1. Buckling and Collapse of Offshore Pipes under
Combined Bending and External Pressure
JENS HAFSTAD 30.09.2020
2. Introduction
Introduction
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
3. Introduction
Steel 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 external
pressure and bending
Infield flowline
Feeder line
Transmission line
4. Pipeline limit states
Limit 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
5. Deep-water pipeline collapse
Oil 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
7. Introduction to buckling
A 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
8. 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
9. Bifurcation buckling
By 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
10. Bifurcation buckling: Example 1 DOF
G. Simitses and D. Hodges (2006). Fundamentals of Structural Stability, Elsevier
13. Energy method
It 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
15. 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
16. 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,
17. 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:
18. Energy method: Example
As before it is shown that the bifurcation load is:
The stability of the equilibrium paths can be checked
19. Suggested exercise 1
1. 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)
20. Ring buckling due to hydrostatic pressure
Brief 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
21. Ring buckling due to hydrostatic pressure
Kyriakides and Corona (2007). Mechanics of Offshore Pipelines Vol I, Buckling and Collapse, Elsevier
28. 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
29. 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
34. 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 bifurcation
pressure lower than the perfectly elastic
bifurcation pressure
36. 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)
37. Elastoplastic collapse of pipes
Comparison of bifurcation pressures (Pc) and collapse pressures (Pco) for an imperfect pipe
38. DNV treatment of collapse
The 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
39. 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
45. 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
46. 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
47. 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
50. 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.
52. 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
54. 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
55. Factors affecting collapse
2. Residual stress
Residual stress may “reverse” ovalization
Reversed collapse mode shown for low
curvatures (circles with “|” in fig.). Normal
collapse for higher curvature (circle with “—”)
56. 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
57. Factors affecting collapse
3b. Initial ovality orientation: interplays with residual stress
Collapse at an angle
with bending axis
59. 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
65. 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
66. 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
70. 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
