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