TWO AND THREE-DIMENSIONAL MODELING OF Claudio dos …

TWO AND THREE-DIMENSIONAL MODELING OF

BUCKET FOUNDATIONS FOR APPLICATION IN DEEP

WATER ANCHORING

Alvaro Maia da CostaClaudio dos Santos AmaralPETROBRAS/CENPES/DIPREX

Abstract - The giant oil reservoirs of PETROBRAS are located in waterdepth varying from 400 to 2500 m. In order to exploit oil in such water depthPETROBRAS developed the technology of Floating Production Platformsassociated with the application of flexible risers . These floating platformslike semi-submersibles (SS) and floating production storage and offloadingships (FPSO) are kept in position through mooring lines and anchors. Inorder to reduce the anchoring radius PETROBRAS introduced the newconcept of taut leg mooring lines using polyester fiber cables. For thisconcept because of vertical load components at the anchor position it ismandatory the application of piles. Due to the water depth these piles will bedriven by suction using the water column. This paper covers the applicationof two and three-dimensional (3D) finite element modeling to determine theholding capacity of such anchors or bucket foundations

INTRODUCTION

The use of piles made of open pipe pile with a length/diameter ratio over 10 iscommon practice in offshore engineering. Steam and oil pressure energy isnormally used for the driving hammers. Hydraulic hammers for underwateruse have been tested in a 1000 m water depth. Beyond this depth operationaland technical barriers could be prohibitive.

To overcome these technical barriers PETROBRAS is introducing a largediameter pipe pile that are suction driven. This new foundation type is

Transactions on the Built Environment vol 29, © 1997 WIT Press, www.witpress.com, ISSN 1743-3509

446 Offshore Engineering

earmarked for use at the fixed anchor points of the floating productionplatforms that will be installed at the continental slope in water depthsbetween 600 and 1800 m.

This technology has been extensively studied by NGI (NorwegianGeotechnical Institute) in multiclient projects cosponsored by PETROBRAS.

The topological difference between suction and impact driven piles is thelength/diameter ratio. Suction driving uses a maximum ratio between 2.0 and3.0 in function of the soil type.

The recommendations of the API code*, with the soil replaced by springs ofnon-linear behavior (P-y and T-z curves), are normally used to establish theload bearing capacity of long piles. Although the experience with fixedplatform foundations revealed serious flaws in the use of this methodology,off-shore platform specialists continue using it on a worldwide scale; some ofthe safety related distortions imposed by the simplifications of the method aremended through experience.

To find out the load bearing capacity of the suction driven piles, NGI use ananalytical method based upon the limit equilibrium and the finite-elementmethod. Field work done in the scope of the multiclient projects validatethese methods (Keaveny, 1991) *.

This paper covers the application of finite element method in order tosimulate the behavior of the suction driven piles at the operational phaseusing PETROBRAS developed simulators comparing the plane strain withthe three-dimensional solution.

ANALYSIS DATA AND GEOTECHNICAL PROPERTIES

In order to show the comparison between the results obtained by two andthree dimensional modeling it is analyzed the behavior of one of the buckedfoundations used as anchors of semi-submersibies at Campos Basin, in waterdepth of 600 m. The final pile loading was deduced from the environmentalload on the platforms and the operational conditions of the anchor system.

The pile dimensioning loads are the following:

- Horizontal component - 4976.5 KN- Vertical component - 4324 KN- Net vertical component (without the pile dead weight) - 3774 KN- Angle of elevation -41° (with horizontal plane)


Offshore Engineering 447

The final topology of the piles under study is:- Pile length - 13 meters- Pile diameter - 4.77 meters- Steel plate thickness - 1 1/2"- Padeye location - 8.5 meters below mudline

Following the geotechnical survey of the Campos Basin, (Costa & Amaral,1992) *, the soil at the anchor area is classified as normally consolidated claywith the following average undrained strength with depth:

- Su (KPa) = 5 + 2 * H, with- H (m), the depth below the sea floor- Total specific weight of clay = 17 KN/nf

The soil/pile contact strength is defined as the undrained strength of the soilmultiplied by an adhesion factor:

- T = a * Su (contact strength)- Adhesion coefficient oc = 0.5 during driving- Adhesion coefficient oc = 1 in operation

The elastic properties used in the model are defined as follows:

PARAMETERS OF THE CONTINUUM

- Su (KPa) = 5 + 2 * H- Esoil (KPa) = 650 * SU- v = 0.49

PARAMETERS OF THE SOIL/PILE CONTACT

-Thickness of the soil adhered to the pile is considered equal a 1.5", h =0.0381m

- CS (coefficient of tangential rigidity) = Gsoil/h = Esoil / 2 h (1+v) =650*Su/2.98

- CN (coefficient of normal rigidity) = Esoil/h

The calculation of skirt penetration resistance is commonly performed by NGIusing the static direct simple shear (sj), while for total load bearingcapacity of the pile they use the compressive undrained shear strength (su***)in the active side, the extension undrained shear strength (s«** ) in the passiveside and the simple undrained shear strength (sj") near the base of the pile.



Based on experience in North sea clays, NGI have proposed the correlationbelow:

sj** = 0.85s»™*

As no such tests were done for clays in Campos Basin, we decided toconsidered for this paper that the effective stress path and strength forundrained loading is independent of the way in which the load is applied. Forthe results presented here in only the compressive undrained shear strength isadopt.

FINITE ELEMENT MODELS OF ANALYSIS

Two models of analysis are considered. In the first one the soil-anchorinteraction is simulated by a three dimensional model, where the external soil,the pile and the soil plug is represented by brick elements of 20 nodes. Thesoil-pile contact is represented by special 3D interface elements. The secondmodel admits plane strain of pile and soil and seeks to find the load bearingcapacity of the pile under consideration of the vertical and horizontal loadcomponents. In both models it is considered the increase of the undrainedshear strength of the soil with depth.

As the analysis is done in undrained conditions, the total weight of soilcolumn and water depth integrate the initial stress condition in both models.

(1)

'o (2)

where:

Ov = total vertical stress;Oh = total horizontal stress;Yw = specific weight of the water;Ys = total specific weight of the soil;Zw= water depth;Zs= depth relative to the sea floor;KO = coefficient of lateral stress at rest.



Model 1 - Plain Strain StateIn this model, the soil and pile are represented by quadratic isoparametricelements of 8 nodes, and the contact soil/pile by interface elements of 6nodes. A total of 9714 elements and 29460 nodes are used. The generation offinite element mesh was done using Mtool that was developed byPETROBRAS/CENPES and PUC/TECGRAF. Figure 1 shows the discretemodel of analysis. In this model the load is applied at the node associatedwith the padeye connecting the mooring line that is located 8.5 meters belowmudline. The necessity of lowering the position of the padeye is related withthe soil pile interaction at the active side of the pile. Lowering the position ofthe padeye will rotate the pile under the environment loads and this conditionwill avoid the soil to separate from the pile, which would reduce the totalbearing capacity of the anchor, due to the elimination of the passive suctionphenomenon.

Figure 1 - Plane Strain Model

Model 2 -Three Dimensional ModelIn this model, the soil and pile are represented by brick isoparametricelements of 20 nodes, and the contact soil/pile by 3D interface elements of 16nodes. A total of 1916 elements and 8011 nodes are used. Figure 2 showsthe discrete model of analysis. In this model, like in model 1, the load isapplied at the node associated with the padeye connecting the mooring line,at a depth of 8.5 meters below mudline. The software PATRAN was used togenerate the 3D finite element mesh.



Figure 2 - Three-dimensional Model

ANALYSIS OF RESULTS

The numerical simulation are done using AEEPECD in plane strain model andAEEPEC3D in three-dimensional model (Costa, 1984) *. The criteria ofMohr Coulomb is used as plasticity law, considering angle of internal frictionequal to zero and cohesion equal to undrained shear strength. Under theseconditions, the yielding surface follows the Tresca model with the soil as anon-tension material.

The programs MVTEW and POS3D, both developed byPETROBRAS/CENPES and PUC/TECGRAF are used as post-processingtools for plane strain and three-dimensional analysis.

Plain Strain ModelIn this analysis, the horizontal and vertical working loading components areapplied to the pile in 30 increments; the difference between each increment is5% of the final project value.

The coefficient of rupture distribution and rupture mode are analyzed for eachincrement unto to point where kinematics conditions caused by the rupturecontour forward the breakdown of the foundation.

Figure 3 shows the distribution of the coefficient of rupture for the incrementcorresponding to 90% of the final project load. The graphic shows the decay



curve of the coefficient of rupture in function of the distance to the regionclose to the pile base, measured along an inclined plane that corresponds tothe favored breakdown plane of the foundation.

At each new load increment, the rupture contour at the foundation soilincreases in direction of the sea floor surface, as shown by the decay curve.At the area contained within the rupture contour, the coefficient of rupturehas a value equal to 1. An increase of the rupture surface at the active andpassive thrust zones of the pile and a higher mobilization of soil/pileinteraction at the active thrust zone are verified.

Figure 3 - Distribution of the coefficient of rupture at the incrementcorresponding 90% of the designing load

Analysis of the rupture contour evolution reveals that the necessarykinematics conditions for foundation breakdown are fulfilled when therupture contour reaches the surface.

Figure 4 shows the rupture line for the increment corresponding to 140% ofthe final project load.



Figure 4 - Distribution of the coefficient of rupture at theultimate load (140% of load)

It can be deducted from these results that a load 40% higher than the finalproject value is required to cause foundation breakdown. NGI recommendsthat three different undrained shear strength should be used in the loadbearing capacity calculation. At the active side of pile should be used thecompressive shear strength. At the passive side the extension undrained shearstrength and at the bottom the simple undrained shear strength, figure 5.When this anisotropy stress depended undrained shear strength is considered,the additional bearing capacity of 40% is no longer obtained. It should benoted that the plane strain model does not consider the soil/pile adherence atthe soil/pile interface perpendicular to the longitudinal axis of the model.Without a calibration by the three-dimensional model or experimental results,it is actually impossible to specify the resistance increase to be expected fromthis.



Figure 5 - Stress conditions along various parts of a failure surface

Three Dimensional ModelIn the three-dimensional analysis, the horizontal and vertical working loadingcomponents are applied to the pile in 14 increments; the difference betweeneach increment is 10% of the final project value

The coefficient of rupture distribution and rupture mode are analyzed for eachincrement unto to point where kinematics conditions caused by the rupturecontour forward the breakdown of the foundation.

Figure 6 shows the distribution of the coefficient of rupture for the incrementcorresponding to 90% of the final project load.

At each new load increment, the rupture contour at the foundation soilincreases in direction of the sea floor surface. At the area contained within therupture contour, the coefficient of rupture has a value equal to 1. An increaseof the rupture surface at the active and passive thrust zones of the pile and ahigher mobilization of soil/pile interaction at the active thrust zone areverified.



Figure 6 - Distribution of the coefficient of rupture at thecorresponding to 90% of the final project load

increment

Figure 7 shows the distribution of the coefficient of rupture for the incrementcorresponding to 140% of the final project load. It can be verified that thereis a reserve of bearing load capacity in comparison with plane strain statemodel, at the same increment.

Figure 7 - Distribution of the coefficient of rupture at the incrementcorresponding to 140% of the final project load along the verticalplane that is applied the load. In this figure it is shown thedeformed configuration of the pile.

Horizontal and Vertical Displacement ComparisonIn order to verify the difference between the results obtained by the planestrain and the three-dimensional models, in figures 8 and 9 are plotted thevertical and horizontal displacement at the position of the padeye. Althoughthe vertical displacement is similar in the two models, we can note that the 3D



model develops higher holding capacity at the horizontal direction, when iscompared with the plane strain model.

Qo

COLUQQ§

16.00 —i

12.00 —

8.00 —

4.00 —

0.00

THREE-DIMENSIONAL ANALYSISPLANE STRAIN ANALYSIS

I I I0.00 0.01 0.04

' I '0.02 0.03

VERTICAL DISPLACEMENT (METERS)Figure 8 - Evolution of the vertical displacement with load

I0.05

Q§

COUJo

0.000.00

I0.01 0.06

I ' I ' I T I '0.02 0.03 0.04 0.05

HORIZONTAL DISPLACEMENT (METROS)Figure 9 - Evolution of horizontal displacement with load

I0.07



CONCLUSION

The results obtained confirm that it is possible to simulate the soil/pileinteractive behavior of large diameter piles with a length/diameter ratio lowerthan 3, through application of the discussed numerical models. The behaviorof these kind of piles at suction driving and while operating as floatingplatform anchors can be derived through numerical simulation.

As could be expected the vertical holding capacity of the bucket foundation iswell represented by a two-dimensional (2D) model. For the horizontaldirection the 2D model shows a conservative result when compared to thethree-dimensional model. The results obtained by the 3D are being used tocalibrate the 2D model and for evaluating the soil reactions that are used inthe structural design of the pile.

PETROBRAS intends to use this technology in several platforms and startthe installation of the first piles in 1997. Suction driven piles as fixed points ofTaut Leg anchor systems will lead to a sensitive reduction in investment andoptimization of the submarine layouts at the new Campos Basin installations.

REFERENCES

[1] API (American Petroleum Institute) "Recommended Practice forPlanning, Designing an Constructing Fixed Offshore Platforms", APIRP2A,1993.

[2] Keaveny, J. M.,"JIP - Foundations for Subsea Systems, Mooring andAnchored Structures on Deepwater Sites - Field Tests an Analyses,Several Reports from NGF, 1991.

[3] Costa, A. M.; Amaral, C. S. & all, "Dados Geotecnicos da Bacia deCampos - Aquisifao , Compilagao e Interpreta ao, Campanha do NavioBucentaur", Internal Report, 1992.

[4] Costa, A M., "Uma Aplica ao de Metodos Computacionais e Principiosde Mecanica de Rochas no Projeto e Analise de Escavafoes Destinadas aMinerasao Subterranea", COPPE, Tese deMestrado,1984.


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TWO AND THREE-DIMENSIONAL MODELING OF Claudio dos …