directed studies-subsea pipelines

Subsea Pipelines

Prepared for Directed Studies CIVL 7006

Nikzad Nourpanah

Under supervision of: Dr. Farid Taheri

Winter 2008/2009

Subsea Pipelines Page 1

Scope

The scope of this document is to give a general introduction on the subject of subsea pipelines, with

reference to design codes as used by the industry. The document covers most important aspects of analysis

and design of subsea pipelines, but it should be noted that some less important topics are left out. Where

applicable, the theory and/or experimental data behind code provisions is discussed with reference to

available technical literature. The main topics are Mechanical design, on-bottom stability, free spanning and

installation of subsea pipelines.


Contents

1. Introduction 9

2. Material Grade Selection 11

3. Diameter Selection 12

4. Wall Thickness Selection 13

4.1. Internal Pressure Containment (Burst) 13

4.2. Collapse Due to External Pressure 19

4.3. Local Buckling Due to Bending and External Pressure 22

4.4. Buckle Propagation 27

5. On-Bottom Stability 35

5.1. Soil Friction Factor 37

5.2. Hydrodynamic Force Calculation 37

5.3. Hydrodynamic Coefficient Selection 39

5.4. Stability Criteria 44

6. Free Span (Bottom Roughness) Analysis 45

6.1. Static condition 47

6.2. VIV 50

7. Installation of Subsea Pipelines 63

7.1. J-lay 68

7.2. S-lay 72

7.3. Reel lay 73

7.4. Towed Pipelines 74

7.5. Shore Approach 75

7.6. Wet vs Dry Pipeline Installation 77

References 80


List of Figures

Figure 1 - US crude oil production trends (S. Chakrabarti, 2005) ................................................................9

Figure 2 - Number of ultra deepwater (>5000 ft) wells drilled in Gulf of Mexico (S. Chakrabarti, 2005) ...... 10

Figure 3 - Roles of pipelines in an offshore hydrocarbon field (Bai, 2000) ................................................. 10

Figure 4 - Free body diagram of a pipe section under internal and external pressure ................................ 13

Figure 5 – Burst pressure (Pb) according to API-RP-1111 (1999) using Equations 4 and 5 for X65 grade

steel, SY = 65 ksi, U = 77 ksi and E = 29’000 ksi .................................................................................... 15

Figure 6 – Pressure level relations (API-RP-1111, 1999) .......................................................................... 16

Figure 7 – Ductile burst sample (API-RP-1111, 1999) .............................................................................. 17

Figure 8 – Brittle burst sample (API-RP-1111, 1999) ............................................................................... 17

Figure 9 – Concept of effective axial force (Fyrileiv et al, 2005) ............................................................... 19

Figure 10 – Collapse pressures of 2900 specimen normalized with collapse pressures calculated by Equation

(15) (Murphey and Langner, 1985) ........................................................................................................ 21

Figure 11 - Collapse pressure vs. D/t per API 1111 (1999) and DNV OS-F101 (2000), (Nogueira &

Mckeehan, 2005) .................................................................................................................................. 21

Figure 12 – Mechanical behavior of pipe subjected to pure bending, (Murphey and Langner, 1985) ........... 23

Figure 13 – Moment vs. strain curves for constant diameter and yield stress but variable wall thickness

(Murphey and Langner, 1985) ............................................................................................................... 23

Figure 14 – Pipe bending tests in air – curvatures at buckling (Murphey and Langner, 1985) ..................... 24

Figure 15 – Pipe collapse due to combined bending and external pressure; comparison of experimental

results with (18) for a perfectly circular pipe (Murphey and Langner, 1985) ............................................. 25

Figure 16 - Rational model prediction of collapse pressure vs. initial ovality, compared to experimental

results for pipe with D/t = 35 (Nogueira & Mckeehan, 2005) ................................................................... 26

Figure 17 - Pressure vs. bending strain predicted by rational model and experiments (Nogueira & Mckeehan,

2005) ................................................................................................................................................... 26

Figure 18 - Pressures vs. bending strain; comparison between empirical formulations of API, DNV and the

rational model (Nogueira & Mckeehan, 2005) ......................................................................................... 27

Figure 19 – Elastic, plastic, collapse and buckle propagation pressures for an X65 grade pipeline based on

API RP 1111 (1999) and Timoshenko (1961) formulations, E = 29’000 ksi ............................................... 28

Figure 20 – Hoop stress associated with elastic, plastic and collapse pressure for an X65 grade pipeline

based on API-RP-1111 (1999) and Timoshenko (1961) formulations, E = 29’000 ksi ................................. 28

Figure 21 – Grouted Sleeve arrestor (Langner, 1999) .............................................................................. 29

Figure 22 – Integral Ring arrestor, which also serves as J-Lay Collar, (Langner, 1999) .............................. 30

Figure 23 - Tested sample of a pipeline with Sleeve type buckle arrestors and the numerical model .......... 30


Figure 24 – U mode buckling of a pipeline; the collapse wave passes through a sleeve type arrestor

(Kyriakides, 2005) ................................................................................................................................. 33

Figure 25 – Comparison of integral ring buckle arrestor design formula with available test data (Langner,

1999) ................................................................................................................................................... 34

Figure 26 - Regions of applicability of different wave theories (API RP 2A, 2000) ...................................... 36

Figure 27 – Relative importance of inertia, drag and diffraction wave forces (DNV-OS-J101, 2004) ............ 38

Figure 28 – Current profile due to tides and wind (DNV-CN-30.5, 1991) ................................................... 39

Figure 29 – CD as a function of Reynolds number and roughness for a cylinder in steady current (DNV-CN-

30.5, 1991) .......................................................................................................................................... 40

Figure 30 – Added mass coefficient Ca as a function of gap ratio H/D (DNV-CN-30.5, 1991) ...................... 40

Figure 31 – CD as a function of KC and roughness (DNV-CN-30.5, 1991) .................................................. 41

Figure 32 – Influence of seabed proximity on CD for current+wave situation (DNV-CN-30.5, 1991) ............ 41

Figure 33 – Hydrodynamic force coefficients CD, CM and CL for regular waves, effect of pipe roughness (a)

and seabed roughness (b) (Bryndum, 1992) ........................................................................................... 42

Figure 34 – Hydrodynamic coefficients versus current ratio for wave plus steady current (Bryndum, 1992) 43

Figure 35 – Free body diagram of pipeline for on-bottom stability analysis (Bai, 2000) .............................. 44

Figure 36 – Free spanning pipeline on seabed ........................................................................................ 45

Figure 37 – Continental shelf and continental slope................................................................................. 45

Figure 38 – Subsea pipelines, Ormen Lange field, Norway (Source: Internet) ........................................... 46

Figure 39 - Typical free span distributions and pipeline profile (Soreide, 2001) ......................................... 46

Figure 40 – Static stresses and deformations in a free spanning pipeline (Mousselli, 1981) ........................ 48

Figure 41 – Static stress and span for pipeline passing obstruction (Mousselli, 1981) ................................ 49

Figure 42 – Vortex shedding due to steady flow at different Reynolds numbers and fluctuating pressures on

pipe resulting in oscillating lift and drag forces (Blevins, 1977) ................................................................ 50

Figure 43 – Classification of free spans (DNV-RP-F105, 2006) ................................................................. 51

Figure 44 – CFD simulation of piggyback pipeline ................................................................................... 53

Figure 45 – Effective length vs. soil stiffness (DNV-RP-F105) ................................................................... 54

Figure 46 – Illustration of the in-line VIV Response Amplitude versus VR and KS (DNV-RP-F105, 2006) ....... 57

Figure 47 – Illustration of the cross-flow VIV Response Amplitude versus VR (DNV-RP-F105) ..................... 58

Figure 48 – Typical two-slope S-N curve (DNV-RP-F105, 2006) ................................................................ 59

Figure 49 – Schematic diagram of free span pipelines with additional local stiffness and damping (Fernes

and Bertsen, 2003) ............................................................................................................................... 61

Figure 50 - Motions due to a prescribed second mode inline deflection. (C) Time series of ry/D close to an

antinode. (D) Time series of rz/D close to an antinode. (Bottom panels) Countours of time evolution of ry/D

and rz/D. (Fernes and Berntsen, 2003) ................................................................................................... 62


Figure 51 - Combined in-line and cross flow motion of a pipeline section (Fernes and Berntsen, 2003) ...... 62

Figure 52 – Schematic of S-lay method for pipelaying (Nogueira & Mckeehan, 2005) ................................ 63

Figure 53 – Schematic of J-lay method for pipelaying (Nogueira & Mckeehan, 2005) ................................ 64

Figure 54 – Taut mooring system .......................................................................................................... 65

Figure 55 – Catenary mooring system .................................................................................................... 65

Figure 56 – Combined station-keeping method for intermediate water depths (Langner, 1973) ................. 66

Figure 57 – Location of stress concentration in sleeve connection, Top: J-lay, Bottom: S-lay (Dixon et al.

2003) ................................................................................................................................................... 67

Figure 58 – Heerema's balder in J-lay mode (Nogueira & Mckeehan, 2005) .............................................. 69

Figure 59 – Dynamics of pipelines during laying: motion, dynamic stresses and tension for different wave

periods (Clauss et al. 1991) ................................................................................................................... 70

Figure 60 – A typical S-lay Vessel (Nogueira & Mckeehan, 2005) ............................................................. 72

Figure 61 – A reel vessel (Guo et al. 2005) ............................................................................................. 73

Figure 62 – Schematic of towed pipeline (Bai, 2000) ............................................................................... 74

Figure 63 – Float and sink method used for shore approach installation ................................................... 75

Figure 64 – Bottom pull method used for pipeline shore approach ........................................................... 75

Figure 65 - Bottom pull method; launching roller track ............................................................................ 75

Figure 66 – Directional drilling method for pipeline shore approach .......................................................... 76

Figure 67 – Comparison of design strategies for 660.4 mm (26 inch) pipeline: wall thickness as a function of

depth (Palmer, 1998) ............................................................................................................................ 78

Figure 68 – Comparison of design strategies for 660.4 mm (26 inch) pipeline: submerged weight in laying

condition as a function of depth (Palmer, 1998) ...................................................................................... 78


List of Tables

Table 1 - Tensile strength properties (API 5L, 2000) ............................................................................... 11

Table 2 - Crude oil sizing guidance (Nogueira & Mckeehan, 2005) ........................................................... 12

Table 3 - Diameters for selected offshore projects (Nogueira & Mckeehan, 2005) ..................................... 12

Table 4 - Temperature de-rating factor, T, for steel pipe according to ASME B31.8 (Nogueira & Mckeehan,

2005) ................................................................................................................................................... 14

Table 5 – Return period for environmental phenomena ........................................................................... 35

Table 6 – Allowable pipeline stresses (Nogueira & Mckeehan, 2005) ........................................................ 47

Table 7 – Response Behavior of free span (DNV-RP-F105, 2006) ............................................................. 52

Table 8 – Different flow regimes (DNV-RP-F105, 2006) ........................................................................... 52

Table 9 – Boundary conditions coefficients (DNV-RP-F105, 2006) ............................................................ 55

Table 10 – Advantages and disadvantages of J-lay (Nogueira & Mckeehan, 2005) .................................... 68

Table 11 – Advantages and disadvantages of S-lay (Nogueira & Mckeehan, 2005) .................................... 72

Table 12 – Advantages and disadvantages of Reel-lay (Nogueira & Mckeehan, 2005) & (Guo et al. 2005) .. 73


Nomenclature

A = Pipeline steel cross section

0A = Pipeline outer cross section

CFA = Stress amplitude due to a unit diameter cross-flow

mode shape deflection

iA = Pipeline inner cross section

ILA = Stress amplitude due to a unit diameter in-line

mode shape deflection

YA = In-line VIV amplitude

zA = Cross-flow VIV amplitude

61 ~ CC = Boundary condition coefficients

aC = Added mass coefficient

DC = Drag coefficient

1+= am CC = Inertia coefficient

LC = Lift Coefficient

CSF=Coating Stiffness Factor

d = Water depth

D = Pipeline nominal outside diameter

fatD = Accumulated fatigue damage

E = Modulus of elasticity

E = Longitudinal joint factor

0f = Collapse factor

1f = 1st eigen-frequency of free span in still water

df = Design factor

ef = Weld joint factor

nf = nth eigen-frequency of free span in still water

pf = Buckle propagation safety factor

tf = Temperature de-rating factor for steel

ivf , = vibration frequency of pipeline due to “i”th sea

state

wf = Wave frequency

F = Construction design factor

DF = Drag force

IF = Inertia force

LF = Lift force

h= Buckle arrestor thickness

H = Wave height

I = Moment of inertia

ID= Pipeline inner diameter

k = Burst coefficient

2

4Dm

K Tes ρ

ξπ= = Stability parameter

DfU

KCw

c= = Keulegan-Carpenter number

L = Wave length

L = buckle arrestor length

mL = Length of pipeline in Miles

em = Effective (modal) mass

)(sm = mass per unit length of pipeline including

structural mass, coating mass and added mass

M = Moment

in = Number of cycles at stress range Si

iN = Number of cycles to failure at stress range Si

)(iP = Probability of occurrence for the “i”th stress cycle

(“i”th sea state)

0P = External pressure

1P = psia at start point of pipeline

2P = psia at end point of pipeline

aP = Incidental overpressure

actualP = Actual measured burst pressure

bP = Burst pressure

cP = Collapse pressure

crP = Free span critical buckling load

eP = Elastic collapse pressure

iP = Internal pressure

idP = Internal design pressure

mP = Minimum cross-over pressure

HydP −max = Maximum hyrotest pressure

pP = Buckle propagation pressure

tP = Hydrostatic test pressure

xP = Buckle arrestor cross-over pressure

yP = Plastic collapse pressure

Q = Cubic ft of gas per 24 hr


υDU c=Re = Reynolds number

iS = Stress range due to ith seastate

uS = Soil undrained shear strength

YS = Specified minimum yield stress

aYS , = Specified minimum yield stress of buckle arrestor

actualYS , = Average measured yield strength of pipe

SF = Safety factor t = Pipeline nominal wall thickness

mint = Minimum measured wall thickness

T = Wave period

T = Temperature de-rating factor for steel

aT = True wall axial force

dT = Design life

effT =Effective axial force (true wall force including

pressure corrections)

lifeT = Fatigue life capacity

U = Steel ultimate tensile strength

actualU = average measured ultimate tensile strength

cU = Current velocity

wcm UUU +=

wU = Particle maximum horizontal velocity due to wave

wU& = Particle maximum horizontal acceleration due to

wave

windU = Current velocity due to wind

tideU = Current velocity due to tide

DfUU

Vn

wcR

+= = Reduced velocity

sW = Pipeline submerged weight

wc

c

UUU+

=α = Current flow velocity ratio

γ = Weight density

υ= Poisson’s ratio, 0.3 for steel υ= Kinematic viscosity, 1*10-6 for seawater ε = critical strain

Tξ = Damping, including structural, soil and

hydrodynamic damping ρ = Mass density

)/()( minmaxminmax DDDD +−=δ = ovality

δ = Pipeline sagging at mid span κ = Curvature η= Efficiency parameter for buckle arrestor

fatη = Fatigue safety factor

µ = Soil friction factor

θ = Seabed slope ϕ= Internal friction angle of soil

φ = mode shape


1. Introduction

In order to understand the importance of subsea pipelines, the importance of offshore oil and gas is first

mentioned. Figure 1 shows the US crude oil production trends from onshore and offshore resources.

Figure 1 - US crude oil production trends (S. Chakrabarti, 2005)

It is seen in Figure 1 that offshore production is increasing and onshore portion is decreasing. This is due to

the fact that most onshore hydrocarbon fields are discovered and under production and some of them are

no longer economic. Also it is seen that production from shallow waters is nearly constant while production

in deepwater (>1000 ft) is increasing. This is due to the fact that almost all resources in shallow waters are

found and being utilized, therefore exploration is active in deep and ultra deep (>5000 ft) waters. Figure 2

shows this fact: the number of wells in ultra deep waters is increasing very fast.


Figure 2 - Number of ultra deepwater (>5000 ft) wells drilled in Gulf of Mexico (S. Chakrabarti, 2005)

In an offshore hydrocarbon production system, pipelines have a connecting role between the facilities.

Figure 3 shows a typical offshore hydro carbon field and the role of pipelines.

Figure 3 - Roles of pipelines in an offshore hydrocarbon field (Bai, 2000)


2. Material Grade Selection

Generally carbon steels are used for subsea pipelines. API-5L "Specification for Line Pipe" (2000) is used for

standard specifications. API-5L covers Grade B to Grade X80 steels with Outside Diameters (OD) ranging

from 4.5 to 80 inch. Table 1 shows tensile strength properties according to API-5L. Generally the most

common steel grade used for deepwater subsea pipelines is X65, regarding its cost-effectiveness and

adequate welding technology. For buried offshore pipeline in the Arctic, the more ductile X52 has been

proven the best choice for limit state design and the need for a high toughness material that could sustain

the high strain based design.

Table 1 - Tensile strength properties (API 5L, 2000)

Generally, higher grades of steel (e.g. X70, X80, Duplex) cost more per unit volume. Welding higher grades

is harder, therefore each joint requires more time so the overall operation time of the lay barge is higher.

On the other hand by using higher grade steels the required wall thickness is reduced. Therefore although

higher grades cost more per unit volume, the cost of pipeline per meter is slightly reduced. Higher grade

steels result in a lighter pipeline, therefore the required tension is lower. This factor is very important in

deep waters, where required tension can be a limiting factor.


3. Diameter Selection

The process for selecting a pipeline diameter involves a detailed hydraulic analysis, especially for multi

phase flows. However, there exist some empirical formulas that produce reasonable accuracy. For example

Equation 1 can be used for sizing single phase gas lines and Table 2 for crude oil pipelines (Nogueira &

Mckeehan, 2005). Also, diameters of some selected offshore projects are presented in Table 3.

mLPPID

Q2

22

13500 −

=

(1)

Table 2 - Crude oil sizing guidance (Nogueira & Mckeehan, 2005)

Table 3 - Diameters for selected offshore projects (Nogueira & Mckeehan, 2005)


4. Wall Thickness Selection

To calculate the required wall thickness for an offshore pipeline, four different failure modes must be

assessed:

1. Internal pressure containment (burst) during operation and hydro-test.

2. Collapse due to external pressure.

3. Local buckling due to bending and external pressure.

4. Buckle propagation and its arrest.

4.1. Internal Pressure Containment (Burst)

The burst pressure of the pipeline is basically calculated by the hoop stress formula for thin walled pressure

vessels. Thin wall theory is valid for D/t > 20 and t < 0.1 inner pipe radius. It assumes uniform wall stress

and gives mean circumferential stress. The burst pressure is calculated by setting the hoop stress equal to

pipeline yield stress and incorporating safety factors. Thin wall equation can be used for D/t < 20 but it

gives slightly higher estimates of stress than thick wall theory. The principal difference between the thin and

thick wall formulations is that for thick wall conditions, the variation in stress between inner and outer

surfaces becomes significant.

Figure 4 - Free body diagram of a pipe section under internal and external pressure

All the major codes (i.e. API, DNV, ASME, ABS and CSA) use the same philosophy. Here the formulation

according to US regulations (CFR, Code of Federal Regulation), which uses allowable stress design is given.

Pid is internal design pressure (CFR, 2002):

FETD

tSP Yid

2=

(2)


F = construction design factor of 0.72 for submerged component and 0.60 for the riser component, T =

temperature de-rating factor (See Table 4), E = longitudinal joint factor (for API-5L steels E is 1.0 for

seamless, electric resistance welded, electric flash welded, submerged arc welded, and 0.6 for furnace but

welded).

Table 4 - Temperature de-rating factor, T, for steel pipe according to ASME B31.8 (Nogueira & Mckeehan, 2005)

According to 30 CFR 250 (CFR, 2002), all pipelines should be hydrostatically tested with water at a stabilized

pressure of at least 1.25 times the maximum allowable operating pressure (MAOP) for at least 8 h. Equation

(3) can be used where F, construction design factor is 0.95 for hydro test:

FETD

tSP Yhyd

2max =−

(3)

API-RP-1111 (1999) which is a limit state code and uses LRFD method uses the following logic for internal

pressure check:

A burst pressure, Pb, is defined for the pipeline:

( )tD

DLnUSP Yb 245.0

−+=

(4)

( )tD

tUSP Yb −+= 90.0

(5)

Any of the Equations (4) and (5) can be used, but API recommends use of Equation (4) for D/t<15.

Regarding geometrical properties, Equations (4) and (5) are only functions of D/t. A plot of the two

equations is given in Figure 5 and it is seen that the two equations give the same results.


Figure 5 – Burst pressure (Pb) according to API-RP-1111 (1999) using Equations 4 and 5 for X65 grade steel, SY = 65

ksi, U = 77 ksi and E = 29’000 ksi

The hydrostatic test pressure should satisfy the following:

btedt PfffP ≤

(6)

Where:

fd is design factor equal to 0.90 for pipelines and 0.75 for risers

fe is weld joint factor and the same as E in Equation (2), originally defined by ASME B31.4 and ASME B31.8.

API-RP-1111 only accepts pipelines with fe equal to one.

ft is temperature de-rating factor and is the same as T in Equation (2) which is given in Table 4.

The Maximum Operating Pressure (MOP) should not exceed 0.80 of the hydro-test pressure:

td PP 80.0≤

(7)

0 10 20 30 40 50 60 70 800

5

10

15

20

25

30

35

D/t

Bur

st P

ress

ure,

Pb (k

si)


Incidental overpressure (Pa) includes the situation where the pipeline is subject to surge pressure,

unintended shut-in pressure, or any temporary incidental condition. The incidental overpressure should not

exceed 90% of the hydro-test pressure. The incidental pressure may exceed MOP temporarily; but the

normal shut-in pressure condition should not be allowed to exceed MOP.

ta PP 90.0≤

(8)

The relation between maximum operating pressure, maximum incidental over pressure, hydro-test pressure

and burst pressure are shown graphically in Figure 6, with fe and ft equal to 1.

Figure 6 – Pressure level relations (API-RP-1111, 1999)

API-RP-1111 (1999) provides Appendix-A as a procedure for testing and qualification of material other than

carbon steel. This code only allows use of ductile material. Figure 7 and Figure 8 show typical failure pattern

of ductile and brittle material respectively. A ductile burst failure has a distinct bulge at the burst location. A

longitudinal fracture extends over the length of the bulge and terminates near the end of the bulge. The

end of fracture turns at roughly 45 degrees from the pipe axis at each end.


Figure 7 – Ductile burst sample (API-RP-1111, 1999)

Figure 8 – Brittle burst sample (API-RP-1111, 1999)


The burst coefficient, k, is defined as:

⎟⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛

−+

=

tt

tDDUS

PkactualactualY

actual

min, 2

ln)(

(9)

Having obtained the burst factor, the burst pressure, Pb, can be written as Equation (10). Note that

Equation (10) is the general form of Equation (4), in which k was set to 0.45.

( )tD

DLnUSkP Yb 2−+=

(10)

The value of k is determined from the burst test data as:

⎪⎩

⎪⎨

⎧

=45.09.0

875.0

min mink

k

kaverage

It is expected that the computed k values will all significantly exceed 0.45.

The effective tension due to static primary longitudinal loads should not exceed the allowable value:

yeff TT 60.0≤

(11)

Where

00 APAPTT iiaeff +−=

AT Aa σ=

AST yy =

Effective axial force is a concept introduced to simplify the treatment of internal and external pressures. By

arbitrarily considering a segment of pipeline as end-capped, the summation of external and internal

pressures result in buoyancy and weight of internal liquid respectively. (Fyrileiv et al, 2005). In order to

justify the end cap assumption, opposite forces are applied and summed with true axial force, Ta, (as seen

in Equation 10). If this simplifying method is not used, the external and internal pressures have to be

integrated over the outer and inner volume surface respectively, which is much more complex than the

effective axial force method. The effective axial force concept is illustrated in Figure 9.


Figure 9 – Concept of effective axial force (Fyrileiv et al, 2005)

Also for the combination of axial force and pressures, API-RP-1111 (1999) suggests the following interaction

equation to be satisfied:

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡≤⎟

⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛ −

loadshydrotestforloadsextremefor

loadsloperationafor

TT

PPP

y

eff

b

oi

96.096.090.022

(12)

4.2. Collapse Due to External Pressure

During installation, subsea pipelines are typically subjected to conditions where external pressure exceeds

the internal pressure. The differential pressure may cause collapse of pipe. Generally, the collapse pressure

is between the elastic and plastic collapse pressures. The elastic collapse pressure, Pe , is found by

examining the stability of a pipe section under hydrostatic load. The plastic collapse pressure, Py , is found

by equating the hoop stress to the yield stress.

3

212

⎟⎠⎞

⎜⎝⎛

−=

DtEPe υ

(13)

DtSP yy 2=

(14)


Each of the major codes gives a transition formula between Pe and Py for calculating the collapse pressure

Pc . DNV (2000) and ABS (2000) give a complicated third order equation. Timoshenko and Gere (1961)

propose a bi-linear transition. API-RP-1111 (1999) gives a very simple formula for Pc, which is the lower-

bound prediction for collapse pressure:

22ye

yec

PP

PPP

+=

(15)

Timoshenko and Gere (1961), propose the following design equation collapse pressure:

32 )1(1

2

⎟⎠⎞

⎜⎝⎛−

+

=

tD

ES

SP

y

yc υ

(16)

Both Equations (15) and (16) are interpolation formulas between Pe and Py. A graphical presentation of

Equations (13), (14), (15) and (16) is given in Figure 19 and the associated hoop stresses (calculated by

assuming thin-wall theory) is given in Figure 20. It is seen in Figure 20 that the collapse hoop stress of the

pipeline has the same typical pattern for column critical stress.

Equation (15) gives nearly the same results as DNV as seen in Figure 11. Equation was originally introduced

by Shell in 1975 (Murphey and Langner, 1985). Comparison of results of Equation (15) with 2900 pipe

collapse tests is shown in Figure 10, and shows that 97% of the collapse data lie above the predictions of

Equation (15).

The design equation according to API-RP-1111 (1999) for external pressure is:

ci PfPP 00 <−

(17)

Where:

0f = Collapse factor, 0.7 for seamless ERW pipe, 0.6 for cold expanded pipe, such as DSAW pipe


Figure 10 – Collapse pressures of 2900 specimen normalized with collapse pressures calculated by Equation (15)

(Murphey and Langner, 1985)

Figure 11 - Collapse pressure vs. D/t per API 1111 (1999) and DNV OS-F101 (2000), (Nogueira & Mckeehan, 2005)


4.3. Local Buckling Due to Bending and External Pressure

During installation with a lay barge, the pipeline is subject to severe bending and external pressure,

however in other situations this might happen, namely in free spans and during depressurization. Most of

the codes have addressed this failure mode and proposed relevant formulations. These formulations are

based entirely on empirical data fitting. API-RP-1111(1999) proposes Equation (18) which can be used for

D/t < 50. DNV and ABS also suggest the same formula except that the strain term is to the power of 0.8.

)()( 0 δεε g

PPP

c

i

b

≤−

+

(18)

Where:

Dt

b 2=ε =buckling strain under pure bending

1)201()( −+= δδg = collapse reduction factor which is maximum 1 for a perfectly circular pipe

The safety factor for bending strain is 2.0.

The buckling strain for a cylindrical shell under the action of uniform axial compression is 1.2 t/D. This strain

is determined by eigenvalue analysis based on the small strain elastic theory, without any account of

imperfections and residual stresses (Fatemi, 2007). The general equation is (Timoshenko and Gere, 1961):

Dt

Dt

bb 2.13.0)1(3

22

=⇒=−

= ευυ

ε

In order to understand the physical meaning of critical strain, pure bending of a pipeline is discussed here.

As bending moment is applied to the pipe, curvature is developed, which is defined as reciprocal of radius of

curvature. A convenient measure of curvature is strain of the material farthest from neutral bending plane:

2Dκε =

For small bending strains, less than the proportional limit strain, the stress at any point and the bending

moment vary linearly with bending strain. With further increase in the bending strain to just beyond the

proportional limit (Point A on the stress-strain curve in Figure 12 (a)), plastic deformation of the pipe

material begins. At this point both the stress-strain curve and the moment-curvature curve move off the

initial straight lines, and the stress distribution, Figure 12 (d), becomes nonlinear. A further increase in

strain, to point B, produces a further departure from the initial linear behavior, including residual curvature

of the pipe centerline. The plastic deformation at this degree of bending is stable, causing little ovaling or

change in cross sectional shape, as indicated in Figure 12 (c), and the pipe itself is not weakened or in any

danger of imminent failure.


Figure 12 – Mechanical behavior of pipe subjected to pure bending, (Murphey and Langner, 1985)

Figure 13 – Moment vs. strain curves for constant diameter and yield stress but variable wall thickness (Murphey and

Langner, 1985)

(b) Moment vs strain

(c) (d) Stress distributions

(c) Ovaling due to bending

(a) Stress-strain curve


As bending strain increase toward point C, ovaling increases rapidly and the slope of the bending moment

vs strain curve tends toward zero. This slope of of the moment-strain curve between points B and C is

determined by two competing effects. Moment is increased as a result of strain hardening and because an

increasing fraction of the cross section reaches yield. At the same time, ovaling of the cross section reduces

the section modulus and the hoop stresses interact with the axial stresses through the plasticity

relationships, which tends to decrease the bending moment. At point C the bending strain reaches a critical

value εb where the ovaling effect just overcomes the strain hardening characteristics of the pipe material.

The bending moment Mb is maximum at this bending strain, and after this point the pipe would buckle

(Murphey and Langner, 1985). Figure 13 shows moment-strain curves for three D/t ratios, where the

diameter is kept constant and wall thickness varies. For undamaged pipeline it has been observed that the

bending strength Mb is approximately equal to fully plastic moment, and the critical bending strain is εb =

t/2D, which is the value used in Equation (18) and is used by most major design codes (API, DNV, ABS).

Figure 14 shows how this value fits the experimental data. Figure 14 also provides some indication of the

detrimental effects of “flat” stress-strain curves and/or inhomogeneous pipe. Note that all the lowest

buckling points on this graph fall into one or both of these categories. “Flat” stress-strain is one that the

slope of the curve goes to zero or becomes negative at any point during the initial yielding process.

Premature buckling is expected for pipes with “flat” stress-strain curve.

Figure 14 – Pipe bending tests in air – curvatures at buckling (Murphey and Langner, 1985)


Equation (18) for a perfectly circular pipe (where the collapse reduction factor is 1) is a straight line which

intersects both axes at 1. For this case, Figure 15 shows experimental results and predictions of Equation

(18) and a good fit is observed.

Figure 15 – Pipe collapse due to combined bending and external pressure; comparison of experimental results with

(18) for a perfectly circular pipe (Murphey and Langner, 1985)

In lieu of the mentioned empirical formulation, Nogueira and Lanan (2001) have developed a rational model

from first principles, and the predictions have been shown to correlate very well with test results. In this

model it is recognized that as a pipe bends, components of the longitudinal bending stresses act into the

cross-section. This, in turn, generates a transverse moment, which ovalises the pipe cross section, or ring,

until it collapses. A pipe under bending will collapse when its cross section (or ring) loses stiffness due to

plastic hinges mechanism formation at the onset of local buckling. Therefore, when rings of the pipe lose

their stiffness, the ovalisation (initially uniform along the pipe length) will concentrate at the weakest point

along the pipe (e.g. a thinner ring) and a local buckle will form. If in addition to bending, external pressure

is applied, its effects are taken into account by noticing that it contributes to reduce the ring capacity to

resist bending. This is due to the effects of the compressive hoop stress. The resulting is an interaction

equation (between pressure and bending strain), which is too long and complicated to be presented here.

Figure 16 shows comparison of collapse pressure predicted by model with those by the experiments which

are in good agreement.


Figure 16 - Rational model prediction of collapse pressure vs. initial ovality, compared to experimental results for pipe

with D/t = 35 (Nogueira & Mckeehan, 2005)

Figure 17 shows the collapse pressure vs. bending strain predicted by the rational model and experiments.

A good match is observed.

Figure 17 - Pressure vs. bending strain predicted by rational model and experiments (Nogueira & Mckeehan, 2005)


Finally the results from empirical formulations of codes (API and DNV) are compared with results of the

rational model in Figure 18.

Figure 18 - Pressures vs. bending strain; comparison between empirical formulations of API, DNV and the rational

model (Nogueira & Mckeehan, 2005)

4.4. Buckle Propagation

If a local buckle is present in a section of a pipeline, for example resulting from excessive bending, the

external pressure may cause the buckle to propagate (travel) along the pipeline. As long as the external

pressure is less than the propagation pressure threshold, the buckle cannot propagate. Codes present

different empirical formulations for buckle propagation pressure which mainly depend on diameter, wall

thickness and steel grade. The equation given by API-RP-1111 (1999) is presented.

4.2

24 ⎟⎠⎞

⎜⎝⎛=

DtSP yp

(19)

It is noted that propagation pressure Pp is smaller than collapse pressure Pc (collapse pressure is the

pressure required to buckle a pipeline section). Figure 19 is a plot of Pe, Py, Pc, Pp for an X65 pipeline. Figure

20 shows the hoop stress associated with the mentioned levels.


Figure 19 – Elastic, plastic, collapse and buckle propagation pressures for an X65 grade pipeline based on API RP 1111

(1999) and Timoshenko (1961) formulations, E = 29’000 ksi

Figure 20 – Hoop stress associated with elastic, plastic and collapse pressure for an X65 grade pipeline based on API-

RP-1111 (1999) and Timoshenko (1961) formulations, E = 29’000 ksi

0 10 20 30 40 50 60 70 800

1

2

3

4

5

6

7

8

9

10

D/t

Pres

sure

(ksi

)

PlasticCollapsePressure,Py

ElasticCollapsePressure,Pe

APICollapsePressure,Pc

TimoshenkoCollapsePressure,Pc

BucklePropagationPressure,Pp

0 10 20 30 40 50 60 70 800

10

20

30

40

50

60

70

80

D/t

Stre

ss (k

si)

PlasticCollapseHoopStress

ElasticCollapseHoopStress

APICollapseHoopStress

TimoshenkoCollapseHoopStress


In order to avoid buckle propagation, the following equation with safety factor fp = 0.8 should be satisfied:

ppi PfPP ⋅≤−0

(20)

In order to satisfy Equation (20) in deep waters, very large thickness is required which is not economical.

Buckle arrestors can be used to mitigate the risk of buckle propagation. In general, the distance between

buckle arrestors should be selected to enable repair of the flattened section of pipeline between two

adjacent arrestors, at “reasonable” cost. For pipelines installed by J-Lay, the buckle arrestors also serve as

pipe support collars. In this case the distance between arrestors is simply the length of each J-Lay joint.

Three types of buckle arrestors are in common use, namely Grouted Sleeve arrestors, Integral Ring

arrestors, and Thick Wall Pipe Joints (Langner, 1999).

Grouted Sleeve arrestors are steel sleeves that are slid over the ends of selected pipe joints and are

grouted in place, as shown in Figure 21, before being installed offshore. Grouted Sleeve arrestors are

preferred, where feasible, because of their low cost. However, this type of arrestor has limited usefulness in

deep water because, as external pressure increases, a collapsed pipe will transform from its normal flat

“dogbone” cross section into a C-shaped cross section which then passes through the arrestor. Hence, for

sufficiently deep water, even an infinitely rigid Grouted Sleeve arrestor is ineffective.

Figure 21 – Grouted Sleeve arrestor (Langner, 1999)

Integral Ring arrestors are thick-wall rings that are welded into selected pipe joints, as illustrated in Figure

22, before being installed offshore. Integral Ring arrestors are used for pipelines in which the strength of

sleeve type arrestors is not adequate, and for J-Lay applications that require a support collar on each pipe

joint. These arrestors are very efficient in terms of strength for a given amount of steel, but are more

expensive than sleeve arrestors because of the additional welding required. Thick Wall Pipe Joint arrestors


are special pipe sections (each designed to prevent collapse propagation), that are welded into a pipeline at

intervals. A Thick Wall Pipe Joint is essentially a very long integral ring arrestor, but is much less efficient in

the amount of steel used.

Figure 22 – Integral Ring arrestor, which also serves as J-Lay Collar, (Langner, 1999)

Figure 23 - Tested sample of a pipeline with Sleeve type buckle arrestors and the numerical model

Due to the complexities of the buckle propagation phenomenon, design relationships are empirical.

The strength of a buckle arrestor is expressed by its crossover pressure, Px, which is the minimum pressure

that can force a buckled section of pipe to “cross over” the arrestor and start buckling the undamaged pipe

on the other side. Obviously, the minimum crossover pressure for a “weak” arrestor is the propagation

pressure Pp (Equation (19)) and the maximum crossover pressure for a “strong” pipe is the collapse

pressure Pc (Equation (15)). An efficiency parameter that varies between 0 and 1 is defined which depends

on the arrestor strength:


pc

px

PPPP

−

−=η

(21)

Providing a safety factor of 1.35 for any buckle arrestor the minimum crossover pressure Pm is defined as:

max35.1 dPm γ=

(22)

Design formulas for each of the three mentioned types of buckle arrestors are given here from Langner

(1999) which is the reference as stated by API-RP-1111 (1999).

Thick Wall Pipe Joint. Thick Wall Pipe Joints have been used as buckle arrestors in situations where

suitable thick-wall joints are readily available and where the weight of the suspended pipeline during laying

is not a critical issue. The design of a thick wall pipe joint arrestor is obtained by equating the minimum

crossover pressure Pm with the design crossover pressure Px which is the same as the propagation pressure

Pp, and solving for the thickness of the Thick Wall Pipe Joint:

4167.0

24 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

Y

m

SP

Dt

(23)

Integral Ring Arrestors. Integral Ring arrestors are forged and/or machined weld-neck rings that are

butt-welded into a pipe joint. A less expensive version slides over the pipe and is fillet welded both sides

onto the outside of the pipe joint. For this technique stress concentration issues must be accounted for.

Integral arrestors are categorized into two types, based on their geometry. Narrow arrestors, in which the

length-to thickness ratio varies between L/h = 0.5 – 2.0, are used primarily for pipelines installed by J-Lay;

here the arrestor doubles as a collar for supporting the suspended pipe span. Wide integral arrestors, where

L/h > 2, are used primarily for pipelines installed by S-Lay, because of the easier passage of this type of

arrestor through the tensioners and over the stinger rollers. The efficiency parameter of the arrestor is

given by:


1≤≥ ηλη andk

(24)

Where:

⎩⎨⎧

><<

=)(2/8

)(2/5.05widehLfornarrowhLfor

k

)( factorstrengtharrestorDPLP

p

a=λ

4.2

,24 ⎟⎠⎞

⎜⎝⎛=

DhSP aYa

The buckle arrestor should be dimensioned such that the crossover pressure Px which is calculated from

Equation (21) is greater than minimum crossover pressure Pm (Equation (22)). As an example, the following

case is examined:

mHmNXMPaYMPaE

mmtmmD

500/10104)65(448199938

9.15457

3 ==

====

γ

Using the given formulas we have:

requiredarearrestorsBucklePP

MPaHPMPaP

MPaPMPaPMpaP

p

p

cye

⇒≤

===

=⇒==

80.0

05.540.3

93.1517.3153.18

0

0 γ

The integral ring buckle arrestor design is as follows:

adequateisarrestorBucklePPMPaP

MPaPkarrestorbucklenarrowhL

MPaYmmhmmLMPaP

mx

x

a

a

m

⇒>=⇒=

===⇒<

====

16.730.05.109.31

5,2/

448407597.6

ηλ


Grouted Sleeve Arrestor. Grouted Sleeve arrestors are forged or fabricated steel cylinders, typically with

dimensions of L/D = 0.5 – 2.0, that are slid over the end of a pipe joint, and grouted in place near the

middle of the joint. Typical grout materials that have been used are portland cement, sand-filled epoxy, and

two-part polyurethane. Sleeve arrestors generally are the lowest cost type of buckle arrestor, but may not

be suitable in deep water due to their limited arrestor strength. At the crossover limit, the cross section of a

buckled pipeline can change from the “dogbone” shape typical of free buckle propagation, to a U mode that

enables the collapse wave to pass through a sleeve-type arrestor, as seen in Figure 24

Figure 24 – U mode buckling of a pipeline; the collapse wave passes through a sleeve type arrestor (Kyriakides, 2005)

Design formulas for rigid sleeve type arrestors are as follows:

),min(5.0/3

21 PPPDLand

x ≥≥≥λ

Where

3,4.2 21

pcpp

PPPPPP

−+==

Choosing the spacing between buckle arrestors is an optimization problem. An approach is given in Bai

(2001).

Figure 25 shows the fitting of design formulas for integral ring buckle arrestors with test data.


Figure 25 – Comparison of integral ring buckle arrestor design formula with available test data (Langner, 1999)


5. On-Bottom Stability

A pipeline laid on seabed is subject to current and/or wave forces. The pipeline withstands these forces by

friction; which is relative to submerged weight of pipeline. It should be noted that in a complete 3D

analysis, the strain energy of the pipeline is also taken into account. The goal of this analysis is to

determine required submerged weight of pipe. If pipeline self-weight is insufficient, additional concrete

coating would be required. Pipeline stability is checked for both operation and installation (pipeline empty)

cases. Return period of environmental phenomena for on-bottom stability analysis is given in Table 5.

Table 5 – Return period for environmental phenomena

Condition Installation*

(Less than 3 days)

Installation*

(Longer than 3 days) Operation**

Return Period Based on weather

forecast

1 year (no threat to human lives)

100 year (threat to human lives)

100 year wave + 10 year

current

10 year wave + 100 year

current

*The installation time is usually short in comparison with operational lifetime of the pipeline. During installation the pipeline might be empty. Regarding the rather short period, less severe design environmental phenomenon are selected (shorter return periods). **Operation lifetime of pipeline might be several decades. The pipeline is usually filled during operation lifetime. Therefore more severe design environmental phenomenon are selected (longer return periods).

Additionally, a minimum pipeline specific gravity of 1.20 during installation is desired.

The on-bottom stability analysis is performed by the following steps:

1. Definition of environmental condition for different return periods, including:

• Water depth (d)

• Significant wave height (H), wave period (T) and angle of attack

• Steady current velocity (Uc) and angle of attack

• Wave only particle velocity (Uw), maximum water particle velocity due to wave and current

(Um) and steady current ratio (UR = Uc/Um)

• Soil submerged weight (γ ), soil friction factor or undrained shear strength (Su)

• Seabed slope (θ ) measured positive in downward loading

2. Determination of hydrodynamic coefficients: drag (CD), lift (CL), Inertia (Cm). These coefficients

should be adjusted for Reynolds number, Keulegan-Carpenter Number, ratio of wave to steady

current and embedment depth of pipeline.

3. Calculation of hydrodynamic forces drag (FD), lift (FL) , inertia (FI)


4. The last step is to perform a static force balance; the hydrodynamic loads are opposed by friction of

pipe over seabed.

Hydrodynamic forces on the pipeline (wave and current) are related to velocity and acceleration of flow at

the pipeline level. Current velocity (Uc) is steady while particle velocity due to a passing wave (Uw) is

oscillatory. Uw is dependent upon wave height, period and water depth. By knowing these parameters a

suitable wave theory can be used to calculate Uw. For most situations linear theory is adequate, because the

particle velocities and accelerations do not vary significantly between theories. As wave height to water

depth ratio increases, Stoke's fifth order theory becomes more appropriate. For shallow water or very high

wave heights, solitary theory is best suited. For breaking waves, a large diameter might affect the flow

regime and other methods may be appropriate, but in general pipelines should be trenched within the

breaking wave (surf) zone. Figure 26 shows the validity of different wave theories for different wave and

depth characteristics.

Figure 26 - Regions of applicability of different wave theories (API RP 2A, 2000)


5.1. Soil Friction Factor

Friction factor is defined as the ratio between the force required to move a section of pipe and the vertical

contact force applied by the pipe on the seabed. The friction factor is dependent upon soil type, pipe

roughness, seabed slope and burial depth. In the absence of site specific data, the following can be used:

• Loose sand: o30,tan == ϕϕµ

• Compact sand: o35,tan == ϕϕµ

• Soft clay: 7.0=µ

• Stiff clay: 4.0=µ

• Rock and gravel: 7.0=µ

The starting friction factor in sand is about 30% less than the maximum value, which occurs after a very

small displacement of the pipe builds a wedge of soil.

5.2. Hydrodynamic Force Calculation

The drag, lift and inertia force can be calculated by the Morrison equation. The general assumption for

Morrison's equation is that the body (pipeline) is small enough not to disturb the flow pattern caused by the

wave. The condition in which Morrison's equation is valid is when the ratio of wave length to pipeline

diameter is greater than 5, and therefore the pipeline is considered as slender. If the ratio is less than 5, the

body diffracts the waves and a diffraction theory should be used. For typical ocean waves and subsea

pipelines the slender body assumption is true. The Morrison equation states that wave loading is summation

of drag and inertia forces. The backbone of the equation can be derived using the momentum conservation

for a control volume containing the pipeline:

22. 1.

)()()( VelocityAreaConAcceleratiVolumeCAdvvdVvtdt

vmdFscvc

⋅⋅+⋅⋅=⋅+∂∂

== ∫∫∑ ρρρρrrrr

rr

(25)

C1 and C2 are constants for inertia and drag, dV is volume element, dA is area element and v is velocity. The

first integration is over a control volume and the second one is over a control surface. Morrison's formula is

usually written as:


mmDD UDUCF ρ21

=

2

21

mLL DUCF ρ=

mMI UDCF &⎟⎟⎠

⎞⎜⎜⎝

⎛=

421 2πρ

(26)

Only velocity and acceleration perpendicular to pipeline axis is considered in Morrison's equation. Figure 27

shows relative importance of inertia, drag and diffraction wave forces. It is seen that as slenderness (L/D)

increases, drag forces are dominant. Although Figure 27 is for a vertical pile, it can be used for a subsea

pipeline if the water depth is not more than half the wave length.

Figure 27 – Relative importance of inertia, drag and diffraction wave forces (DNV-OS-J101, 2004)

The magnitude of particle horizontal velocity and acceleration due to waves according to linear (Airy) theory

are as follows (L is wave length and z origin is at water surface and negative downward):

]/2cosh[]/)(2cosh[

2 LdLdz

LgTHU w π

π += (Horizontal particle velocity at elevation z)

]/2cosh[]/)(2cosh[

LdLdz

LHgU w π

ππ +=& (Horizontal particle acceleration at elevation z)

)2tanh(2

2

LdgTL π

π=

(27)


Currents have different sources but the most important ones are due to tides and wind. Tidal currents have

a 1/7 power law profile in depth. Wind driven currents have a linear profile and affect a limited depth (50

m). The combined current profile is shown in Figure 28. In the absence of site specific data the profile given

below can be used (z is distance from free surface and positive downwards):

⎟⎠⎞

⎜⎝⎛ −

+⎟⎠⎞

⎜⎝⎛ −

=50

507/1 zUd

zdUU WindTidec

(28)

UWind is wind-driven current velocity at surface and can be approximated as 0.015 x wind velocity at 10 m

elevation. Velocities of tidal currents depend strongly on the location and no approximate formulas are

established.

Figure 28 – Current profile due to tides and wind (DNV-CN-30.5, 1991)

5.3. Hydrodynamic Coefficient Selection

CD, CL and CI are dependent on one of the following situations:

Steady current only

Steady current and waves

For steady current conditions acting on a pipeline resting on seabed, CD ~ 0.7 and CL ~ 0.9. CD is generally

dependent upon Reynolds number (Re) and roughness, but for post critical state it is constant. Figure 29

can be used to evaluate these effects on CD for steady current.


Figure 29 – CD as a function of Reynolds number and roughness for a cylinder in steady current (DNV-CN-30.5, 1991)

In the case of steady current and waves, the coefficients are dependent on Keulegan-Carpenter KC number,

roughness and steady current ratio. The added mass coefficient (Ca = Cm-1) is given in Figure 30 as a

function of gap ratio. Physically KC is the amplitude of fluid particle displacement in each period normalized

by pipeline diameter, and is interpreted as measure of drag to inertia ratio.

Figure 30 – Added mass coefficient Ca as a function of gap ratio H/D (DNV-CN-30.5, 1991)

D

Ca

CD


If Uc is large with respect to Uw, the situation is similar to steady current alone (If Uc/Uw is greater than 0.4

this is true). For situation where the ratio is << 0.4, Figure 32 can be used for CD. The influence of seabed

proximity can be seen by using correction factors obtained from Figure 35.

Figure 31 – CD as a function of KC and roughness (DNV-CN-30.5, 1991)

Figure 32 – Influence of seabed proximity on CD for current+wave situation (DNV-CN-30.5, 1991)

Extensive experimental studies by Bryndum et al. (1983 and 1992) have led to hydrodynamic coefficients

graphs, as seen in Figure 33 and Figure 34.These experiments cover a wide range of flow conditions. Tests

for wave only have been done for 0<KC<160. Also effect of superposition of a steady current on the waves

is investigated for current ratios of 0<Uc/Uw<2. They have also concluded that increasing the current ratio

decreases all hydrodynamic coefficients, as seen in Figure 34. These studies are used in the comprehensive

on-bottom stability program by American Gas Association (AGA 1993).

Subsea Pipe

Figure 33 –

elines

Hydrodynamiic force coefficients CD, CM

roughne

and CL for re

ess (b) (Brynd

egular waves,

dum, 1992)

effect of pipee roughness (

Page

(a) and seabe

42

ed

Subsea Pipe

Figure 34

elines

– Hydrodynamic coefficiennts CD, CM andd CL versus cu

1992)

urrent ratio foor wave plus ssteady curren

Page

nt (Bryndum,

43


5.4. Stability Criteria

The last step of the simplified on-bottom stability analysis consists in assessing stability using a simple

lateral force equilibrium equation. Figure 35 shows a free body diagram of the problem.

Figure 35 – Free body diagram of pipeline for on-bottom stability analysis (Bai, 2000)

The following formula assumes a coulomb friction model and is over-conservative if the pipe is embedded. A

safety factor (SF) is included to account for actual values of soil friction, environmental data, particle

velocity and acceleration and hydrodynamic coefficients. Recommended SF is 1.05 and 1.1 for installation

and operation conditions respectively. The rather low safety factors are due to the very conservative nature

of this simplified 2D method. Ws is pipeline submerged weight.

)sin()cos( θθµ SMDs WFFSFFW ++≥−

(29)


6. Free Span (Bottom Roughness) Analysis

The goal of this analysis is to identify possible free spans that exceed the maximum allowable span length.

Figure 36 shows a schematic of a pipeline laid on a rough seabed in which free spans are possible.

Figure 36 – Free spanning pipeline on seabed

The irregular seabed profile is seen on the continental slope; a steep slope where the mild slope continental

shelf reaches ultra deep waters as seen in Figure 37. Figure 38 shows visualizations of a rough seabed

topography and subsea pipelines of the Ormen Lange field (Norway) passing a rough seabed.

Figure 37 – Continental shelf and continental slope


Figure 38 – Subsea pipelines, Ormen Lange field, Norway (Source: Internet)

The length and height of the span have a random distribution and lengths as long as 300-400 m is possible.

A typical distribution of free span length vs height and also the resulting profile of the pipeline is shown in

Figure 39.

Figure 39 - Typical free span distributions and pipeline profile (Soreide, 2001)


6.1. Static condition

The pipe span is checked for stresses under static conditions. Both Von-Mises and longitudinal stresses

should be checked and limited to the values given in Table 6.

Table 6 – Allowable pipeline stresses (Nogueira & Mckeehan, 2005)

A typical pipeline span free body diagram is shown in Figure 40, along with dimensionless diagrams for

calculation of stress at mid-span and span shoulders, and also mid-span deflection and induced pipe span.

The stresses depend on span length and pipeline tension.


Figure 40 – Static stresses and deformations in a free spanning pipeline (Mousselli, 1981)

w is submerged weight of pipeline per unit length


Another scenario is that the pipeline passes over an obstruction. A schematic of the pipeline is given in

Figure 41, along with dimensionless diagrams for pipeline span and maximum stress at mid-span. For this

situation the span is a function of obstruction height and pipeline tension, while mid-span stresses do not

depend on tension.

Figure 41 – Static stress and span for pipeline passing obstruction (Mousselli, 1981)

T

f

W

w

V

f

Subsea Pipe

6.2. VIV

The free spa

cross-low VI

fatigue dam

When free s

water) may

oscillate due

are caused

VIV and lift

oscillation n

frequency of

Figure 42

elines

an should al

IV do not o

age has to b

spans occur

y cause dyn

e to vortex s

by symmetr

t forces cau

normal to th

f inline VIV

– Vortex she

so be assess

occur. Recen

be assessed

due to seab

namic effects

shedding. Tw

ric and asym

se cross-flo

he flow, tw

is approxima

edding due to

resulting

sed for VIV.

ntly codes ha

and shown

bed irregula

s. The fluid

wo forms of

mmetric vort

ow VIV. As

wo cycles of

ately twice c

steady flow a

g in oscillating

Regarding V

ave added a

to be allowa

arities the pr

d interaction

f oscillation a

ex shedding

can be seen

f pressure o

cross-flow VI

at different R

g lift and drag

VIV, the free

an option w

able.

resence of b

n with the p

are observed

g, as seen in

n in Figure

oscillation p

IV.

Reynolds numb

g forces (Blev

e spans mus

which VIV is

bottom curre

pipeline can

d namely in-

n Figure 42.

42, for eve

parallel to th

bers and fluct

vins, 1977)

st be such th

allowed to

ent (and wav

n cause the

-line and cro

Drag forces

ery one cycl

he flow occ

tuating pressu

Page

hat in-line a

occur but t

ves in shallo

free span

oss-flow whi

s cause in-li

le of pressu

cur. Therefo

ures on pipe

50

nd

the

ow

to

ich

ne

ure

ore


Generally the following tasks have to be performed in the assessment of free spans for VIV:

• Structural modeling

• Load modeling

• A static analysis to obtain the static configuration of the pipeline

• An eigen-value analysis which provides natural frequencies and corresponding modal shapes for in-

line and cross-flow vibrations

• A response analysis using a response model or force model in order to obtain the stress ranges from

environmental actions

It is necessary to predict if a free span is isolated or affected from adjacent spans. Generally if the shoulder

length between two spans are relatively short, and also length of two adjacent spans are comparable, the

two spans interact, as seen in Figure 43.

Figure 43 – Classification of free spans (DNV-RP-F105, 2006)

A pipe over a short span behave like a beam (bending mode is dominant), while a pipe over a long span

behaves like a cable (axial mode is dominant). Table 7 shows this classification, where L is free span length

and D is pipeline diameter.


Table 7 – Response behavior of free span (DNV-RP-F105, 2006)

Another important parameter is the current flow velocity ratio which distinguishes between current and

wave dominated flow regimes and is defined by Equation (30). Table 8 shows different regimes.

wc

c

UUU+

=α

(30)

Table 8 – Different flow regimes (DNV-RP-F105, 2006)


The state of the art code for free spanning pipelines is DNV-RP-F105. This code recognizes three methods

for VIV assessment, and the first one is the most commonly used:

1. “Response Models” approach to predict the vibration amplitudes due to vortex shedding. These

response models are empirical relations between “reduced velocity” response amplitudes. Hence the

stress response is derived from an assumed vibration mode with an empirical amplitude response.

“Reduced velocity” is a function of still-water natural frequency and flow velocity.

2. Semi-empirical lift coefficients, or generally “Force Model” (Larsen, 2002). If the loading is defined,

the response can be achieved from solution of governing equations. The main disadvantage is that

appropriate formulations for loading –especially for cross-flow VIV- do not exist.

3. As a third option, Computational Fluid Dynamics (CFD) simulation of the turbulent fluid flow around

one or several pipes can in principle be applied for VIV assessment to overcome the inherent

limitations of the state-of-practice engineering approach. The application of CFD for VIV assessment

is at present severely limited by the computational effort required. In addition, documented work is

lacking which shows that the estimated fatigue damage based on CFD for realistic free span

scenarios gives better and satisfactory response than the methods described above. Figure 44 shows

results of a CFD simulation for the case of a pipeline with a piggyback pipe.

Figure 44 – CFD simulation of piggyback pipeline


Natural Frequency

Natural frequencies of the span can be found using FEM including pipe-soil interaction effects, geometric

non-linearities and static equilibrium conditions. Also approximate formulations are available (DNV-RP-

F105). The formulas are valid for single span on relatively flat seabed (almost horizontal spans), L/D is less

than 140 and sagging deflection/D is less than 2.5. Also compressive axial force should be less than half the

buckling load. The static deflection can be estimated as:

cr

eff

eff

PTCSFEI

qLC

++⋅

=1

1)1(

4

6δ

(31)

C6 is boundary condition coefficient and is given in Table 9, and CSF is a factor accounting for stiffness of

coating. Teff is effective axial force (true axial force with consideration of in external and internal pressure

effects) and Pcr is the critical buckling load. The formulations are based on fixed-fixed boundary conditions

and Leff account for this. Boundary conditions are a function of shoulder soil stiffness. As this stiffness

increases the conditions are more like fixed, as seen in Figure 45 (β represents soil stiffness).

Figure 45 – Effective length vs. soil stiffness (DNV-RP-F105)


The first eigen-frequency can be approximated by (32). For a (geometrically) linear structure, natural

frequencies are a function of stiffness and mass only. For a geometrically nonlinear structure natural

frequencies are dependent also upon deflection (sagging of pipe span), as can be seen in Equation (32).

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛+++⋅≈

2

3411 11D

CPT

LmEICSFCf

cr

eff

effe

δ

(32)

Where C1 – C3 are boundary condition coefficients given in Table 9, E is Young’s modulus, I is moment of

inertia and me is effective (modal) mass. Effective modal mass is defined as:

∫

∫=

L

Le dss

dsssmm

)(

)()(

2

2

φ

φ

(33)

Where m(s) is mass per unit length of pipeline including steel and concrete coating mass, content mass and

added mass, and Φ is assumed mode shape (i.e. half wave cosine for first mode).

Equation (32) predicts the eigen-frequency with ±30% accuracy (DNV-G14, 1998). In this Equation, the

three terms in the parentheses represent bending, axial and sagging effects respectively (Bruschi & Vitali,

1991).

Table 9 – Boundary conditions coefficients (DNV-RP-F105, 2006)


Important Parameters for VIV

VIV response depends on these parameters (Blevins, 1977):

• Reduced velocity: as a structure vibrates in a flow, it traces out a path. For steady vibrations the path

length normalized by diameter is termed reduced velocity:

DfUUV

n

wcR

+=

(34)

• Reynolds number:

υDUc=Re

(35)

Kinematic viscosity (ν) is defined as ratio of viscosity to density.

• Keulegan-Carpenter Number:

DfU

KCw

w=

(36)

• Damping factor: dependant on ratio of energy dissipated by the structure per cycle over total energy of

structure. A non-dimensional parameter named reduced damping or stability parameter is used instead:

2

4Dm

K Tes ρ

ξπ=

(37)


Response Models

Amplitude response models are empirical models providing the maximum steady state VIV amplitude

response as a function of basic hydrodynamic and structural parameters mentioned above. The response

models are based on experimental laboratory test data and full-scale tests. Figure 46 shows a curve relating

reduced velocity (Equation 19) to maximum in-line VIV amplitude. As with an SDOF system, increasing the

damping (which increases stability parameter Ks (Equation 22)) reduces the vibration amplitude.

Figure 46 – Illustration of the in-line VIV Response Amplitude versus VR and KS (DNV-RP-F105, 2006)

The effect of flow regime (Table 8) is included with a correction factor applied to stress range. In-line VIV

stress range is calculated as:

ILY

ILIL DA

AS ,2 αψ⎟⎠

⎞⎜⎝

⎛=

(38)

Where the correction factor for current flow ratio is defined as:

8.08.00.15.03.0/)5.0(5.00.0

, <<⎪⎩

⎪⎨

⎧

>−

<= α

αα

αψα

forforfor

IL

(39)


Equation (39) shows that for wave dominant flow regimes (according to Table 8), in-line VIV is negligible or

does not occur.

For cross-flow VIV, Figure 47 can be used to relate reduced velocity VR to maximum vibration amplitude.

Figure 47 – Illustration of the cross-flow VIV Response Amplitude versus VR (DNV-RP-F105)

Cross-flow VIV stress range can be calculated as:

kZ

CFCF RDAAS ⎟

⎠⎞

⎜⎝⎛= 2

(40)

The effect of damping is included via the amplitude reduction factor Rk:

⎩⎨⎧

>

≤−=

− 42.3

415.015.1

ss

ssk KK

KKR

(41)

Fatigue Criteria

Having calculated the stress for each sea state (for example by using the above mentioned Response

model), the fatigue damage can be calculated by using S-N curves. An S-N curve gives the number of cycles

required for failure of a structure (N) for a given stress range (S). Three methods are available for

generating an S-N curve:

1. Dedicated laboratory test data

2. Accepted fracture mechanics theory

3. Use of codes


DNV-RP-F105 (2006) gives the following formulation for S-N curves:

⎪⎩

⎪⎨⎧

≤⋅

>⋅=

−

−

SWm

SWm

SSSa

SSSaN

2

1

2

1

(42)

a1 and a2 are characteristic fatigue strength constant defined as the mean minus two standard deviation

curve. SSW is stress at intersection of the two S-N curves, defined by:

⎟⎟⎠

⎞⎜⎜⎝

⎛ −

= 1

1 loglog

10 mNa

SW

SW

S

Where NSW is the number of cycles for which change in slope appear. Log NSW is typically 6-7.

By plotting Equation (42) in a logarithmic plane, a bi-linear curve is obtained in which m1 and m2 are the

slopes of each segment. Figure 48 shows a typical two-slope S-N curve. Log NSW is typically 6-7.

Figure 48 – Typical two-slope S-N curve (DNV-RP-F105, 2006)

For a given sea state number i, the stress range, number of cycles (ni) and number of cycles to failure (Ni,

from S-N curve) are known. The accumulated fatigue damage of different sea states during the pipelines

life can be evaluated using the Palmgren-Miner law (DNV-RP-F105, 2006) with Equation (43), which states

that fatigue damage due to each individual stress range can be summed up to give the total damage D. the

value D = 1 is equivalent to fatigue failure:


∑=i

ifat N

nD

(43)

Where:

ivlifeii fTPn ,××=

mii aSN −=

By equating Equation (43) equal to unity, the fatigue life capacity, Tlife, is formally expressed as (DNV-RP-

F105):

∑⋅⋅

=

aiPSf

T miiv

life )(1

,

(44)

The fatigue life is the minimum of the in-line and cross-flow fatigue lives.

The design life, Td, should be less than Fatigue life. Various codes give safety factors. The general equation

is as follows:

lifefatd TT ⋅≤ η

(45)

DNV-RP-F105 (2006) defines the safety factor fatη as 1.0, 0.5 and 0.25 for “Low”, “Normal” and “High”

safety classes respectively. On the other hand API-RP-1111 (1999) defines the safety factor as 0.1. The

difference between the numbers is because DNV uses partial safety factors for VIV.


On-going Research

Recently, it has been shown that in-line and cross-flow vibrations are not independent (Fernes and

Berntsen, 2003). Excitation in a cross flow mode shape might lead to in line excitations and vice versa.

Fernes and Berntsen (2003) have approached by a “Force Model” technique. A general geometrically-

nonlinear beam-cable with additional local damping and stiffness (which can be used to model shoulder soil)

is formulated, as seen in Figure 49. The governing equation of motion is given in Equation (46)

Figure 49 – Schematic diagram of free span pipelines with additional local stiffness and damping (Fernes and Berntsen,

2003)

)()(24

4

1 axkraxtrRGiF

xrT

xxrEI

trR

trM

t−−−

∂∂

−+=⎟⎠⎞

⎜⎝⎛

∂∂

∂∂

−∂∂

+∂∂

+⎟⎠⎞

⎜⎝⎛

∂∂

∂∂ δδ

(46)

Where:

M is mass, r is deflection vector (y and z components, r = ry + irz), T is tension, F is hydrodynamic forces

calculated by Morrison’s equation, G is submerged weight per unit length, i is imaginary unit, R1 and R2 are

global and local damping respectively, k is local stiffness and δ is Kronecker delta function. The above

partial differential equation has two sources of non-linearity: time dependency of tension and hydrodynamic

forces. At any instant, tension can be calculated as:

LLSEATT −

+= 0

Where:

T0 is the residual lay tension, L is initial length and S is elongated length, calculated from:

2

1 ⎟⎠⎞

⎜⎝⎛+=

dxdr

dxds

Equation (46) is solved using the Fourier Sine Transform technique (Fernes and Berntsen, 2003), (Kreyszig,

1993). Coupling of cross-flow and in-line mode shapes can be investigated using this model. As an example,


a unit diameter in-line second mode shape is imposed as initial condition (ry). The coupling of cross-flow

mode shape (rz) is observed, as seen in Figure 50.

Figure 50 - Motions due to a prescribed second mode inline deflection. (C) Time series of ry/D close to an antinode. (D)

Time series of rz/D close to an antinode. (Bottom panels) Countours of time evolution of ry/D and rz/D. (Fernes and Berntsen, 2003)

An example trajectory of a point on a pipeline free span is generally 8 shaped; as seen in Figure 51.

Figure 51 - Combined in-line and cross flow motion of a pipeline section (Fernes and Berntsen, 2003)


7. Installation of Subsea Pipelines

There are four methods for installing pipelines on the seabed, namely S-lay, J-lay, Reel-lay and Tow. J-lay

and S-lay methods are schematically shown in Figure 52 and Figure 53 respectively. The shape of the

suspended pipeline from lay barge to seabed justifies the corresponding name. In the reel-lay method, the

pipeline is spooled around one or more spools and un-spooled during offshore works. The unspoiled pipeline

departs the vessel in an S-lay or J-lay shape depending on the vessel method employed. In the J-lay

method the pipeline departure angle is large. This geometrical condition results in a single curvature for the

pipeline, or J-shape. On the other hand, the departure angle in the S-lay method is smaller and therefore

the pipeline has a double curvature, or S-shape.

Figure 52 – Schematic of S-lay method for pipelaying (Nogueira & Mckeehan, 2005)


Figure 53 – Schematic of J-lay method for pipelaying (Nogueira & Mckeehan, 2005)

Apart from the tow method, the three other ones require a lay-barge that can store line-pipe onboard, and

also additional supply barges as required. The lay-barge needs to be positioned in a specific position for

some time during the laying operation. Generally two methods exist for station-keeping:

• Mooring and anchoring

• Dynamic Positioning System (DPS)

There are two mooring types, namely taut and catenary which are shown in Figure 54 and Figure 55

respectively. The taut system withstands the environmental forces acting on lay-barge with its axial

stiffness. Taut mooring can be made of steel cables or nylon ropes. Taut mooring is suitable for shallow

waters. The catenary mooring withstands forces by its weight. Catenary moorings can be made of chains,

and are mainly used in deep waters but by using intermediate buoys they can be used in shallow waters

too. Moorings are not effective regarding angular motions of the vessel, namely roll, pitch and heave.


Figure 54 – Taut mooring system

Figure 55 – Catenary mooring system

A DPS vessel has thrusters in every direction. It has sensors which sense the environmental forces acting on

the vessel. Based upon the magnitude of environmental forces sensed, the thrusters are activated and exert

a force opposite that of environmental ones, and thus the vessel achieves relative positioning. It should be

noted that accuracy of DPS is generally less than mooring, but for ultra deep waters, DPS is the only option.


Any unexpected movement away from the planned laying route may severely bend the pipeline either in a

sag-bend or in an over-bend and the pipe may buckle or kink, therefore station-keeping is very important

during pipelaying.

A DPS lay-barge has substantial advantages in deepwater (e.g. 100 ft and deeper). At shallower depths, a

DPS lay-barge has disadvantages which are uncompensated. In shallow water any motion of the vessel

other than the prescribed forward motion, if unrestrained, can damage the pipe. It is apparent that engines

of substantial size are required to limit the control vessel motions with this high accuracy. At greater depths

the pipe assumes a nearly vertical attitude as it sags to bottom. Consequently, the lay-barge has greater

freedom of movement before the pipe is endangered. A combined station-keeping method was patented in

1973 (Langner, 1973) which utilizes both DPS and anchoring: lateral positioning is done via moorings and

longitudinal positioning is achieved via thrusters, as seen in Figure 56.

Figure 56 – Combined station-keeping method for intermediate water depths (Langner, 1973)


Regarding the new strain based design method of pipelines, strain and stress concentrations during offshore

installations have to be carefully considered. For example a new (and faster) installation method for pipe-in-

pipe welding is as follows: Typically two offshore welds are required for connecting two pipe-in-pipe joints

together (i.e. one for inner and one for outer pipe). In the new technique the outer pipe is swaged and fillet

welded to inner pipe onshore, and only one offshore weld is required for welding two inner pipes together. A

sleeve is slided over the connection area. These types of innovative techniques have to be carefully

examined regarding stress and strain concentrations. Dixon et al. (2003) performed a FEM analysis of the

mentioned connections. They have found different locations of stress concentration for J-lay and S-lay, as

seen in Figure 57.

Figure 57 – Location of stress concentration in sleeve connection, Top: J-lay, Bottom: S-lay (Dixon et al. 2003)


7.1. J-lay

The J-lay installation method is a relatively new type of installation method specifically aimed at deepwater

and ultra-deepwater projects. This method is characterized by a steep ramp, typically 65 deg or higher

departure angle, therefore the pipeline has a suspended J-shape. Figure 58 shows a J-lay vessel laying pipe

with the aid of a side tower. During J-lay, the stresses and strains close to the top and the horizontal

tension component and also the horizontal tension at the seabed are minimized. The advantages and

disadvantages of the J-lay method are described in Table 10.

Table 10 – Advantages and disadvantages of J-lay (Nogueira & Mckeehan, 2005)

Adv. Best suited for ultra deepwater pipeline installation.

Adv. Suited for all diameters.

Adv. Smallest bottom tension of all methods, which leads to the smallest route radius, and allows

more flexibility for route layout. This may be important in congested areas.

Adv. Touchdown point is relatively closer to vessel, thus easier to monitor and position.

Adv. Can typically handle in-line appurtenances with relative ease, with respect to landing on the

seabed, but within the constraints of the J-lay tower.

Disadv. Regarding the near vertical ramp, fewer welding stations are available, typically one or two.

Therefore the laying rate is generally less than S-lay.

Disadv. Some vessels require the use of J-lay collars to hold the pipe (as mentioned in section 4.4.

Buckle Propagation, these collars may be used as buckle arrestors too).

Disadv. If shallower water pipeline installation is required in the same route, the J-lay must be

lowered to a less steep angle. Even then, depending on the water depth, it may be not

feasible to J-lay the shallow end with a particular vessel and a dual (J-lay/S-lay) installation

may be required.


Figure 58 – Heerema's balder in J-lay mode (Nogueira & Mckeehan, 2005)

In order to assess the pipeline structural integrity during any installation method where the pipeline is

suspended from the vessel to the seabed, a structural analysis by FEM method has to be performed. A FEM

package has to be used. Depending on the degree of accuracy required, several aspects have to be

modeled namely:

• Geometrical nonlinearity

• Material nonlinearity: the pipeline in the sagbend and overbend usually undergoes plastic

deformations

• Material anisotropy: the new higher grade carbon steels which are being developed (e.g. X80 and

above and Duplex) are anisotropic; the yield stress and modulus of elasticity may be different in

hoop and longitudinal directions

• Seabed soil: the seabed soil serves as an elastic foundation for the pipeline. Also the seabed resists

horizontal and longitudinal pipeline movement with friction. The seabed also damps the vibrations of

the suspended span

• Effect of wave and current forces on the suspended pipeline

• Effect of wave, current and wind forces on lay-barge which induce movement of top of suspended

pipeline. Some researchers in the early 90’s have addressed this topic namely Vlahpoulos et al.

(1990), Clauss et al. (1991) and Clauss et al. (1992). All these researches neglect the Material

nonlinearity and material anisotropy. It should be noted that these researches are basically two

uncoupled analyses:


First, analysis of the vessel motions from a seaway neglecting effect of pipeline on vessel motions

which can be done using standard packages (e.g. WAMIT, ANSYS AQUA, MOSES, etc). Result is the

time history of stinger motions, which is used as input boundary condition for the second analysis.

Second, analysis of a geometrically non-linear beam-column moving in fluid (which is subjected to

boundary condition derived from first analysis

The results of an analysis of this kind, including motions of the suspended pipeline, dynamic stresses

and dynamic tension range are shown in Figure 59.

Figure 59 – Dynamics of pipelines during laying: motion, dynamic stresses and tension for different wave periods

(Clauss et al. 1991)


General FEM packages such as ABAQUS and ANSYS can be used for this means. Other packages are also

available which are specifically aimed at subsea pipelines, the oldest and most common one being OFFPIPE

(www.offpipe.com). The goal of the installation analysis is to check the wall thickness of the pipeline, the

top tension required during installation and seabed tension. The top tension has to be checked with capacity

of lay-barge tensioners. The tensioner force is equal to the submerged weight of the suspended span minus

seabed tension. Some modeling features of OFFPIPE are as follows:

Dynamic analysis capability, lay-barge RAO’s (Response Amplitude Operators) and regular wave or wave

spectrum can be specified, the resulting vessel motions are incorporated in the analysis.

• The finite element method considers both geometric (large displacement) and material (nonlinear

stress-strain curve) non-linearities.

• Provides a detailed model of the lay-barge and a simplified structural model of the stinger which

includes the effects of the ballast schedule and hinges between stinger sections.

• Includes detailed pipe support models, which can include angled horizontal and vertical rollers,

overhead restraints and finite length roller beds.

• The seabed is modeled as a continuous elastic-plastic foundation (not a series of point supports).

The lateral soil resistance is bilinear, elastic for small horizontal displacements and frictional for large

displacements.

OFFPIPE uses the Ramberg-Osgood material model, expressed as: B

yyy MMA

MM

K ⎟⎟⎠

⎞⎜⎜⎝

⎛+=

κ

Where:

EDS

K yy

2=

DIS

M yy

2=

A = Ramberg-Osgood equation coefficient

B = Ramberg-Osgood equation exponent

In lieu of the detailed analysis mentioned above –which is required for the detail design stage of a project-

preliminary analysis using the stiffened catenary equations can be used. The original catenary equations

consider only tension in the line. By modifying the original catenary equations to include the effect of

bending stiffness, the stiffened catenary equations result. These equations yield very accurate for the J-lay

configuration (Langner, 1984) and the output is top and bottom tension and pipeline stresses and strains,

therefore a preliminary check of wall thickness and vessel tensioner can be done.


7.2. S-lay

The majority of offshore pipelines are installed using S-lay. For shallow waters the stinger and departure

angle are near horizontal. Recently S-lay vessels configuration is modified such that the stinger can reach

very steep angles of departure, which enables it to operate in deeper waters. This method is termed steep

S-lay. An S-lay vessel is seen in Figure 60.

Figure 60 – A typical S-lay Vessel (Nogueira & Mckeehan, 2005)

All offshore welding is done with the pipe in a horizontal position; therefore S-lay is very efficient compared

to J-lay. The main advantages and disadvantages of S-lay are given in Table 11.

Table 11 – Advantages and disadvantages of S-lay (Nogueira & Mckeehan, 2005)

Adv. All welds are done in horizontal position, making for efficient productivity of multiple welding

stations (typically 5-6).

Adv. Suited for all diameters.

Adv/Disadv. Can typically handle smaller, more compact in-line appurtenances with ease, but larger in-

line structures may be too large to go through the stinger.

Disadv. Buckle arrestors will induce concentrated higher strains in their vicinity within the stinger

Disadv. Typically, pipeline will twist (rotate axially) during installation. Bai (2000) describe this

phenomenon as a result of plastic strains.

Disadv. Requires a very high component of horizontal tension.


7.3. Reel lay

Reel-lay is a method of installing pipelines from a giant reel mounted on the lay-barge. Pipelines are

assembled at an offshore spool-base facility and spooled onto a reel which is mounted on the deck of a lay-

barge, as seen in Figure 61. Reel-lay was first patented in USA in 1968.

Figure 61 – A reel vessel (Guo et al. 2005)

Reeled pipelines can be installed up to 10 times faster than conventional pipelay. The greater speed allows

pipelines to be laid during shorter weather windows. Reel-lay can be used for pipelines up to 18 inches in

diameter. The reel can be either horizontal or vertical. Horizontal reel vessels lay pipelines in shallow to

intermediate water depths using a stinger and S-lay. The vertical reel-lay vessel is used for intermediate to

deep waters. The main advantages and disadvantages of real-lay are given in Table 12.

Table 12 – Advantages and disadvantages of Reel-lay (Nogueira & Mckeehan, 2005) & (Guo et al. 2005)

Adv. Almost all welds are done onshore, minimizing offshore welding.

Adv/Disadv. Well suited for smaller diameter lines and smaller D/t ratios. Maximum diameter is 18 inches.

Adv. If all pipeline can be stored on-board, a very fast installation campaign is achieved, making

this method very cost effective.

Disadv. If the route is too long or the diameter is too large, all the pipes may not be able to be

stored on-board and a number of recharging trips to the spooling base may be necessary to

reload, thus offsetting the high lay rate.

Disadv. Very high pipeline strains (3-5%) are applied to the pipeline. also the pipeline is plastically

deformed and then straightened. Some thinning of the wall and loss of yield strength of the

material in localized areas can occur (Bauschinger effect)

Disadv. Due to high strains, welding methods and acceptance criteria are more stringent.

Disadv. Pipeline will rotate during installation and may coil on the seafloor

Disadv. Inline structures are typically more difficult to handle and install.

Disadv. Concrete coated pipelines cannot be reeled.

Disadv. Only specifically designed pipe-in-pipe pipelines can be reealed.


7.4. Towed Pipelines

In this installation method, the pipeline is constructed onshore and towed into place, as illustrated in Figure

62. There are different ways to tow the pipeline string to site: surface tow, mid-depth tow or bottom tow.

In the surface tow the pipe is positively buoyant, towed to location on the surface, and sunk in position by

flooding. Wave action is a factor; therefore this method is used typically where rough seas are not likely. In

the mid-depth tow typically the pipe or pipe bundle is negatively buoyant, suspended above the seabed and

towed by a lead tug with a tail tug at the end of the pipe string. If the pipe is positively buoyant, mid-depth

tow may be achieved by incorporating the use of drag chains at specified intervals along the pipe string, so

that the pipe string assumes an equilibrium position above the seabed. For the bottom tow method, the

pipeline rests on the seabed, and a tug pulls it.

Figure 62 – Schematic of towed pipeline (Bai, 2000)

The length of the towed string is limited to about ten miles in the most favorable conditions.

The tow methods are challenging due to the effects of the environment such as waves action, oscillations

during pull or abrasive effects of the seabed during bottom tow. However, the onshore construction may

significantly reduce cost when compared to the installation methods described in the previous sections.

Several failures of pipe bundles during tow attest to the precautions that the offshore pipeline engineer

must take when using the tow method of installation.


7.5. Shore Approach

The methods mentioned above may not be able to install the subsea pipeline as it approaches very shallow

waters and the shore. Three methods exist:

• Float and sink, illustrated in Figure 63:

Figure 63 – Float and sink method used for shore approach installation

• Bottom pull method: the pipeline is pulled from shore to sea, illustrated in Figure 64. The required

roller tracks installed onshore are seen in Figure 65:

Figure 64 – Bottom pull method used for pipeline shore approach

Figure 65 - Bottom pull method; launching roller track


• Directional drilling method: the pipeline is drilled from shore under the seabed to a point where

water depth is sufficient, as illustrated in Figure 66:

Figure 66 – Directional drilling method for pipeline shore approach


7.6. Wet vs Dry Pipeline Installation

Conventional design in deep water requires the pipeline to withstand hydrostatic pressure of the sea,

because the pipeline is normally installed air-filled (dry). Collapse under external pressure usually governs

the establishment of wall thickness, and the calculated wall thickness is very large. In the design studies of

Oman-to-India pipeline in maximum depths of 3000 m, for example, experimental and analytical studies

indicate that the required minimum wall thickness is well over 30 mm even for modest diameters of 20 and

26 inches (Palmer, 1998). These wall thicknesses burden the economic feasibility of projects attractive on

other grounds.

Once the pipeline is in service, the internal pressure during operation is almost invariably higher than the

external pressure. 2000 m of seawater corresponds to 20 MPa: most flowlines operate at higher pressure

than this, because if the internal pressure were less than the external hydrostatic pressure the produced

fluid would normally go back down the hole. The conclusion is that:

Most of the wall thickness of a conventionally designed pipeline is only required while the pipe is being laid.

In a real sense, the additional steel required to resist external pressure during laying is wasted.

Generally, two methods are available for installing the pipeline:

• Air filled (dry)

• Liquid filled (wet)

The advantage of air-filled installation is reduced submerged weight which results in lower force required by

vessel tensioner, and as mentioned above the biggest disadvantage is large wall thickness required to

withstand external pressure. On the other hand in the liquid filled technique, the submerged weight is

higher, but internal and external pressure counter act and wall required thickness is not governed by

external pressure. In shallow water this is true. In ultra deep water it is no longer true, if we take

advantage of the reduced wall thickness that wet installation grants. Also wet laying enhances on-bottom

stability immediately after installation.

Alternative liquids might have advantages for wet installation. A lighter liquid fill reduces the submerged

weight. Pentane (626.2 kg/cu.m), Methanol (791 kg/cu.m), Gasoline and water have been used for

installation. If the pipeline is filled with lighter liquids the external and internal pressures don’t counter act

completely, and the pipeline has to be designed for the pressure difference. The advantage of wet

installation in ultra deep waters is illustrated in the following example:

An X65 steel pipeline with D = 660.4 (26 inch) is designed for the worst of the following two cases:

The pipeline must withstand an operating gauge pressure of 20 MPa

The pipeline must withstand the difference between external and internal pressure

The required wall thickness for different depths is shown in Figure 67. It is seen that liquid filling reduces

the required wall thickness substantially.


Figure 67 – Comparison of design strategies for 660.4 mm (26 inch) pipeline: wall thickness as a function of depth

(Palmer, 1998)

The pipeline submerged weight (which has to be in the range of vessels tensioner capacity) is shown in

Figure 68. In water depths up to about 1000 m, the pipeline designed and constructed air filled is lighter

during construction than the liquid filled one, as would be expected. However if the depth exceeds 2700 m,

the pentane filled procedure gives a submerged weight during construction smaller than air filled. At these

ultra deep waters, a liquid filled installation allows large reductions in wall thickness without any penalty in

submerged weight.

Figure 68 – Comparison of design strategies for 660.4 mm (26 inch) pipeline: submerged weight in laying condition as

a function of depth (Palmer, 1998)

The liquid filled strategy clearly allows huge reductions in the cost of steel. In the above example and a

maximum depth of 3000 m, air filled installation has a steel weight of 566 kg/m, whereas pentane filled

requires 367 kg/m and water filled requires 216 kg/m. for a 1000 km pipeline the reduction in tonnage of

steel with Pentane fill is therefore 200’000 tonnes, which at a round figure of $1000/tonne corresponds to a

saving of 200 M$.


References 1. ABS (2006), “Guide for Building and Classing Subsea Pipeline Systems”, American Bureau of Shipping

2. AGA (1993), “Submarine Pipeline On-bottom Stability”, American Gas Asociation

3. API-5L (2000), “Specification for Line Pipe”, 42nd Edition, American Petroleum Institute

4. API-RP-1111 (1999), “Design, Construction, Operation, and Maintenance of Offshore Hydrocarbon

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