Understanding pipeline
buckling in deepwater applications
Finite element
model predicts local conditions
D. DeGeer - C-FER
Technologies
With ultra deepwater
pipelines being considered for water depths of nearly 3,000 m, pipe collapse,
in many instances, will govern design. For example, bending loads imposed on
the pipeline near the seabed (sagbend region) during installation will reduce
the external pressure resistance of the pipeline, and this design case will
influence (and generally govern) the final selection of an appropriate pipeline
wall thickness.
To date, the deepest
operating pipelines have been laid using the J-lay method, where the pipeline
departs the lay vessel in a near-vertical orientation, and the only bending
condition resulting from installation is near the touchdown point in the
sagbend. More recently, however, the S-lay method is being considered for
installation of pipelines to water depths of nearly 2,800 m. During deepwater
S-lay, the pipeline originates in a horizontal orientation, bends around a
stinger located at the stern or bow of the vessel, and then departs the lay
vessel in a near-vertical orientation. During S-lay, the installed pipe
experiences bending around the stinger (overbend region), followed by combined
bending and external pressure in the sagbend region.
Initial bending in the overbend
during pipe installation may result in stress concentrations in pipe-to-pipe weld
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In light of these
bending and external pressure-loading conditions, analytical work was performed
to better understand the local buckling behavior of thick-walled line pipe due
to bending, and the influence of bending on pipe collapse. Variables considered
in the analytical evaluations include pipe material properties, geometric
properties, pipe thermal treatment, the definition of critical strain, and
imperfections such as ovality and girth weld offset.
Design
considerations
As the offshore
industry engages in deeper water pipeline installations, design limits
associated with local buckling must be considered and adequately addressed.
Instances of local buckling include excessive bending resulting in axial
compressive local buckling, excessive external pressure resulting in hoop
compressive local buckling, or combinations of axial and hoop loading creating
either local buckling states. In particular, deepwater pipe installation
presents perhaps the greatest risk of local buckling, and a thorough
understanding of these limiting states and loading combinations must be gained
in order to properly address installation design issues.
Initial bending in
the overbend may result in stress concentrations in pipe-to-pipe weld offsets
or in pipe-to-buckle arrestor interfaces. Initial overbend strains, if large
enough, may also give rise to increases in pipe ovalization, perhaps reducing
its collapse strength when installed at depth. Active bending strains in the sagbend
will also reduce pipe collapse strength, as has been previously demonstrated
experimentally.
Overall modeling
approach
In an attempt to
better understand pipe behavior and capacities under the various installation
loading conditions, the development and validation of an all-inclusive finite
element model was performed to address the local buckling limit states of
concern during deepwater pipe installation. The model can accurately predict
pipe local buckling due to bending, due to external pressure, and to predict
the influence of initial permanent bending deformations on pipe collapse.
Although model validation is currently being performed for the case of active
bending and external pressure (sagbend), no data has been provided for this
case.
The finite element
model developed includes non-linear material and geometry effects that are
required to accurately predict buckling limit states. Analysis input files were
generated using our proprietary parametric generator for pipe type models that
allows for variation of pipe geometry (including imperfections), material
properties, mesh densities, boundary conditions and applied loads.
A shell type element
was selected for the model due to increased numerical efficiency with
sufficient accuracy to predict global responses. The Abaqus S4R element is a
four-node, stress/displacement shell element with large-displacement and
reduced integration capabilities.
All material
properties were modeled using a conventional plasticity model (von Mises) with
isotropic hardening. Material stress-strain data was characterized by fitting
experimental, uniaxial test results to the Ramberg-Osgood equation.
Pipe ovalizations
were also introduced into all models to simulate actual diameter imperfections,
and to provide a trigger for buckling failure mode. This was done during model
generation by pre-defining ovalities at various locations in the pipe model.
Bending case
A pipe bend portion
of the model was developed to investigate local buckling under pure moment
loading. Due to the symmetry in the geometry and loading conditions, only one
half of the pipe was modeled, in order to reduce the required computational
effort. The pipe mesh was categorized into four regions
- Two refined mesh areas located over a length of one pipe diameter on each side of the mid-point of the pipe to improve the solution convergence (location of elevated bending strains and subsequent buckle formation)
- Two coarse mesh areas at each end to reduce computational effort.
Clamped-end
boundaries were imposed on each end of the pipe model to simulate actual test
conditions (fully welded, thick end plate). Under these assumptions, the end
planes (nodes on the face) of both ends of the pipe were constrained to remain
plane during bending. Loading was applied by controlled rotation of the pipe
ends.
In terms of material
properties, the axial compressive stress-strain response tends to be different
from the axial tensile behavior for UOE pipeline steels. To accurately capture
this difference under bending conditions, the upper (compressive) and lower
(tension) halves of the pipe were modeled with separate axial material
properties (derived from independent axial tension and compression coupon
tests).
In general, the
local compressive strains along the outer length of a pipe undergoing bending
will not be uniform due to formation of a buckle profile. In order to specify
the critical value at maximum moment for an average strain, four methods were
selected based on available model data and equivalence to existing experimental
methods.
Collapse case
The same model
developed for the bending case was used to predict critical buckling under
external hydrostatic pressure. This included the use of shell type elements and
the same mesh configuration. In the analyses, a uniform external pressure load
was incrementally applied to all exterior shell element faces. Radially
constrained boundary conditions were also imposed on the nodes at each end of
the pipe to simulate actual test conditions (plug at each end). In contrast to
the pipe bend analysis, only a single stress-strain curve (based on compressive
hoop coupon data) was used to model the material behavior of the entire pipe.
Bending case
validation
The pipe bend finite
element model was validated using full-scale and materials data obtained from
the Blue Stream test program, both for “as received” (AR) and “heat treated”
(HT) pipe samples. Geometrical parameters were taken from the Blue Stream test
specimens and used in the model validation runs. Initial ovalities based on
average and maximum measurements were also assigned to the model. The data
distribution reflects the relative variation in ovality measured along the
length of the Blue Stream test specimens.
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Axial tension and
compression engineering stress-strain data used in the model validation were
based on curves fit to experimental coupon test results. As pointed out
previously, separate compression and tension curves were assigned to the upper
and lower pipe sections, respectively, in order to improve model accuracy.
In the validation
process, a number of analyses were performed to simulate the Blue Stream test
results (base case analyses), and to investigate the effects of average strain
definition, gauge length, and pipe geometry. These analyses, comparisons and
results were:
- The progressive deformation during pipe bending for the AR pipe bend showed the development of plastic strain localization at the center of the specimen
- A comparison between the resulting local and average axial strain distributions for two nominal strain levels indicated that at the lower strain level the distribution of local strain is relatively uniform, at the critical value (peak moment) a strain gradient is observed over the length of the specimen with localization occurring in the middle, the end effects are quite small due to specimen constraint and were observed at both strain levels
- The resulting moment-strain response for the AR pipe base case analysis found the calculated critical (axial) strain slightly higher than that determined from the Blue Stream experiments
- The effect of chosen strain definition and gauge length on the critical bending strain for the AR pipe base case analysis, using the four methods for calculating average strain, gave similar results
- The critical strain value is somewhat sensitive to gauge length for a variety of OD/t ratios
- The finite element results are seen to compare favorably with existing analytical solutions and available experimental data taken from the literature. For pipe under bending, heat treatment results in only a slight increase in critical bending strain capacity.
Collapse case
validation
Similar to the pipe
bending analysis, the plain pipe collapse model was also validated using
full-scale and materials data obtained from the Blue Stream test program, both
for “as received” (AR) and “heat treated” (HT) pipe samples. Pipe geometry and
ovalities measurements taken from the Blue Stream collapse specimens were used
in the validation analyses. Initial ovalities based on average and maximum
measurements were also assigned to the model at different reference points.
Hoop compression stress-strain data was used in the model, and was based on the
average of best fit curves from both ID and OD coupon specimens, respectively.
To validate the pipe collapse model, comparison was made to full-scale results
from the Blue Stream test program which demonstrated a very good correlation
between the model predictions and the experimental results.
In addition to the
base case, further analyses were run for a number of alternate OD/t ratios
ranging from 15 to 35. Similar to the pipe bend validation, the OD/t ratio was
adjusted by altering the assumed wall thickness of the pipe. The finite element
results have compared favorably with available experimental data taken from the
literature.
The beneficial
effect of pipe heat treatment for collapse has resulted in a significant
increase in critical pressure (at least 10% for an OD/t ratio of 15). The
greatest benefit, however, is observed only at lower OD/t ratios (thick-wall
pipe). This can be attributed to the dominance of plastic behaviour in the
buckling response as the wall thickness increases (for a fixed diameter). At
higher OD/t ratios, buckling is elastic and unaffected by changes in material
yield strength.
Pre-bent effect
on collapse
Finite element
analyses were also performed to simulate recent collapse tests conducted on
pre-bent and straight UOE pipe samples for both “as received” (AR) and “heat
treated” (HT) conditions. The intent of these tests was to demonstrate that
there was no detrimental effect on collapse capacity due to imposed bending as
a result of the overbend process. In the pre-bend pipe tests, specimens were
bent up to a nominal strain value of 1%, unloaded, then collapse tested under
external pressure only.
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To address this
loading case, a simplified modeling approach was used whereby the increased
ovalities and modified stress-strain properties in hoop compression due to the
pre-bend were input directly into the existing plain pipe collapse model (the
physical curvature in the pipe was ignored).
A comparison between
the predicted and experimental collapse pressures for both pre-bent and
straight AR and HT pipes indicates that the model does a reasonable job of
predicting the collapse pressure for both pipe conditions. It is also clear
that the effect of moderate pre-bend (1%) on critical collapse pressure is
relatively small.
While the pre-bend
cycle results in an increased ovality in the pipe, this detrimental effect is
offset by a corresponding strengthening due to strain hardening. As a result,
the net effect on collapse is relatively small. For the AR pipe samples, there
was a slight increase in collapse pressure when the pipe was pre-bent.
Conversely, for the HT pipe, the opposite trend was observed. This latter
decrease in collapse pressure can be attributed to two effects: the larger
ovality that resulted from the pre-bend cycle and the limited strengthening
capacity available in the HT pipe (the HT pipe thermal treatment increased the
hoop compressive strength, offering less availability for cold working increases
due to the pre-bend).
Similar to previous
experimental studies on thermally aged UOE pipe, the beneficial effect of heat
treatment was demonstrated in the pre-bend analysis. The collapse pressure for
the pre-bent heat treated (HT) pipe is approximately 8-9% higher than that for
the as received (AR) pipe, based on both the analytical and experimental
results. This increase, however, is lower than that observed for un-bent pipe
(approximately 15-20% based on analysis and experiments).
This unique case of
an initial permanent bend demonstrated that the influence on the collapse
strength of a pipeline was minimal resulting from an increase in hoop
compressive strength (increasing collapse strength), and an increase in ovality
(reducing collapse strength). This directly suggests that excessive bending in
the overbend will not significantly influence collapse strength.
Future work includes
advancing the model validation to the case of active bending while under
external pressure. This condition exists at the sagbend region of a pipeline
during pipelay and, in many cases, will govern overall pipeline wall thickness
design.
Acknowledgments
The authors would
like to acknowledge the support of this program by Medgaz SA and the technical
contributions of Medgaz personnel throughout the model development phase.
Editor’s Note: This
a summary of the OMAE2006-92173 paper presented at the 2006 OMAE conference in
Hamburg, Germany, June 4-9, 2006
11/01/2006
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