buckling and collapse of offshore pipes under combined

Buckling and Collapse of Offshore Pipes under Combined Bending and External Pressure

JENS HAFSTAD 30.09.2020

IntroductionIntroduction

Brief introduction to bifurcation buckling◦ Introductory example

Elastic ring buckling due to hydrostatic pressure

Collapse of offshore pipelines due to hydrostatic pressure◦ Timoshenko collapse formula

◦ Code treatment of collapse

Factors affecting collapse pressure

Collapse of offshore pipelines due to hydrostatic pressure and bending◦ Factors affecting collapse

◦ Collapse formula and pressure-moment interaction

IntroductionSteel pipelines often form an important part of offshore developments

◦ As steel-catenary risers (SCR)

◦ Infield Flowlines – small size (<12 in), short distances of a few km

◦ Feeder line – medium size (6-20 in), longer distance (order of 100 km)

◦ Transmission (trunk) lines – large size ( up to 48 in) and long distances (e.g. Norway-UK 1200 km)

Need to be designed to withstand external loadings (pressure, bending, axial tension)

◦ Focus of this lecture is collapse due to externalpressure and bending

Infield flowline

Feeder line

Transmission line

Pipeline limit statesLimit state (DNVGL-ST-F101) - a state beyond which the structure no longer satisfies the requirements

◦ serviceability limit state (SLS): A condition which, if exceeded, renders the pipeline unsuitable for normal operations

◦ ultimate limit state (ULS): A condition which, if exceeded, compromises the integrity of the pipeline

Local collapse of an offshore pipeline is characterized by the loss of roundness and gross deformation of the cross-section – ULS

Deep-water pipeline collapseOil and gas exploration is moving towards deeper waters with future developments that may approach 3500-4000m

◦ Deep water: 300-1500 m, ultra deep-water: >1500 m (EIA)

Where (ultra) deep-water field developments are likely to take place:

◦ Gulf of Mexico (1800-2000 m)

◦ Brazilian Pre-Salt (excess of 2000 m)

◦ West Africa

Some trunklines are also installed or planned in ultra-deep waters

◦ Oman-India pipeline (planned) – up to 3500m

◦ South Stream pipeline – up to 2250m

The burst limit state (due to internal pressure) is usually the most critical loading in shallow water. For (ultra) deep-water the hydrostatic loading may become the dominant loading and critical design factor

◦ Pipeline installed without water filling experiences hydrostatic pressure without internal pressure to balance

Trend towards deeper waters

Introduction to bucklingA brief introduction to the buckling phenomenon will be given in the following

◦ An in-depth treatment requires a course in itself

Consider an infinite and perfectly round pipe loaded by hydrostatic pressure

◦ The primary (sometimes called fundamental or pre-buckling) solution is a uniform compression of the pipe

◦ At some load, this configuration becomes unstable and a different configuration becomes more energetically favourable – in the case of the pipe, this is (at least initially) an ovalization deformation

◦ Buckling is the process of changing (suddenly) from one configuration to the other

The concept of stability• Assume that external loading is applied quasi-

statically to a structure. The structure will then deform while static equilibrium is maintained

• If at any load level a small disturbance is applied and the structure:

a) Oscillates about the equilibrium state, and

b) The level of external loading remains constant, then

the structure is said to be in stable equilibrium

• If the structure tends to remain in the disturbed state, or diverge from the deformed equilibrium state, it is said to be in neutral and unstable equilibrium respectively G. Simitses and D. Hodges (2006). Fundamentals of Structural

Stability, Elsevier

Bifurcation bucklingBy bifurcation is meant the intersection of two static equilibrium paths at the same external load level

◦ That is, two solutions exist to the equilibrium equation(s) at some point

Changes in stability along the primary path occur at bifurcation points

◦ The path denoted OA denotes a stable static equilibrium path

◦ The path AB denotes unstable static equilibrium

As the load passes through its critical state, the structure passes from its unbuckled equilibrium configuration to an infinitesimally close buckled equilibrium configuration → bifurcation buckling

It is of interest to determine: ◦ Load level for which buckling takes place

◦ Stability of post-buckling solution

Pre-buckling or fundamental solution

Post-buckling or secondary solution

Bifurcation point

Bifurcation buckling: Example 1 DOF

G. Simitses and D. Hodges (2006). Fundamentals of Structural Stability, Elsevier

Example (small rotation)

Energy method

G. Simitses and D. Hodges (2006). Fundamentals of Structural Stability, Elsevier

Energy methodIt is possible to show that the following must hold true for stable equilibrium:

Note: Dn is the determinant

G. Simitses and D. Hodges (2006). Fundamentals of Structural Stability, Elsevier

Energy method

G. Simitses and D. Hodges (2006). Fundamentals of Structural Stability, Elsevier

Energy method: Example revisited

1. Energy stored in the system (in this case the spring)

2. Total potential energy:

3. Static equilibrium requires the total potential to have a stationary value

4. Linearized equilibrium

That is, we are concentrating our analysis to the vicinity of the fundamental solution 𝜃 = 0

Energy method: Example

• Second derivative of potential energy = 0 (the criterion for bifurcation)

• Moreover, the second derivative gives an indication of the stability of equilibrium,

Energy method: example

• Previously small rotations were assumed.

• Consider the total potential energy for finite rotations:

• First derivative of potential energy gives the nonlinear equilibrium equation:

Energy method: Example

As before it is shown that the bifurcation load is:

The stability of the equilibrium paths can be checked

Suggested exercise 11. Consider all equilibrium configurations for the presented example. Evaluate stability of each

equilibrium configuration

2.

Hints:• Use symmetry• Loading is hydrostatic, when

finding external energy, consider area (Uext = ΔA x P)

Ring buckling due to hydrostatic pressureBrief overview of procedure to evaluate bifurcation buckling:

1. Establish kinematic relations

2. Constitutive relation (linear elastic)

3. Determine potential energy

4. Stationary potential energy → equilibrium

5. Perturbing and linearizing equilibrium equations, as well as substituting our fundamenal solution → bifurcation load

6. Finally, consider imperfections

Ring buckling due to hydrostatic pressure

Kyriakides and Corona (2007). Mechanics of Offshore Pipelines Vol I, Buckling and Collapse, Elsevier

Ring buckling due to hydrostatic pressure

Ring buckling due to hydrostatic pressure

Ring buckling due to hydrostatic pressure

Ring buckling due to hydrostatic pressure

Ring buckling due to hydrostatic pressure

Ring buckling due to hydrostatic pressure

Ring buckling due to hydrostatic pressure

a=0.1, 0.05, 0.01, 0

A “real” pipe will inevitably contain initial imperfections. Rather than suddenly buckle when the bifurcation load is reached, the pipe gradually deforms with increasing load.

• The figure shows increasing ovalization for three different initial ovalities as determined from eq. 4.9

• Note that the equilibrium equations were linearized, and are therefore lacking “information” – the post-buckling behavior is unknown

• Moreover, the material behavior is assumed to be purely elastic. At some point the stresses in a metallic pipe will reach yield

w

Ring buckling due to hydrostatic pressure

Different post-collapse behaviors are shown for three different types of hardening.

◦ Numerical method is used to solve for the post-buckling behavior

◦ For the elastic behavior (material II), the post buckling behavior is shown to be stable → load increases after buckling

◦ Metallic materials will behave like material model (III). The post-buckling behavior of the ring then becomes unstable

“On the determination of the propagation pressure of long circular tubes”, Kyriakides, Yeh and Roach, 1984

Timoshenko formula

Timoshenko formula

Timoshenko formula

Timoshenko formula

Plastic bifurcation buckling

Bifurcation buckling need not occur only in the elastic regime

◦ Plastic bifurcation may occur for initially perfectly round rings – plastic deformation occurs prior to the bifurcation

◦ Numerical treatment needed

Elastoplastic behavior leads to bifurcationpressure lower than the perfectly elastic bifurcation pressure

Plastic bifurcation bucklingComparison of elastic and plastic bifurcation Note normalized by yield pressure

Elastoplastic collapse of pipes

Collapse of offshore pipelines is usually a limit load instability phenomenon

◦ Initial imperfections cause a gradual ovalization of the pipe with increasing load. Ovalization accelerates as the bifurcation pressure is approached

◦ A peak load occurs due to yielding of the pipe wall – the peak load corresponds to the collapse pressure

◦ The load to maintain static equilibrium drops until touchdown

For very thin pipes bifurcation type instabilities might materialize under some load conditions (bending)

Elastoplastic collapse of pipes

Comparison of bifurcation pressures (Pc) and collapse pressures (Pco) for an imperfect pipe

DNV treatment of collapseThe collapse pressure is found by solving for Pc:

The external pressure at any point shall fulfill:

pmin = the minimum internal pressure that can be sustained. Normally taken as zero

Ym and Ysc are safety factors

Characteristic material strength: yield stress modified by some safety factor

Fabrication factor: depends on manufacturing

Comparison of collapse expressions and experimental data

No application of safety factors

f0=1%, material with E=210,000MPa, v=0.3 and fy=450MPa, no reduction due to fabrication method and safety factor equal to unity

Factors affecting collapse - Overview

• Imperfections• Ovality• Thickness eccentricity

• Material parameters• Yield stress• Hardening behavior

• Residual stresses• Anisotropic yielding• Type of loading

• Hydrostatic• Plane strain• Lateral pressure

Factors affecting collapse 1. Initial ovality

As shown: 1% ovality can reduce collapse pressure by approx. 30%

Factors affecting collapse

2. Wall thickness eccentricity

Of less importance if smaller than 10%. May be neglected

Factors affecting collapse

3. Material yield stress

• Yield stress governs transitional value of D/t that separates elastic and plastic buckling

• Collapse pressure is roughly proportional to yield stress for plastic buckling

• Increasing the yield stress increases the collapse pressure for low D/t

0,00

20,00

40,00

60,00

80,00

100,00

120,00

12 14 16 18 20 22 24 26 28 30 32 34 36 38

Collapse pressures - X65/X80

X65 QUART Ovality = 0.25 % X80-T QUART Ovality = 0.25 %

Co

llap

se p

ress

ure

[M

Pa]

D/t

X65: SMYS = 65 ksi = 448 MPaX80: SMYS = 80 ksi = 551 MPa

SMYS: specified minimum yield stress

Factors affecting collapse

3. Material stress-strain response

n: hardeing parameter in Ramberg-Osgood law

Factors affecting collapse

4. Residual stresses

• Residual stresses may be introduced in the manufacturing process

• Effect increases with D/t until some point• For high D/t the effect of residual stress is

lower (see D/t=40 in graph)• High D/t buckle elastically, thus

plastic effects are less important

Factors affecting collapse

5. Anisotropic yielding

• Anisotropy also introduced during manufacturing process

• Usually consider only longitudinal and circumferential direction, altough anisotropy in thickness diretion may be present

• Again, effect is less pronounced for high D/t

Factors affecting collapse 6. Types of pressure loading

• Lateral pressure loading lowers collapse pressure

• Effect is apparent for low D/t• For higher D/t inelastic effects are

reduced, which reduces the difference between collapse pressures

• Hydrostatic pressure is more representative of operational conditions

Pipe collapse due to pressure and bending

Pipe collapse due to pressure and bending

Pipe collapse due to pressure and bending

• Previous figures showed the possible scenario of collapse due to pressure and bending• In sagbend during laying (S- or J-lay) if

tension is lost (tension has stabilizing effect)• Seabed instability (rockslide) may also bend

pipe

• Bending ovalizes pipe (Brazier effect). Together with pressure leads to earlier onset of collapse

• For low D/t, the pipe will ovalize with increasing curvature until a point of dynamic collapse

• For high D/t, the pipe may experience a bifurcation instability

Mean diam.

Pipe collapse due to pressure and bending

Pipe collapse due to pressure and bending

• Finite element analysis of pipe collapse – the combined loading case is first pressurized then subject to bending

Progressively collapsing cross sections

Hydrostatic pressure Pure bending Bending + pressure

Onset of dynamic collapse

Pipe bifurcation due to pressure and bending (thin pipes)

Factors affecting collapse

1. Loading path

• Pressure → bending loading path is more critical

• Radial loading path (i.e. Increasing curvature and pressure “at the same time”) falls between P→k and k→P

Factors affecting collapse

2. Residual stress

Residual stress may “reverse” ovalizationReversed collapse mode shown for low curvatures (circles with “|” in fig.). Normal collapse for higher curvature (circle with “—”)

Factors affecting collapse

3a. Initial ovality orientation

• Initial ovality oriented at an angle with bending axis creates a “cusp” in the collapse envelope

• Collapse profile can become angled with respect to the bending axis

Factors affecting collapse

3b. Initial ovality orientation: interplays with residual stress

Collapse at an angle with bending axis

Factors affecting collapse

3c. Initial ovality orientation: effect of increased residual stress or initial ovality

Factors affecting collapse

4. Wall thickness eccentricity

• For the case of no ovality imperfection a 5% thickness eccentricity oriented at 45° reduces collapse pressure by less than 1%

• Wall thickness eccentricity has the effect of “rounding” the cusp region when initial ovality is present

Orientation of thickness eccentricity

Factors affecting collapse

5. Material stress-strain response

Factors affecting collapse

5. Material stress-strain response

Factors affecting collapse

6. Anisotropy

Collapse envelopes

Pressure-moment interaction

a=0.6

“Tube Collapse Under Combined Pressure, Tension and Bending Loads” Bai, Igland and Moan, ISOPE Vol. 3 No. 2, 1993

Pure bending collapse formula

Collapse curvature:

Note that the stress-strain relation for this formula is characterized by:

“Tube Collapse Under Combined External Pressure, Tension and Bending” Bai, Igland and Moan, Marine Structures 10, 1997

Suggested exercise 2

Consider a pipe of X-52 steel grade, with D/t=20 and initial ovality ∆0= 0.002 (i.e. 0.2%)

1. Assume that the Timoshenko formula is valid (is it?), calculate the collapse pressure

2. Calculate the pure bending collapse moment, and curvature

3. Draw the pressure-moment, and pressure-curvature interaction diagram

4. Compare your results with the interaction diagrams of the next two slides. Comment on differences

See also nomenclature at end

Suggested exercise 2

Suggested exercise 2

NomenclatureUnless otherwise noted

References

1. Kyriakides and Corona (2007). Mechanics of Offshore Pipelines Vol I, Buckling and Collapse, Elsevier

2. G. Simitses and D. Hodges (2006). Fundamentals of Structural Stability, Elsevier

3. T.A. Netto (2016), Collapse of Rigid Pipes under External Pressure and Bending – An Introduction

4. Bai, Igland and Moan (1993) ,“Tube Collapse Under Combined Pressure, Tension and Bending Loads” ISOPE Vol. 3 No. 2

5. Bai, Igland and Moan (1997), “Tube Collapse Under Combined External Pressure, Tension and Bending”, Marine Structures 10