine Pipeline Systems

DNV-OS-F101, Det Norske Veritas, 2000.

[2] Crystal Ball 2000 (Standard) version 5.1 Decisioneering Inc

Denver, Corolado USA.[3] Hobbs, R. E., 1986. In-Service Buckling of Heated

Pipelines, Journal of Transportation Engineering,

Trans.ASCE, Vol 110, No. 2, pp. 175 - 189.

[4] Brennodden, H. and Stokkeland, A. 1992 Time dependant

pipe-soil resistance for soft clay, OTC 6846

[5] Verley, R.L.P. and Lund, K.M. 1995. A soil resistance

model for pipelines placed on clay soils, Proc. OMAE,

Conf. Copenhagen, Vol V: 225-232.

[6] Ballet, J. P. and Hobbs, R. E (1992), Asymmetric effects of

prop imperfections on the upheaval buckling of pipelines.

Thin Walled Structures Vol 13, (355-373)

[7] BP course notes to Theory and Application of Structural

reliability to Pipeline Engineering provided by C-FERTechnologies, May 2001.

[8] Taylor, N. and Gan, A.B., 1986. Submarine Pipeline

Buckling-Imperfection Studies. Thin Walled Structures

(295 - 323)

[9] DNV Recommended Practice for Free Spanning Pipelines

DNV-RP-F105, Det Norske Veritas, 2002

[10] Timoshenko, S. P. and Gere, J. M. 1961. Theory of

Elastic Stability.

[11] Richards, D.M. and Andronicou, A. 1990. Ultimate

strength of pipelines. 1st European Offshore Mechanics

Symposium, Trondheim, Norway.

[12] ABAQUS/STANDARD Finite Element Program. Version

6.6, Hibbitt, Karlsson and Sorensen Inc., Pawtucket, RI.[13] Nystrm, P.R., Trnes, K., Bai, Y., and Damsleth, P.A.

1997 3D Dynamic Buckling and Cyclic Behavior of

HP/HT Flowlines Proceedings 7th

International Offshore

and Polar Engineering Conference.

[14] Mrk, K. J., Collberg, L., Levold, L and Bruschi, R, 1999

Hotpipe Project: Design Guideline for High

Temperature/Pressure Pipelines 9th

Int Offshore and

Polar Engineering Conference Brest, France.

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