Finite Element Analyses in Offshore Foundation Design

th
The 12 International Conference of
International Association for Computer Methods and Advances in Geomechanics (IACMAG)
1-6 October, 2008
Goa, India
Finite Element Analyses in Offshore Foundation Design
L. Andresen, H.P. Jostad, K.H. Andersen,K. Skau
NGI, Oslo, Norway
Keywords: offshore, foundation, design, FEM, FEA
ABSTRACT: Offshore structures for oil and gas exploitation are designed for severe environmental loads. These
structures are either placed directly on the seabed or they are moored to anchors installed in the seabed soil. The
foundation or anchor design is a key activity for the successful performance of the structures. The cyclic loading,
geometry and soil behaviour may be very complex and there are large cost savings in obtaining an optimal
design. Finite element method (FEM) based analyses and simulations are used increasingly in the design
process. The FEM has the potential to increase the accuracy, efficiency and reliability and reduce the uncertainty.
This paper presents examples of finite element analyses performed at NGI for various topics in offshore
foundation design.
1 Introduction
Offshore structures for oil and gas exploitation are subjected to severe environmental loads from waves, wind,
current and possibly ice and earthquakes. Strict requirements are set for the optimum performance of their
foundation systems and the foundation design is a key activity in the overall engineering process of these
structures. The foundations must be designed for the expected cyclic load history. The capacity under cyclic
loading may be higher or lower than the monotonic capacity, depending on the cyclic degradation.
Various types of structures and foundation systems are used such as piled jackets, jackets with caissons (bucket
foundations), jack up rigs on spud-cans or mats, floating structures moored to different types of anchors and steel
or concrete gravity base structures (GBS) with or without skirts.
The major foundation design topics are:
1.
2.
3.
4.
5.
6.
Bearing capacity
Installation aspects
Foundation stiffness
Consolidation and settlements
Soil reactions against the structure
Soil-structure-interaction (SSI)
Even if hand calculations and limit equilibrium methods have been and still are used extensively, finite element
analyses (FEA) are used increasingly to deal with the above topics. FEA have many advantages including the
ability to include complex geometries, spatially varying soil properties, advanced non-linear and anisotropic
constitutive models, and partial consolidation under long term loading, to name a few. This paper presents
examples of FEA performed at NGI within these different topics of foundation design. The objective is to
demonstrate that FEA may lead to a more optimal design and to help reducing the uncertainties in the design
process. However, these examples also illustrates that great care must be taken and that speciality knowledge in
FEA is required. The paper is organized in Sections 3 to 8 for the various design topics. In Section 2, the
framework used to account for cyclic loading in the soil behaviour is presented.
2 Cyclic loading and soil properties
2.1 Loading
Offshore structures are subjected to multi-directional loading F=[Fx,Fy,Fz,Mx,My,Mz] that may be separated into
average loads Fa, e.g. weight W' of the structure and the average components of the storm like wind and
currents, and cyclic loads Fcy, e.g. wave, ice and earthquake actions. The wave action will in addition cause cyclic
pressure variations Δpw,cy(x,y) on the seabed outside the structure. Reference is made to Figure 1.
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The real irregular cyclic load history is in the design normally simplified into a design composition with a certain
duration, e.g 100 year storm with 18 hrs. build-up and a 6 hrs. peak period. The cyclic loading within each period
is grouped into several (i..n) load packages at different load levels [Ni, fcy,i] with Ni being the number of cycles and
fcy,i (Fcy = Fcy/Fcy,max) the load level respectively for package i. Each cycle has a certain period Tp, typically 10-15
sec for wave loading and about 1 sec for earthquake loading.
y,N
a)
Fy , M y
Mz
Δpw(x,y)
b)
z
x, E
Fx , M x
Wave direction
Topside
Fz
Δpw(x,y)
c)
Fy , M y
y, N
τ
τa
τ
0
τcy
τ
τ
Δτa
0
0
0
time
τ
τa
0
Δτa
τcy
τa
Δτa
time
τcy
time
N
fcy= Fcy/Fcy,max
340
0.30
160
0.42
75
0.54
30
0.68
10
0.83
1
1.00
Figure 1. Example of geometry, wave loads and potential failure surface for a gravity offshore structure a) Plane
view b) z-y cross-section with simplified stress conditions c) Number of waves (N) of each load level (fcy > 0.3).
Figure 1 shows the geometry, the loading and a simplified picture of the shear stresses along a potential failure
surface for an offshore gravity base foundation. The average shear stress τa is composed of the initial shear
stress τ0 = 1/2σ'v0(1-K0) from the anisotropic in situ consolidation stresses and an additional shear stress Δτa =
f(Fa) induced by the average loading. The cyclic shear stress τcy = f(Fcy) is induced by the cyclic loading. The
initial shear stress τ0 has been acting under fully drained conditions while the additional average shear stress Δτa
and the cyclic shear stress τcy may in general act under partly drained conditions depending on drainage
conditions, loading rate and soil drainage characteristics.
2.2 Cyclic soil properties
A soil element subjected to cyclic loading will develop average ua and cyclic ucy excess pore pressure and
average γa and cyclic γcy shear strains that increase with number of cycles, as illustrated in Figure 2. Ultimately,
the strains will become very large (γa and/or γcy > 15 %) and the soil element is considered as failed.
Figure 2. Shear stress, shear strain and pore pressure during cyclic loading (Andersen, 2004)
The development of pore pressure and shear strain will depend on the combination of average τa and cyclic τcy
shear stresses. By running several laboratory tests with different combinations of τa and τcy, diagrams of the type
presented in Figure 3 may be established. The diagrams show the strain response after N=100 cycles for a soil
element in direct simple shear (DSS) and triaxial compression and extension mode of loading. It is seen that the
response depends on the stress path and the average shear stress τa. Similar diagrams may be established for
various number of cycles, e.g. N = 1, 10, 1000.
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1.0
N=100
γcy = 15%
τcy
τa
γcy,a
1
N=100
0.6
0.5
0.25
τcy/suC
τcy/suDSS
0.5
0.1
γa
γa
0.5
-4
a)
-0.4
1.0
τa/suDSS
=
5 1
0.5 0.25
0.1
0.05
5%
-1
-1
5
0.
.5
-0.2
0.0
γa
=
15
%
1
5
0 .2
0
%
15
5
3
1
2
0.5
0.25
=
0.2
0.0
0.0
0.0
15%
γ cy =
0.4
0.25
3
0.2
0.4 0.6
0.8
τa/suC
b)
Figure 3 Accumulated average shear strain and cyclic shear strain amplitude for combinations of average and
cyclic shear stresses. Example for DSS test (a) and triaxial compression and extension tests (b) on normally
consolidated Drammen Clay after N=100 cycles. (Andersen, 2004).
The cyclic shear strength is the maximum shear stress that can be mobilized, i.e. the sum of average and cyclic
shear stresses at failure (i.e. 15 % strain), τfcy = τa,f + τcy,f . The cyclic strength depends on the number of cycles
N, the average shear stress τa and the stress path α, i.e. τfcy = f(N, τa, α) and can be determined from the
diagrams in Figure 3 by reading out and calculating the sum of average and cyclic shear stresses at 15 % strain
for various values of τa. The diagrams in Figure 3 not only give information about the cyclic strength but also the
shear stress - shear strain relationship as a function of the cyclic shear stress. Examples are given in Figure 4.
TRIAX
N=10
1.0
1.0
0.0
0.2
0.8
0.8
0.4
τ cy/s u
= 0.0
0.2
0.4
τa/suDSS
0.6
τa/suC
DSS
DSS
N=10
0.4
0.2
Compr.
Extension
0.6
0.6
0.4
0.8
0.0
-0.2
C
τ cy/s u
= 0.4
0.2
0.2
0.0
-0.4
-12
0.0
-8
-4
0
0
4
γa (%)
a)
2
γa (%)
b)
4
6
Figure 4. Average shear stress - shear strain relationship as function of cyclic shear stress amplitude. Example
for triaxial tests (b) DSS (a) and on normally consolidated Drammen Clay after N=10 cycles. (Andersen, 2004).
The diagrams in Figures 3 and 4 give the soil behaviour for a cyclic load history with N cycles of constant cyclic
shear stress. In a storm, however, the cyclic shear stress is likely to vary from one cycle to the next, as seen from
Figure 1c. The equivalent number of cycles Neqv of the maximum cyclic shear stress that would give the same
effect as the real cyclic load history is therefore determined. For clays (i.e. undrained conditions), Neqv may be
determined by keeping track of the cyclic shear strain during the cyclic load history by the "strain accumulation"
procedure (e.g. Andersen et al., 1992). For sands (or conditions with drainage), Neqv can be determined by
keeping track of the permanent pore pressure accumulated during the cyclic load history (Jostad et al.,
1997;Andersen et al., 1994). The reason for using the pore pressure accumulation procedure for sand is that
some drainage is likely to occur during the load history in sand. It is assumed, however, that drainage does not
have time to occur within each cycle. To account for drainage, it is necessary to keep track of the accumulated
pore pressure.
1%3% 15%=γcy
0.5%
0.15
0.20
τa=0
0.25%
τcy/σvc’
τcy/σvc’
0.20
0.10
0.1%
0.10
up /σ
1
10
100
1000
10000
Number of cycles
0.0
0.1
vc ’=0
0.05
0.05
0.0
τa=0
0.15
1
10
Fail
u
0.5 re enve
lope
0.2
5
.05
100
1000 10000
Number of cycles
Figure 5. Contour diagram with cyclic shear strain (a) and accumulated pore pressure (b) as function of number
of cycles and cyclic shear stress. Example for DSS tests with τa = 0 on normally consolidated Drammen Clay
(Andersen, 2004).
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The accumulation procedures use strain or pore pressure contour diagrams of the type presented in Figure 5 and
storm load compositions of the type presented in Figure 1c. The diagrams in Figure 5 are established based on
the same laboratory tests that are used to establish the diagrams in Figure 3.
In principle a constitutive model could be formulated that follows each individual cycle and thus used in a time
series FE-analysis of the complete load history. At the present NGI does not have such a model for that purpose
that is sufficient robust and fits laboratory data accurately enough. Instead the relationships given in Figures 3, 4
and 5 are used in the constitutive models that are implemented into the FEM programs used for offshore
foundation design at NGI. Since the average shear stress and the cyclic strength are functions of the cyclic shear
stress, it is necessary to know the cyclic shear stress when entering the diagrams in Figures 3-5. This is done by
calculating the shear stresses in the soil as function of the cyclic loads Fcy. In FEA, iterations are performed to
update τa(τcy) as the τcy distribution changes.
3 Bearing capacity
Bearing capacity calculations are performed to check that the foundation can carry the design loads with an
adequate safety against failure or excessive deformations. Usually limit state design is used and different limit
states are considered, e.g. the 100-year storm load. Traditionally the limit equilibrium method (LEM) has been
used in such calculations, however FEA is increasingly used and has the advantages that more complex
geometries and loading may be accounted for, it is more rigorous and the governing failure mechanism is
identified automatically by the method, i.e. no search through possibly governing mechanisms is needed. In this
Section examples are given of the bearing capacity analyses for a concrete gravity base platform, the holding
capacity of a suction anchor and the capacity of a Jacket platform founded on bucket foundations.
3.1 Bearing capacity of a gravity base platform
The bearing capacity problem shown in Figure 1 was analysed using 3D FEA, a more detailed presentation is
given by Andresen et. al (2007). This concrete structure, used for storage and processing of Liquid Natural Gas
(LNG) is 200 m long, 100 m wide and 60 m high. The water depth is 25 m. Underneath the foundation base slab
a system of steel skirts are penetrated 1 m into the soil to prevent sliding along the seabed surface from being the
governing failure mechanism. The submerged weight W' in the operational condition including ballast is 2000 MN.
Trial analyses were run to identify the governing failure mechanism and the sufficient model dimensions. It was
important to minimize the model dimensions to obtain a fine mesh discretization with a reasonable computation
time (overnight). The Plaxis 3D Foundation program (Plaxis, 2008) was used with 9000 15-noded wedge
elements discretizing the soil and the foundation base slab.
The soil consists of a medium stiff clay layer to 5 m depth and then medium dense fine sand below the clay to
large depths. The effect of consolidation from the platform weight W' and the pore pressure build-up and partial
drainage during the storm are accounted for when assessing the strength. The strengths were assessed on the
basis of site specific laboratory tests and the storm composition shown in Figure 1c using the accumulation
procedures in Andersen et al. (1994). Only the waves with load level higher than 30 % of the maximum waves
were used as lower load was found to have no degrading effect on the strength. This resulted in Neqv = 10 and the
shear strength profiles shown in Figure 6b. The figure shows the cyclic shear strength for τa=0 for the clay layer
(layer II) and the sand layer (layer III) below the platform and outside of the platform. The wave loading is being
symmetrical with Fa = 0 which results in τa = 0 on the horizontal plane that constitutes nearly 90 % of the failure
mechanism. The strength below the platform is higher than outside because of the increased effective stresses
from the platform weight. The effect of the platform weight load spread (distribution of Δσ'v below the platform) is
accounted for by an approximated simple 1:3 rule as shown on Figure 6a.
+1.0
Found.
II-Out
-1.0
II-Below
-5.0
III-Below
Load
spread 1:3
-10.0
III-Out
a)
b)
Figure 6. (a) Cut into FE-model at one foundation corner showing the element discretization and the material
below the foundation and outside of the foundation. (b) Cyclic shear strength τf,cy profiles for triaxial compression
(TXC), direct simple shear (DSS) and triaxial extension (TXE).
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The resulting failure mechanism is shown in Figure 7, consisting mainly of sliding in y-direction along the top of
the weaker layer at 5 m depth. Passive and active earth pressures develop along the 200 wide and 5 m deep
windward and leeward planes. Side shear develops along the 100 m wide and 5 m deep side planes. This is the
main mechanism, however torsion, overturning moments and the uneven distribution of seabed pressure also
affect the mechanism. Figure 7a shows that the torsion causes some rotation of the foundation.
z
y
x
Gravity Base
Foundation
Fy
a)
Failure surface
b)
Figure 7. Failure mechanism depicted as contour shadings of displacements at failure. a) Top view showing
rotational displacements caused by the torsion moment. b) z-y cross section.
3.2 Discretization error
Capacity calculations with the FEM will always contain discretization errors, i.e. there will be an overshoot in the
calculated ultimate capacity. This error is a result of representing a continuous variable by a finite number of
element interpolations. The discretization error can be reduced by using a finer mesh, with the penalty of an
increased computational cost. It is not possible to quantify the error from the result of one run with only one mesh
realization, and one must then often rely on experience from similar problems to judge if the discretization error is
acceptable.
For the problem presented in section 3.1 the discretization error was quantified by calculating the horizontal load
capacity with the same FE model but with different meshes with varying number of elements. The results are
shown in Figure 8. It is seen that by increasing the number of elements (reducing the average element size AES)
the calculated capacity is reduced. It is possible to fit a curve to the results which can be extrapolated to AES = 0
(infinite number of elements) where the discretization error vanishes.
400
380
370
360
350
340
320
310
9 720 El.
16 480 El.
330
42 354 El.
Horizontal Capacity (MN)
390
300
0
0.5
1
1.5
2
2.5
3
Average Element Size, AES (m)
Figure 8. Horizontal load capacity calculated by FEA using the same model but with varying number of elements.
The dotted curve represents a proposed extrapolation towards AES= 0.
The example from section 3.1 demonstrates that 3D FEA are suited for calculating bearing capacities of offshore
foundations with multidirectional loading and complex geometries such as skirted bases. However, one should be
aware that there may be a need for a very fine mesh discretization to avoid overshoot. Furthermore, care should
be taken as little experience and only limited validation examples exist for the application of 3D FEA to such
problems.
3.3 Holding capacity of suction anchors
An industry sponsored study on the design and analysis of deepwater anchors in soft clay was completed in
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2003, where NGI participated together with OTRC in the USA and COFS in Australia (Andersen et al., 2005). In
this study, independent 3D finite element analyses for several hypothetical cases were performed by NGI, COFS
and OTRC.
One case, C2, consisted of an anchor with weight W' = 300 kN, diameter B = 5 m and depth D = 7.5 m, giving a
DSS
C
DSS
E
DSS
= 1.25·z, su = 1.2· su , su = 0.8· su
and
depth to diameter ratio D/B = 1.5. The soil strength data was: su
with su along the outside skirt wall equal to 0.65·suDSS. Figure 9a shows holding capacities for this case
calculated by the three different groups for various load angles from pure horizontal to pure vertical loading. In
each case the load is attached to the anchor in the optimal attachment point such that the anchor is prevented
from rotating.
3000
2500
Vf (kN)
2000
α = 600
1500
α = 450
1000
α = 300
NGI 3D FE
500
OTRC 3D FE
UWA 3D FE
0
0
a)
500
1000
1500
2000
Hf (kN)
b)
Figure 9. Holding capacities of a suction anchor calculated by 3D FEA a) Capacities for the optimal loading point
calculated for various combinations of horizontal H and vertical V loads. b) Deformed mesh and contour shadings
o
of displacements illustrating the failure mechanism for the case C2 with 45 loading angle.
o
Figure 9b shows the failure mechanism for load angle 45 calculated by Bifurc 3D (NGI, 1999). The mechanism is
illustrated by the deformed mesh and the contour shadings of displacements at failure. It is seen that the anchor
is not rotating and that the mechanism involves some of the soil underneath the skirt tip-level.
The overall conclusion from this study was that the 3D FEA results were in good agreement. The difference in
capacity calculated by the different groups was generally less than 3 % and the capacities were about 10 %
higher than NGI's results obtained from using limiting equilibrium methods. Hence, it was demonstrated that by
3D FEA, less conservative and reliable results were obtained. From this and other studies it is found that it is
important to model the reduced undrained shear strength along the outside skirt adequately. It is also proven to
be very efficient to use special zero thickness interface elements along the skirt outside and underneath the skirt
tip. If such elements are not used, it may be necessary to use an extremely fine mesh discretization in these
areas to allow for a possible full slip between the anchor and the soil.
3.4 Capacity of the Draupner Jacket foundations
The Draupner-E platform is a steel jacket located 160 km offshore Norway at water depth of 70 m (Tjelta, 1995).
Unlike most jacket platforms, which are founded on piles, Draupner is founded on steel bucket foundations, see
Figure 10a.
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Pull out force (MN)
100
20 MN/s
200 MN/s
80
Dense
sand
40
20
1·10-5 MN/s (Drained)
0
a)
b)
0.2 MN/s
60
10
20
30
40
50
Displacement (cm)
Figure 10. a) The Draupner jacket being lifted onto a barge (photo by Statoil). b) Uplift capacity of a bucket
anchor versus vertical displacement for different loading rates calculated by a fully coupled FEA.
The four circular foundations each of 12 m diameter are equipped with 40 mm thick steel skirts that are
penetrated 6 m into the seabed by undepressure. The soil conditions consist of very dense sand with relative
density Dr in the range 90-100% in the top 23 m.
While clay generally is undrained during a typical storm history, sand may be fully drained during changes in the
average load at the same time as it is undrained during short term single wave cycles. The long term drained
vertical uplift capacity of these foundations is therefore quite low and consists only of drained inside and outside
wall friction. However, the capacity for the short duration (Tp ~ 11 sec) wave load with a typical rate of 0.2 MN/s is
much higher as illustrated in Figure 10b.
NGI has implemented a special constitutive model for the analysis of such jackets with skirted foundations in
sand into the in-house finite element program Bifurc (NGI, 1999). The main parameter in this model is the
accumulated pore pressure ua as function of the cyclic shear stress amplitude τcy and number of cycles N. The
soil response for average load Fa is calculated using the mobilized friction model (Nordal et al., 1989). The
accumulated pore pressure is calculated based on the cyclic shear stress amplitude τcy(x) calculated from the
cyclic loads Fcy in a separate analysis with input of the actual equivalent number of cycles in each integration
point Neq(x). The equivalent number of cycles is found from pore pressure contour diagrams of the type shown in
Figure 5 b.
By using this constitutive model together with a coupled stress equilibrium and pore water flow (consolidation)
finite element formulation, it is possible to analyze pore pressure accumulation and dissipation problems. The
procedure is described in more detail in Jostad et al. (1997). As a validation of the procedure the response of a
bucket foundation resembling the ones for the Draupner platform was calculated. The average vertical load on
each foundation prior to the storm loading is 10 MN. Figure 11 shows the idealized cyclic load history, with
increasing average Va and cyclic Vcy vertical load, and the calculated vertical displacements (maximum, minimum
and permanent) during a 6 hours peak design storm period. The results are for the skirted foundation that
experience increased average vertical load during the storm (leeward leg). The horizontal load component is
assumed to be taken by the less mobilized foundations. It is seen that the failure mode is development of large
vertical settlements.
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Vertical load, V (MN)
60
Vmax
40
Va
20
Vcy
0
Vmin
Time (sec)
-20
0
5000
10000
15000
20000
0
5000
10000
15000
20000
Vertical displac. (cm)
0.0
-40
25000
30000
max/min
-60
-5.0
-10.0
25000
30000
Permanent
displacement
-15.0
Figure 11. Idealized cyclic vertical load history and calculated vertical displacements of leeward leg of a Jacket
during a 6 hours peak storm period.
4 Installation
Suction anchors and skirted gravity base foundations have steel or concrete skirts that protrude into the soil
during installation. The skirts are penetrated down into the soil by the weight of the structure or by a combination
of the self weight and an applied underpressure under the base. The installation method and process affect
important aspects of the design such as the penetration resistance, the distribution of contact stresses between
the foundation structure and the soil and the shear strength along the skirts (friction capacity of the skirts).
Numerical analysis of installation processes such as the penetration of a steel skirt into the seabed is extremely
challenging. Ideally the analysis should account for large deformation, continuously changing contact area and
remoulding of the soil. Methods that handle large deformation such as the Updated Lagrangian (UL) or the
Material Point Method (MPM) (Coetzee et al., 2005; Beuth et al., 2007) are promising but still under development
and not used regularly in design practise. In this Section results are presented from a study where small- and
large deformation FEA were carried out to study how the soil displaced by a penetrating skirt may affect the
horizontal stresses along the outside skirt wall.
4.1 Set-up effect along bucket anchor outside skirt wall
An important part of bucket anchor design in clay is the determination of the shear strength along the outside skirt
wall in the operational condition. This shear strength is affected by the horizontal stress increase due to soil being
displaced outward from the advancing skirt tip during installation. The strength is also highly affected by the
sensitivity of the clay, the dissipation of excess pore pressures with time and thixotropy as shown by Andersen
and Jostad (2002). The strength increases with time and this effect is often referred to as set-up.
During self-weight penetration, a significant part of the soil displaced by the skirt will move outside the skirt wall,
as for driven piles. When underpressure is applied, however, most of the clay displaced by the skirt is expected to
move into the anchor. The outward soil movement during weight penetration will cause a significant increase in
the horizontal stress outside the skirt wall, whereas the movement of soil into the anchor during underpressure
penetration may give significantly smaller horizontal stress build up, or even stress reduction.
The soil movements and horizontal stress build-up were studied by a small deformation stepwise geometry
update FEA procedure for both a flat and a tapered skirt tip by Andersen et al. (2004), using the Plaxis program.
Later this process has been studied more in detail at NGI by large deformation FE analyses with the ABAQUS
and Plaxis programs using the Updated Lagrangian method. An example of a FE-model from these studies is
shown in Figure 12a. The anchor has a diameter D = 5.5 m, skirt thickness t = 0.05 m, penetration depth Z = 16
m and a tapered tip. Interface elements were used to model the disturbed zone of clay between the "intact" clay
and steel skirt and in the interfaces between the clay and the skirt tip. An undrained shear strength profile su = 2.0
+ 1.25·depth (kPa) was modelled.
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1/2D
3D
Anchor
D = 5.5 m
Z = 16 m
t = 0.05 m
Interface
elements
skirt
wall
skirt tip
Entire mesh
Detail of skirt tip
a)
b)
Figure 12. a) Finite element model of installation of bucket anchor with tapered skirt tip. b) Vectors of horizontal
displacements around a tapered skirt tip during penetration by underpressure.
To model accurately both the in- and outside skirt friction and the skirt tip bearing capacity a mesh with extreme
refinement and interface elements around the skirt tip was used. For the mesh shown in Figure 12a the ratio
between the model width (20 m) and the skirt thickness (0.05 m) is about 400. The ratio between the dimensions
of the largest and smallest element in the mesh is about the same.
Figure 12b shows vectors of horizontal displacements around the tapered skirt tip during penetration at 14 m
depth. It is seen that the soil along the tapered part of the skirt moves outside the skirt wall. However, the
underpressure causes a portion of the soil to move inside the skirt at some depth below the advancing skirt tip.
The soil being continuously moved outside of the advancing tip during penetration is causing a stress build-up
along the skirt outside wall. Figure 13a shows contours of added horizontal stress in the vicinity of the skirt tip for
a case with self weight penetration.
Distance from skirt inside (m)
40
2-3
30
a)
Δσmean (kPa)
Depth (m)
3-4
4-5
7-8
6-7
self-weight
20
10
0
suction
-10
5-6
Δσh/su
Flat tip
Tapered tip
-20
-30
b)
Depth = 13.7 m
su = 17.1 kPa
2
4
6
Radius (m)
8
10
Figure 13. a) Build-up of horizontal stress outside the tapered skirt tip during self weight penetration. Contours of
increase in horizontal stress Δσh normalised with the undrained shear strength su. b) Mean stress distribution
outside the skirt wall at 13.7 m depth for the skirt being penetrated to its final depth of 16 m depth.
In Figure 13b the permanent stress change, after final penetration, outside the skirt wall is shown. There is a
significant permanent stress increase outside the skirt wall for self-weight penetration whereas there is a stress
reduction for penetration by underpressure. Using a tapered skirt tip gives only a slightly different stress
response. The results from the small strain stepwise updated geometry procedure (Andersen et. al, 2004) agreed
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very well with results obtained with large deformation Updated Lagrangian analyses.
5 Foundation stiffness
The assessment of the foundation stiffness and the cyclic displacements are important topics in the design of
foundations for offshore structures. The maximum cyclic displacement amplitudes in a storm may be of interest
for e.g. the design of pipelines connected to the foundation, and the foundation stiffness may be used in the
dynamic analyses carried out for the structural design of the platform superstructure (shafts or legs and topside).
5.1 Rotational stiffness of the Troll-A platform
The Troll A platform is a huge concrete gravity base structure located in the Norwegian trench at water depth of
305m. The platform was installed in 1995. The foundation design performed by NGI is described in Hansen et al.
(1992).
36 m
303 m
The foundation rotational stiffness and cyclic displacements during storm have been calculated using the NGI inhouse FE code INFIDEL (NGI, 1991) and the ABAQUS FE-program. The platform and the FE model of its
foundation are shown in Figure 14. Symmetry and anti-symmetry were utilised and an one-quarter model of the
foundation including the four shafts, the nineteen concrete caissons and the 36 m deep concrete skirts protruding
into the subsoil was established. The soil layering is shown with different colours down to 100 m. Infinite boundary
elements with initial stiffness (not shown) are used around the model periphery. The FE- one quarter model has
1.3 million degrees of freedom.
Figure 14. The Troll-A platform with its concrete gravity base structure and an ABAQUS model for calculation of
the rotational stiffness of the foundation.
The stiffness is calculated for various stages of cyclic loading, i.e. one cycle of the maximum wave (N=1) or 300
cycles of the maximum wave (N=300). Figure 15a shows the calculated normalised platform rotation as a function
of the normalised overturning moment and Figure 15b shows the secant rotational (rocking) stiffness during the
moment loading. Note that the rotational stiffness represents the cyclic displacement amplitude during the
maximum wave as a function of the maximum wave load amplitude and is thus not the load displacement
behaviour in individual cycles. Because the soil is degraded during repeated cyclic loading, the stiffness is lower
for the 100-year design storm (N=300) than during the application of one cycle (N=1). Non-linear stress-strain
relationships of the types shown in Figure 4 for the relevant N and τa were used to obtain the results shown in
Figure 15.
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N=1
N = 300
0.6
0.4
0.2
0.2
a)
Norm. rotational stiffness K/Kmax
Norm. overturning moment - OTM, M/Mmax
0.8
0.4
0.6
0.8
1.0
N=1
0.8
N = 300
0.6
0.4
1.0
Norm. rotation (θ/θmax)
b)
0.2
0.4
0.6
0.8
Norm. overturning moment - OTM, M/Mdesign
1.0
Figure 15. Relationship of amplitudes of moment and rotation (a) and secant rotational stiffness as function of the
overturning moment caused by the maximum wave in a storm. (b) During installation (N=1), and maximum wave
at the end of the 100-year design storm (N=300).
160 m
In some cases the foundation may be regarded as rigid compared to the soil stiffness, those cases do not require
any sophisticated modelling of the structure. However, in other cases there may be considerably flexibility in the
structure and in its foundations. In these cases it may be necessary to perform a more sophisticated SoilStructure-Interaction (SSI) analysis with realistic representation of the structure geometry and stiffness. Figure 16
shows an example where the flexibility of the structure relative to the soil is significant and where a full SSI
analysis has been performed. The figure shows the rotation and contour shadings of deformation during
application of the maximum wave moment.
Shafts
36 m
deep
skirts
Figure 16. Deformed mesh and contour shadings of deformation during maximum wave loading from the
ABAQUS model of the Troll-A platform.
5.2 Rotational stiffness of the Shah Deniz “jack up” foundations
The Shah Deniz platform is a permanent steel jack up unit (TPG500 concept from Technip) located in the
Caspian Sea at water depth about 100 m. The jack up legs are founded on large steel bucket foundations as
shown in Figure 17. The three foundations are 30 m in diameter and equipped with corrugated steel skirts that
are penetrated 9 m into the seabed. The soil conditions are mainly sand down to 18 m depth and clay
underneath.
The load distribution between the legs and the maximum leg-moment during a storm is highly dependent on the
rotational stiffness (fixity) of the foundations. An increased fixity reduces the leg-moment and also the lateral
displacement of the topside. The dynamic load amplification is also dependent on the dynamic foundation
stiffness. The assessment of the static and dynamic foundation stiffness was therefore a key activity in the design
of both the platform and its foundations. A complicating factor was that the large diameter foundations, and in
particular the top plates, were quite flexible relative to the soil.
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u(x,y)
Foundation
125m
30 m
SAND
9m
CLAY
30m
a)
b)
Figure 17. A "jack up" platform (a) and the FE-model (b) of one of its 30 m diameter bucket foundation embedded
9 m.
The foundation stiffness was calculated by 3D FEA using the Bifurc 3D (NGI, 1999) in-house program. Non-linear
elastic stress-strain relationships of the types shown in Figure 4 were used for both the average Ma and the cyclic
Mcy moment loading. Figure 17b shows the 3D FE-model. The foundation was modelled with shell elements with
interface elements below the top plate and along the in- and outside of the skirt walls. Prescribed displacements
were applied over the top plate. Because of the highly non-linear behaviour, an iterative procedure was used
where the deflection pattern u(x,y) of the foundation top plate was calculated by the Technip structural engineers
based on soil springs calculated by NGI.
6 Consolidation settlements
Foundation design generally involves establishing the time-settlement relationship during the lifetime of the
structure. This becomes especially important for gravity base platforms on clay where the high weight can cause
substantial settlements and the low permeability may cause the consolidation process to last several years.
6.1 Time-settlement for a gravity base platform
In this Section an example is given for the FE - analysis of the time-settlement relationship for a gravity base
platform and for the seabed in the vicinity of the platform. The settlement of the seabed was used as input in the
design of a pipeline connection to the platform.
The input data for the analysis is the geometry, soil layering, soil permeability and stiffness, drainage conditions
and the load history. The permeability and the stiffness are both stress dependent. Cam-clay type of models like
the one shown in Figure 18a are well suited for representing the stress dependent stiffness and have memory
that accounts for the preconsolidation stress.
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κ*
Base
stress (kPa)
Base effective stress(kPa)
ln σ'
oct,c ln[p’ln σ'oct
ln[p
p]
κ*
virgine
loading
1 cycle on/off loading
200
1 cycle on/off loading
160
120
Loading history
1 year
loading history
80
40
0
0
0.2
100
200
300
400
Time (days)
Time (days)
Settlement
(m)
Settlement (m)
0.0
unloading/
reloading λ*
a)
εvol = εv + 2εh
b)
Seabed
-0.2
20 m off
15 m off
10 m off
5 m off
-0.4
1st
1 yr.year
resultsresults
st
-0.6
GBS
GBS
-0.8
Figure 18. a) Cam-clay type of stress-strain relationship. b) 1st year loading history and vertical settlements for a
gravity base platform (GBS) and nearby seabed calculated by FEA.
Figure 18b shows the 1st year load history and calculated settlements for the gravity base platform (GBS) and for
points on the seabed being 5, 10, 15 and 20 m off the platform. The fully coupled pore pressure dissipation and
equilibrium analyses were performed using the Plaxis FE-program with a cam-clay type material model. The load
history reflects the gradually increasing ballast weight during the first 90 days after installation. One cycle of onand off-loading represents the situation where the platform is filled to maximum weight with liquid natural gas and
then off-loaded to the average weight. It is seen that the platform settles about 80 cm during the first year while
the seabed settles 10-20 cm. The pipeline connection was then designed for a relative settlement of 70 cm over
the nearest 20 m from the platform. Other important components contributing to the total settlement of offshore
foundations like immediate settlements, creep and effects of cyclic loading are not considered here.
7 Soil reaction distributions
For the structural design of the foundations, the distribution of reaction stresses on the foundation for the different
loading conditions must be known. Aspects that are of particular interest may be the distribution of contact stress
underneath the base and how large part of the load is carried by the skirt wall and skirt tip compared to the base.
Normally soil reactions are provided to the structural engineers in the form of a number of possible distribution
diagrams for a set of unit load cases. There are aspects such as uneven seabed, installation effects and
redistribution with time that makes it very difficult to accurately calculate reliable distributions. The reactions are
therefore in most cases based on engineering judgement and conservative estimates in order to provide a robust
structural design. FEA may, however, provide valuable insight into the mechanisms of load transfer between the
foundation and the soil. For skirted gravity base foundations such as the one shown in Figure 19a, the main
interest is to assess the fraction of the submerged weight carried by base contact stresses, skirt friction and skirt
tip resistance respectively. A reasonable estimate may be provided by applying the submerged weight W' to a FE
model such as the one shown in Figure 19a for the subsoil and the foundation with base and skirts.
7.1 Redistribution during cyclic loading
The loads will, however, redistribute with time. During cyclic loading there will be a tendency for redistributing
weight from the skirts to the base. This is due to the degradation of strength and stiffness for combinations of
average stress (caused by the weight) and cyclic stress. A constitutive model for cyclic loading has been
developed at NGI where the input is diagrams of the type shown in Figure 4. This model has been used in FEA of
this load transfer mechanism from skirt to base. The mechanism is illustrated in Figure 19b. The soil below the
skirt tip is highly mobilised due to weight loading and has to reduce the average stresses (weight) when the cyclic
stresses increase. Other parts of the foundation, such as the base, are less mobilised by weight loading and may
increase both the cyclic and the average stresses, i.e. carry more of the weight.
3259
a)
b)
c)
Vcy
τa(w')
SOIL
1.0
1
0.8
τa/suDSS
STRUCTURE
d)
1.0
DSS
w'
τcy/s u
= 0.0
0.4
w' + vcy
0.6
0.8
0.4
0.6
S
DS
τ cy/s u
w' + vcy
w'
= 0.0
0.4
0.8
0.4
0.2
0.2
2
1
2
0.8
τa/suDSS
w'
0
2
4
γa(%)
6
0
2
4
γa(%)
6
Figure 19. Ilustration of redistribution of average stress from a skirted GBS foundation during cyclic loading. a)
FE-model b) Consentration of average shear stress under the tip after application of weight loading W' c)
Reduction of average stresses (weight) under skirt tip d) Increase of average stresses (weight) underneath the
base during combination of weight W' and cyclic loading Vcy.
8 Soil-Structure-Interaction (SSI)
Structural design of offshore platforms is often based on highly simplified uncoupled foundation behaviour. In
reality there may be a large degree of interaction between the behaviour of the soil, the foundations and the
superstructure. In some cases, and in particular for quite flexible structures such as jack up's, there is a potential
benefit of accounting for this interaction. In this Section an example is given of a full SSI analysis of a jack up
platform using FEA.
8.1 Moment fixity of a Jack up platform
Normalized cyclic shear stress, ξ
Three legged jack up units founded on spud-cans are widely used offshore as mobile drilling units. In the
conventional design the spud-can reaction forces are obtained from a structural analysis with pinned footing
conditions. There is a potential benefit in accounting for the rotational stiffness of the footings as an increased
rotational stiffness will reduce the maximum bending moment, hull displacement and dynamic load amplification.
Accounting for vertical and horizontal flexibility of the footings will, on the other hand, have the opposite effect.
a)
b)
OCR = 40, Neqv = 10
OCR = 4, Neqv = 7
Cyclic shear strain, γcy
Figure 20 a) 20 m diameter skirted spud-can footing for jack up platform. b) Normalized cyclic shear stress versus
shear strain curves for the clay.
In Jostad et al. (1994) a FEA procedure is presented for an integrated analysis of a jack up platform and its soil
foundation system where the non-linear relationship between the spud-can displacements and reaction forces is
incorporated. Redistribution of the reaction forces between the spud-cans is allowed until the overall bearing
capacity of the jack up platform is reached. The procedure is based on the following:
1. The cyclic force displacement characteristics of the spud-can are calculated by FEA using the 3D code
INFIDEL (NGI, 1991) and stress-strain relationships of the type shown in Figure 4 or Figure 20b.
2. The 3D bearing capacity envelopes (V,H,M) are established by a limiting equilibrium analysis as proposed by
Andersen and Lauritzen (1988).
3. The cyclic force displacement curves and the bearing capacity envelopes are implemented into a non-linear
structural FE-program for the soil-structure-interaction analysis of the jack up.
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The potential benefit of the procedure was demonstrated by an example calculation (Jostad and Andersen, 2006)
of a three-legged jack up rig of the Gorilla Class installed in a stiff clay site at a water depth of 94 m. The rig has a
longitudinal leg spacing of 56 m and a transverse leg spacing of 64 m. The available leg length below the hull is
132 m. The weight of the platform during operation is 204 MN, which gives an average leg load of 68 MN. The
geometry of the spud-can including the proposed skirt configuration is shown in Figure 20 a. The moment fixity
was increased by equipping the footings with skirts that penetrate into the soil. The inner and outer circular skirts
are stiffened by 12 radial steel plates with thickness of 10 mm connected to the spud-can tip.
The design storm is a 6 hours storm with a 50 years return period. The equivalent maximum lumped
characteristic environmental load caused by waves, wind and current are 33.5 MN. The load accounts for
dynamic amplification assuming pinned footings. The stiff clay profile has an undrained average undrained shear
av
strength su of 60 kPa that is constant with depth. The overconsolidation ratio is 40 in the top 5 m and 4 below 5
m depth. By the strain accumulation procedure it is found that the equivalent number of cycles Neqv is about 10 for
the upper clay with OCR = 40 and about 7 for the clay below 5 m depth with OCR= 4. The corresponding
normalized cyclic stress-strain relationships are shown in Figure 20b.
The cyclic load-displacement relationships for the individual foundations are computed by the 3D finite element
program INFIDEL. Since the loads on the individual footings depend on both the stiffness of the structure and the
load path dependent non-linear stiffness of the individual footings, the analyses are performed by an integrated
SSI analyses as described in Jostad et al. (1994).
The main results from these SSI analyses are the maximum horizontal cyclic displacement component of the hull,
the critical moment in the leg and the global bearing capacity of the jack up platform as functions of the load
factor p multiplied to the characteristic environmental load. The analyses gave in addition displacements and
rotation of the individual footings and the corresponding reaction forces. Results for the windward and leeward
legs are shown in Figures 21a and b.
From Figure 21a it is seen that the load factor p where the moment in the lower leg guide become critical (i.e.
equal to 1 GNm) is increased by about 16% by equipping the spud-cans with skirts. The results without skirts are
in this case about the same as for pinned footings. Furthermore, it was found that by using skirts the global
bearing capacity of the jack up platform was increased by about 60%.
a)
b)
Figure 21 a) Calculated leg moment at the lower guides versus load factor for spud-can with and without skirts in
stiff clay. b) Cyclic horizontal footing load versus total vertical footing load for spud-can with skirts in clay when
loaded in the direction that gives one single leeward leg.
This type of analysis involving load path dependent non-linear analyses of embedded circular foundations in a
layered soil for all load levels including the combination of the average vertical load and the cyclic loads that
cause failure (large displacements) of the individual foundation, is practically impossible without using the finite
element method.
9 Final remarks
In this paper various topics within the design of foundations for offshore structures for hydrocarbon exploitation
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have been presented. The main difference between onshore and offshore foundation design is that the offshore
foundations are always subjected to cyclic loading which may cause soil strength and stiffness degradation.
A framework for accounting for the cyclic load history in determining the static and cyclic soil stress-strainstrength relationship has been developed at NGI and has been briefly presented in Section 2 in this paper. This
framework is validated by comparisons to field and laboratory model tests and prototype structures (e.g.
Andersen et al., 1989 and 1993) and has been used successfully in combination with limiting equilibrium and
finite element analyses in foundation design for numerous offshore structures safely operating all over the world.
The finite element method is increasingly used, offering several benefits over the limiting equilibrium method. In
this paper examples, within various design topics, are presented where FEA have proved to be favourable.
10 References
Andersen K.H., Dyvik R., Lauritzen R., Heien D., Hårvik L., Amundsen T. 1989. “Model tests on gravity platforms. II:
Interpretation. J. Geotech. Engrg., ASCE, 115, pp. 1550-1568
Andersen, K.H., Dyvik, R., Kikuchi, Y., Skomedal, E., 1992. ”Clay behaviour under irregular cyclic loading”. Proc. Int. Conf. on
the Behaviours of Offshore Structures, London, Vol.2., pp 937-950.
Andersen, K.H., Dyvik R., Schrøder K., Hansteen O.E and Bysveen S. 1993. Field tests of anchors in clay II: Predictions and
interpretation. J. Gecotech. Engrg., ASCE, 119, pp. 1532-1549.
Andersen, K.H., Allard, M.A., Hermstad, J., 1994. “Cetnrifuge model tests of a gravity platform on very dense sand; II:
Interpretation”. 7th Int. Conf. on Behaviour of Offshore Structures. BOSS’94. Cambrid
Andersen K.H. and H.P. Jostad. 2002. "Shear Strength Along Outside Wall of Suction Anchors in Clay after Installation". Proc.
12th Conf. ISOPE. 26-31 May. Kyushu. Japan.
Andersen, K.H. 2004. "Cyclic clay data for foundation design of strcutures subjected to wave loading". Keynote lecture: Proc.
Int. Conf. on "Cyclic Behaviour of Soils and Liquefaction Phenomena", CBS04, Bochum, Germany, pp. 371-387
Andersen K.H., L. Andresen, H.P. Jostad, E.C. Clukey. 2004. "Effect of skirt-tip geometry on set-up outside suction anchors in
soft clay". Proc. 23rd Int. Conf. Offshore Mech. Artic Eng. OMAE04. 20-25 June. Vancouver. BC Canada.
Andersen K.H., J.D. Murff, M.F. Randolph, E.C. Clukey, C. Ebrich, H.P. Jostad, B. Hansen, C. Aubeny, P. Sharma and C.
Supachawarote. 2005. "Suction anchors for deepwater applications". Keynote lecture: Int. Symp. on Frontiers in Offshore
Geotechnics, ISFOG. September 2005. Perth. Western Australia.
Andresen, L., Andersen K.H., Jostad H.P.J and Rahim A. 2007. "Bearing capacity of offshore gravity platforms by 3D FEM".
Proc. Num. Model. in Geomech. - NUMOGX, Rhodes, pp. 509-515
Beuth, L., Coetzee, C.J., Bonnier, P. and van den Berg, P. 2007. "Formulation and validation of a quasi-static material point
method." In 10th International Symposium on Numerical Methods in Geomechanics, 2007.
Coetzee, C.J., Vermeer, P.A., Basson, A.H. The modelling of anchors using the material point method. Interl J Numer Anal
Meth in Geomech., 29 (2005), 879-895
Hansen B., Nowacki F., Skomedal E and Hermstad J. 1992. ”Foundation design, Troll platform”, BOSS’92, London
Jostad, H.P., Andersen K.H., Tjelta T.I. 1997. ”Analyses of skirted foundations and anchors in sand subjected to cyclic loading”.
Proc. of BOSS’97 Behaviour of Offshore Structures, Vol. 1. pp. 149-162
Jostad, H.P., Andersen, K.H., 2006. ”Potential Benefits of Using Skirted Foundations for Jackup Platforms”. Proc. OTC 18016
Jostad, H.P., Nadim F., Andersen K.H. 1994. “A computational model for fixity of spud-cans on stiff clay”. Proc. BOSS’94
Behaviour of Offshore Structures, Vol. 1 Geotechnics, pp. 151-171
Nordal S., Jostad H.P., Kavli A., Grande L. 1989. ”A coulombian soil model applied to an offshore platform. Proc. 12th ICSMFE.
Rio de Janeiro.
Norwegian Geotechnical Institute (NGI). 1999. Bifurc-3D. "A finite element program for 3 dimensional geotechnical problems".
Report 514065-1. 31 December 1999.
Norwegian Geotechnical Institute (NGI). 1991. “Description of INFIDEL – A nonlinear 3D Finite Element Program”. NGI report
514093-3, Rev. 1.
Tjelta, T.I. 1995. “Geotechncial experience from the installation of the Europipe jacket with bucket foundations”. Proc. OTC
paper 7795. pp. 897-908
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