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.
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| Initial bending in the overbend during pipe installation may result in stress concentrations in pipe-to-pipe weld offsets or in pipe-to-buckle arrestor interfaces. |
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.
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.
To address the
pre-bend effect on collapse, 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).
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.
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