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TheMcClellandLecture
ATributetoBram
OBJECTIVES
Demonstratethetechniquesofplasticlimitanalysis(PLA)andtheadvantagesofsameforestimatingfoundationcapacity
Outline OffshoreFoundation ABriefHistory AnalysisofTypicalCasesIncluding
IndividualandSystemsof ShallowFoundations PileFoundations
ShowSimilaritiesandDifferencesinPLAandLimitEquilibriumTechniques
History TheEarlydays
History ShallowWaterStructures
History DeepWaterStructures
History ShallowFoundations
howcanmathematics,whichissoclearandprecise,andinsomanywayssimple,beappliedtothephysicalworldwhich,althoughapparentlyconsistent,ismanysidedandextremelycomplex?.
Calladine,1969
IDEALISATION
Thepurposeofcomputingisinsight,notnumbers.
RichardHamming
COMPUTING
thissolutionwasobtainedusingtheanalyticaltoolsavailabletous
thissolutionwasobtainedusingtheanalyticalfoolsavailabletous
ANASIDE
SHALLOWFOUNDATIONS
ConventionalMethods
PlasticityApproach
ConventionalPlaneStrainBearingCapacitySolution
Mechanism
Prandtl Reissner Terzaghi
V/A=cNc +qNq +0.5BN
Mathematiciansareusefulanimalswhoshouldbekeptingoldencagesandfedproblemsjudiciously.
KarlTerzaghi
ThePlasticityApproachwithSomeWordsofCaution
TheUpperBoundMethodofPlasticLimitAnalysis
Defineanadmissiblemechanism
Assumeavirtualvelocityoftheunknownloads
Setexternalworkratesequaltointernalenergydissipationrates
Solvetheresultingequation
Optimizethemechanism
AWordofEncouragement
Remember nooneeverreallyunderstandsanything,wejustgetusedtoit.
Example InclinedLoadMechanism
V
45
B
vo
B
C
DAE
Example1 Solution
EccentricLoadMechanism
D
M
H
yh
B
R BA
.
Brinch HansenMechanism ScoopMechanismRandolph,etal
AlternativeFormulationsforShallowFoundationSystem
DetailedorExplicitMechanism MacroorImplicitMechanism
StepByStepProcedureforMacroPLAPlanarModel(V&H)ofSystem
1. VirtualrotationaboutXo,Yo2. Findfootingvelocitiesv&h3. Usenormalitytoformratiosof
velocitiese.g v/h4. Equatethesetoratiosfrom
mechanism=>2equations5. Interactionsurface=>3rdequation6. SolveforV&H7. Dissipationrate=Vv+Hh8. Setdissipation=externalworkrate9. SolveforunknownForce10. Optimizee.g.wrt Xo ,Yo
MacroSolutionsofTwoFootingSystemWithVaryingVerticalLoad
PileFoundations
ANASIDE
Thesepileswillhavetobedrivenwithconsiderablebatter.
Thesepileswillhavetobedrivenwithconsiderablebutter.
PileFoundations LateralCapacity
DeepflowaroundofaflatplateH=11.42SuB
LateralMechanismforTranslation
PileFoundations DetailedRotationMechanismforRigidPile
PileFoundations AnalysisofaFourPileGroup
xo ,yo
R
Parameter Value
0and2 0.10 0.40
TypicalResultsMomentvs.LateralLoadInteractionDiagramforaFourPileGroup
ShearMode
OverturningMode
InteractionMode
ComparisonofUpperBoundvsLimitEquilibriumAnalysis
S3