Drag Anchor Fluke
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Bransby & O’Neill: Drag anchor fluke-soil interaction in clays 1 Drag anchor fluke-soil interaction in clays M.F. Bransby & M.P. O’Neill Centre for Offshore Foundation Systems, The University of Western Australia, W.A., Australia ABSTRACT: Finite element analysis of the fluke-soil interaction behaviour of drag anchors in undrained soil has allowed calculation of plastic yield loci for characterisation of fluke failure states. The yield loci produced are examined in terms of soil deformation mechanisms and kinematics and are incorporated into a novel method for drag anchor design. 1 INTRODUCTION The movement to offshore developments in deeper water has led to increasing reliance on offshore structures which are tethered to the seabed rather than resting upon it. In addition, these are often re- quired to be anchored in soft, normally consolidated silts and clays. One common seabed mooring system is the drag anchor and chain system (Figure 1). The anchor is lowered to the seabed surface and then installed into the seabed by dragging the chain laterally. Due to the shape of the anchor, kinematics govern so that it must embed during displacement and hence signifi- cant holding capacity may be achieved. Most hold- ing capacity is achieved by soil resistance against the fluke, but the kinematics are controlled by the length of the shank and the orientation of the shank with respect to the fluke. The use of drag anchors in offshore mooring sys- tems requires knowledge about the anchor’s holding capacity, embedment depth and drag length required for mobilisation of the working load. These all vary for different soil conditions and drag anchor designs. Historically, drag anchor design has been empiri- cally based (Vryhof Anchors, 1990). More recently, Figure 1. Drag anchor and chain system approaches have been introduced which seek to pre- dict the entire drag trajectory of an anchor from in- stallation to mobilisation of working load capacity (Neubecker and Randolph, 1996; O’Neill and Randolph, 1997; Thorne, 1998). These approaches are based on combined kinematic and equilibrium analyses. They use basic geomechanics principles to find the geotechnical resistive loads acting on the anchor in the equilibrium solution and simple as- sumptions about the anchor movement in the kine- matic solution. The above design approaches use empiricism for solution (for example, the anchor form factor f, Neubecker and Randolph, 1996). There appears to be room for non-empirical prediction methods using basic soil mechanics. When drag anchor holding capacity is approached in soft undrained soils, soil failure consists of local plastic flow around the fluke and shank. Thus, the behaviour will be independent of the orientation of the anchor with respect to the soil surface and so analysis of the soil around the fluke will lead to in- sight about the general anchor behaviour. This paper presents analysis of the soil around anchor flukes using finite element analysis. The work allows investigation of the anchor under gen- eral loading conditions and the behaviour has been characterised in terms of a plastic yield envelope. The findings can be used to validate previous design methods (e.g. Neubecker and Randolph, 1996) or alternatively will lead to novel numerical design methods using the yield envelope approach which are introduced briefly. 2 PLASTICITY CONCEPTS AND THE YIELD LOCUS Recently, the analysis of offshore foundations such
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Drag Anchor Fluke
Transcript of Drag Anchor Fluke
Bransby & ONeill: Drag anchor fluke-soil interaction in clays 1Drag anchor fluke-soil interaction in claysM.F. Bransby & M.P. ONeillCentre for Offshore Foundation Systems, The University of Western Australia, W.A., AustraliaABSTRACT: Finite element analysis of the fluke-soil interaction behaviour of drag anchors in undrained soilhas allowed calculation of plastic yield loci for characterisation of fluke failure states. The yield loci producedareexaminedintermsofsoildeformationmechanismsandkinematicsandareincorporatedintoanovelmethod for drag anchor design.1 INTRODUCTIONThemovementtooffshoredevelopmentsindeeperwaterhasledtoincreasingrelianceonoffshorestructureswhicharetetheredtotheseabedratherthanrestinguponit.Inaddition,theseareoftenre-quired to be anchored in soft, normally consolidatedsilts and clays.Onecommonseabedmooringsystemisthedraganchorandchainsystem(Figure1).Theanchorislowered to the seabed surface and then installed intothe seabed by dragging the chain laterally. Due to theshapeoftheanchor,kinematicsgovernsothatitmustembedduringdisplacementandhencesignifi-cantholdingcapacitymaybeachieved.Mosthold-ing capacity is achieved by soil resistance against thefluke, but the kinematics are controlled by the lengthoftheshankandtheorientationoftheshankwithrespect to the fluke.The use of drag anchors in offshore mooring sys-tems requires knowledge about the anchors holdingcapacity, embedment depth and drag length requiredfor mobilisationoftheworkingload.Theseallvaryfor different soil conditions and drag anchor designs.Historically, drag anchor design has been empiri-cally based (Vryhof Anchors, 1990). More recently,Figure 1. Drag anchor and chain systemapproaches have been introduced which seek to pre-dicttheentiredragtrajectoryofananchorfromin-stallationtomobilisationofworkingloadcapacity(NeubeckerandRandolph,1996;ONeillandRandolph,1997;Thorne,1998).Theseapproachesarebasedoncombinedkinematicandequilibriumanalyses. They use basic geomechanics principles tofindthegeotechnicalresistiveloadsactingontheanchorintheequilibriumsolutionandsimpleas-sumptionsabouttheanchormovementinthekine-matic solution.Theabovedesignapproachesuseempiricismforsolution(forexample,theanchorformfactorf,NeubeckerandRandolph,1996).Thereappearstobe room for non-empirical prediction methods usingbasic soil mechanics.When drag anchor holding capacity is approachedinsoftundrainedsoils,soilfailureconsistsoflocalplasticflowaroundtheflukeandshank.Thus,thebehaviourwillbeindependentoftheorientationoftheanchorwithrespecttothesoilsurfaceandsoanalysisofthesoilaroundtheflukewillleadtoin-sight about the general anchor behaviour.Thispaperpresentsanalysisofthesoilaroundanchorflukesusingfiniteelementanalysis.Theworkallowsinvestigationoftheanchorundergen-eralloadingconditionsandthebehaviourhasbeencharacterisedintermsofaplasticyieldenvelope.The findings can be used to validate previous designmethods(e.g.NeubeckerandRandolph,1996)oralternativelywillleadtonovelnumericaldesignmethodsusingtheyieldenvelopeapproachwhichare introduced briefly.2PLASTICITYCONCEPTSANDTHEYIELDLOCUSRecently,theanalysisofoffshorefoundationssuchBransby & ONeill: Drag anchor fluke-soil interaction in clays 2as spudcan and shallow foundations have used plas-ticityconceptstoexpressthebearingcapacityoffoundationsundercombinedvertical(V),horizontal(H)andmoment(M)loading(Murff,1994;Tan,1990; Martin, 1994; Bransby and Randolph, 1998).Aplasticyieldlocusisintroducedwhichex-pressesthecombinationofV-H-Mloadsthatresultin foundation failure.Thiscanbegivenasamathe-matical expression, f where f(V,H,M) = 0 at yield, orshown graphically (Figure 2). Not only may the yieldlocusbeusedtocalculatefootingcapacityundercombinationsofloads,butmayalsoformaplasticpotential (g(V,H,M)) for description of plastic verti-cal,horizontalandrotationaldisplacementsofthefootingatfailure(Figure2).Indeed,plasticitytheo-rems(e.g.Chen,1975)showthattheconditionofnormality or associated flow will exist for undrainedfailureconditionswhenthesoilalsoremainsat-tached to the footings.Consideradraganchordeepinundrainedsoil(Figure3).Loadsexertedontheanchorcanbeex-pressedintermsofforcesparallel(H)andperpen-dicular (V) to the fluke and moment load (M) aboutanyoneparticularreferencepointonthefluke.Combinationsoftheseloads(H,VandM)willcausefailureoftheanchorwithconsequentanchormovementsparallelandperpendiculartotheflukeand rotationally about the same reference point.Becausetheanchorisdeep,soilfailurewillbefullyconstrainedandlocaltotheanchorwhateverthe direction of the load. Thus, the failure loads H, VandMwillbeindependentofanchororientation,andsothelocalloadanddisplacementdefinitionsintroduced in Figure 3maybeappropriategenerallyforallfailureconditions.Inaddition,thedeepcon-ditionensuresthatthereisnosoil-anchordetach-ment.Thus,plasticdisplacementswillbegovernedby normality to the failure yield locus, f(H,V,M) andso determination of the failure locus also allows pre-diction of anchor displacement directions at failure.Anchor failure loads (H, V and M) will be a resultofverycomplicatedthree-dimensionalsoildis-placements around a complex drag anchor geometry.To examine this in detail, full 3D analysis would berequired and the detailed 3D geometry of the anchorwould have to be incorporated. This would be extre-Figure 2. The yield locus and plastic potential function.Figure3.Loadsanddisplacementsatfailureforasimplifieddrag anchor.mely time consuming. It is believed that much of thecomplexmechanisticbehaviourmaybeunderstoodbyexaminingasinglepartofthedraganchorsys-tem:thefluke.Thiswillprovidealargeproportionoftheholdingcapacityoftheanchorandgovernmuch of the anchor kinematics.Thefluke-soilinteractionbehaviourisexaminedusingthefiniteelementanalysisbelowandthere-sultsareexpressedasplasticyieldloci.Methodsofutilisingtheyieldlocusinanchordesignareintro-duced and discussed in following sections.3 FINITE ELEMENT ANALYSISThe aim of the finite element analyses was to exam-inesoil-flukeinteractionbehaviourduringundrained,deepfailureconditions.Inparticular,theaimwastodeducetheshapeoftheH,V,Myieldloci for flukes of different shapes.Theflukeshapewasidealisedasbeinginfinitelywide to allow planestrainanalysis.Althoughthisisnotnecessarilyagoodapproximationtoreality,itwillallowdetailedanalysisofasimplergeometrywhichmayenablebetterunderstandingofthegen-eral soil-fluke interaction problem.Two simple fluke geometries were investigated: arectangularflukeandaneccentricwedge.Dimen-sionsweredefinedasshowninFigure4.Forbothflukes,alengthoverdepthratioL/d=7wasadopted,asthisissimilartothatofaVryhofStevpris anchor fluke (Vryhof, 1990).The finite element package CRISP, CRItical StateProgram(BrittoandGunn,1987)wasused.Intheanalyses,approximately80015-nodedtriangularelements with 27 degrees of freedom were employed(cubicstraintriangles).Trescaelastic-plasticsoilwasusedwithG/su=500whereG istheshearFigure 4. Simplified fluke geometry and definitions.Bransby & ONeill: Drag anchor fluke-soil interaction in clays 3modulusandsuistheundrainedshearstrength.Thesoil was modelled as undrained by use of total stressanalysis together with a Poissons ratio, = 0.49.Displacementcontrolledanalysesaremostsuit-ablefordeterminationoftheyieldlocus(Bransbyand Randolph, 1997). For these present analyses, thefootingwasdisplacedslowlyinacertaindisplace-mentdirection(i.e.v/,h/ constant)untilaplastic failure load was reached. The full yield locuswascharacterisedbythefinalloadpointsaftercar-ryingoutarangeofthesedisplacementprobeswithdifferent v/ and h/.3.1 Rectangular flukeResultsfromaseriesofdisplacementprobesundervariouscombinationsoftranslationparallel(h)andnormal (v) to the fluke direction are shown in Figure5.Bothparallelandnormalloadisnormalisedbyfluke length and undrained shear strength so that theyieldlocusispresentedindimensionlessH/(Lsu)V/(Lsu)space.Aconvexyieldlocusresultswithmaximum horizontal load, Hmax/(Lsu) = 4.29 (V andM = 0) and Vmax/(Lsu) = 11.87 (H and M = 0).The peak loads Hmax and Vmax can be compared tosolutions with upper bound calculation. Figures 6(a)and6(b)showkinematicmechanismsfortheupperboundplasticitycalculationofVmaxandHmaxre-spectively. The upper bound calculations give:
,_
+ + ,_
+ cos21Ld42tan4LsVumax(1)
,_
+ + ,_
+ cos2142tanLd4LsHumax(2)where is defined as in Figures 6(a) and 6(b) and isvaried to minimise Hmax or Vmax.ThepredictionsofVmaxandHmaxareshownonFigure 5 for the rectangular footing. Good agreement024681012140 1 2 3 4 5 6H / (L su)V / (L su)Upper bound: V / (L su) = 12.10Curve fit (M = 0)Upper bound: H / (L su) = 5.15Vvh HVmaxHmaxFigure 5. Rectangular fluke yield locus in V-H space.Figure 6. Upper bound mechanisms for calculation of Hmax andVmax.isobtainedbetweentheFEandupperboundcalcu-lation of Vmax. However, less good agreement is ob-tained in prediction of Hmax.Examination of soil deformation mechanisms cal-culated at the horizontal and vertical capacities in thefiniteelementanalysisrevealwhyVmaxiswellpre-dicted by upper bound analysis, but Hmax is not (Fig-ure7).ThesoildeformationmechanismintheFEcalculation at Vmax is very similar to that of the upperboundsolution,butthereisasignificantdifferencebetweentheFEcalculatedmechanismandupperboundmechanismforpureparallel(h)movement.FurtherrefinementofthemethodsforHmaxcalcula-tion is required.TheyieldlocuscanbededucedinfullH,VandM space when rotational displacements are includedwithtranslationinthedisplacementprobes(Figure8). The yield locus is symmetrical about the axes andis convex.Figure 7. FE calculated soil displacements at Hmax and Vmax.Bransby & ONeill: Drag anchor fluke-soil interaction in clays 400.40.81.21.60 3 6 9 12V / (L su)Curve fit (H = 0)0369120 1 2 3 4 5V / (L su)Curve fit (M = 0)00.40.81.21.60 1 2 3 4 5H / (L su)M / (L2 su)Curve fit (V = 0)Figure 8. H-V-M yield locus for rectangular fluke.The moment capacity with V, H = 0 was found tobeMmax/(L2su)=1.49.Thiscanbecomparedtoanupperboundsolutionusingarotationalscoopmechanism(Figure9)ofMmax/(L2su)=1.60(ThegeneralsolutionisMmax/(L2su)=/2(1+(d/L)2).ThereisgoodagreementbetweentheFEandupperbound solutionsbecauseofthesimilarityofthesoildisplacement mechanism (Figure 9).3.2 Wedge shape flukeThefullyieldlocusinH-V-Mspacewasobtainedfortheeccentricwedgeshapedfluke(Figure10).Unlikefortherectangularfluke,theyieldlocusisnotsymmetric.Forexample,underpureHloading,theresultantfailuresoildisplacementswillgivepositivehandpositivev;theanchorwillmoveup-wardstotheright,partlyfollowingthebottomsur-faceofthewedge.Thus,duetonormality,themaximum H load will be sustained with negative V.Themaximumhorizontalloadisalsosustainedwithasmallnegativemoment.Adetailoftheyieldlocus in H-M space is shown on Figure 11. The shiftFigure 9. Upper boundmechanismforcalculationofMmaxandFE calculated soil displacements at Mmax.-0.600.61.21.80 1.2 2.4 3.6H / (L su)M / (L2 su)Curve fit (V = V1)-0.600.61.21.8-3 0 3 6 9 12V / (L su)Curve fit (H = H1)-30369120 1.2 2.4 3.6V / (L su)Curve fit (M = M1)Figure 10. H-V-M yield locus for wedge fluke.ofthepeakHpositionisduetothechanged(andasymmetric) kinematics of the wedge fluke.3.3 Curve fittingThe yield loci are shown in full H-V-M space for thetwo fluke shapes in Figures 8 and 10. It is more use-fultoexpresstheyieldlociasseparateyieldfunc-tions. Preliminary curve fits are suggested as an off-set form of the Murff (1994) equation:p1n1 max1m1 max1q1 max1H HH HM MM M1V VV Vf11]1
,_
+
,_
+
,_
(3)wheretheexponents,q,m,nandparechosento-getherwiththeoffsetsV1,M1andH1aftertheFEanalyses. The parameters used in the curve fitting areshown in Table 1, and the fitted curves are shown inFigures 8 and 10.Both equationsgive reasonably good curve fits to-0.600.61.21.80 0.6 1.2 1.8 2.4 3 3.6H / (L su)M / (L2 su)HhMCurve fit (V = V1)h/LM = 0H1, MmaxHmax, M1 ( = 0)Figure 11. H-M yield locus for wedge fluke.Bransby & ONeill: Drag anchor fluke-soil interaction in clays 5Table 1. Yield locus curve fitting parameters.Parameter Rectangular fluke Wedge flukeHmax/(L su) 4.29 3.34Vmax/(L su) 11.87 11.53Mmax/(L2 su) 1.49 1.60H1/(L su) 0 0V1/(L su) 0 -1.25M1/(L2 su) 0 -0.57m 1.26 2.37n 3.72 2.14p 1.09 0.93q 3.16 3.41thefullyieldlocus.However,forthepurposesofanchordesignitistheloadconditionsclosetothepeakHloadwhicharemostimportant.Morecom-plexcurvefittingtoallowforthedetailedshapeofthe yield locus in this region may be required.4 KINEMATIC ANCHOR ANALYSISTheyieldlocicurvefitsproducedbythefiniteele-mentanalysesforthefluke-soilinteractioncanbeusedinthekinematicanalysisofdraganchors.TheapproachissimilartothatbyNeubeckerandRandolph (1996), but plasticity concepts are used todeterminetheforceontheflukeintheequilibriumsolutionandtheassociatedplasticanchordisplace-ments are used to determine the anchor kinematics.First,theanchoriswishedintoplacenearthesoil surface. Next,equilibriumoftheanchoriscon-sideredwhichrequiresfindingtheflukeloadthatwill cause yield. The plastic normal at this load pointwillthendictatetheplasticdisplacementofthefluke.Thisgovernsthedirectionofthenextanchormovement and the anchor is stepped to the nextpo-sitionwheretheprocedureisrepeated.Hence,theentireembedmenttrajectoryoftheanchorcanbecalculatedtogetherwiththechainforceateachin-stant. This is explained in slightly more detail below.4.1 Geometrical simplificationThesoilstratigraphyisconsideredasasinglelayerofsoil withundrained shearstrength, suo at the soilFigure 12. Simplification of the anchor-chain geometry.surface and a shear strength gradient k.The drag anchor is simplified as shown on Figure12. The fluke is wide enough such that it can be ide-alised as being plane strain. The shank is treated as aplateoflengthslandofwidthsw.Thechainofdi-ameterbisconnectedattheanchorpadeye.Thefluke-shank angle, fs, is also defined in Figure 12.At any instant, the padeye is at a depth, zpbelowthesoilsurfaceandthetopfaceoftheflukeisin-clinedatangletothehorizontal.Thechainisin-clined at an angle a to the horizontal at the padeye,whereaisgovernedbythepadeyedepth,zp,thechain width, b, the force on the chain, Ta and the lat-eralcapacityfactorofthechain,Ncusingtheequa-tion of Neubecker and Randolph (1996):( )21a2p p uo caTkz 5 . 0 z s bN 211]1
+ (4)4.2 Equilibrium solutionThe forces acting on the anchor are shown on Figure12.Forthepurposeofthisanalysis,theanchorisassumedtobeweightless.Theshankdragforce,Hsactsatthemidpointoftheshankandparalleltothedirection of fluke travel. It is calculated as the prod-uctoftheprojectedshankareaperpendiculartothedirection of travel, a bearing capacity factor, Nc = 9,andtheundrainedshearstrengthattheshankmid-point. The unknown chain force, Ta is resisted by theshankdragforce,Hsandtheflukedrag(H,V,M).Giventhatf(H,V,M)=0astheflukeisatfailure,there is enough information to calculate all the forcecomponents.4.3 Normality displacementsIfitisassumedthatelasticdisplacementsarenegli-gibleincomparisontoplasticdisplacements,theflukemovementdirectionwillbegivenbythenor-mal to the plastic yield locus at the load state calcu-latedbytheequilibriumsolution.Thus,/(h/L)=(f/(M/L))/(f/H) and v/h = (f/V)/(f/H).Assuming that the anchor fluke moves a distancex in the direction parallel to the top fluke face in adisplacementincrement,thenh=x,v=((f/V)/(f/H))xand=(f/(M/L))/(f/H)x/L.4.4 Re-calculation of anchor positionTheanchorpositionisrecalculatedafterchoiceofxusingthedisplacementequationsabove.Thechainangleisrecalculatedforthenextequilibriumstep and the direction of the last anchor displacementisrecordedsothatthedirectionoftheshankdragforce,Hs is known.The procedure isrepeated fromBransby & ONeill: Drag anchor fluke-soil interaction in clays 602468100 100 200 300 400Draglength (m)Padeye load (MN)01020304050Padeye depth (m)Padeye loadPadeye depthFigure 13. Results from kinematic drag anchor analysis.theequilibriumstepuntilthechainforce,Tabe-comes constant and the trajectory of the anchor flat-tens.4.5 Typical resultsA typical drag trajectory is shown in Figure 13 for ananchorinanundrained,normallyconsolidatedclaywithsuo=0kPaandk=1kPa/m.Theanchorhasdimensionssimilartothoseofa32tonneVryhofStevprisanchorwitha50fluke-shankangle(Vry-hof,1990).Figure13alsoshowstheholdingforceon the chain, Ta as the drag progresses.Boththedragtrajectoryandholdingcapacityre-sultsaresimilartothoseseeninmodelanchortests(ONeillandRandolph,1997)withagradualin-creaseinholdingcapacityastheembedmentdepthincreases.Afinalholdingcapacityof8.7MNequates to an anchor form factor f of 1.7. This com-parestof=1.4derivedexperimentally,suggestingthattheyieldlocusapproachtotheanalysisofan-chors in clays is promising.5 CONCLUSIONSLocalsoilfailurearoundtheflukeofdraganchorshasbeenanalysedusingfiniteelementanalysistoinvestigate how drag anchor capacity and kinematicsareaffectedbythefluke.Fluke-soilbehaviouratfailurehasbeencharacterisedwithaplasticyieldenvelope in terms of loads parallel and perpendiculartotheanchorflukeandmomentload,usingtheframeworkemployedrecentlyforshallowfounda-tion analysis.Yieldenvelopesarepresentedforidealplanestrainflukesofvariousshapesandupperboundre-sultsarepresentedtoverifythesefindings.Thevarying yield envelope shapes are seen to be the con-sequenceofdifferentsoildeformationmechanismsaroundtheanchorgovernedbytheanchorflukege-ometry.However,thesecanbeexpressedsimplyintermsofcurvefitsinH-V-Mloadspace,andtheseyieldlociwillalsoformplasticpotentialsallowingcalculation of fluke displacement direction at failure.Theworkhasleadtotheintroductionofanewnumericaldesignmethodforpredictingdraganchortrajectoryandholdingcapacityusingtheyielden-velopeapproach.Despitethesimplificationsinher-entintheanalysisandthesimplifiedformofthefluke-soilyieldlocuscurve-fitused,theanalysismethodgaveresultssimilartothoseseeninmodeltestsofanchorsinsoftclays.Thissuggeststhatthemethodhaspromisewithfurtherrefinementoftheyieldenvelopeandbetterapproximationtothean-chor geometry.ACKNOWLEDGEMENTSTheworkdescribedinthispaperformspartoftheactivitiesoftheSpecialResearchCentreforOff-shoreFoundationSystems,establishedandsup-portedundertheAustralianResearchCouncilsRe-searchCentresProgram.SpecialthanksareduetoMr.NicholasSpadacciniforhiscontributiontothework presented in this paper.REFERENCESBransby,M.F.,Randolph,M.F.,1997.Shallowfoundationssubject to combined loadings, Proc. of the 9th Int. 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Centrifuge and theoretical modellingofconicalfootingsonsand,PhDThesis,TheUniversityofCam-bridge.Thorne,C.P,1998.Penetrationandloadcapacityofmarinedrag anchors in soft clay, Journal of Geotech. and Geoenv.Eng., Vol. 124, No. 10, pp 945-953.VryhofAnchors,1990.AnchorManual,KrimpenadYssel,The Netherlands.
