Abstra ct

BEHAVIOUR OF HIGH-STREN GTH CONCR ETE UND E R BIAXIAL LOADIN G CO N DIT IONS

by

©

AmgadAhmedHussein,B.Sc.(E ng.},M.Eng.

A thesis sub m itt ed to the Schoolof Graduate Studiesin partialfulfilment of the

requirementsfor the degreeof Doctor of Philosophy

Facultyof Engineeringand Applied Scien ce Mem orial Unive rsityofNewfo und land

April 1998

St.John's Newfoundland Canada

Abstra ct

Wit htheincreas in g applica tions ofhigh strengthconcreteintheconstruct ionin- dustry.the unde rstanding ofitsbehaviourunder mult iax iaJloadingis essent ialfor reliableanalysis and safe design.Thisthesis encompassesaninvestigationof tbebe.

haviourof highstre ngt h concreteunderbiaxialloadin gcond itio ns. and aconsue u rive modelling study toenablenum ericalpredict ion.through the finite element method . ofsuch a behaviour.

The experimentalphase includedthe evaluationanddesign ofthe loadingplatens.

The test set-upandsupports arevery crucialto'this typeoftestingdueto the fricti on that exists betweenthetestingplatensandthespecim en.Atheo reticalst ud y usiag the finite elementapproachwasconducted toinvestigatetheeffectof confinement on thedisplacement fieldin additionto thestressdistributioninthe loading direct ion.

Three types of load ingplatens were exami ned:the drysolid platens. thehrushsup- portandteflonfric t ion reducing pads.The resultsofthesimulat ionindicated that themost homogeneous st ressand displacemen tfield are achievedthrough the brush pla te ns.Based onthefinite element inve st igation , thesizeand dimensions ofthe brush platens wererecommen ded.Theywer e usedin theexperimental study.

Atest set-upwasdesigned and manufactured.\Iod erncont rolschemesandhigh- speeddata acquisitionsystem werebe usedtomonitor the materialresponse and collecttheexperi mental results.Four different types of high stre ngt hconc retepla te specimens weretested unde rdifferent biaxialload combina tions.Theprincipaldefor- mationsinthespecimen wererecorded andthecrackpatt ern s andfail ure modeswere examined.Based onthestrengthdata,failure envelopesweredeveloped foreach type ofconc rete. Thetest results revealed thatthefailureenvelopes of concretedepends ontheconcretest rengt h andonthetypeofaggregates.Apronounceddifference was

foundbetwee n the highstrengt hlight ....eight andthe highstrengt h norm a lweigh t concret e.The deformat ioncharacte risticsindica tedthathighstr engthconcrete shows a linearbehavio ur upto a higherstressthannormal strengt hconcrete. Italso has a higherdisconti nuitylimits. Th.. observed failuremodes showedthatthe reis no fundame ntaldifference in the crac kpatterns and failuremodesduetotill'inc reasein the comp ressivestrengt hoftheconcreteor due tothf'useoflightwf'ight aggr{"gatPS underdifferentbia.ti al loadi ngcombi nat ions.

The testresults wereused to modifyandca librate a frac t ureenergy- base d non- associatedmodelforhigh-st rengt hconcrete.The model was im plemented in a general purpose finiteelementprogramand wasverifiedagainst thetest results.LOsingthe proposed eonst tt uuve model.a finiteelementstudyWB..'icar ried outtoanalyzethe st andardcompressionrest ona concretecylinde r.The effectsof the compressive strength.cylindersize.loadingplatens and sulphu rcappingwereInvestigated.The stu dy confirmedthata triaxialcompressivestressstateexist satthecyli nderend . and alarge Stressconcentraticaoccurs at rbe cornet.ThE'simulation resultsrevealed that the use ofa standardbeari ngblock is essennelintestinghigh strengthcone-rete.

\Ioroo\·er.insome cases.the useof anonstandard hearingblockcanresultin alow..r strength.which was observed experime nta lly.The simulationprovidedan explanation for sucha behavio ur.Finally.the finiteelemenr ana lysisdemonstratedtha t the use of softmaterials.asfrictionred ucers. couldcreate drastic chan ges in thestateof stress inthe specimenaswell as itscompressivestrength.The use ofsoft materialsshould.

therefore.becarriedout withca ution.

iii

Acknowl edgement s

Iamgreatly Indebted toDr.H.:\Iarzouk.PrOfl"SSOfofCivilEngineering,under whose guida nce andsupervision theprojectwascarried out.Hisexcellent guida nce.

suppo rt.and pa tiencehelpednil'to compler e thisthesis.

)Iyspecia lthankstoDrs.P.Morinand.\1.Booto n.fortheirsupportanden- coura ge ment.andalsoforser vingonthe supe rv isory com mittee.Tha nksare due

[0 Dr.J.J.Sharp.AssociateDeanofEngineering forGraduat eStudies andH...

sea rch.forhis unders tan din g,encoura gemen tand[Itt'facilities provided.Further- more.Dr..1•.J.Sha rpand),[5.),I.Crocker.secretaryoftheAssociateD..an'soffice.

are acknowled ged forensuringsmootItand t'fficientoperationoftheassocia tedad- miuistra rivs[asksofmy gradu ate program.

Iwouldliketothank Dr.A.Elwi.ProfessorofCivilEngineering,l"ni\l' rsity of Alberta.for his assistanceandhelpfuldiscuss ionregardi ngrhefiniteelementim- plement ationof theleon:\Iodt"i.Itform edthebasis oftnt"lmplernenta tionof the Extendedleonxlodelthatwas carriedoutinthisthesis.

Sincerethanksare-duetorheTechnical Staffwho madethe-irservicesilnilab[e-at eve rystageof thisproject.especiall y Slessrs A.Bursey.C.Wardand R.O'Dnscoll.

r

express mywarmappreciationtothemembersofthe-TechnicalServicesofXlernorial Lniversitv,~I r.L.Spu rrellforhisinvaluableassistanceinmanufact uring all theparts used illthetest set-up .~Ir.B.Burkeforperfornungalltherequired weld ing.Thanks arealso due[Q:\Ir.H.Dye .machin e shopsupe rviso r,and~fr.J.Andrews.\I.'t'lding shopsupervisor .fortheircontinuousaccommoda tionandhelpduringthemanufac- turingof thetest set-up.Thegeneroussupport fromthe CenterforComputer Aided Engineeringandits staff.especia lly xlessrsD.Press,andT,Gala\\'ayandLlittle.

oncomputingservicesis verv much appreciated.

Thisthesis...·as completed at :\IemorialCni\"e'rsit~·ofXewfoundlandas part ofa project fundedbytheXacuralScience'SandEngin eerin gResearchCouncilofCanada.

Funding in the fonn of graduatefellowshipand gradua t.. supplementfrom).If'morial l'nive rslty is gratefully acknowledged.

Iamgrate fulto thefellowgradu atestudentsfor their encouragemen t andcom- pany.Iwo uldliketo thankmy friend S.Awada llah for hisrrue friendshipand his mor al supportto me thro ugho utthecourse of my thesis.

r

wouldliketotake thischance toexpressmy profoundgratitudetoallmyfam ily mem bersfortheircontinuingencouragementand affection.

Finally.a specialword mustgotomy wife.:\"ancy.for the sacrificesshe made and theprivationssheend ured duri ngthe tenure ofthis thes is.

Contents

Abstra ct

Ackn ow le dgements Listof Figures

ListofTables 1 Introd u ction

1.1 Scope 1.2 ResearchOhjecnves. 1.3 Thesis Ou tline.

2 ReviewofLit erature 2.1 toadApplica tionSystem.

'J'J ResponseofConcreteCoderBiaxialLoadingCondit ions 2.2.1 XcrmalStrengthConerere.

2.2.2 High-St rengt hConcrete 2.2.3 LightWeightAggregateConcrete. 2.2.-1 PostPeakBehavi ourinLniaxlalCompression. 2.2.5 PostPeakBehavi ou r inBia:rial Compression.

iv xii

15

IS 22

2.2.6 loading Path 2.3 Consti tutive~Iodels

2.3_L Elastieit yBased~Iodels '1.3.2 Plasticit:!.BasedModels '1.3.3 Endochronicmodels '1.3A Damage~Iodels. 1.3.S ~Iicro plane~Iodels.

"2.3. 6 AdoptedMod elfortheCurr entSt udy

'18 28 '1A FiniteElementSimula tionofConcrete Tes t SpecimeninCompression 30

2A .l Analytical and Finite ElementStudies of L'nlaxlalTt'StiDl~of ConcreteCylin ders.

2A.2 Finite Elemen tSimulat ionofthe BoundaryConditionsusedin Biaxial Test ing ofConcrete

3 Fin ite Element Evaluat io nofthe Boundary Condit ions used.in Bi- axia lTestingofConcrete

3.1 Simula tionofrheInte ra ction Betwee n rheTest Spe-cimen andthe load- ing Plate ns

3.2 Ccnsriturive~Iaterial ~Iodel. 3.2.1 Elastopl as ticBehaviour.

3.2.2 Behavi our underCompressiveSrr£'SSState . 3.2.3 Crac king.

.

1 3 Spec ime n-Plat enInte raction 3.4 Surfac e Constit utiveBehaviour 3.5 Geo metric~Jodelling. 3.6 ~I a[eria lProperties.

vii

30

34

Vi

3.

3.

. 18 39

'0

'3

3.7 Results of the Xumerical Evaluation of the Set-up. :3.7.1 Cniaxial Loading

3.7.2 Linear Analysis versus Xonlinear Analysis 3.7.3 Buckling Capacity ofthe Brush Rods 3.7.4 Biaxial Loading

3.8 Recommendations for theTest Sl'I-L'p

4 Experimental Program -t.l Bia xia l TestingApparatus

-L1. 1 LoadingFrame

-t.1.2 Loading Platens -t.1.3 Hyd ra ulic Actuators -t.1.4 Measurement Devices

-1.1.5 Data AcquisitionSystem.

4.1.6 ControlScheme. -t.2 TestingProcedure

4.2.1 SpecimenLoading -t.2.2 SpecimenMouurmg. -t.3 Test Specimens -t.--t Matenals Used

4.4.1 Cementtttous Materials -t.-t.2 Aggregates. 4.4.3 ChemicalAdmixtures 4.4.4 High-rangewater Reducers 4.4.5 Retarder

4.5 Concrete Mixes

viii

69 72 72 75

76 '9 79 '9 80 81 81 81 82 82 85 85

.l.f \lixlng Procedure -t.7 Propertiesof FreshConcre te. -1.8 Spf,<,IIlWIl Fabrication.

t.8.1 Casung -1.8.2 Curing -1.8.3 Grind ing. -l.9 Summaryof Experiments

5 TestResultsan d Discussion 5.1 Strength Data

5.1.1 Compressive Streugrh of the Different \lixturf'S 5.1.2 BiaxialStrengt hData

5.2 T~'pj('alSt ressStrainCurves 5.3 Post -P('akBeha viour 5... Failure Modes.

6 ACon stit u tiveMod elforHighStrengt hConcrete 6.1 A Fracture-Energy-BasedPlasticity \10<1('1 6.2 Leon'sTriaxial Strength Failure Criterion. 6.3 Extr-udedLI'OIl'STriaxial Strength FailureCriterion.

6... Isot ro picHa rdening Xlodel for Pre-PeakBehaviour 6.5 XonlinearHardeningHes po nse.

6.6 Xonassociau-d Flow.

6.7 Isotr opicSoftening \lml,·1 forPost-PeakBehaviour 6.7.1 \IOOeIType Fracture

6.7.2 Degradationof Triaxial Strength

ix

8' 8'

8 '

8' 88 88 90

92 92 92 9,j lOG 122 127

6.t.3 ~lixl!d :\IOO~frac ture. 1·; 5

6.8 The Basis ofXumericalImplementation I.;;

6,8.L Xume nc alIm plementationof Plast icit y, 1-)8

6.8.2 Elasuc-PredtctorStl"P 1·;8

6.8.3 Plastjc-Corr ectorStep 1.;9

6.8.-1 Crossing theYieldSurface 159

6.8.5 Retu rningto theYield Surface 161

6.8.6 The plasti c ).lult iplier..lA 162

6.9 Implementat ionof theModel 163

6.10Calibra tio nandVertficanenofthe )'IOOel. 163

7 Applicationof the ProposedModel: Eval ua ti onof theSt andard

UniaxialCom p ress ionTest 171

r.1 lnt roduction. 171

.,2StandardUniaxialCom pressionTest 1.2

r.3 Specificationsforthe Standard CylinderTesc, 1.2

;..1 Standar d Specimen Size 1;5

7.5 Stateof Stress in a Test Specimen. 105

;.6 finiteElement Simulation 1.6

r,

6.1 Geometric ).Iodellin ,ll; 1.8

t.t ~Iater ial)'IOOel

irs

;.S Simulati onof the CompressionTest 18.

•.9 Effectsof DifferentTestVaria bles 190

r,9.1 Concre te Co mpressive Strengt h 190

r.

9.2 Specimen Size, 19.

;.9.3 Bearing BlockDimensions 203

.,10End Preparation of tllf' Specimen 210

t.11Summa ry 216

8 Con cl us io ns 219

8.1 Summary 219

8.2 Evaluation of DifferentLoadi ng Platens for Biaxial Testing of High-

Strength Concrete . 220

8.3 ExperimentalFindings 221

8...1 Finite Element Model. 223

8.5 Application of the Finite ElementModel:Evaluationofthe Standard

Lniaxial CompressionTt'S1. 22-1

8.6 Contribunon. 226

8.. Reco mme nda t io nsfor Further Resea rch. 22.

Refer en ces 229

xi

Li st of Figures

2.1 Biaxial test methods[5J 10

2.2 Average shearstress-straincurvesfo r differentloading systems[201 12 2.3 Exploded viewof fluidcushioncubical cell[221. 13 2.4 Biaxialstrengthenvelopeof concrete[l el]. 15 2.5 Schematic of the stress straincurves obtainedform a uniaxial test

specimenin compression

3.1 Constitutive model used in the FE analysis 3.2 Isoparametric interfact'r-h-ment

3.3 'con-local interface frictionmodel.for which the condition of no relative motion is approximatedby stiff elastic behaviour. as shown by the dashes line .

.3.4 TIl(>fin ite elementmesh

3.5 Stresscontoursin the direction of loading(S22)and displacement con- lours inthe orthogonal direction(e llforthe uniaxialcases

U : =

100

~IPa) ,at ulti mate load

3.6 Shear stresses induced illtill:'specimen.(It H>tothe brush loading platens.

foruniaxialcase

U : =

100~IPa)

3.7 Shear stresses inducedillt1H'specimen.dur-to the lubricated teflon pads,foruniaxialcase

U;

=100~IPa)

xii

19

.n

51

52

3.8 ShearS!rl:'SS('Sinduced in the specimen. due tothe solid loadin g platens.

for uniaxia lcase

U;

=100),IPa)

3.9 Shear stresses inducedinthespecime nat theultimau- strength.due tothe different loading systems .for uniaxial case

U; =

100),IPa),at ultimateload

53

3.10St ressconto urs in rhr-direct ion of loadin g (522) and displacenu-ut con- tours intheort hogo naldirectio n(L"l) for the uniaxia lr-lastir- analysis 56 3.11Conto ursofthe principa lstrecses(SPI ) anddisplacementcontours in

oneoftheorthogonaldirect ions(L"l )for the biaxial ce,...

U; =

100 ),IPa).at ulti mateload..

3.12Shea rstresses inducedintbespecime n. dill"tothebrus hloadingplatens.

for biaxialcast>

U;

=.100 ),IPa)

3.13 51H'arstresses induce-d in thespecimen. dUE'10 till'lubricated n-Hon pads.for biaxialcase

U: =

100),IPa).

3.1-1Shea rstrPSS{'S indu cedinthe specimen.due tothe solidloadi ng pla tens.

for biaxia lcase

U; =

100),IPa)

3.15Shea rst resses induced in the specimen at the ultim atestrength.due '9

60

61

62

to thedifferentloadingsystems. for biaxialr-ase

U; =

100),IPa) 63

-t.I Test set-up(fro nt alview) . 66

4.2 Test se-t-up[sideview] ti7

4.3 ThE' brushloading platens 71

-lA ...test specimen mou nt edillthetest setup 73

-l.5 ...test specimenwith two orthogonalstraingall~1'Smounted at the centre '-l -l.6 ... photographofthe data acquisition S:'-'stl'llland the ),!TSmain control

pancl.

xiii

.&. ,

Block diagr a m highlightingthedet a ils of theclosed-looptestscheme ,S

·t S Gradingofaggrega tes. g~

~.9 Photographof thegrinder usedforgrinding thetr"St specimen S9

·5.1 Ahigh st reng t hco ncretecylinderatfailure. 93 5.:! Biaxial strengt h envelopesfor~SCundercombined tensionandcorn-

pression.biaxi altensio nandbiaxialcom pression.

.5.3 Biaxia lst rength. envelo pesfor HSCundercc rnbtnedte nsio n andcom - pressio n.biaxialte nsio n and biaxialcompression

5.~ Biaxia lstrengt h.envelo pesforl"HSCundercombined te nsionandcom- pression.biaxial tension and bia xialcompress ion. .

5.·5 Biax ial strengthenvel o pesfor HSL\\ 'Cunder combinedte nsionand' compression.bia xia l tens ionand biax ialcompression

5.6 Bia xia lstrengt h envelopes for the fou r ditff'renttypesofconcreteunder combinedte nsionandcompression.biaxialtensionand biaxialrom- press ion

5., Stress-strain relationshipsforthenormalstrength concrete mixI~SC, underbiaxia lcom press io n

5.S Str ess-strainrelationshipsfotthe normalstrengrhconcrete mixI~SCJ underco mbined tens ionandcomp ression.

:5.9 St ress-s t rain relationshipsfortil...normalstrengt hconc retemix(~ S C) underbiaxialte nsio n..

5.10Stress-strainrelations hips fortbehighstrengthconcretemix(HSC) underbiaxialcompression

5.11Srress-srrainrelat io nshi psfor thehig hst ren gt h concretemix(HSC) undercombined tens ionand com pression

100

101

1O:?

103

ltj.'

108

109

110

111

II:?

5.12Sm-ss-stratn rela t ionship sforthehigh strengthconcretemix(HSC) underbiaxialtensi on

5.13 Stress..strainrelar icnships for thehighstrengthconcrete mix(e HSe) underbiaxia lcompression

;U~Strcs....strain relat ionsh ipsfor the high st rengthconcretemix(l"HSC) under combinedtension and comp ressio n"

5.15 Stress-strainrelationsh ipsforthe high strength concrete mix(L"HSq under biaxial tension

5.16Stress-strainrelationships for the lightweight concrete mix(HS L\ \"C) under biaxialcom pression

5.1iStress-strain rela t ionship s for the lightweightconcrete mix(HSLWC) under combined tensionand com pression

5.18St ress-st ra inrelationshipsfor thelight weightconcrete mix(HSL\ \"C) 113

111

115

116

Iii

118

underbiaxia ltension 119

5.19Poisson'sra t io versusappliedst ressfor thedifferenttypl'S of COIlI'Tef('

in unia xial com pressi on. 123

5.20 Uniaxial st ress-st rai ncurve(Ol•f')for a typica l:\SC speci me n 125

;j.21 Failur e modi 'S ofSP f' d Ill I' Il Ssubjected touniaxial com pressio n 131 5.22 FaiIUTI'modesofspecimenssubject edtobiaxialcompress ionstn'ssl's

132 5.23 Failure modes of specimens subjected to biaxial compressionst re-sos

133 5.2·t Failure modi'S ofspecimenssubj ect ed torombi nr -d tension and1"011\_

pression(0] /01

=

-1/ 0.10)

5.25Failuremodes ofspeci me nssubjected tounia xial tensio n

131 135

112 139 6.1 Triaxial failure envelope. deviatoric sections. of the Pramono and willaru

1ll00t^p

I I· o j)

6.2 Deviatorie \'iew ofthe EDl[. 1]

6.3 Plane sr n-ss sections ofsmooth(EL~I)anti polygonal (Loon) failure

envelopes 1.t2

6A Comparison of themodelwith thecurrent biaxialtest data. U.t 6.5 Loading surface of isotropic hardening model. I.t6

6.6 Fictitious crack model

[ID.t]

150

6.. Composite fracture model for tensile cracking 152

6.8 The forward-Euler procedure: (a ) Locating the intersection point A:

(b) Moving tangeuttallv fromAlOe(and correcting 10 D), , 160

6.9 Verifiratiou of plane stress elements , 166

6.10 Comparison of the finitel'IPIIII'ntresults with the biaxia lexperimental data on normal strength concrete byH. Kupfer et al.

lUI

6.11 Comparison of the finite element results with the experimental data for theCHSC mix.

6.12 The finite element mesh for a cylindrical specimen subjected to triaxial loading ,

16.

168

169 6.13 Comparisonof the finite f'1"III£'lIt results with the triaxial experimental

data on high strength concrete bvJ. XiI' l't a!'

[90] 1.0

•.1 ,"\ST~tC 39-1993a standard bearingblock forcompression testing li3

•. 2 State of stress on a rompression test specimen 1.7

7,3 The finite element mesh 179

'A Forces acting on all axi-symmetric element 180

1~1 7.~ Pri ncipalst ressesfor a150 x 300 mmcylinder,/:=30~IPa.tested

witha 152mmbearingblockatnominalaxialstress=-12~IPa correspo nd ing to-10S{loading.

7.6 Principalst resses for a1~0x300mm eylinde r./:=30~I Pa.rested wirha152 mm bearingblockat nominal axial srress

=

-1;~IPa

correspo nd ingto905f:loading. 18-1

7.7 Principa l stresses for a1.50 x .100 mmcylinde r./:

=

30~rPa,tested with a152 mm bearing block atnominaJ axiaJst ress

=

-30~IPa correspo ndi ngto100%loading

i.8 Shear stressinducedinthespecim en.atdifferentloadinglevels. /;

=

30"IPa.1.>0x300 mmcyli ndersthatare testedwith 150 mmbearing block

7.9 Displacem entconto urs fora

no

x300mmcylinder./;=30~IPa, testedwirh a 152mmbearingblock atnominalaxialstress:::::-30

~IPacorres pon d ingto 1009iloadi ng

7.10Principalstresses fora 150x300mmryhn d er./;=30~IPa.reseed witha 152mm bearingblockat nom inalaxialstress=-.10 "IPa correspo ndi ng to100%load ing and usinginterfaceelement10simula te theinter acti on betweentheplat en andthe specime n

i. l1Shearstressinduced inthespecim en. alongcylinderend.150x.100mm cvlindersthatare testedwith150 mm bearing block. usingdiff..rent modellingassumpt ions.

18·5

ISO

18;

1S9

\91

7.12Displacement contoursfor a 150x300mmcyli nder.

f:

^=30:l.lPa.

tested witha152mmbearin gblock atnominalaxialstress

=

-30

~IPacorres pond ing to 100~loadingand usinginterf ace'elementto simulat etheinterac tionbetwee ntheplatenandthespecimen 192 7.13Principalstresses fora150 x 300 mmcylinder,/:=;0\IPa. rested

with a152mmbea ring blockatnominalaxialstress=-;0:l.IPa correspo ndi ng to ioo'ifloading

i.UPrincipalstresses fora 150 x 300 mmcylinder./:=100 \IPa.tested witha152 mm bearingblockat nominalaxialstr ess=-100\IPa correspo nding toIDa

'*

^loading

7.15 Shearstr ess inducedinthespecimen. along cylinde r end.for different compressivestrength.150 x 300 mmcylinderstha taretested with

no

mmbearingblock.

i.16Principal stressesfora 100 x 200 mmcy linder./:=30\IPa.rested witha102 mm bearing blockatnominalaxial stress

=

-30 :l.IPa corres ponding to1005{loading

i.1i Principalstresses for a 100 x 200 mmcylinder./;=70 :l.IPa. tested witha 102 mmbeari ngblockatnominalaxialstress

=

^-;0:l.IPa

correspo ndi ngto 100%load ing

i.IB Principalstresses fora100x200mmcylinder. /;=100 :l.IPa.tested witha102 mmbearingblock at nominalaxialsnE'SS=-100 :l.IP"

corresponding toIDa%load ing

;.19Shea rstress inducedinthespecimen.alongcylinderend. fordifferent compressive st rength.100 x 200mmcylindersthat aretestedwith102 mm bearingblock.

xviii

19'

195

19i

199

:!OO

201

202

7.20Principalstresses for aViax300mmcylinder.

t: ⁼

³⁰~( Pa.tested witha102 mm bearing block at nom ina laxialstress

=

-.10~(Pa co rresponding to100<.kloading

7.21Princi pal stresses fora 150 x 300 mmcylinder.

t;

⁼30:\IPa.reseed wit h a102 mm bearing block atnomi nal axial stress= -.10~IPa corres po ndingto100<.kloadingandusinginterface elementto sim ula te the interactionbet ween the plate nand thespecimen

7.22 Shearstressinducedin thespecimen.alongcylinde rend.1-:50 x 300mm cylindersthatare tested with 102mm bearing block.usingdifferent modellingassumptio ns

7.23 Principa lstressesfora 100 x200mmcylinder.

t:

^{=30~IPa.tested}

wit ha152 mm bear in g blockat nominal axial stress=-30~I Pa correspo ndingto1009{loadi ng

•.24Shea rstressinducedin the specimen.alongcylinderend.for different romp ressive strength.100 x 200mm cylindersthat aretestedwith 1·50 mm bearingblock.

•. 25 Principa lstresses for a 1.50x300 mmcylinder.

t:

⁼30 ),IPa.tested with a152 mm bearingblockatfailure. specimen test ed usingal..i mm rubberpad.

7.26 PrincipalStressesfor a150x 300 mmcylinder.

f: =

30),[Pa.tested with a152 mm beari ngbloc katfa ilure.specim en testedusing a.1mm sulphurcappingcompound.

7.27Principa lstressesfor a 150x300 mm cylinder.

t; =

30 :\IPa. tested with a 152 mm bearing blockat failure.specimen testedusing a 6 mm sulphu rcappingcompound

xix

20.5

20.

208

:109

:HO

213

214

215

•.28 Shearstress inducedinthe specimenca pped withsulphu rcompo und for150J(300 mmcy lind ersthat aretested with 150mm bearing block 21.

List of T ables

3.1 Xumberofelementsfordifferent testset-ups. 3.2 Shear stresses ind ucedin thespecimen

.J.l Gradingof aggregates.

.1.2 Physical properties of normalweightaggregates .1.3 Physical properti es oflight weight aggregate. . -1.-1~( ixproportionsof0.1cubicmeterofconcrete.

"

&1 83 36

5.1 Uniaxialcom pressivest rengthforthe differentmixturesatdifferent

agesfor the 100x 200 mmc~rlinders 9-1

5.2 Splitt ing tens ilest rengt hC\IPa) forthe differentmixtures at91days 9-1 5.3 Biaxialstrengthdat aforthl"normalst rengthconcrete mix \"SC 96 5..1Biaxialstrengt h datafor thehighstre ngt hconcrete mi."HSC 9, 5.5 Biaxialstrengthdata for the highstr ength concrete mixL-HSe 98 5.6 Biaxial strengthdata forthelight wei ghtconcretemixHSlWC 99

6.1 ),Iate rial parameters for thedifferent typesofconcr ete. 165

i.I Differentcasesofthefinite dementsimulat ion. l iB

i'.2 Xumber of elements.. IBI

;.3 Displace ment values in tbe lateraldirection(1:1),andintbedirection ofloading(1:2).attbe ultima teload.forone-quarterof the test cylindl'r 202

Chapter 1 Introduction

Inrecentyears, consid erable att entionhas been givento tbeuse ofsilica fumeas apartial replacement for cementin theprod ucti on of highst rength concret e.High stren gthconcretepossessesfeaturestbat could beused.advantageously inconcre te structures;these featuresinclude:lowcreepchar ac t eristics,low permeability.low deflection of members resultingfromhighelast icmodulus,andthe reducedloss of prest ress force because of lowercreep deformation. Hence.theapplication of high strengthconcreteisrap idly gainingpopularityin the concreteindust ry.

Concretes withst rengt hsexceeding 60 :\IPa are prod ucedcommerciallyusingcon- ventionalmet hodsand mate rials andare notunus ualin constructiontoday.High str engt hconcret e bas beenusedforoffshoreplat forms.marine structures.tallbuild- ingsandlongspan bridges.Theconst ructio nofCh icago'sTowerPlace.wouldnot have been possiblewithouthighstrengt h concret e.Highstrengt h ready-mixed con- crete wasusedontheFirst PacificCent rein Seattl e.Washington;inthis case the designstren gt hofthe concrete was 97MPa[I).High strength concrete wasalsoused fortheworldtallestbuilding, theMalaysia'sTwins.

The modemconcrete offshore st ructuresin theNorthSea are built withhigh strengthconcrete,with a minimum compressivestr engthof60 MPa[3]. Over twentj..

concrete gravuv platforms heve beenconst ructed in the Xorth Sea. IIIf' Baltic Sea andoffshoreBrazil{-IJ.Forexample.rhespecified strength(56~IPa)for Gullfaks C platfo rm (1986-87)concret ewas 50%higher tha nthestreng thof BerylA.platform (1973-,5)concrete(36~IPa).TheactuaI28-da~..compressivestrengthnf theGnllfaks concrete con'samples was found tobe-approximately,0~IPa13].

Hecent.ly,a gra vitybased structu reutilizinghigh strength concrete was\ISf'{!for theHibernia development offtheeaster ncoast of Xewfoundland. It is IIII' firstgravity basestructureto be built in Xort hAmerica. High strengthconcrete. containing minera l admixture such as silicafume. isrela t ively impermeable.Hence.it offers great promiseforthe durabilityprobl em associa ted withmarin e andoffshorestruct ures situated in the harshXort hAtlanticwaters. The specified design strengt hfor the Hibe rn ia GBS was,-I~I Pa. The actual strength was found to be much higher. Xormalweig htaggrega tesaswell as light weight aggregateswereUSN !intill'high st re ngt hconcretemix.In the des ignof thesetvpe ofstructuresmany loading cast's are considered. The state of stress insuch a massive structure is quite complicated and finiteelementana lysishadto be used.

TIll' behaviourof reinfor ced concretemembersandst ructuralsystems,spe-ifi- callv their responseto loads and other actions. has been the subject of Intensive tnvesngauons since the beginning of the present century. Because of the complexities associated with thedevelo pment ofra tional ana lytic alprocedu res, present-day design methods continueillman y aspects tobeba srdOilthe empiricalapproaches. which usethe results of alarge amount of experimental data.

Such an emp irica lapproac hhas 1)\"('11m-o-ssarv in the past, and maycont inue to 1)(' the most convenie nt method forordina rydesign. However . thE' finite element method now offers a powerful and generalanalytical tool for studying the behaviour of

reinforced concret e.Cracking.tensio nsoft ening.non- linearmulriaxialmar erial prop- erues.complexsteel-co ncrete interfa cebehavi our.andothereffects previousl yignored or trea tedinaveryapproximatewaycan now bemodelledrationall y.Throughsuch studies.in which the imp ort an t parametersmay beva ried convemenr lvandsys tem- atically.new insightsaregainedthatmayprovid e a firmerbasisfor thecodes and specificationson which ordinarydesignisbased.

Thefinite element method has been used directl y forthe anal ysis anddesignof comp lexstruc t ures.such asoffshort'oil platforms and nuc lea rccnratnmenestruct ures.

Thesecannotbetrea ted pro per f r~.rbe mor eappr o:cimatemet hods.However.the finiteelement methodrequires agooddescrip tion ofthe actual materialbehaviour underdifferent load combinations. inord ertoyieldaccura te andrea llsncresults.For norm alstre ngthconcrete. reasonableamounts of dataart' available.Tbis isnot th..

case for highstrengt hconcretefor whichexistingdata arescar ce.

Considerable expe rime nta lresearchhas recently been directed towardsapplying new techniquesin concretetestin g.Special testset-ups andservocontro lledtesting haveprovidednew experimental evidence whichwasnotavailableearlie r from pre- domi nantlyload-controlledtest data. For example.a stab ledescending portionof the stress-strataCUC\"eof concre tein compressionanddirect tension\\"85observed.

The uniaxi al st ress-str ai ncurvesobtai ned haveprovid edaninsightto the mate rial's post-peak behaviour thatwasneverknownbefore.

Althou gh concreteis subject ed.inpractice. to awiderange ofcomplexsta tesof stress.mos t of the avail a ble informationon highstrengthconc rete. elas tic andin- elastic deformationalbehaviour.has been obtainedfrom simp leuniaxial compression and bendingtests.Suchtestaart'usually carr iedout undershort-term sta ticloading Theseexperiments provideasmal l part of the vastamount of datarequi red under all

possib le combina tio ns and typ es ofst resses.

\-er~'few experimentshavebeen carriedout to ascertainthe behaviour of high stre ngt hconcrete underbia xial andtria xia lstatesofstress. There fore.anexton- sivcexperimental programisrequiredto investigat ethebehaviour of high stre ngt h concrete Hilder biaxialloading.

1.1 Scop e

The currentst ud y is ca rriedouttoexaminetbr-behaviourof highstrengthconcrete whensubject edtobiaxial state ofstress. Thescope of the experimental program is asfollows:

I.Inves ngate the behaviour of high stre ngt hconcrete mad e with norma l weight aggregatesand light weight nggregates.

2.To exam ineandevaluate thetes tdata.

3.Recordthe deforma t ioncha racte rist ics.

.t.Observethefa ilure 1II001l's.

5.Developthefai lur e envelopes.

6. Compa rethe beha viour of high strengt hconcrete with that of nor mal st re ngt h concrete.

TIl(>experimenta lresultscanthenbe usedto modify a suita blecons ti t utive mod el for highstrengthconcrete. By imple ment ingtheconstitutivemod el in a general purpose finite elementprogram .one can then predictrhe beha viourof differenthigh stre ngt h concret est ruct ures. Modellingof the reinforcementcall be easily added tothe finite elementprogra m, Howe ver .abond characte risticsst udy, forhigh st rengt hconcre te.

should be carried outfirsttoprodu ce propermodellingassum ptio nstoyieldgood results.

1.2 R es earch Objectives

Themai nobject ive ofthe current resear chisto investigatethe behavio urofhigh strengthconcrete underbia xialloading.The researchobjectivesof this invest igatio n can be summarized asfollows:

1.To exami netheavailablemet hodsused inbiaxialtestingof normal strength concreteand toidentify thesuitab lemethodsthatcanbeusedforhighstrength

.JToensure thatselectedtest set-ups will notimpose any limitationswhen used forhighstrengthconcretetesting.To performthis task . a finite element cval- uationof theexist ingtestset- ups used in biaxialtestingof concreteshouldbe carriedout.

3. To design anappr op ria te test set-upforbiaxial testingofhigh strength concrete thatcanproduc ereliab letestdata.

-l.To collectandanalyze the strengthdata andtheload-deformationbehaviour ofhigh strength concre teunderbiaxialload ing condition s.

5. To examin e the failuremodes andcrackpa tt erns for differentstress rat ios.

6.To adopta theoreticalconstitu tive model suitableforthe finiteelement analysis ofhigh strengthconcrete and tocali brat e it using the experimenta ltest results.

7.To implement the proposedmodelinageneralpurpos efiniteelement program capableof dealingwithcomplexstress analysis problems.Thevalidityof the

high strength concrete model should be established by appropriate comparisons with the test results.

8. To conduct a finite element analysis of the standard compression test in order to provide some insight intotha t importanttest. The parameters should be selected to simulate the actual ones used in the standard compression tests

1.3 Thesis Outline

Chapter 2 is divided into four parts The first part reviews the different methods of load application used in biaxial testing of concrete.The second part reviews previous research conducted on normal strength concrete underbiaxial state of stress. The third part contains a brief review of the different constitutive models used in idealizing the behaviour of concrete. The fourth part is a literature review of previous analytical and finite element studies of uniaxial testing of cylindrical specimen.

Chapter 3 contains a non linear finite element study of the effect of different load application platens used in the biaxial testing of concrete. The findings of the study are used to recommend the loading platens for the test set-up.

Chapter 4 describes the experimental investigation. Details of experimental facil- ities, test procedures andinst rument a t ion are presented.

Chapter 5 presents the test results and observations obtained from the experimen- tal investigation, as well as the subsequent analysis of these results.

Chapter 6 deals with an adopted constitutive model and its applicationto high strength concrete. The implementation of this model in a general purpose finite element program is also described.

Chapter 7 presents a finite element study of the standard uniaxial compression test on concrete cylinders.

Finall y.a summaryor the currentin...estjgaricnand theconclusionsreached are gh-eninChapte ri.

Chapter 2

Review of Literature

In thischapt er.a shortreviewof literaturepertainingto the differentaspectsofthe curren tresearchworkis given. Inthefirst section.abriefreview ofthe existing tes t set-ups andthedifferentmethods of load application usedinbiaxialtestingof norm al strengthconcreteispresented.Secondly. the earl ier work onbiaxialtesting ofconcrete.as reportedby differentresearc hers.is discussed.Highlights of differen t constit utive modelsusedfor ideali zing theconcrete behav iourarebrieflysum ma- rized.Finall y,previousworkon finite elementsimulationof atest specimen under compressive loadingisdiscussed .

2.1 Lo a d A p p lication System

Variousvariablesof thetes t set- upcanexertaninfluence onthespecime n'sresponse under biaxial stateofstresses. Typically,thespecimensusedin biaxial tests are eit herconcreteplatesorconc re tecubesloaded in two direct ions.Thus,the boundary condit ionsst and out as themostinfluential factorinaspecimen'sresponse,asthe aspect ratioofa biaxialtestspeci me nis equalto one.Theinteract ion between the test speci men and the loadin gplatens couldInfluencethesp eci men'sbehavio ur,strengt h and mode offailure.

frictional forcesdevelop betweenthe concretespecimen andtheloadi ngplatens as aresult of the differe nces in la teral expansionbet ween the concretespecimenandthe steelplate ns.frict ionconstr ainsthespecimen boundary against lateral displacem ents whichleadsto additio nalshearstresses onthe surface.andthusinduces forcesinthe concrete specimen whichareaddedto the nom inaltestload.[0addition.the stress dist ribution in thespecimenis notuniform.As a result.the specimenis in a biaxial stateof stress whichisnotwell defined.

Variousmet hods of load applicatio nhave beenproposedfor biaxialtesti ngof normal concretetoelim ina tethe frictionproblem(seefigure 2.1).Adetailedand comp rehensiveclassificati onofthe loadingsyste msis given by the internationalcoop- erat iveprogramcarried outbyGerstl e er al.[51.Therat ionale of suchmethods is to reducethe effectof late ra lconfinementof the test specime n.The met hods available in the literatu recanbe classifiedinto t...."I)mainca tegories as follows :

a)The use offriction reduci ngpadstored ucethe frictio nbetween therest speci- men and the loadingpla tens.

b)Flexib leloading platenstoallow forthe specime ndeformationwithout intro- ducinganyrestrai ntssuchasthe brush support andthefluidcushion system.

The simplest meth od for elimina tion offrictionforces is theuse of alub ricant between the loadingplate nsandthe testspecimen.Sheppa rd16jobserved thatsuch treat mentmayleadto the oppositeeffect:excessivelubricationmay leadtooutward- directed frictional forces caused by the squeezingoutofthe lubricant.The lateral extrus ionofthelubrica ntwillinduce latera ltensi lest ressesandanonuniform st ress dist ribut ion in the specimen'sendresulti ng in a reduction of its apparentstrength.

In ordertoredu cefriction . Sheppard[61used frict ion-re du cing padscomp osedof twolayers of plasticfilm0.0076ernthickcombinedwit halayer of axlegrease.Hugues

10

Figure2.1:Biaxial test methods[5}

and Bahararnian[7J examined those pads in uniaxialcompression and noticed that the cube results were much lower than the expected strength values. They at.tributr-d that to the expansion of the plastic film between the grease and the concrete specimen which would haveled to premature failure of the concrete.

Hugues and Baharamian[8J used a sandwich made of layers of alum inumsheets and grease to reduce the friction between the test specimen and the loading platens.

Schickert[9}showed the limitationof this solution in the case of high applied stresses.

The frictional forces were much stronger shortly before fracture occurred than at the start of load application.

~1illsand Zimmerman {1O] found that pads made withaxlegrease between 0.0075em teflon sheets had a very low coefficient of frictionfor normal stresses up to 350 MPa.

Nojiri et al.[11] used two sheets of teflon (0.05 mm) lubricated with silicon grease as a friction reducing pad.The friction pads were able to reduce the coefficient of

11

frictionbetween tbe testingplatensand thespecimens toaval ueof0.0..1.

Itshouldbe noted thatifintermediatelayers are used.theirthicknessshoul dbe kept very small. Increasingthethicknesswilllead toasign-reversalof theconstraint atthe interface between the specimen andtbetest ingmachi ne.This"illlead to a splittingactionatthespeci men end.Acom p re hens ive..studyonthe useofinter me- diat elayersisgivenby~ewman1121.

Brushbeari ngplatenswerefirstintrod uced by HiLsdorf[131.and have beensub- sequentlyusedby several researchers(forexample[1-1.15.16.17.181.amongorh- en).Theload ingapparatusconsistsofassembled steelrods, with a crosssectionof 5 x 5mm.The lengt hoftherodsvaries fro m 100-1·10mm,depending onthemax- imum concretestrengthforwhich the particularbrus h platen can be usedwithout bucklingofthe filaments.This supportislaterally deformabletofollowtheconcrete deformation and hence eliminate the late ralconfinement.However.theapplica bil- ityofthistechniquemaybelimitedby the allowedmaximumpressure loa d ofonly 69MPa. above whichthe brus hbuckling mayoccur [Schickert[1911.

Vonk etaI.{201carriedoutastudy to inves tig a tetheshearstr essesinducedin the specimendue to differen t sup po rt systems.[0that investi gat ion.three different systemswere employed:solid platens. brush pla tens(short andlong brush es)and teflon pads.The resultsof thestudyindicatedthattheshearstressesinducedinthe specimens wereveryhigh inthecase of dry solidplat en s.Withthebrush bearing platens , theshearstresses increasedathigherappliedloads dueto thebend ingof thebrushrods.The use ofteflonpads produced theopposite results. Theinduced shearstressesincreased asthe appliedloadwasincreased;it then started to decrease as the appliedload was furtherincreased(Figu re2.2). van Mier and Vcnk[2 1]

attri butedthis behaviourtothe slip-stickbehaviourexh ibited bytheteflon padsat

12

... ---

/ I I

/

I

i I

II

Figure2.2:AVtmJ.gt: sheJ;Jr.nru.,,-.stnl' lIcu.rvu fordlJJerenlloading systems:(-r:-J dryplaten. (- - ) .shOTtbrush.(---)longb~h,(- ..-)teflon{f O!

smalldeformatio ns(highshear stresses).

TheDuid cushion supportsyste mwasdeveloped byAnden ees etaI.[22Jatthe university of Colorado.The specim enwasloaded bymeans of flexible membranes under hydrau lic pressure;and thefluidpressureswereappliedat theopposingsurfaces of the test specime nsothat thespecimen floatedwithin theloadcell(Figure2.3).

Thismet hod eliminat ed anyfrictionbetween thetestspecimenandtheloadingdevice.

Fluid andfluidcushion(tbinmembrane)boundary devices,howev'er,can leadtoearly failure duetointeractionwit hthespecimen microstructure (231.In additio n,the)' limitthenature ofload ing to comp ressiveload ingsonlyastheycannot produce tensionload ing.Toperform tensiontests,brusbplatensshouldbeadded[241,

Asallof theabove cases show,theloadi ng devicesusedinbiaxial testingofcon- creteimpose some boundaryconstraintsinthenormal aswell asthe lateraldirections,

13

Figu re2.3:Exploof'AJview of fluIdc'l.~hi.onC1Jbical cell{22}

For thelat er alboundaryconstraint ,thefluid cushio ns aresufficient lydeform able so as topermit la ter aldisp lace ments, withzero shea rst resseson thesurface.Rigidsteel pla te nswithout surface lubrication prod uce sufficientlyhigh frictionto constrain the specimen boundaryagainst lateral displacements,leading to shear stresses on the surface. To reducela teral friction. different methods of lubrication or brush platens are used to allow lateral displacement.

As for norma l boundary constraints,rigid steelplatens,which cause uniformnor- maldispl acemen ts but variable norm al stressesmaybe grouped at one end ofthe sca le; fluidcushions, whichens ureuniformstresses butpermi t variablenorma l dis- placem ents , areatthe opposite end . Ot her devices (such as brushplatens orlubrica nt ) produce anintermedi a te degree of boundaryconstraint.

14

2.2 Response of Concrete Under Biaxial Loading Conditions

2.2.1 NormalStrength Con cre te

Several researchershavestudiedthe behaviourofnormalstrengthconcrete subjected tobiaxialstresses114.16,17,25.26,15J.Someof the muchearlier informa tionis questiona blebecauseof thetechnicaldifficult iesinvolved in achievi ng the desiredstate ofstressandin obtainingaccuratemeasurements of the extre mely small multiaxial strains. Iyengaretal.[251 reportedbiaxialstrengt hvalues as highas350%of tbe uniaxialcompressionst rengt hof an ident icaltestspecimen. Thismisleading result couldbeattri buted.tothe three-dim ensional st ateofstressexisti ng in their testsdueto friction betweenthetestingplatens and thetestspecimens.App lying different methods toreducethefrictionbetweentbetestspecimensandthetesting platens yielded moreaccura te results.Nevertheless.tbereponed results had alarge scatte r(26J.

The mosteffect ive method to alleviatethefrict ionproblem wasthebrush bearing platensdeveloped byHilsdorf(131. Thebrushpla tens minimizetheconfinement duetofrictio n andyieldmorereliable stress-strai n and strengt hresults.Kupferer al.(14) utilizedtheseplatensandcarri edoutanexperimentalinvestigationon the behaviourofconcreteunderbiaxialload ing. Theirresearchprovidedsomeofthe most complete andreliable experimentallydeterminedinformatioD.on thebiaxial behaviourandultima testrengthof normalst rengthconcrete.Theresultshave been widelyaccepted and wereverified byLiuet at.[161and Tasujieeal. [171,usingsimilar testset-ups.Moreover,the resultsofthe fluid cushiontestscarriedout hyAndenaes etal.{22Jwere in goodagreementswith Kupfer's observations.

The strengt h ofconcretesubjectedtobiaxi al compression wasfoundtobe higher

15

",__ p.-t90~~(7llXla-ol

_ J1•....3'I5~ ""~P.<l

._I!..-MO~.:r..opa(l

Figure

:q:

Dumal strength envelope of concrete {l-4J

thanthe uniaxialst rengt h114. 16,17J. A strengt h increase of approximately16% was achieved at an equa lbiax ialcompressionstate(0,/(13

=

1). A maximum strength increase of about 25%wasreached at a stress ratio of

°2/(1\ =

0.5.The strength decreased almost linearly as the applied tensile strengthwas increased forthe biaxial compression-tension case. The biaxial tensile strengthwas almost the same as that of uniaxial tensile strength(Figure 2.4).

2.2.2 High-Strength C o n cr e t e

Veryfewdata is availa bleonhigh-strengt hconcre te underbiaxial state of st ress[11, 2i,28].Nojiriet al.[11] carried out anexperimentaltest ingprogra m011fourCOIl- cretemixeswith differentcompressivestrength subjected onlyto biaxialcompressive loading.ThE"specimen used wert' tOOmm cubes.Thehighest concret estrength used in the study was 67.9~IPa. Theauthors concluded that failure envelopes for the

16

fourdifferentstrengt h levels ofconcrete(in biaxial com pression)were verysim ilar.

However.thewholerange ofthebiaxialfailureenvelope was not covered.

Herri n[211 studiedthebehaviourofmodelconcrete plate specimens.composed of nine aggreg atediscsembedded in ahigh-st ren gthmortar matrix...hen subjec t ed tobiaxialcompression.Cbea[281 tested thesam e modelspecimenaswellashigh- strengthconcreteplates(127x 127 x 12.7rom)made with different types of ag- gregatesandsubject edto biaxial load ing.Themaximum compressivestrengt hof the tested plateswas 60 MPa. Albeitthe maximumstrengt hofthe control cylin - ders reached almost95 ;\.fPa. no explanation wasgiven forsuch discrepancy.Only com pression-eompressiontestswere performedandthewholeran geofbiaxialfailure envelope wasagain not covered.

Theonly availabledatain the literaturethat covers the entirebehaviourof a relativelyhigh-strengt hconcretemix. subjectedtobiaxial load ing,wasreported.

byKupferetal.[141. [0this experiment alwork.one set ofthetestedspecimens hadacompressive strength of59 \lPa. The specimens weresubjected to three ran ges ofbiaxial stresses:compressicn-cempressic n(C-C), tension-tension(T-T), andcompression-tension(C-T).The aut hors concludedthattheneithertheconcrete composition northeconcretestrengthhas anyeffect on the biaxial strength.andthat the str engt hchar acteristicsaretypicalforanytype of concrete.Nonetheless,some researchers noticed thatthebiaxial strengthofconcretedecreases withthe increase o(compressivestrength117.291.

The behaviourof high-st rength concretecouldbedifferentfrom normalst rengt h concretefordifferent biaxial load combinations1311.Forthe C-Ccase. the mien>

cradring andthe stress-st raincharacteristicsof high-strengthconcreteunder uniaxial load ingisquit edifferent tban nonn al strengt h-concrete. As(or theT-T ease, a

17

decreasein theratio oftensilestrengt hto com pressivest rengt h maybe observed for higher-strengthconcrete,as notedforuniaxialcases(301. Alar ge differencecouldbe notedfortheC-Tcase(311.A small arnoun toftensionwoulddecrease the compressive ca pacity moreradi call yforhigh-str ength concretetha n fornormalstrengt hone.

2.2.3 LightWe igh tAggrega t e Concrete

few experime ntalinvestig at ionsofthe behavio urofnormalstrengt h tight weight aggregateconcrete under biaxialstr ess were performed[32, 33,

:HI.

Tayloretal.[331 test edthreedifferentconcre temixesmad e withalllight weightaggregate in biaxial compression.The specim enswere50 mmcubes andtheyweretested using brush loadingpla tens.The results ofthe invest igation indicated tbatthefailureenvelope ofIigbtweightconcr eteisdifferentthan tha tof normalweightconcrete.This finding isincontrast toapreviousinvest iga tion by~iwaet aL{32] (w inggreasedbearing pads)which concludedthattheshape offailure envelope(in biaxialcompression)is similartothatof normalstr ength concrete.However.bot hinvestigations indicat ed tbat themaximum biaxial compressionresistance.for light weight concrete,occurred at aratio ofapp lied loadsequal to 0.8.

Atan and Slate[34\carriedoutalimited biaxialcompressiontestingprogram on two typesof light weightconcrete(one with light weight fineaggregate andthe other withnaturalsand).Theexperimen tswereperformed on a 130x 130 x 13 mm concrete plates usingthebrush platens.The resultsof theinvestiga tionindica ted that.incontradict ionto the above mentionedinvestigations, theshapesofthe failure stressenvelopes(inbiaxial com pression) forlight weight andnormalconcreteare general ly similar andthe biaxialcom pressionresistance,forlight weightconcrete.

occurredata ratioofapplied loads equalto 0.4•0.5.

18

2.2.4 Po stPeakBeha v iourinUn iaxialCom p ress ion

Inorde r10obt aina stabledeseendingportion duringarompress io ntese,a closed- loop dtsplacemenr control. ofthe test.hasto be em ployed.Experiment scarriedoutin loadcontrol[constant d)do nOIca pturethis phenom en on.Inadisplaremenrccmrol comp ression test.someselecteddeforma tio n inthespecimenisUSE'dasafeed-beck signal.figure"2.5providesaschema t icoftheStressstrai ncur-..ewhichisobralned fromsucha test.

Thepostpea k behav iour of acompress ionspecimenis mainlyaffecterlbyfour interactingparame ters(351:(a ) thest rengthof concre te.(hithecomposi t ionofrbe feedbacksignalthat cont rolsthetest: lc ]thefric t ionres tr aintat the podzones:and (d)the areasof strainlocalization inthespecimen.

Earlyresearch work(36.20]revealedtha t asthe supportsystemis changed. the postpeakbehavi ou r ofnorma lstrengt hconcretebecomes significanrly different.In thesetests. plate n topla tendisplacementwasusedas thefeedbacksignal.Onthe ot her hand. exte nsiveexperi ments[3,.38. 39J havedearlydemonstratedthatusing theplatentoplatendisplace ment.as afeedb ack signal.doesnotprod uce a stable dt'SCendingportio n ofthestressstra inrun'" forhighstrengthconcretecylinders.lr was suggestedthat a snap-bac k phenomenonoccursandthatcould b"considered the reasonforthe absenceofany post peakbehavio urfor highstrengt h concrete.

Se...ralcontrol techniqu e'Shavebeensuggestedtoproduc e a sta blecont rolcapableof rapturingthisphenomenon forhigh strengt hconcrete cylindricalspecimen.Among them is the useofcircumferentialstrainas afeedb acksignal[-10.38..ILJ. POSt peak behaviourof high-str ength concret ewasobtainedusinga combinatio nofcross-head displacement.axialandcircumferentialdefonnationof the specimenasthefeed- hack signalH2J.Asimilarmethodusingacombination of axialand circumfere ntialdis-

J '

Compressiontestcylinde r

Sv=platendisplacement Sc=gauge displace men t

NormaJstre ngthconcrete

a

Highstrengthconcrete {snap back phenomenal

19

Figure2.5:Schem aticofthe srressJtruincunJe$QbtaiTied form a unitU1a1t~.•t$peCI- men tTlcomprtJJlon(plate TitoplateTidi.~pfacem ~T1ti...useda.'afeedback.1IgT1 al)

20

placement asafeedback signal wasusedbyGlavind andStang[35j.Anot hermethod offeedbackcont ro lusinga linearcombinationofforceanddlsplaremenrwasem- ployedby[.13.39.441.Thismet hod wasoriginallyproposedforcompression ttstinK of rocks[451_ The fact orsthataffectthepostpeak behavioursuchasthe spee-i- men'sroodrestraint exist for bothhighstrengthaswe llasnorma l strengthcon Cff' tf'

specimen.l"sing aplatentoplatendisplacementas afeedback signalproducesa sta ble descending portionfor norma lstrengthspecim enbutisnotsuccessful for high strengthspecimen.This was att ributedto theso called snap-backphenomenon.The snap-backphenome nonwasonlyobserved. forhigh stren gt hconcretespecim en.WI'WD thecircu mferentialstrai nisusedasa feedback signa l. .-\.logicalinrerpreranonfor suchaphenomen onwas givenby[351.In normal strengt hconcrete.thecracks get arrestedbytheaggregate.In highst rengt h concrete.thecementpasteandlilt'ag- gregat~aresimilarinstrength and sti ffness.Thus. thecrack extendsth roughrh..

aggregate. Asaresult.when a crackdevelopsin high st rengt hconcrete.thereis asudden increaseincircum ferentialstrain.causingunloading to takeplaceinthe axialdirectio ninordertoregulate theerrorsignalthatcontrols tbemoveme ntofthe hydr aulic actu ator.Ontheother handthe research workby Jansenet al.[-1-1)shows thatthesnap-backis a materia lphenom enon for highstreng thconcrete.Inthatre- search program.thestrainwas st illmeasu redever a bigportionofthespecimenand close to theregions with end restrai ntduetothespecimen-plateninteraction.This couldin8uence the result s to someextent.Inconclus ion.it seems as more research workis neededbeforeasolidconclusioncanbe reac hedrega rdi ng theissueofsnap hackphenome nonin highstrength concrete.

Anot her outs tan d ingissueis whatdOE'Sthe com pression postpeak behaviou r repre sentand overwhat portionofthespec imenshould itbemeasured"!Also. does

21

this measurementreflecta true materi albehaviour oris it astructu ralrespo nse as tbe resultofseveralfactorsincludingthestiffness oftheloadingplaten andtheregions of the test specimensthatare affectedbytheend restraint"

Theexperimenta l resul tsIndicatedthatcompressionfailureis subjectto localize- noneffects.Thepost peak behaviourwasfoundtobe dependentonthespecimen geometry.boundarycond it ions.andthegaugt'lengthusedtoobtainthestra ins[18.

20.-161.Conside r the uniaxial compressionevlind rir al testspecimenshown in Fig 2.:).

Duetoend restraint.thest ress distribution inthe specimen isnotun iform.During the post peakbehaviour.thereexisttwodifferenrzonesin the specimen.The area tha t isadj acen t to thepla ten switha smallerstress[han the middle portion of the specimenand the failurezoneloc ated closetothe cent reofthe specimen,The middle portionof thespeci m en.thefailurezone.deformsin a way thatis different than th..

end zoot".Some expa nsio noutsidethe failure zonewilltakeplace asunload ingOlC- curs .Thusthe totaldeforma tion inthespecime nis the combi neddeform ationofthe intac tpartas ....~IIas [heloca lized failurelone.Thus thepla ten toplatendeforme- tioncannotbeconsideredasthe -rrue'mat erial behavio ur .Asa resu lt.itis ra tio nal that themeasurem entof the strainshouldta ke placein themiddleport ion ofthe spec imen.Also.this measurements shouul beI~as the feedbacksignaltoproduce asrabledescending port ion ofthe stress straincurve.Ot her wise.the meas ure ments will rep resent a struc turalbehaviourrat herthan amat er ial behaviour,

In multiax ialtesting.the natureofthe testpreventsmountingany sensor,in asecureway. directly on thespecimen. Thus. unfortunately.it is only poss ibleto measurethe globaldeformat ions. thatis. isplatento platenmeasurements.Inbiaxial tes ti ng.however,surfacemeasurements. on thefree surfaceof the specimen.can be attained. Still.thesesensorsare subject edtocrackingand spallingunder the

anaehmempoi n tsof rhe transd ucerinthepostpeak behaviou r[35. ·11.-16].Thus . sucha sensorcanno t be used t'fficit'ntlyinthe postpeakregime asloss ofcon trolmay occuranddamage'ca noccur totheload ing actuators.

2.2.5 PostPeakBehav iour inBiaxial Co mpre ssion

Post peak behaviourofconcre teisofvi ralimportan cewhennonlinear finit e element analysisisused foraccur atepredictionofstruc turalresponse. Theexisten ce ofa descendingbranch of the stress-straincurves under biaxialst ressstateshas norgen- erallybeen observed. Xelisse n1151 atte mpt edto obtainthedescendin g portionof theStressstrain curve und er biaxialloading.Constantrateof strainingwas used.

How ever .Xelissen found thatthis partofthe st ressst raincurve depended onthe situ at ionofthemeasu rem en t instrum ents.As aresult,the descending branchwas nOIreported forany biaxialtest.

van~lit'r[18Jcond uc ted a notable-test program[0study thesoftt'ningbehaviour ofconc reteundertriaxial st ateofstress . Theexperimental program containedavery limited portionon biaxialcompressionloading.Thedescendingportion. for anormal strengt h specimen."asreported fortu·o low confineme ntstressratios.~dal

=

0.0.') and 0.10.Lnfcrt unat ely. atahigherconfinement ratio(a2/a3=0.331,thedescending portio nsofthe stress- straincurve.could not besUC"Ce'SSfuUv obtained.In addition . thespecimen'sresponse(stress strai ncurve]wascalcula ted fromtheplatentoplat en dlsplacemenr.Due tothe bendingofthebrush rods . corr ec t ions totbe stressstra in curvehad tobemad e usinga similaraluminumspecimen.Itshouldbenoted that sucha correctionmaynot beaccu rate.Inthe postpeakregime. concretewillcrack.

As aresult.the deformation.duetothe bendingof t be brushrods,willbesignificantly differentfora concret espec imen. Xc nerheless.thetriaxia ltes t data obtained from thatexperimen talprogramis considered tobefairly good and itiswidely accepted.

23

2.2.6 Loading Pat h

Taylor etal.

t -l'1

investiga tedthef'fft'(;[of rhe loading path on thl"biaxial respo nse of lig ht9.-eiglueggregareconcre te.Thefind ings of theirstudyindica ted that two- step sequent ialload ingsresult ed instrengths significantlyIOWE'1thanIhOSf'obtai nedfor proponionalloa dings.For nonn alstrengthconcrete.Xelissen[151observed that the maxi mum-sr rengrhenvelopewas lnde pende nrofthe loadpath.However. inhis study.

tbet'fectoftheload ingpathwasnotinvestiga tedforconcretewteh hig herst rength.

In conclusion.fromtheahm."f!'menno ned reasoning.itappearstha tfurt her in- vesrigations shouldbededicatedtostudy thebehaviourofhigh-strengthconcrete underhiaxialloading.Inthisthesis.an experimentalinvest igation.covering the en- tire loadpath is ca rriedoutto dete rmine the behaviourofhigh-strengthconcrete whensubjectedtobiaxialstateofsU('SS.

2.3 Const it ut ive M odels

Overrhe past:!5 yea rs.severalconstitutivemodels have been proposedandusedfor thefiniteelementanalysisofconcretest ructures.Anextensivereview ofthesemode ls was undertakenbyChenandSaleeb{-lSI.Che n{-l9]andrheASCEComm itteeon FtniteElement Analysisof Reinforced ConcreteStruct ures150].:\1E'an whilE'.CEatE'-- port{5l1provides a crit icalreviewof theconstitutivelawsusedformodelling concrete undermulrlaxtelsta teofstress.Inthis section.highlightsofthe availa bleconst it utive relationshipsforconcrete and theadvantagesand disadvantagesof these mod els are brieflysum marized. Ratherthanreviewingeachindivid ua l researchsepa rately. the mai n features ofeach familyofmodels are presented.

2-1

2.3.1 ElasticityBas ed Models

Tnt'elasneny-based modelscanbe dividedinto:a)linearelasnc.h)nonlin earelasth-.

andcl incremental[hypoe lastrc ]model.

Linearelas tic mod els

Thelinearelast icmodels art'basedODtherelat ion:

whereC".1ismateria lma t rixf(E.lll .and a' land

t. ,

arerbestressand strainvectors.

respectively.

ThesemodelsaresimpleandeasytoformulateandUSE'.Howes...r.suchmod..ls areDOlo ngerusedintheanalysis ofconcretestructures.Themain drawbackofthl"S'"

modelsis thattheyfailtoidentifythe inelast icdeformation.Also.thesta teofstress dependsonlyonthecurrentstat eofstrain.

Nonline ar elasticmode ls

Thenonlinearelastic(secant]model152.:>'1..j-ljcanbe expressedas:

whereF"isthe elastic-res ponsefunctionanda"and

f.,

art'thecompo nentsofthe stressand strain tensors .respecriv-ely,

Thesemodelsprovide a simple approachforproblemsinwhichmonotonically proportionalloadsprevail.Thedisadvantageofthesemodelsisthat the stateof stress dependsonl~..onthecurrentstateofstrain.These typesofmodels are limited to st ructures subjectedtospecifictypes of loading(monotonicand proportional)[.j -lJ.

25

Thein cre ment al(hyp oelastic)mode ls

The incrementalih~..poetasde]models[55.·56..5T]arebased on:

whereD'/tlisa mate rialpro pe rty matrix.which isa functionof stressorstra intensor.

andiI'land(tjare thestress andstr a in- incre me nt tenso rs.

These modelsareca pa ble ofmodelling manyof the charac terist icsofeoncre re behaviourunder monotonic load ings. In additio n.theyaresimple to formulatein comparisontoplasticandendcchronicmodels.The main disadva ntage ofsuchmodels istha ttheydonotapply insit uationswheretheprincipalstress directio ns rotate[;)8!.

Inaddition.theycannotaccountforthebehav iourofconcr eteinthestrainsoft e ning region.Also.thesemod e ls do notaccura tely describe thebehaviourofmnl·TN Punder c)·d icloading.

Recently,anort hotropicmode l was usedbyLink andElwi(591.ThemodelWiIS buih on theequivalent uniax ialstr a in concept advoc atedin;55..')6.57).link and Elwi[591.based onthatmod el.ca rr iedouta finiteeleme nt analysis(twodimen - siona l)ofcomposite ice resistingwalls.Good agreeme ntbe tweenthe experim ental and theoreticalresu ltswereachieved.Howew..r.it was foundthat the mod el poorly predictedthebehavio urofthewallssubjectedtosignifica nt lo ngit udin alcompressive loads.Thatwas attributedtotheoveresnm a uonofrbeco nfine menteffects

2.3.2 Plas t icityBas ed Models

Thetradi tio nalplasticity-basedmod els canbe classifiedas:a)elasticper fect ly plastic.

and b)elastichardeningplas tic.

26

Elas t ic perfectlyplast ic

Theetasnc perfectlyplastic:models areincrementa l innatu re and thl'Ycan represent inelasticstra ins inconcrete.HO\\""I'\~r ,the normaliryruleusedinthese modelsdol'S not applyaccurate lytofractured concrete. Thedisad van tage ofthese modelsis that they predicthighervolumet ric expa nsion upo nfail urethanobserved in practice. Also.since the failuresurfaceis fixedin theSltPSSspace, itcanno taccountforthe behaviourof concreteinthestr ai nsoftening region.

Elas tichar deningplast icmode ls

Earlierelastichardeningplasticmodels are basedon acertai n~'ieldsurfa ceandthe evolu rlonof a subsequent loadingsurface1[60.61.62. 6.11.amongot hers). rhey account fortheplas t ic strainsinconcrete and [her describeaccuratelymanyof rhe cbareceensncsofcoucr..te. Th e majordisadvantage of these modelsis that they cannot accountforthe microcra cking ofco ncrete since the normal ityruleis used.

Xlorerecen telastoplasnc models(6-1.W.66.67]are ohenUSE'dto describe the behaviourof conc re tein compression. ThPSt'mode lsmay('O'-errhesrress histor y dependr-ntbehav iour.They allow.inconnect ionwit hanonassociared flow rule.the simulationofthe nonli nearvo lume cha nge.Howeve r,theseelastoplasticmodelshac....

someinadeq uac iesinthetensionandmixed compression-t ension regions.Themain dlsadvanrageisthei r inabilityto model crackedconcrete. Therefore.in thesemodels

theel~lO plasticconce pthasto be abando nedrorallywhen tensile cracksoccurs.

Recently.the plasticity based model shan'made considerableprogress. Such modelsincorporated the useofthe recentconceptsof fracturemechanics{58. 691.

andconti nuum damag emechan ics (in theform of elast ic degradation)(;0.n].Thus.

plasticity -basedconsrttuttvelaws are capableofmode llingplainconcreteillcrac ked

'2,

and un-crarked states with the same elastoplasttcCOIlCl'Pt.

2.3 .3 End och ro n ic mod el s

Theendoc hronicmodelsarebasedontheconcept ofintrinsicrime.whichdpscrilws the inelastic st ra in accumulation[, 2,,3].Th<'SI'modelsan' ca pa bleof modelli ng a wide range of nonlinear behaviourof concrete. ThelISI'of such models requires a largenumberofmaterialparamet ersthat areincr em ent all y nonlinear .resultingill heavycomputationaliter ationinafinite eleme nt program.

2.3 .4 Damage Model s

A cont inuumdamagemechanics approachis USl'dtointerrelatedistribut eddefects and the macroscopic behaviour ofconcrete.Extensive researchwork011the applicati on of damagemechanic stomodelcon cret ebehavi ourwas..carr iedout and numerou s papl'rs WNepublished.for exampleI'~',5.,6_.._'8J. A review ofsome ofthe ava ila ble damage models IISM for concretera nhe found ill[,81. Ast a t e ofthe art reviewof damagemechanics can ht'foundin[, 9. 80.811.Recent implementationof damage mechanics tostudy the behaviourof plainconcr etedams wassca rr iedout by[82,83J.

The fundam entalnotionofthesemodelsis torepresentthedamage st a teofmate ri- alsb~-an internalvariable.which directlycharacterizes thedistributionof microcr acks formedduringtheloadingproc{'ss . Eachdamage model established nnx-hanicaloqua- nonsto describetheevolu tionofthe internal variablesand themecha nica l behaviour of damaged materials .Althoughther ehasbeenaprofounddisagreem entamongre- sea rchers rega rdingtheproper choice forthecha ract eriza t ionof dama ge. thefurther developmentof a moregeneral.and unified.damage approa chwillprovide a powerful tool in modelling concrete beh avio ur.

28

2.3.5 Microp lan eModels

The micro pla ne moodrepresents a mieromechan icsapproach tomod ellin g ccncrere behaviour.Originallypresented byBaia nt[8-11.the funda mental assumptionis thar thest ress-st rainrela ric ncan be specifiedlndependen rly on va rio usplanes inthemare- rial. assum ing that ebestr aincompone ntsonthe plan earetheresolvedcompo nents ofthestra in tensor.Thederivationofthe incrementalconsrit utiverolanr mship is given in BazanrandPrat[&>j.Incorpor ationofanonloeal softeningmodelintothe microplan emodel waslater performed byBaian tandOzbolt[861.

Althou gh themicro planemode lshows goodpromise forgeneralmulriaxialsim- ulat ion ofconcreteccnsruunverespo nse.muchmor e developme nt work needsto be unde rta ken. for example.inthe researc hworkbyBazant andOzbolt[8,]on cyclic triaxialbeh aviour of concrete.only uniaxialloa di ngcases wereconside red.In addition.thedeeay parameters used todetermine the consriruri ve mod uli arenot calibratedsufficie ntly. The spherica l integralsused inthe derivationof theccnstit u- riverelat ionshiprequiretheuse of severalinteg rat ionpointsonthehemisphere per GaUM point.which increases solutionrimedramatically.Thf'5E'shortcomingsmake themicroplan emod elunwieldyfortheanalysis ofgeneralconcretestructures.Fur - rhermore.the util izationofa micropla nemodelto analyzefullscalestr uct ures has yettobetac kled.

2.3.6 Adopt ed Mode lfor theCurrent St udy

Some mey contest thattheplasticity basedmodelsmaybeinadequate inrep resenting the crackingofconcrete.on the macro-leve l.asmicromech anicswould.Xeverrheless.

in the pheno me nologicalapproach to modelling a frictio nalmat er ial like concrete.it can bearguedthatall theessentialresponsefeatur es can berepr esentedin a tractabl e

29

model without theexplan atio n[ha l wouldbeprovidedb~"nncrom echa mcs.Suchan approachisjus tified by "needtoprovide engineering analysisofstructuralsys tems made wit h concrete.Thus theadequacy ofaplasticitybasedmodelcan heevalua ted on amacrcmecha nica lbasis.raths-r[ha n on amtcromecban tcel basis.as r..pn,spnrf'<f bytheexperimentsonspedmens on alaboratory.

The modeladopted in[his stu dyisbasedonErse andWillam1;1]mod el.Iti...

referred10 as theExtend ed Leon:\Iodt"i.Thedevelo pmentof tha tmoodoccurred gra duallyoyer the yearsattheLniversityofColorado.TheLeonmod el[881was firstemp loyed. byWillam I'tal.[891 10 characterize[hetriaxial[estdaraof medium strengthconcrete.Subseq uently.i[wasextendedbyPramoncandWilla m

fo Ol

ro formulate anelasto-plasri cconstiturivemodelfor hardening and softe ningbehaviour of concrete when subject ed[0arbitrary triaxial loading. The model"·ASfurthe r extendedbl-"Etseand Wiflam1;11[0become[he-Exten ded Leonmod el.

Theelasto- plas ticconstitut ivemodelbyPramonoand\\"iIlam{TO]waslmple- memedinto[he generalpurpose finit e element program AB.-\Q l"Sb~"Sit"t"[al.[90].

IIwas usedinanumerical inves tigationofhighstrengt hconcretecolumns.IIis worthment ioningherethatthelmplementatlonoftheEtse andWilla m[;11model.

inthecurrent thesis.is based ontheSit>Nal.{90]implement aion ofthe Pramono and\'"iIIam[;01.

Tha tparticular mode lwas ChOSf"Dfor[lit,purposes ofthisstudybecause it pus- sesses differentchar acteristics[hatmakeitauracnveforusewith finite elementanal- ysts.Thedevelopm ent oftbe adoptedmOOI"I.togetherwiththe mod ificat ion. calibra- tion.andimpl ementati onin a generalpurposefiniteelem ent programispresentedin Chapter

s.

.10

2.4 Finite Element Simulation of Concrete Test Specimen in Compression

The finite element meth od can be applied(0provide someinsight intodifferenttypes of basictes tin g ofaconc re tespecime n.Itcanb4' used toprovi desomeunderstand ing of thestress stateinthe specimen aswellas theinteractionbetwee nrh ..specimen andthe testing mach ine. Inthe following sections.a literat ure review ofsome of (hi' ana lyt ica l and finiteelement work usedin simulatinga compressiontest cylin de r.

ispresented.In addition. previo us worklnvclvi ng thesimulation of a brushplaten suppo rtfor bia xialtestingis reported .

2.4.1 Analytical an d Finite Element Studies of Uniaxial Test in g of Concr eteCylinders

Analyt icalestima tes ofthestr essdisrrib u ticnwithinacircu larcylind rica lspec imen under compression.withperfectlyconstrained ends.were made as early asthe begin- ning of thiscentu ry in 1902 byFilon[911using linea relasticity,Filon showed that thesta teofstress inthespecimenisnotpt'rfecrl~'uniform anda stressconcen trat ion exists atthecorn erends. Otherclosedform solutionsusingthetheory ofelas tici ty ban' beenproposed[92.93.

9-IJ ..

Al-Chal a biandHuan g{951provideda compariso n of someof thesepredictions andshewed that theydiffersignifican tly. linea rfinite elementanalysisofa test cylind erhave alsobeen providedforuns pecified rockand soil mater ials[961.Theeffects ofinsertsonthe behaviou rof cylinders. in uniaxia l compression. wasst ud ied byBrady{9-IJ. linearelasticanalysiswasperfor medon acylinder withinsertsusedtominim ize rhe end-plate-spec imeninterfacialfrict ion.

Threedifferent modu liof inse rtswereexam ined.Becauselinearelasncmod el was used .suchanalysis can becons idereduseful for theelast icrange only.The material