Proceedings of OMAE04
23rd International Conference on Offshore Mechanics and Arctic Engineering
June 20-25, 2004, Vancouver, British Columbia, Canada
OMAE2004-51425
PIPELINE-SEABED INTERACTION IN SOFT CLAY
M. Hesar
KBR
Hill Park Court, Springfield Drive,
Leatherhead, Surrey, KT22 7NL, UK
Email: majid.hesar@halliburton.com
ABSTRACT
Offshore pipelines laid on the seabed in a snake
configuration and transporting hydrocarbon products under
high pressure/high temperature are becoming a cost effective
alternative to trenching and burial. However, there appears to
be a major disparity between the level of sophistication and
accuracies inherent in the structural FE models used for
expansion and lateral buckling analysis of pipelines, and the
degree of crudity in adopting and using Coulomb friction
values.
This Paper reports the findings of a programme of
geotechnical finite element analyses performed for a project
where some 91km of 26” gas pipeline was designed to be laid
in a snake configuration. The seabed soils were predominantly
very soft clay. The ABAQUS/Explicit finite element program
was used with an adaptive meshing technique to analyse the
embedment and large lateral ploughing movements of the
pipelines by a distance of several diameters. It was found that
the FE model predicts the initial pipeline embedment into soil
accurately and rectifies the inaccuracies inherent in published
plasticity-based closed form solutions. A new non-dimensional
relationship is proposed for estimating pipeline embedment in
soft clays. The effect of important parameters such as the soilpipeline interface friction, operating submerged weight and
initial embedment, were all captured. Predicted cyclic lateral
ploughing showed similarities to the observed response in
reported model tests. The results were used in the structural FE
model of the pipelines to analyse the expansion and lateral
buckling problems and hence design the number and critical lay
curvature of snakes as well as other important features.
by a robust buckle management strategy. Important design
features such as the frequency of snakes or sleepers and
minimum snake curvature are determined by sophisticated
finite element analyses which take into account all pertinent
operating data for the pipeline, such as temperature and
pressure profiles, submerged weight, and stress-strain
properties of pipeline material. These FE models are relied
upon to provide the stresses and strains in the pipeline
accurately. A very important element of such FE models is the
contact interaction of pipeline with the seabed in both
longitudinal and lateral directions.
The seabed in these analyses is usually represented as a
rigid surface. The contact interface friction between pipeline
and seabed is modeled by the classical Coulomb friction law. In
current practice the values of friction coefficient are obtained
from Codes of Practice which quote numbers with widely
varying ranges for generic soil types, e.g. [2]. There appears to
be a major disparity between the level of sophistication and
accuracies inherent in the FE analyses of pipeline expansion or
lateral buckling and the degree of crudity in adopting and using
Coulomb friction values.
NOMENCLATURE
ALE
AGA
CPT
co
c1
D
d
FE
Eu
Fc
Ff
Fh
Fl
Fr
Fv
INTRODUCTION
Offshore oil and gas pipelines and flow-lines carrying
fluids under high pressure and high temperature and laid on the
seabed, either in a snake configuration or straight with buckleinducing devices, are becoming a cost effective alternative to
trenching and burial solution, e.g. see [1]. The success of this
system strongly depends on whether it can be demonstrated that
the required levels of safety and reliability will be maintained
Arbitrary Lagrangian-Eulerian
American Gas Association
Cone Penetration Test
Undrained shear strength at mudline
Gradient of undrained shear strength
Pipeline diameter
Effective averaging depth for Su
Finite element
Undrained Young’s modulus of elasticity
Pipeline-soil contact pressure
Frictional component of soil lateral resistance
Total horizontal soil lateral resistance
Hydrodynamic lift force
Remainder lateral soil resistance
Pipeline submerged weight [10]
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Ir
P
PRC
ro
SI
Ws
Wo
γ'
µ
í
Rigidity Index
Pipeline vertical penetration
Pipeline Research Committee
Pipeline outer radius
Site Investigation (geotechnical)
Pipeline maximum submerged weight
Pipeline operating submerged weight
Submerged unit weight of soil
Classical Coulomb Friction coefficient
Poisson’s ratio
CURRENT METHODOLOGY FOR LATERAL
BUCKLING ANALYSIS
In current practice FE models are used to perform
structural design of the pipelines and to ensure that stresses in
the pipeline are within acceptable limits set by the appropriate
Codes. A typical FE model may consist of a few hundred 3D
pipe elements capable of modeling the Poisson effect of hoop
stress and the end-cap effect due to internal pressure loading.
The pipe-to-seabed interface is modeled via the contact
algorithms. The classical Coulomb friction law is used for the
pipe-seabed contact, with different friction factors in the axial
and lateral directions. The orientations of these lateral and axial
directions rotate with the pipeline during large deformation
analyses. The lateral buckling behaviour of a pipeline is a
complicated combination of axial and lateral soil resistance
forces. For example, a low axial and high lateral friction
combination means that the onset of lateral buckling will be at a
higher temperature/pressure. However, once buckling starts the
“feeding” will be easier and the buckle radius will be smaller,
resulting in a sharper bend and hence higher stresses.
It is well known that both the axial and lateral interaction
response of pipelines with seabed soils are highly nonlinear and
that the classical Coulomb type friction law does not strictly
apply, e.g. see [3]. This is particularly the case in very soft soil
conditions. In such soft clays the lateral resistance of soil to
pipeline movement, and hence the equivalent lateral friction
coefficient is much more strongly influenced by the passive soil
resistance than by the Coulomb interface friction component.
Since the passive soil resistance of soil is directly related to
settlement of the pipeline it is important to predict embedment
of the pipeline correctly.
CURRENT METHODS FOR PREDICTING PIPELINE
EMBEDMENT AND AXIAL FRICTION COEFFICIENT IN
SOFT CLAY
Several researchers have suggested analytical closed form
solutions for prediction of pipeline embedment, e.g. [4-8].
However closed form solutions, by nature, make a number of
simplifying assumptions which detract from their accuracy and
reliability in design work. For example Fig. 1 shows the
relationships given in the AGA/PRC manual [9], and clearly
shows the large degree of discrepancy between different
closed-form solutions proposed. One of the most recent and
rigorous analytical solutions is due to Murff et.al. [10], and is
based on plasticity solutions. They assume a rigid-plastic
response for clay and zero friction between the pipeline and
clay and present the non-dimensional relationships shown in
Fig. 2 between pipeline submerged weight and penetration.
Some of the published field and laboratory test results are also
shown in Fig. 2 which illustrates the degree of scatter in the
reported physical test results. One possible reason for the
scatter in test results may be inaccurate measurement and
reporting of undrained shear strength. In low shear strength
clay measurement of Su itself is difficult and in high shear
strength clay penetration measurements may not have been
accurate. In the past soil-pipeline interaction tests have suffered
from apparatus faults as well, e.g. see discussion of TAMU
tests by Verley and Lund [11]. All closed-form solutions and
tests reported refer to a “constant” undrained shear strength.
Real field data invariably shows strengths increasing with depth
due to consolidation of clay under its own weight over a
geological time scale, as well as other reasons such as ageing.
CURRENT METHODS FOR PREDICTING LATERAL
SOIL RESISTANCE AND FRICTION COEFFICIENT IN
SOFT CLAY
Considerable research effort has been spent in recent years
to try and develop empirical lateral soil-pipeline interaction
relationships [3, 6-9,12-16]. In the empirical relationships that
emerged from the interpretation of these tests the total
horizontal soil resistance, Fh is divided into two components as
given below [3], see Fig. 3:
Fh = ì . (Ws-Fl) + Fr
……………………….……………. (1)
A constant value of 0.2 is adopted in the above relations
for ì, the contact interface friction coefficient. The equations
for the remainder term, Fr have been empirically derived and
include the energy terms to account for the work done by the
pipeline in cyclically deforming the soil and causing further
embedment. Later Verley and Lund [11] proposed a
simplification of the equations both for pipeline embedment
and remainder lateral resistance based on a dimensional
analysis. They presented a re-interpretation of the tests
performed at SINTEF [16] and corrected some of the errors
due to apparatus faults in the TAMU tests. Their work showed
that the most important parameters are undrained shear
strength, Su and clay submerged unit weight, γ'. Less important
are the amplitude of environmental cyclic force and pipeline
submerged weight.
Wagner et al [17] presented a best fit analytical
relationship to the data reported in the SINTEF tests [16].
It should be noted that the above research effort and hence
the resulting equations are only useful for environmental
stability assessment of the pipelines e.g. an AGA Level 3
assessment. They are not applicable for the case of lateral
buckling of pipelines, since in the latter case no lift forces are
present. In the author’s opinion separation of the lateral soil
resistance into the two components in the manner of Eq. 1 has
no rational basis, particularly in clays, since interface friction
(or adhesion) between pipeline and soil is not contact stress
dependent. Furthermore, real seabed clays almost never have a
constant undrained shear strength profile with depth.
For these reasons it is the author’s opinion that, in the
absence of costly field tests, advanced FE methods are the most
appropriate way to proceed in determining the most realistic
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relationships for both pipeline embedment and lateral soil
resistance.
shear strength profile reported for each section was assigned to
the clay in the model for that section.
The undrained Young’s modulus of elasticity was
estimated as:
GEOTECHNICAL CHARACTERISATION OF PIPELINE
ROUTE
A geotechnical SI programme executed along the route
corridor consisting of vibro-core sampling and CPT probing,
showed that soil conditions along the route of the pipelines are
predominantly soft clay overlying either sand or stiff clay. At
some locations along the route sand layers of significant
thickness are exposed at the seabed.
The site investigation report divides the route into a
number of “Geotechnical” sections based on the near seabed
soil conditions. The strength profiles show that the undrained
shear strength of clay varies with depth below mudline. Within
some of these sections the pipeline characteristics such as
submerged weight and outer diameter also change. For the
purpose of present FE analyses further subdivisions were
included in those sections to accommodate these specific
characteristics. Due to the variability of soil conditions at
different sections the FE model was run with the actual soil
strength profile reported for that section. Other relevant data
such as the submerged unit weight under hydro-test and
operating conditions were changed to reflect the actual
conditions for each individual section.
THE FINITE ELEMENT MODEL
In this project both hand calculation methods published in
the literature and finite element techniques using
ABAQUS/Explicit were utilised to obtain embedment of the
pipelines and lateral resistance-displacement relationships. Two
plane strain models were developed, a coarse model for bulk of
the runs and a finer mesh model used to calibrate the coarse
mesh and hence account for mesh sensitivity effects.
The coarse FE mesh is shown in Fig. 4. The plane strain
mesh extends to a depth of 2.5m, and 12m laterally. For
computational economy the soil was modeled in two layers, an
upper layer with an optimal mesh size relative to pipeline
radius and a lower layer defined with a coarser mesh. The
purpose of this lower layer was to include sufficient volume of
seabed so that settlements due to elastic deformation of the
seabed would be included in the predictions. The two surfaces
along the interface plane were bonded together. The pipeline
was modeled as a rigid circular surface with its outer diameter
equal to the finished concrete coating. The interface frictional
stress between the concrete coating and clay contacting
surfaces was limited to the remoulded undrained shear strength
of clay at mudline. Self-contact was defined for elements
forming the seabed to account for the case when a hump of clay
folds back and touches the seabed itself. The finer mesh model
had the same overall dimensions and characteristics, except
with a mesh density of five times higher.
In the absence of good quality soil laboratory test data
appropriate for FE work, a linear elastic perfectly plastic
response was assigned for the constitutive behaviour of clay.
All analyses were performed with the clay modelled as an
undrained single-phase material obeying the von-Mises yield
criterion; no coupled stress-pore pressure (consolidation)
effects were considered. Actual depth-dependent undrained
Eu = Ir x Su , Ir = 50 to 200 (depending on Su)
These low values of Rigidity Index for soft clay are
considered appropriate, following the recommendations of
various references reported e.g. [18]. Poisson’s ratio was taken
as: ν=0.49. In order to account for the possible soil disturbance
caused at the touch down point by installation vessel
movements, the insitu soil shear strength was reduced by a
nominal amount. From experience of similar pipeline
installations this disturbance was not anticipated to be
significant.
The pipeline was initially located 2m away from the left
edge of the model in order to eliminate boundary effects, see
Fig. 4. Initially an Implicit FE model in ABAQUS/Standard
was used with the geometric nonlinearity effects switched on.
However, the large amounts of settlement that resulted,
particularly in the weakest clays, caused very large mesh
distortions. Subsequently, in order to eliminate numerical errors
due to mesh distortion effects Adaptive Meshing had to be
used. At present Adaptive Meshing capability is not available
in ABAQUS/Standard, and hence ABAQUS/Explicit had to be
adopted. ABAQUS/Explicit uses an ALE (Arbitrary
Lagrangian-Eulerian) adaptive meshing algorithm. The domain
being adaptively meshed follows the material originally inside
the mesh. No material actually enters or leaves the mesh
boundaries and the mesh is moved and reformed at each time
increment, using the original topology. The algorithm
accurately remaps the solution variables onto the new mesh,
keeping track of the stress fields within the solution domain
accurately. It should be noted that this technique is different
from “adaptive mesh refinement” often used in small strain
implicit FE analyses, which would not be appropriate for
advanced simulations in the present work. The analyses were
conducted in the following steps:
1.
2.
3.
4.
Establish the correct initial stress conditions in the soil.
Apply the pipeline self-weight corresponding to the hydrotest conditions
Unload the pipeline to operating submerged weight
conditions
Push the pipeline laterally in a displacement-control mode
whilst still under the operating weight.
The settlement obtained in Step 3 was used for the purpose
of calculating the axial friction. The ultimate axial friction force
was obtained as the product of pipeline/soil contact area and
clay strength at mudline. This is regarded as conservative, since
due to the cyclic action of waves and currents during the period
prior to the design event the pipeline is expected to settle a
further small amount into the soil. This further settlement will
increase the frictional soil response both axially and laterally.
Vertical elastic rebound of the pipeline when unloaded from the
hydro-test conditions in Step 3 was found to be small, as
expected, since nearly all the settlement is due to plastic
deformation of the clay, see Fig. 7.
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All analysis steps were performed sufficiently slowly so as
not to be affected by inertia effects. The kinetic, total, and other
energy quantities of the model were monitored to ensure that
inertia effects were eliminated and static conditions prevailed
throughout the analysis, and that the results were free from
numerical errors.
All aspects of pipeline-seabed interaction are influenced by
the embedment in soft clay prior to the design event.
Traditionally pipeline embedment is separated into two parts,
one due to initial embedment and the other resulting from the
cyclic hydrodynamic forces generated by the environmental
forces (waves and currents) during the period between
installation and design event. The latter are expected to be
small in the relatively benign environment of the Caspian.
submerged weights under hydro-test conditions were greater
than the touch down point loads.
For lateral buckling analysis a “range” of possible variation
in seabed friction is required. Again, in order to minimise the
number of FE runs, at three representative sections additional
runs were performed with the clay strength corresponding to
the lower bound and upper bound profiles of each of these
sections. As mentioned earlier the elastic re-bound of the
pipeline in soft clay is negligible since nearly all the settlement
is due to irrecoverable plastic deformation of the soil.
Fig. 7 shows an example vertical displacement history of
the pipeline as it undergoes hydro-testing and subsequently
carries the product (operation condition) for two different
operating weights.
PREDICTED PIPELINE EMBEDMENT
For comparison with the Murff et. al. [10] predictions
shown in Fig. 2, the results obtained from the present
ABAQUS/Standard and ABAQUS/Explicit models for a test
case of a pipeline placed in a clay with constant strength with
depth are shown in Fig. 5. The ABAQUS/Standard model does
not provide a satisfactory prediction because of gross mesh
distortions. However, the ABAQUS/Explicit model using the
Adaptive Meshing capability performs very well. At small
settlements the ABAQUS/Explicit solution appears to over
predict pipeline settlement relative to the closed form solution
curves. However, Murff et. al. [10] warn against using their
solution for small pipeline settlements (<5% diameter).
Furthermore, the distribution of actual test data points shown in
Fig. 2 appears to be biased towards the ABAQUS/Explicit
solution at small displacements. The ABAQUS/Explicit results
are therefore an improved solution to the pipeline embedment
problem in soft clay.
It should be emphasised that closed form solutions should
not be presumed as “exact” yardsticks against which FE
predictions can be compared. Rather, the argument should be
pitched the other way round. The FE model does not make any
unrealistic simplifying assumptions adopted by the closed form
solutions, such as
• Zero pipeline friction during settlement
• Constant undrained shear strength of soil with depth
• Infinitely rigid-perfectly plastic soil behaviour
• No soil heave around pipeline, which is known to have 1015% effect on collapse load, [10]
PREDICTED LATERAL SOIL RESISTANCE
When a pipeline which has partially penetrated the seabed
undergoes substantial lateral displacement (of the order of
several diameters) without rotation, the soil’s response depends
principally on the submerged weight of the pipeline. Other
factors include clay shear strength, interface friction coefficient
(traditional Coulomb friction), and the magnitude of lateral
displacement itself.
It was observed in the present work that under these
conditions, lateral displacement generally results in either a
gradual sinking or very gradual uplift of the pipeline as it
“ploughs” the soft clay in front. In order to account for these
effects adaptive meshing is vitally important, otherwise the
finite element mesh becomes grossly distorted and the analysis
stops prematurely because of excessive mesh distortion.
One drawback with using FE analyses in a project time
scale is the time consuming aspect of this type of analysis,
particularly if many different analysis runs have to be
performed. In order to overcome this problem two FE models
were utilised, a coarse mesh model and a fine mesh model, as
discussed earlier. The coarse model was used for bulk of the
analysis runs at all the geotechnical sections, as the run times
with this model were short. Typical run times with the coarse
model were approximately 20 minutes compared to more than 8
hours of the finer model on a 1.8GHz processor PC. The mesh
density in the fine model was 5 time higher. The coarse model
was calibrated against the fine mesh model and the results were
corrected.
A typical deformed mesh of the coarse model after the
pipeline has been displaced laterally is shown in Fig. 8. The
good proportion of element shapes is evidence of the adaptive
meshing algorithm re-meshing the domain correctly. Fig. 9
shows the deformed mesh of the fine model after the pipeline
has been pushed laterally by 4m and then brought back
(simulating a heating/cooling cycle).
The lateral force versus lateral displacement response from
the coarse and fine models in these runs are shown in Fig. 10.
The slightly oscillatory nature of soil reaction behaviour in Fig.
10 is due to the following reasons:
For the case of clays with a linearly increasing shear
strength with depth Murff et.al. [10] found that their solutions
(Fig. 2) can be utilised, providing the shear strength averaged
over a depth, d, is used. They found that the depth d is given to
a good approximation from the relationship:
d/ro = P/ro + 0.075
…….……………………………… (2)
In order to rationalise the number of finite element runs,
use was made of the good correlation obtained (Fig. 5). In a
spreadsheet the penetration was iterated and the average
strength given by Eq. 2 was used to obtain the solution
matching the non-dimensional ABAQUS/Explicit curve.
As an example, the deformed mesh presented in Fig. 6
illustrates the contours of vertical settlement under the
application of hydro-test weight in the coarse model. The
•
•
The clay is almost incompressible (ν = 0.49)
The clay behaviour has been modeled as an elasticperfectly plastic material (there were no high quality data
available to allow a more sophisticated constitutive model
for clay to be used).
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•
Only a small value was assigned for the bulk viscosity of
clay, since viscosity, which helps smooth out oscillations,
also lowers the minimum stable time increment in an
explicit analysis. Smaller time increments increase the run
time too much for it to be a viable tool in a project timescale.
The coarse model over-predicts soil resistance to lateral
movement of the pipeline by about 13% relative to the finer
model. Hence in the subsequent analyses which formed bulk of
the analysis runs for the geotechnical sections the coarse model
was used to gain economy in terms of run time, and the results
were corrected.
The influence of pipeline operating submerged weight (for
the same hydro-test weight) is illustrated in Fig. 11. The
pipeline experiences a higher lateral soil resistance the heavier
it is, even though the initial penetration is the same.
The effect of interface friction (the value of Coulomb
friction) between the pipeline concrete coating and clay is
illustrated in Fig. 12. Results for two values of interface friction
are shown, a low value of 0.3, and a value of 1.3 corresponding
to the remoulded clay shear strength. An increase of
approximately 22% in peak lateral soil resistance is obtained
with the higher interface friction value, although at larger
displacements the resistance values appear to become closer.
An example selection of lateral resistance versus lateral
displacement curves are plotted for some of the geotechnical
sections in Fig. 13. Most of the curves appear to experience a
peak which corresponds to a displacement of the order half to
one diameter. Thereafter the resistances reduce and in some
cases increase again at larger displacement. In some cases
where the initial penetration is not substantial the response does
not exhibit a peak and a near-plateau response is observed.
The ordinates on lateral resistance curves can be divided
by the individual operating submerged weights of the pipeline
at each section to obtain the “equivalent lateral friction
coefficient” see Fig. 14. These curves illustrate that the
equivalent lateral friction coefficient itself varies as the pipeline
moves on the seabed. Additionally this variation is widely
different for different sections, depending on the soil and
pipeline characteristics discussed earlier.
CONCLUSIONS AND RECCOMMENDATIONS
The finite element technology and developments in
computer hardware have now sufficiently progressed to the
point where advanced geotechnical simulations can be
performed as routine tasks in pipeline projects. This Paper has
shown that even for a pipeline system traversing widely varying
seabed conditions pipe-soil interaction data can be generated
that can be used as input to the structural FE analyses.
Provision of such site and project specific interaction data
avoids the need for resorting to generic values of friction
coefficient quoted in the Codes. This approach can results in
bespoke solutions and hence economy through avoidance of
unnecessarily excessive conservatism.
The ABAQUS/Explicit finite element package employing
an adaptive meshing technique was used to model the soil
medium. It was found that the FE model predicts the initial
pipeline embedment into soil accurately and improves the
predictions of previously published plasticity-based closed
form solutions. Elastic rebound of the pipeline due to reduction
of self-weight from hydro-test or touch-down loads to the
operating condition is found to be small. The intricate manner
of soil resistance against pipeline lateral movement, as well as
the effect of important parameters such as the soil-pipeline
interface friction, operating submerged weight, and initial
embedment, were all captured.
It is recommended that the ideal approach for incorporating
the “equivalent friction coefficient” relationships typified by
those shown in Fig. 14 is to define them as displacementdependent friction coefficients for use in the structural FE
analysis of pipeline. This can be done, for example by use of a
user subroutine, e.g. FRIC subroutine in ABAQUS.
It was found that pipeline-seabed interaction is strongly
dependent on the embedment of pipeline prior to lateral
movements. The main parameters influencing the embedment
of pipeline are submerged weight of pipeline and undrained
shear strength of near-seabed soils. It is not only the strength
intercept at mudline, parameter co, but also the rate of increase
of undrained shear strength with depth c1 that influence pipeline
behaviour. It is therefore strongly recommended that in future
pipeline projects, attention is paid to obtaining high quality
soils data from the shallow soil layers. The upper one to two
diameters is the most important for determining the actual
pipeline response. In very soft clays the CPT probe is not
accurate enough and newer more accurate instruments such as
the T-bar and insitu vane should be used to calibrate the CPT
and to profile the strength of seabed soils more reliably.
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implementation”, Paper OTC 15310 .
[2] BS8010 - British Standard, Code of Practice for Pipelines.
[3] Lieng, J.T. , Sotberg, T. H., Brennodden, H. 1988,
Energy Based Soil Pipe Interaction, SINTEF Report
Number STF69 F87024.
[4] Small, S.W., Tambruell, R.D. and Piaseckyj, P.J., 1971,
Submarine pipeline support by marine sediments, Proc, 5
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[6] Wantland, G.M., O’Neill, M.W., Reese, L.C., and
Kalajian, E.H., 1979, Lateral stability of pipelines in clay,
Proc. 11 OTC, Vol. 2, pp. 1025-1034.
[7] Karal, K., 1977, Lateral stability of submarine pipelines,
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5
Downloaded From: https://proceedings.asmedigitalcollection.asme.org on 06/30/2019 Terms of Use: http://www.asme.org/about-asme/terms-of-use
Copyright © 2004 by ASME
[8] Ghazzaly, O.I., and Liam, S.J., 1975, Experimental
investigation of pipeline stability in very soft clay, Proc 7
OTC , Vol. 2, pp-314-326.
[9] AGA/PRC, 1993 Submarine pipeline on-bottom stability,
Vol. I, Analysis and Design Guidelines, American Gas
Association, Report PR-178-9333.
[10] Murff J.D., Wagner D.A., Randolph, M.F., 1989, Pipe
Penetration in Cohesive Soil, Geotechnique Vol. 39, N. 2,
pp 213-229.
[11] Verley, R. and Lund, K.M., 1995, “A soil resistance
model for pipelines placed on clay soils”, OMAE –Vol. V,
Pipeline Technology ASME.
[12] Allen, D.W., Lammert, W.F. and Hale, J.R. 1989,
Submarine pipeline on-bottom stability: Recent AGA
Research, Proc. 21 Offshore Technology Conference,
OTC 6055.
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Proc. 21 Offshore Technology Conference, OTC 6059.
[14] Karal, K., 1985, A concept for design of Submarine
pipeline to resist ocean forces, Trans. ASME, 107, 42-47.
[15] Lyons, C.G., 1973, Soil resistance to lateral sliding of
marine pipelines, Proc. 5 Offshore Technology
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[16] SINTEF, 1986, Pipe-soil interaction tests, soft clay, STF
60 F86023.
[17] Wagner D.A., Murff, J.D., Brennodden, H., 1987, “Pipesoil interaction Model”, Paper OTC 5504.
[18] Brand, E.W, and Brenner, R.P. (Ed.) 1981, Soft clay
Engineering, Elsevier, ISBN 0-444-41784-2.
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Figure 1 AGA/PRC [9] pipeline embedment curves.
Figure 3 Lateral soil resistance curves, [3].
Figure 2 Murff e al [10] normalised embedment curves.
Figure 4 The coarse finite element mesh
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7
6
Fv/(2roSu)
5
4
3
Murff et. al. Upper Bound
2
Murff et. al. Lower Bound
Randolph &Houlsby Upper Bound
Figure 8 Deformed mesh plot at pipeline lateral displacement
of 3m (coarse mesh).
ABAQUS/Standard (Implicit)
1
ABAQUS/Explicit
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
P/ro
Figure 5 Comparison of ABAQUS and Murff etal [10] results.
Figure 6 Typical contours of vertical displacement under
Hydro-test loading conditions.
Explicit analysis time (seconds)
Vertical Pipeline Displacement (m)
0
5000
10000
15000
20000
25000
30000
0.00
-0.05
-0.10
Wo=2117 kN/m
Wo=2611kN/m
-0.15
Lateral Soil resistance (kN)
Figure 9 Deformed mesh plot after one cycle of lateral
displacement (fine mesh)
Fine
mesh
-0.20
Lateral displacement (m)
-0.25
Figure 7 Pipeline vertical displacement v. time, showing
small elastic re-bound (Wo=operating weight).
Figure 10 Lateral load-displacement using coarse
and fine meshes.
8
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4.50
3.50
Horizontal soil reaction (kN)
4.00
Lateral Soil Resistance (kN)
3.0
Wo=2117 kN/m
Wo=1590 kN/m
Wo=1060 kN/m
Wo=530 kN/m
3.00
2.50
2.00
1.50
1.00
2.5
2.0
1.5
1.0
0.5
0.50
0.00
0.000
1.000
2.000
3.000
4.000
5.000
6.000
0.0
7.000
0
Lateral Pipeline Displacement (m)
0.5
1
1.5
2
2.5
3
Horizontal pipeline displacement (m)
Figure 11 Effect of pipeline operating weight on lateral
soil resistance.
Figure 13 Example lateral load-displacement responses.
3.00
1.2
Equivalent lateral friction coefficient
Lateral Soil Resistance (kN)
2.50
2.00
1.50
1.00
Fric Coef=1.3
0.50
Frci Coef=0.3
0.00
0
1
1
2
2
3
3
4
4
5
Lateral Pipeline Displacement (m)
Figure 12 Effect of pipeline-seabed interface friction
on lateral soil resistance.
1.0
0.8
0.6
0.4
0.2
0.0
0
0.5
1
1.5
2
2.5
3
Horizontal pipeline displacement (m)
Figure 14 Example equivalent lateral soil friction coefficients.
9
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Copyright © 2004 by ASME