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FiniteElementAnalysesinOffshoreFoundationDesign

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The 12th 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. Bearing capacity 2. Installation aspects 3. Foundation stiffness 4. Consolidation and settlements 5. Soil reactions against the structure 6. 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.

Fx , Mx

Fy , My

Mzx, E

y,N

Wave directionΔpw(x,y)z

Fz

y, N

Fy , MyΔpw(x,y)

τ0

ττcy

Δτa

time

τa

0τ0

ττcy

Δτa

time

τa

0

τ τcy

Δτatime

τa0

τ τcy

Δτatime

τa0

τ0

τ

τcy

Δτa timeτa

0τ0

τ

τcy

Δτa timeτa

0

Topside

a)

b)

1.001

0.8310

0.6830

0.5475

0.42160

0.30340

fcy= Fcy/Fcy,maxN

1.001

0.8310

0.6830

0.5475

0.42160

0.30340

fcy= Fcy/Fcy,maxNc)

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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a)

N=100

τ cy/s

uDS

S

τa/suDSS

0.50.00.0

0.5

0.25 0.5 1 2 3 5

0.1

1

0.5

0.25

3

γcy = 15%

γa = 15%

τa

τcyγcy,a

1.0

1.0

b)0.2-0.4 0.4 0.6 0.80.0-0.2

0.0

0.2

0.6

0.4

0.25

τa/suC

τ cy/s

uC

γcy = 15%γa = 15%

γ a= -1

5%

0.050.10.5

15

0.25 0

0.25 10.5-1.5-4

N=100

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.

a)

0.40.2

0.0

τcy/suC = 0.4

0.20.0

γa (%)0 4-4-8-12

TRIAXN=10

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Compr.Extension

τ a/s

uC

b) γa (%)4 620

DSSN=10

0.0

0.2

0.4

0.6

0.8

1.0τ a

/suD

SS

0.8

τcy/suDSS = 0.0

0.2

0.4

0.6

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.

3%

Number of cycles1 10 100 1000 10000

0.1%

0.25%

1%0.5%

15%=γcy τa=0

τ cy/σ

vc’

0.0

0.05

0.10

0.15

0.20 3%

Number of cycles1 10 100 1000 10000

0.1%

0.25%

1%0.5%

15%=γcy τa=0

τ cy/σ

vc’

0.0

0.05

0.10

0.15

0.20

τ cy/σ

vc’

0.0

0.05

0.10

0.15

0.20

10000Number of cycles

τ cy/σ

vc’

0.0

0.05

0.10

0.15

0.20

1 10 100 1000

τa=0Failure envelope

up/σ

vc ’=0.05

0.1

0.250.5

10000Number of cycles

τ cy/σ

vc’

0.0

0.05

0.10

0.15

0.20

1 10 100 1000

τa=0Failure envelope

up/σ

vc ’=0.05

0.1

0.250.5

Number of cycles

τ cy/σ

vc’

0.0

0.05

0.10

0.15

0.20

τ cy/σ

vc’

0.0

0.05

0.10

0.15

0.20

1 10 100 1000

τa=0Failure envelope

up/σ

vc ’=0.05

0.1

0.250.5

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.

a)

II-Below

III-Below

III-Out

II-Out

Found.+1.0

-1.0

-5.0

-10.0

Load spread 1:3

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.

a)

yz

x

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.

300

310

320

330

340

350

360

370

380

390

400

0 0.5 1 1.5 2 2.5 3

Average Element Size, AES (m)

Hor

izon

tal C

apac

ity (M

N)

42 354 El.

16 480 El.

9 720 El.

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

Gravity Base Foundation

Failure surface

Fy

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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 depth to diameter ratio D/B = 1.5. The soil strength data was: su

DSS = 1.25·z, suC = 1.2· su

DSS, suE = 0.8· su

DSS and 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.

a)

0

500

1000

1500

2000

2500

3000

0 500 1000 1500 2000

NGI 3D FEOTRC 3D FEUWA 3D FE

V f(k

N)

Hf (kN)

α = 450

α = 300

α = 600

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

of displacements illustrating the failure mechanism for the case C2 with 45o loading angle.

Figure 9b shows the failure mechanism for load angle 45o 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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a) b)

1·10-5 MN/s (Drained)

10 30 40 50200Displacement (cm)

Pul

l out

forc

e(M

N)

20

40

60

80

100

0.2 MN/s

20 MN/s

Densesand

200 MN/s

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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-60

-40

-20

0

20

40

60

0 5000 10000 15000 20000 25000 30000

Vmax

Vmin

Va

Vcy

-15.0

-10.0

-5.0

0.00 5000 10000 15000 20000 25000 30000

Time (sec)

Ver

tical

disp

lac.

(cm

)V

ertic

allo

ad, V

(MN

)

Permanent displacement

max/min

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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a)Entire mesh Detail of skirt tip

1/2D 3DAnchorD = 5.5 mZ = 16 mt = 0.05 m

skirt wall

Interface elements

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.

a)

7-86-7

5-6

4-5

3-42-3

Δσh/su

Dep

th (m

)

Distance from skirt inside (m)

b)

self-weight

suction

2 4 6 8 10-30

-10

0

30

20

40

10

-20

Radius (m)

Δσm

ean

(kPa

)

Flat tipTapered tipFlat tipTapered tip

Depth = 13.7 msu = 17.1 kPa

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

skirt tip

3255

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). The foundation rotational stiffness and cyclic displacements during storm have been calculated using the NGI in-house 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.

36 m

303

m

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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a) 0.2 0.4 0.6 0.8

0.4

0.6

0.8

0.2

Norm. rotation (θ/θmax)1.0

N = 1

N = 300

Nor

m. o

vertu

rnin

g m

omen

t -O

TM, M

/Mm

ax

b) 0.2 0.4 0.6 0.8

0.6

0.8

1.0

0.4

Norm. overturning moment - OTM, M/Mdesign

Nor

m. r

otat

iona

l stif

fnes

s K

/Km

ax

1.0

N = 1

N = 300

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).

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 Soil-Structure-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

160

m

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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a)

30m

9m

30m

9m

125m

b)

CLAY

SAND

Foundation

u(x,y)

30 m

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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a) εvol = εv + 2εh

ln[p’

λ*

κ*

κ*

ln[pp]

ln σ'oct

unloading/reloading

virgineloading

ln σ'oct,c

b)

0 100 200 300 400Time (days)

0

40

80

120

160

200

Bas

e ef

fect

ive

stre

ss(k

Pa)

-0.8

-0.6

-0.4

-0.2

0.0

0.2

Set

tlem

ent (

m)

5 m off10 m off

15 m off20 m off

GBS

Loading history

1 cycle on/off loading

1st yr. results

1 year loading history

1 cycle on/off loading

1st year results

Base

stre

ss (k

Pa)

Settl

emen

t (m

)

GBS

Time (days)

Seabed

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 on- and 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.

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w'

Vcy

22

11

a) b)

τ a(w

')

STRUCTURE

SOIL

τ a/s

uDS

S

γa(%)

τcy/suDSS = 0.0

0.2

0.4

0.6

0.8

1.0

0.4

0.8

20 64

τ a/s

uDS

S

γa(%)

τcy/suDSS = 0.0

0.2

0.4

0.6

0.8

1.0

0.4

0.8

20 64

11

w' + vcy

22

w' + vcy w'

w'

c) d)

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 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

Nor

mal

ized

cycl

icsh

ears

tress

, ξ

Cyclic shear strain, γcy

OCR = 40, Neqv = 10

OCR = 4, Neqv = 7

Nor

mal

ized

cycl

icsh

ears

tress

, ξ

Cyclic shear strain, γcy

OCR = 40, Neqv = 10

OCR = 4, Neqv = 7

Nor

mal

ized

cycl

icsh

ears

tress

, ξ

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 strength su

av 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-strain-strength 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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