Implementation and Inspection of a High-Cycle Accumulation Model

86 Pages·2016·6.44 MB·English

by  Thijs L. Lukkezen

I I
MPLEMENTATION AND NSPECTION OF A
H -C A M
IGH YCLE CCUMULATION ODEL
THESIS REPORT
by
ThijsL.Lukkezen
MasterofScience
inCivilEngineering
Thesiscommittee: Prof.dr.M.A.Hicks, TUDelft
Dr.ir.P.Hölscher, TUDelft,Deltares
Drs.G.A.vandenHam, Deltares
Dr.F.Pisanò, TUDelft
Dr.ir.R.B.J.Brinkgreve, TUDelft

A
CKNOWLEDGEMENTS
BeforeyouliestheresultofthehardworkduringmygraduationinternshipatDeltares. Mygrad-
uationtrackhasnotbeenasmoothride,butwasratherabumpyroadfrombeginningtotheend,
filledwithchallenges,deadends,newbeginnings,butalsosatisfactionwhenthingsfinallyworked
out. Of course, I could not have done this simply on my own and therefore there are a couple of
peoplethatIwouldliketothankinparticular.Firstofall,Iwouldliketothankmydailysupervisors
atDeltares:PaulHolscherandGeeraltvandenHam.Thankyoubothforthepleasantmeetingsand
coffeebreakswehadwhereyougavemeplentyofvaluableadviceonmythesis,butIalsoenjoyed
ourchatsonnon-thesisrelatedtopics. NextIwouldliketothankVahidGalaviandJonathanNuttal
from Deltares for your support with the Plaxis implementation. I have asked plenty of your time
andknowledgeonPlaxisUDSMroutinesandFortranprogramminglanguage,ofwhichIamabso-
lutelythankful.IwouldalsoliketothankAndrzejNiemunisforprovidingmetheUMATcodeofthe
HCAmodelandTorstenWichtmannforourcorrespondenceandtheveryusefuladviceandanswers
to my many questions about the HCA model. Also a warm thanks to Ronald Brinkgreve, Michael
HicksandFedericoPisanòforjoiningthecommitteeonbehalfoftheTUDandprovidingmewith
feedbackandguidanceduringthevariousmeetingswehad. FurthermoreIwouldliketothankall
otherpersonswhohelpedmeoutatDeltaresonsmallerandbiggerissues;theDeltaresgraduation
student community who provided a welcome distraction during the lunch and coffee brakes; my
roommates,whoprovidedalisteningeartomyincomprehensiblegibberishduringtimesofstress
andwerealwaystheretocheermeup;andmyotherfriendsandfamilywhosupportedmethrough
theprocessinmanyways.
ThijsL.Lukkezen
Delft,June2016
iii

A
BSTRACT
Thepredictionofpermanentdeformationaccretioningranularmaterialsasaresultoflong-term
cyclicloadingisacomplexchallengethatreceivesgreatattentioninengineeringfields,includingin-
frastructuraldesignanddesignofoffshorewindturbines.Manymodelshavebeenproposedinthe
pastwhichaimtopredictthiscyclicdeformationaccumulationforspecificorgeneralpurpose.One
ofthemostadvancedmodelsavailableisthe"High-CycleAccumulation(HCA)model"byNiemunis
etal(2005)[1].Althoughverypromising,thismodelisasofyetrarelyusedinDutchgeotechnicalen-
gineeringpractice. Oneofthepossiblereasonsforthisisthelackofunderstandingandavailability
ofthemodel.Thisthesishastheaimtoovercometheseproblemsbygatheringrelevantinformation
ontheHCAmodel,implementingitinPlaxis2Dfiniteelementsoftwareandinspectingthecapabil-
itiesoftheresultingFEroutine.Aftergatheringtheinformationonthemodelfromliterature,itwas
concludedthatthemodelhasgreatpotentialandisthemostextensivelyvalidatedmodelavailable.
However, therearealsosomeboundaryconditionsforwhichthemodelfailstopredictthedefor-
mationscorrectly.Themodelalsorequiresavastnumberofadvancedlaboratoryteststobecarried
outinordertocomputethemodelparameters.
TheimplementationoftheconstitutiveequationsinPlaxis2Dwasperformedsuccessfullyand
wasverifiedforasingle-elementtypecase.WhenapplyingtheFEroutinetoaboundaryvalueprob-
lem,numericalissuesarisingfromthefiniteelementcalculationkernelconflictwiththesensitivity
oftheHCAmodeltothestateparameters,resultinginasevereover-estimationofaccumulatedset-
tlements. Asensitivityanalysiswascarriedout, whichshowsthatthemodelishighlysensitiveto
the parameters of the hypoplastic model (which is used in the initial calculation phase of the FE
routine). ItisconcludedthatfortheHCAroutinetobeusedinPlaxis,thenumericalissuesshould
beinvestigatedandpossiblyanumericalinterfaceshouldbedesigned. Thehighsensitivitytothe
modelparameters,combinedwiththevastamountofrequiredeffort(andcost)tocomputethese
parametersforasandsamplemakethemodellessfavourableforpracticaldesignapplications.
v

C
ONTENTS
Acknowledgements iii
Abstract v
ListofFigures ix
ListofTables xi
1 Introduction 1
1.1 GeneralContext . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 JustificationofResearch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Objectives&Methodology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 ThesisOutline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 CurrentModelsandPractices 5
2.1 GeneralConcept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 TypesofAccumulationModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Sawicki . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 Suiker&deBorst. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.5 Françoisetal.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.6 Niemunisetal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 TheHigh-CycleAccumulationModel 11
3.1 ConstitutiveModel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.1.1 DecompositionoftheAccumulationRateε˙acc. . . . . . . . . . . . . . . . . . . 12
3.1.2 StiffnesstensorE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1.3 PlasticStrainRateε˙pl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 PropertiesandCompliances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2.1 CompliancewiththeMinerRule . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2.2 CyclicStrain"Memory" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3 DeterminationofSoilParameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3.1 HCACoefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3.2 DensityLimits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.5 TheHypoplasticityModelwithIntergranularStrains . . . . . . . . . . . . . . . . . . . 26
3.5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.5.2 ConstitutiveModelandParameters. . . . . . . . . . . . . . . . . . . . . . . . . 27
3.5.3 IncreasedShearStiffnessModification . . . . . . . . . . . . . . . . . . . . . . . 29
3.5.4 IntergranularStrainExtension. . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.6 Summary&Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4 FEImplementation 31
4.1 UserDefinedRoutines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.1.1 AnalysisandComparisonofUMATandUDSM . . . . . . . . . . . . . . . . . . 32
vii
viii CONTENTS
4.2 ConversionoftheHCAUMATRoutinetoPlaxisUDSM. . . . . . . . . . . . . . . . . . 33
4.2.1 StepsofConversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2.2 MaterialProperties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2.3 StateVariables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.3 ModificationtotheElasto-PlasticPredictor . . . . . . . . . . . . . . . . . . . . . . . . 36
4.3.1 TheNumericalCalculationScheme. . . . . . . . . . . . . . . . . . . . . . . . . 36
4.3.2 TheHCAStiffnessTensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5 Verification 41
5.1 ModelParameters&BoundaryConditions. . . . . . . . . . . . . . . . . . . . . . . . . 41
5.2 Results&Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
6 2DShallowFoundationCalculation 45
6.1 MaterialConstants&BoundaryConditions . . . . . . . . . . . . . . . . . . . . . . . . 45
6.2 MeshDependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
6.3 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
6.4 NumericalIssues. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
6.4.1 Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
6.4.2 DiscreteLoadfunction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
6.4.3 NumericalTensileStraining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
6.5 PredefinedDisplacementBoundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
6.5.1 SensitivityAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
6.6 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
7 Conclusions&Recomendations 55
7.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
7.2 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
7.3 Recommendations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
A Symbols&Notations 59
B ModificationstotheHypoplasticityModel 61
C FEImplementation 63
D ShallowFoundationCalculations 67
D.1 CalculationResults. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
D.2 SensitivityAnalysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Bibliography 71
L F
IST OF IGURES
2.1 Thoughtexperiment:squareboxfilledwithsandsubjectedtoauniformverticalpres-
sure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Evolutionofε,εampl andεc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 The common compaction curve of Sawicki’s model compared to observations from
labtests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.4 ThefourstressregimesofthemodelofSuiker&deBorst, eachdefiningspecificsoil
behaviour. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.5 BasicconceptoftheHCAmodel[1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.1 AvisualizationoftheprocesswithwhichthetensorialamplitudeAε isderivedfrom
thestrainpath[1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Theeffectofcyclicloadinghistoryontherateofdensificatione˙[1] . . . . . . . . . . . 14
3.3 Examplewhichillustratestherequirementoftheplasticstrainrateεpl.Thestrainrate
ε˙ isindicatedwithDandthestressrateσ˙ withTinthisfigure. . . . . . . . . . . . . . . 16
3.4 Discretizationofirregularinputtoblocksofconstant-amplitudecycles.From[2]. . . 17
3.5 Fourtestswithdifferentloadblocksequences[2] . . . . . . . . . . . . . . . . . . . . . . 18
3.6 Accumulationduetostresscyclesconsistingtwodifferenttypesofharmonicoscilla-
tions[3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.7 Testresultsfrommulti-stagecyclictriaxialtestwithachangeinηav betweenthestages
totesttheeffectofcyclicpre-loadingonthedirectionofstraining[4]. . . . . . . . . . . 19
3.8 Correlationsbyvariousauthorsforliquefactionresistance[5] . . . . . . . . . . . . . . . 20
3.9 CorrelationbetweenCSRN=15andgA forthesandinvestigatedin[5] . . . . . . . . . . 21
3.10 Accumulationcurvesofmulti-stagetestwithappliedmonotonicloading[6] . . . . . . 22
3.11 Scatterinobtainedvaluesofunitweightusingvariousstandardtestmethodsfortwo
ofthesandsinvestigated.From[7]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.12 PlotsofHCAmodelpredictionsandtestdataforthreesandsamples.[8] . . . . . . . . 25
3.13 Thedependencyofthereferencevoidratiosonthemainstress[9] . . . . . . . . . . . . 28
3.14 Influenceofn(a)andh (b)onoedometriccurves[9]. . . . . . . . . . . . . . . . . . . . 28
s
3.15 Increaseofincrementalstiffnessduetochangeinthedirectionofstraining[10]. . . . 29
4.1 PlaxisHCAUDSMinternalcalculationscheme. . . . . . . . . . . . . . . . . . . . . . . . 34
4.2 Schematicrepresentationofthewrapperfunction. . . . . . . . . . . . . . . . . . . . . . 35
4.3 Iterationschemes:(a):ModifiedNewton-Raphson;(b):FullNewton-Raphson. . . . . 38
4.4 Hybriditeration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.1 Schematicrepresentationofverificationcase. . . . . . . . . . . . . . . . . . . . . . . . . 42
5.2 StrainaccumulationresultsfromPlaxisimplementation. . . . . . . . . . . . . . . . . . 43
6.1 FEcalculationofashallowstripfoundation . . . . . . . . . . . . . . . . . . . . . . . . . 46
6.3 Resultsofthemeshdependenceanalysis.. . . . . . . . . . . . . . . . . . . . . . . . . . . 47
6.2 Meshrefinements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
6.4 FoundationsettlementresultsofthePlaxis2DFEcalculation. . . . . . . . . . . . . . . 48
6.5 Thedependencyofthecalculationofaccumulatedsettlementonadifferentchoiceof
numericalstabilizationparameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
ix
x LISTOFFIGURES
6.6 Resultsofthe Plaxis2D FE calculationwithprescribedfoundationdisplacementsin
the implicit phases, compared with the observed results from the centrifuge test of
Helmetal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
6.7 Relative sensitivity values η of the investigated model parameters. A value of 1.0
SR
means that a certain percentage change in input will lead to an equal percentage
changeinoutput. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
6.8 Sensitivity valuesη ofthe investigated inputparameters, normalized by their (ap-
SS
proximated)inputrange. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
C.1 Plaxismaterialpropertiesinputscreen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
D.1 VerticalStressdistributionafterthefirstloadpeakonthefoundation(164kPa) . . . . 67
D.2 Detailledclose-upoftheverticalstressdistributionnearthefoundationcornerinFig-
ureD.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
D.3 Distributionofverticaldisplacementsatthefoundation. . . . . . . . . . . . . . . . . . 68
D.4 Closeupoftherecordedstrainamplitudeεampl beneaththefoundation. . . . . . . . . 69