SHIPS IN ICE:

INFORMATIONTO USERS

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51_1ohn's

SHIPS IN ICE:

THE INTERACTION PROCESS AND PRINCIPLES OF DESIGN

BY

©BINZOU.M.ENG •• B.ENG.

AThesissubmittedtotheSchool ofGraduateStudies inpaniaIfWfilJmeraofthcdegreeof

Doctor otPhilosopby

FacultyofEngineeringandApplied Science Memorial Universityof Newfoundland

MaY,l996

.+. ^-..., """"'"

Aoquisiliansand

~Servic:n

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^=ONIUAONI

BibfioNquIrwionale

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Ac:quisibonI«

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The authochasgromedaece- exclusivelicenceallowing the Nationallibraryof Canadato reproduce,

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distributeor sell copies aflbisthesisinmicroform,.

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The author retainsownershipofthe cop)rightinIbisthesis.Neitherthe thesis norsubstantialextractsfromit may beprintedor otherwise reproducedwithouttheauthor'5 permission.

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Canada

n

Abstract

For ships operating inarcticand5l.l~arctic:waters. ice loadisa major threat. Due tothe unccnaimiesinice cond itionsandvarying open.tinSsituations. anaccu rl teeslima.

tionondesign iceloadisdifficult.Theobjectiveofthe presentresearchis(0investigate theiceloadsand theassociatedsauc=turaIstrengthfromasp«.Uofmedw1ics,swistics and design principles.

F"aru,theice-structureinteraction. processisinvesrig&ted fromtheviewpointof mechanics.TheinteractionisdwKterizedbyicelhaaureand damage.'Theiceload is highlylocalizedwithinhighpressw't:ttgionstermedcriticalzones_Anumerical analysis wascarriedOllila investigate howI.crackmay propagatein anicesheetand how theice materialisdamaged during anice-structu reinteractio n.The analysis showedthatsmall shearcrac ks. withmixedmodes, aremore likelythe candidates forthefracturespall.and the formationof criticalzones.

Criticalzonesvvyinspaceand time.Thesecril~zones aredtaracterindusing paramelers suchISspatialdensity.zonalIta.andthezonal Ibrce_These paramctmin themodelwereca1ibntedunashipbiaIdataofeCGSLouisSt.Uurenl.Theseeloads on •designara. weremodelledas •rmdom. number"ofc;:riticalzones,each withI.random fbrce.Buedon thismodeland extremevaluetheory••desilPlcurvewupro posed forthe estimation ofenrerne iceloads.

Third,thestrengthof thestructure was investigated.A long plate.loadedbyuni- form pressure wasproposedasthe designmoodfor thepllting.Duetolhe randomness ari ceload.thereareuncertainties associatedwiththedesignmodel.Toundencand this uncertainty,variousloadscenarioswereinvestigated usingthefiniteelement method_The resulushowthat theplatefails~•domilW1tsection.whichfailsin•way silTlllarto an '"equivalentlongpl~eM FutonAffecting the failureoflhepanelarelatenl5I.Ippon and

III

interactionberweenaiticaIZOMS.Thesefactorswereinvestigatedandempirical.formula wen:derived basedOftfiniteeIernencmodellins-

Asimplifiedmodelwasproposedtoimtesrip te thefailureofthe"equMJmtlong plate".Thismodelwasused,togetherwithfactors oflatenlsupport.locationandinter- actions~criticalzonesfromempiricalformula,inMonteCarlosimulation scheme tomodeltheunc:en aintyof thedesign modeloflhestnlCNre.Thesimulatedresultsof the uncertalnryfact orwereapproximatedbyalognormaldistnbutioft.

Finally,theresultsfromtheanalysisOftthe ice loadsandthestm e turalresist anc e were usedindiscussion ofthe designprinciples.Twodesignmethods. i.e.,reliabilityde- signandcode designmethods. were discussed.Principlesin selectingdesignlowandre- sistancewere discussed.Theseprincipleswereappliedin an example designofanoff·

shoreoiltanker.Reliabi lityof theplatesfromdifferentdesignstrategieswereeval~ted Itwasfoundthat.forultimaterupNfC,&yearlymaximumwithap~i1ityofQ~

of 10'"is appropriate1$the designload.

IV

Acknowledgments

[ amgreatlyindebtedto my supcMsor,Dr.Ian Jordaan,NSERClMobil Industrial ResearchProfessorinOcean Engineering, MemorialUniversity,for his inspirationand supponthroughout theproject.Hetaughtme anewmethodin approachingan engineer- ing problem,whichalsoaffectedmy way of everydaythinking.

I wouldalsolike tothankmy co-supervisors,Dr.M.R.Haddan.Chairman.Naval ArchitectureandOcean EngineeringatMemorialUniversity,andDr.G.Timco, National ResearchCouncil Canada,for their advisesand suggestions.Their help,especially inthe latter stages of theproject. is very much appreciated.

Duringtheprojel;t.Ihadtheopponu nitytowork withDr.Fredcrlting,Dr.B.Par- sons. Mr.D.SpencerorNational ResearchCouncil. Dr.1.Dempseyof Clarkson Univer- sityandOr.M_KachnovofTuft's University. Their suggestionsand encouragement are appreciated.

Thehelpandencouragement offered by my colleagues.Mr.lingXiao.Dr.R.

McKenna,Mr.MarkFuglem, Ms.M.Johnston, Dr.Sanjay Singh., Dr.Dmitri Mal- skevitch.Mr.BarryStone,Ms.Katen Muggeridge.Mr.TrevorButlerandMr.Bin Liuare greatlyappreciated.

[ amdeeplyindebtedtomy familymembers,mywife June, mysonJamie.,mypar- entsand parentsintawwho kept meinthestatewithfullofhopeandenergy.

Financialsuppon for thiswork was providedbytheNatural SciencesandEngi- neeringResearch Council of Canada(NSERC). Centre for Cold Ocean Resoun:eEngi- neering(C-CORE).Oft'ihore OevdopmentFund.NationalEnergyBoard.The courtesy andgenerosityoflheseorganizalionsis gratefullyacknowledged.

v

Contents

Ac:ka owledam en tl _

Coate.""' VI

Li5to(F"'IU""~

..x

USto(Tabln XV

Nomenc..lure.._ _ .._.._ ._ _._ XVI

ChapterIlntrodutti on_ _.._ _ _ _ _ . .__ _ I

1.1Xop:oC~WClf1r.. • ••__••••_ •••• .

Oapttr21u-Sh1Ittart •• terac1kt.Pro«u' - _

2.1~_ ._. ._•. . _ . _.._._._.__._••_.__6

2.2IccfrKtllft _. .__ __. ._ _..__ .._ ••.••.•.•.9

HAnalysi.01Bum ModeiByHulthi _ .1IdSuo. 2.SAna/ylUoiSmallCradA.DifrcRntLoc:atiolol...

2.6IccDamaac

2.'C~.__...__..__. ._

VI

...11

.. 22

. 21

... . ...l! .J<

...31

a.apln'JProbabilisticAaafysilol(uLoads JI

l.llllU'Odul:tioll.•__...._..•...._._.__••••__ ••••_ ... ••_..._

).2ExuanaIAnaIysi.l....•_••.•.••~••.•._._•••••••••••.••.••.••.•...•.•..•... ... •... .. ....•••.•...•..•... •. ....13 l.lPm-iauIExpmen.;einSwi.sticaIAtIalysisollceLmds.

J.J .law....-__._ .._ _ _.__ __ _ _ _ .__

J.J.JA"APP'O«*&.d_Dt1uJtifSJupR_,.,TnlJlJ .._ .._. .._ _47

UScMislicalAufrlilGlCrilQl Z -. .. H

J.4.1INj;,a#o#t0/.P70b1nl _

.._.._._..._ ..._ .._61 ...•.._.. _.._.._.._..._._ ...•.._.67

... ... . ... ..._ 72 J.J.ISltJIlnlQo{fuLt»dsi"1JII8tJltic.•..... ... ...7J

l.6Co1ldudiIll ~···__·_··_ ····_·__ ··· _

...]8

•••.••111

CbpCn' 4SC".ct1InlSlrnetlll "

~.II~ ._- - - -- - II

UTheLoocPlaeModcl.. ._.__._ _ ._ ... . ..._ ... U

4.1.1 T-Hi ...dn.--ffmpF..' _.._ __ _ ___

./.1.JFI"i~EJ~_"tA1III'ysUo/.~

l.Dn,

PltJI~.•.. . ... ... .. ... ...91 UThe PatchLoOII4 Model

4.J.I.'JodrIDrw~t .

.....9.&

••..•_.9-1 J.J.1RI... lu..__._. . ..._. ..._ .._ .._ .._._ ..__..._..__. ._ ._I Of

VII

~.~ ~ ~.. Critical z-£FORllS_ _.•.. .. _.•_.•_ .... _ _...IOS

HDcs:ip Stnqr ....__... ...1I0

UConcl_and.~ .._ _. ._ ....112

CUpcer 5 A Probabilistic: A• .."...rne Oesip MocId

.14

S.llrwoduaioll_ _ .._..__ _. . ._ __ ...•

UStruduql~..RaIistic Loads_ ._._ . 1.:UCtutt$Wiu.~C"tjc"' z-..._.._.._

... ...•._.IIS

1.J.2.\f~""'rt1tWAdi<lootINi(,1ti_ R..pnue. _ J.J.JkJll'I"DIttIC~lf'idlFi",~~"t.\fOtklli",,_ _ ...

1.! .!n.~C~WitIlTwoOl".lfonC'ilicaI ZCJMs 1].1

5lALongPlateLoackdBy I'lon-Uniformforces III

S.J,ITJr,,"Hi~ J,f~j_ _ _ _ _ _ /J/

... ...._.._/J,I

..._ .._ .../J1

U ModdiJta:ofthcU-wmyill l!lcDaip Mldd • _

J.4./Tlw.\.Iod61_ .._ . ... .__..._...._..._ ..._ ....__ /J'J

J.,I.!RLDIIlS. .._ _.__•._ _ .. . _ _ _._ /J!

S.6C oad U5ioesand ~ ...__.__.. _ ...._ ..._ ...I..S

CIIa p lft' 6DmtaPriHiplpl.... _

6.1lJwodul;tioa _. _ _~ _.•_ _ _ .

6.2OaipMelhc:ds_ _ _ _ _ .

'"

•••••••••.•.•.•.••.••.•..•••_._•.•.•••• •• • ••••••.••.••.•..•.•.../JO 6.!.!CO<klNsip.•.• . .. ....... ...JJJ

6.lDesign Load.. IS..

... •.../J1 .../J1 If.J_JDd1P'/ct l.otJdfo'r~CO<'t«fXlNSlf"...• ...•. ....•...•... ......./If/

\10

6,~~olt!ll:5cnIaure.. ._..__ .. ... ..._.._.._._._. •._._

6.'Desip olthe Pbc:i..,.. _

6.1.1~r~IdQllt/ ~icL1ti-~ Slrrssu--.---_-.

'"

._..1604

Ct••pler1CoodudidlRt ...rIu 171

Ibf~. ' "

LX

List of Figures

Figure 2. I SchematicIJlustrationofACriticalZoncwithSpalls

Figure2.2AngleotCracIc Propaption{Palaniswamy and Knauss, 1914) 12 Figure 2.)Dataof Sben and Lin (1916) FinedtotheMaimumSERRAnalysis of

PalaniswamyandKnauJs(1974).DataNormaflZed withKf'O.I07MP.m^H 12

Figure 2.4Kendalrsdoublecantilevezo beam I]

Figure2.5Kendall's modelforlheaackoff'thecenter line (fromKendall 1978) IS

Figure2.6StrutS withno (:onstrail1Jatfree ends 16

Figure2.7 DoubleCantilcver Beam withrestrainedends from DeFranco andDempsey

(1990) 17

Figure2.BAnicesheetwidt•central crack,loadedby an indentor 18 Figure2.9 (a)Resultsofstrainenergyreleaserate.(b)dec:ailof6gurc(a) 20 Figure2. 10Anicesheetwithcrackindifferentverticallocations 21 Figure2.IIGvaluetforaxbatdifferentlocations 22

Figure2.t2 ABeam ModdbySoo(l 990) 2J

Figure2.IJAIIldeal.izedIce-SlI\JCtUte Imeracrton 2S

Figut t 2.14Ana/ysisonthntTcaoClocationoftheaack 26

Figure2.ISAnalysisonetfcaofw 21

Figure2.16:Analysisontheeffectofw. 27

Figure2.17 Resultsof MonteCarloSimulations 29

Figure2.18Tensile StressZoneandShear stressZones ) I

Figure2.19GValuesofDiffemrt CrackLengths 32

Figure2.20 Schematic Illustration ofPressure VanuionDuringtheInteraction Process3:5

Figure2.21 Effect of Spalis onTotal Force 36

Figure].ISchematic:VIeWof ThreeRegionsofPressurewithin aDesignWindow ]9 Figure]_2 Critical.ZoneActivityWithinthe ContactArea.,(buedonBlountet:&I.,1981.

~O ~

X

Figure3_3TheTailof.Distnbution 46 Figure3.4RankedDmonLoc.a1PressureMeasured Onboard theUSCGC Polar Sea..

(IordaanetaI.199 3.) 49

Figure 3.5Resultsofaror Inp.vs.x Plots(Jordaan etaI.•1993.) 50 figure3.6Probabilitydensityofexuemepressure(Iordun etaI.•1993.) 53 Figu re3.7SchematicIIIustraIionofContactArea.CriticalZonesandDesignWindoW154 Figure3.8LocationofVariousPressureSensors(dashedc:iedesindicatesemoninieac-

rive region.eachm:ungularin solidlinesindicatesthearea.pressure sensorrepr~

senuinapproachB) S6

figure ).9ApprolcimationofCriricalZones 57

Figure3.10 TimeSlicesCormpond toPeakPressures 61

figure3.IIProbability of CriticalZonalForce 62

Figure3.12 Schematic VIeWofADesignwithTheCriticalZones Figure3.lJModelling of CriticalZonalForces

Figure3.14 ProbabilityorLocai Pressure(Result s ofApproach A) Figur e 3.15 ProlnbiliryorLoca1Pressure(ResultsofApproac h B) Figur e 3.16 Results ofa. Values

6'

66 69 69 70

figure].17 Resultsoh.Values 70

Figure3.18ModifiedValuesofx. for MaximumPressurePerRam.

n

Figure3.19Scht:maticDiagram Showing TimeTrxesfOf"a).Ramandb)a Continuous

Intcraction(fi"txnJordaaneaI.•1993') 74

Figure3.20 Themostprobableextremeloadsobtainedu a functionof days in icein vari- ousseaarearortbebowframe(FFR2)(fromKujala.1991.Figure14) 76 Figure 3.21 ComparisonBetween CanadianArcticClusandBaltic Ow 79

Figu re 4.I AShip Panel Subjectedby IceImpactLoads 83

Figure 4.2Schematic D1U1tcu ion of PlasticFailur eMechanism(basedonCaneretal.,

1992). 85

XI

FiKUre 4. )(a) SC:hematic: Diagram of a Plate With FilledEndsandLoadedbyLateral

Pressure, (b) Distribution of Bending Moment. 87

Figure 4.4 Sc:hematic: Diagram ofThree Hinge Mechanism. 88

Figure4.5 Schematic:DiagramofMembrane Action 89

Figure 4. 6Sc:hematicDiagram ofMembrane Action Failure Mechanism. 90

Figure4.7 Mechanic:aIPropertiesof Materia! 91

Figure 4.8Asection ofthedeflectedplateand the distribution ofthe princ:ipalstrains 9)

Figure 4.9mustrationof Different Failure Mechanism 9)

Figure 4. 10AnIdealized Plate UnderLareral Pressure. 95 Figure 4.II RigidPlastic Defonna tionandElasto-plastic:Defonnalion 96 Figure4. 12 IUuSlrationofThree PossibleFailure Patterns. 97 Figure4.Il Variation ofNonn alizcd Pressure al Collapse against B 102 Figure 4.14 The NonnaJizedSlrengthofthe Plalewilh Different LoadedWidlh 102 Figure4.15 Nonnaiized Strength for Different Deflectionsat MidspanPrior to Failure10)

Figure 4.16Deformedpanel(H.0.)m) 104

Figure 4. 17Pressure vs.displacementat midspan 104

Figure 4.18 Strengthatvariousload widdIS 105

Figure4.20 Selected Load Cases 107

Figure4.21Defonned paneL,shawin!contoursofprinc:ipaJstrains(Case I) 108

Figure4.22Pressurevs.DisplacemeJlut midspan 108

Figure 4.2) Deformed panel and distributionsof principal strain(Case21) 109 Figure4.24Deformedpanel and distribut ions of princ:ipalstrain(Case 22) 109 Figure 4. 25Deformedpandand distribulions of principal strain(Case 2) 110 Figure4.26 AnaI)'1isof designpressure fO"CACIVessels withr=O.46,n=10000 112

Figure 5.IProbabilityof theNumberofCriticalZones ona

o.n

m!Panel 116 Figure 5.2 ProbabilityDensity ofCritical ZonalArea(fro m ApproachAofChapter3) 117 Figure5.)ZOnal Forces vs.ZonalArea(fromApproac:hAof Chapter) 117

Figu re5.4 A panelloaded by onecritical zone 119

XJl

FigureS.S Thecasewithone criticalzone 120 Figure S.6Analysisof the effect of the lengthof criticalzone,h 122 FigureS.7Analysisofthe effect ofthe locationofcriticalzones 122 FigureS.8 Relative locationsbetweenCriticalZones 126

FigureS.9Caseswithtwoor morecriticalzones 127

Figure S.10Effect ofh(theanalysis issupponedbythepreviousanalysisofh) 129 Figure S.11 Analysis on theeffectofinteractionbetween criticalzones 129

FigureS.12AnalysisofCASE C 132

Figure S.13 Schematic Diagram ofaBeamLoadedbymultiplePointloads 133

FigureS.14ThreeHingeMechanism 134

Figure S.IS Schematic View of Membrane ActionofaBeam Loadedwith point Loads13S FigureS.16 Beamunder DifferentLoading Conditions,(a)Beam.LoadedbyUniform

PointLoads, (b) Beam Loaded by Tent ShapePointLoads.(c) Beam Loadedby A

Single PointLoad 138

FigureS.17Differentloadcases 138

FigureS.18Variationoft be locationofacriticalzone Figure 5.19 A randomlychosenloadcase Figure5,20A Scheme of MonteCarlo Simulations Figure5.21ModelUncenaintyfor PlasticCollapse Figure S.22ModelUncertaintyfor UltimateRupture

14 1 141 143 144 144

figure 6.1 Anal)'lisofaDesignDecision 148

Figure 6.2Comparison ofFailureProbabilitiesa)ASafe Structure.b)AnUnsafe Struc-

tur e.

andc)An Over-designedStructure lSI

Figure6.]Schematic View of theProcessofOptimaiDesignofSlfUcture 152

Figure6.4Load-ResistanceProblem 154

Figure6.SSchematicillustrationofditferentrulesofspecifjingtheload 158

Figure6.6Threeclasses ofloads(Maes,1986) 158

Figure6.7Relationship betweenSafetyFactors and ExceedanceProbability [60

xm

Figw-c6.•ProbabilityofFailurefocDifferentPllte Thidcness Figure6.9PlateThiclcnt-uforDifferentDesign5rmegies Figure6.10Probability ofFailure(ullimau: Rupture) Figure6.II Probability of Failure(Three hingeFailure)

XIV

,.7

169 170 170

List or Tables

Table 3.1 Areausigned foreachprnsute sensor 57

Table 3.2Mean zonalAreaand the SpatialDensity 60

Table l.)Panmet m ofexponemialdistributionofcritica1zonalforce 60

Table4.1Puticuian oftbeplatebeam 92

Table4.2

P

valuesfordifferentases. 97

Table S.I Results offiniteeIemenI~IforCasesIto 20 123 TabfeS.2Rnultsof6niteel~analysiJforCasa2110)9 IJO TableS.lTheMeanPressureatThree HingeCollapseforDifferent Load Type 137 TableS.4ComparisonofPointLoadModel.withlheApprollimalt Solutions 138

Table 5.SResultsfor Casesd,eand( 139

Table S.6 ProbabilityDensityFunctions COI'ModeiUnceruiJYY(lognormal) 142

Table 6.I PrincipalParticularsof the Vessel 148

TaiMe 6.2PlateTbicImessforDifferentClassShips 167

xv

Nomenclature

AN zonewithhighpressure A! regionwithlow pressure

A" spalledregion designarea("r)

uncertaintyindesign model orthe structure cdl cumulativeprobabilityfunction COV coefficientof variance D.v damagedue10microcraclcing

£ Young'smodules(MPa)

fJII~. J/ factor ofJatlCfa1suppoct forplastic collapseand ultima terupture,respectively fJ~A,/..,t factorof locationfor plasticcollapseand ultimate rupture, respectively h~:.f,.: factor ofinteractionsupport forplasaiccollapseandultimaterupture, respectively Fzf:J cumulativeprobabilityof Z

G SlnlinEnergyRelease rate (Jlm^J)

length ofthecriticalzone(m)

K, Stressintensityfactor for modeI (tensile)fracture(MPaml.'2) Krc fracturetoughness (MPam^V2)

K11 stressintensity factorfor modeIT(shear) fracture(MFa m^li1) load

XVI

M bendingmoment(N.m) M, plasticbendingmoment (N.m)

numberoframsperyear Pm pressure at2-Hingecollapse (MPa) Pm pressureatJ-Hinge collapse(MPa) p. probabilityof«ceedance p~ pressure at ultimate rupture (MPa)

proportionofhits R resistaneeof thestrueture Ft resiSlancefrom the design mode!

r, specifiedresistance framespacing(m)

damageparameterdefinedin Shaperay'stheory.

platethickness(m) Ur totalenergyofthesystem

designload specifiedload

Z themaximumof asetofrandomquantities dispersionof doubleanexponential distribution loadfactor (Chapler6)

p mareriatfsctor

xvrr

~ deflectionatmidspan aspectratio ofapanel AI expected numberof events It parameteroflocation

IJ,E(X) meanofX Poisson'sratio

directionoffracturepropagation(cad.) spatialdensity ofcritical zones(zoneslm^l) O'r yieldstress(MPa)

O'y' (O'y"'0',J/2

ultimate strength (MPa) 0:VAR(X) Variance ofX

parameterfor interaction betweencriticalzones

XVUI

Chapter I

Introduction

1.1Ov.rvl~

Thehullofashipisexposedtoditrerenc environmemaifOl'CC$.duringttsliferime. These fon:ainclude hydrostaticloads.waveloads.wind loadsandiccimpact loads.The load during interaction withiceisamajor consideration for the designofshipsin arctic and subarct ic waters.Considera ble forcesdue toiceimpactmay resultwhenan arctic class vesselstrikes multi-year ice orice island fragments.orwhen asubarctic vesselstrikes anundetected growlerorberg)'biroForJ.designeroran engineer.choosing.designicc load basalwaysbeena cba1Iengebecauseoftheuncertaintiescf'iceloadsin nature.These uncertaintiesarepartiallyduetothevaryingiceconditionsandthecomplicatednatureof

Fromtheviewpoint of mechanies.,ic:e-struc:tureandte:e.-vessdinteraction(except atverylowratn)is chatal;terizcdbyicefractureandice damageprocesses.Themeture usuallyinitiatesfromftawsandirregularities in theice andresults in discretepieces of ice spaIlingall Consequently,thecontactareabetweeniceandstructureisreduced andthe pressureontheice-structureinterfaceisredistributed.Inaddition.the stress within1M ice musisredianDuIed.wbK:h QUKS additionalspalls.The pressure in

me

reducedcontact:

areas.especi&Ilytow ardsthe ceeree.is veryhighandlheice is subjeaed10severedamage

Thesehighpressureregions(termed criticalzones)cornspondtotheareasonthe strue.

turewhereIouIizediceloadsoccur.TheaiticaJzones arelmpottantin the estimation of ice loadsandstructural designand are the focusof the prnent. research.

Thel'racturctrajectories dictate sizesandgeometryof spalled ice piecesand thereforegovern dieformation, number.sizesandimensiti esof aitical zones.Fr~is randomin nature due to therandomnessofftaW1andirregularitiesinice.Asaccese- quence,aitiaJ zonesare alsorandom..Ithasbeenobservedfromtheshiprammingtrials {eg.men and Bklunt,1984 )andinmediumscaleind emarion tests(e_s- Frederlcingetal.•

1990 ) thathighpressure zonesconstantlydisappear andreappear.move&-omone placeto another and chan8e inimmsity.The randomnessoficeload and eritical zonescanbeac- counted forbya probabilistic analysis.Usually, the probability distributionof ice load can bederived frommeasurements of fieldtests and ship ramming trials.Suchadist ributio n can thenbeusedinthedetennination of the designiceloadcwthe designrtsistance forthe

The structureofaship'shull isa complexcombinationof plating.stitfenmand suppo rtingframes.[nprw;:tK:e,thestrengthoftheship suuctureisdividedintothree components.These are primary,secondary and tertiary (paulling. 1988).Theprimary,or global, strength is associatedwith the hull girder.Loads affecting the hullsirderare gen- erallyglobalimpact loads.The secondary,or semi-localstrength is concerned with the strength ofa luse plate panel(orJril1as e).Theterti ary.orlocal.strengthis concerned wit hthestrengt hof plating betweentwostifTenenortwoframes-Thisregionmust resist

localized ice1oacIs.,especially theaitic:alzonesdwresultfrotntheice fallure medwUsrn.

This region is thefocusoftheprnentSlUdy.

Fora ruleNseddesignfor ice, such as the Proposals for ArcticShippingPollution PreventionRegulations(theASPPR ProposaJs.Melville Shippingltd.•1989),theplaling is usually rreatedualongplate.,loadedbyuniformlateralpressure.Theplate mayfailin oneofthree limit sutes.,e.g.thethree-h.ingeeoIIapse,pmnanenrsecandul1inwerupture. Thethree-hinsf:coQapseandpermanent-sec areusually associatedwithsmricability whereasultimateruptuJ"eis concernedwithsafety.ThekJng platemodeliseasytoimple- ment.Inreality.the iceloadson aplatearemore complicated thuItheidealizeduniform load.Criticalzonesmoves fromplace10place,andchangeininlensity.Depending onthe exactdislribution oftileload.the responseofthe plate could be quite differentfromone case toanother.Thisresultsin an uncenainty inthe design modelofthestructure.

Thesuength ofasuuctureis also random.Thisis because ofuncertainliesrelated 10stI'lIClW'aIsizeandmaterial strength.Aswas IeamedfromthereviewandYf:rilication ofT1wASPPRProposalsbyMemorial Universtryof Newfoundlancl(Carter eal-199'2).

theship sttueturalstrengthmightbeaffectedby unceruintiesinplatethidcness,material strength,weldeffectandheat.atfectedZOlles.

Anoptimaldesignof the structure shouldaccountfor all uncertaintieswociated wilh the environmental loadsanddesignmodel.Sucha designcan beviewedasI decision process. The designermustgivedueconsideratio n10twoconflictingobjeaives.i.e.

safetyandeconomy.TbeomicaJ.Iy.thereisnoabsolulelysafestNclurebecauseofuecer- laintiesof environmentalloadand stNClUrairesistance Thesafetylevel:of asructure can

be evaiua.tedby!heprobabilitYof struauralsunival.This probabilitycanbeobcained fromtheprobabilitydensitiesoftheload and resistance.Anoptimalstructu reshouldhave aprobabilityoffailureclose toataradvalue whichis acceptedbythe~ginceriniprac_

tice.Therearetwomethods inItruCruraIdesign.namelyreliabilitymethodandcodede- signmethod.Forthefirst.the5lJU<:tUnistrengthis selectedbased on thetargdreliability. III thesecond.thestnIdureis designedaccording10.designrule.Therulehasan inlrinsic safetymargitI accepted by theprofessiocL Newrulesare also calibratedbyreliability

...."..

1.1Scorn

ofth~

Work

Mechanicscrtce-seucrureinteraction,statistics of iceloadsand reliab ilityana.Iysis ofstructuralstrength are threeimponanrandinterlinkedaspectsforrbedesignof a struc- ture.TheproposedresearchpresenlJ an approachwhichintegrates

an

threeupecu.The focusof theresearchiscriticalzona (~iudIUghprusureregionswhicharethe key dementSof ice loads).Iwillinvestigatehow theyformand how they affecttheovenIlice loadsand theresponseof the5tNChJre

Fint,IwiDinvestigate theice-structure interaction processfromtheviewpointof mechanics.Iwill investigateexistinlfracture modelsandtheirapplicabilityto theprob- lemsof spallinland formationofcritical zones.Iwillinveuigatethe propagationofsmall cracksindltferenlsuesszoneswithinanicesheet.

r

willalsoinvestigate thefraaure damageintaplayprocusby.numericalexample

Second.we propose a probabilisticapproachto the estil'lUtionoficeloads.Extre- malanalysis andits applicationinevaluating designjceloadistiBl discussed.Critical zones arequantifiedbyparameters suchu theirspatia!detlsity.sizesandintensities.

These parametersare calibratedusing theship rammingtrial dataof LouisSt.ullrent.A probabilisticmodelofaitical zonesis~whichassumesthat the iceI<ndonade- signareaisappliedthrougharandomnumber ofc:ritiaJzones..each witharandom fom:

Thismoddisthen usedinderiving theprobabilitydistributionofextrema!teeloads.

Third..wcwill investigate thestrengthofthe5U'UCtUn!.WewillfocusouranalyS:s on the s1Upplating.The longplatemodel.which isused inpracricaIdesign, wiDbere- viewedand differentfailure mechansims willbe investigated.Theresponseof . plateto variousrealisticloads willbeanalyzed using afinite clementmethod.Along plate model.

which accountsforthe nolHlniform loads.willbe developed.Thismodel.togetherwith the resultsfromthe finiteclementmodellingofvarious~scenarios., will beused to analyzethe~IIIYof lbe design moddof the struerurc.

Finally,wewilldiscuu theprinciplesof desiglt Theseinclude•discuS5iorlon differentdesignmethodsinpracticeandrationaleinsdcctingthedesignloadsandresi,.

taoce. Theprinciplesare appliedfor thedesignof platingof a tanker foroffshoreNew- foundland waters.Platethickn essaccordingtodifferent designstrategiesarederivedand theprobability of failurefor eachdesignisevaluated

Chapter 2

Ice-Structure Interaction Process

2.1 ln trothlction

Ice-structureandice-YnSdirucraaion(accprIt\'ftYlowrates}is dwacterized byicefractureanddamagepnxc:ues.Thefractureusuallyoccunnear thefree edge bee- dering theaetuaIcontact ueabetweenthe ice andthesuueture.Such fractures resultin largepiel:esofice spallingoff and•reducricnin theremaininJcontact areas.The pres- sureinthesecontACtareasisveryhigh, especiallytowuds theeemee.Theareas havebeen termed mlkalzona.Extensivedamage toice usuallytakesplaceinthesezones,There isevidencetNt icehasbeenmicrofractured..brokenintOsnWlpiea:s,sub;«tedto pressu.remeltinlandsinter-edlOj:etMrinthesezones(Jordwl,)Ciaoandlou.1993) Thesezones aboCU1'Ymoltof the iccloadand aceauci&ltotheInOddlingofthe g10baI scaleetfeclandto the analysis ollocalpressure.Spa.lling by fracturegovernsthevariation ofsize,numberandlocationofthese zones during theinteractionprocess Figure 2.1 schematicaUyillustratesan interactionwithonecriticalzoneandspalls.

Spalling byfracturehasbeenanalyzed..using finiteelementmodcl.ling.byXiaoand JOfdaan(1991)inttnnSofw propaptionofafLawlocatedneartheice-structure

Spall Event

\ - ~""-

~/

/

/ /

Fip n2.ISd wWlDlic:JJalNlJionojACrltiaU " - withSpaJh

icespalling offand a reduaion ofiaforce.Furtbennore,theyround1Iw tlaWipropapte morereadilyinzones oflowconfiningpressure.Thesezones arelowednearthefree surfaceof theicewherespaIIsareoftenobserved. ARawmay propagateina tensile mode,ashearmodeoramixedmode.Theyalsofound thatW lensilezones nearthefree edgeofanicesheetare often small.Zoneswith highshearSlress tend10belarger, witha higherprobability ofcomaining a flaw.Fractur eisunlikely tobeiniliatedfromCTlCIa underhigh confininSpt"essure

Evansetat (1984 ) proposed asemi-quantiwivemodelforthe spallingof edge.

loaded ice sheds.Themodelwasbl5ed on. the plairHtraincavity expansiontheory (Hill.

1950)and elasticplate bending theory.II confirmed thai the forca required 10 propagate spall cracks are relativelysmall bul the authors experienced difficultiesincalibratingthe parametersinthe modelbyaperimcnts

CriticalzonesandspalIsarerandominnature. This!wbeendemonstratedin mediumsale indentation tests (i.e.Fredcrtinget&I.1990)and shiptrials (i.e.Glenand Blount1984).wherehigh pressureareuconswttfydisappe:arandreappear,move from one placetoanother,changinginintensity.The prob.blIisticnatureofcritical~and spalls isassociatedwiththerandomness offlaws inice.whichlead to the initial ionof spal ling.Similarto other material s.iceco ntainsmanydefectssuchas cracks.inclusions, pores,grain boundaries andotherweakness.Boththesizeandthelocat ion ofthese are genenJ.lyrandom.Forthisreason,IprobabilisticanalysisofexistingBawsis needed.A probabilisticmodelbasbeenproposedbyMae!et al_(1916),byassu.mingthat thecracks arerandomlydispenedin ..malerialvolumeaccordingto..Poissonprocess.Onthe other hand,Kendall(1971)refemdto theprobabilistic:approachu~dubiousstati sticalargu- mentsinvoMnginvisibleflaws".HepropoKd ..detmninisricmodd.,wdIlcnownu"'thc double cantileverbeam",which usumestllat .. eentr21ly located crackdivides..beaminto twocantilevers andthatthemultins bendingmomentoneach canlileverresultsin crack growt h.It hasbeenfoundbylouet&I.(1996) thai thebasicassumptioninKendalrs model,tha iis. treati ngtwoSlIUtSu elasticbeam,isonl.y validforlargec:rac:klengthJ (ie Thethicknessof an ice sheet).Cradtsofsuch lengthand of such Ioation can be rarely

berarelyfoundinnature.Although.longcentralcrackshavebeenobservedinsome indentation tnts(K1miand Muhonen1990). they aremorelikely fonnedu • resull of thepropagllion ofsma1Imc:ks rather thanbeingpresentasinilialflaws.Inaddition, DcFnncoandDempsey (990)foundthat thebounduycondilioninKendall'smodd is nor

wen

defined.which may resull inthefractureforceestimatedbeingcJose10 one tltird of the realvalue. Therefore., thercplacemenl: of"imisble flaws"(forexampleanin boundaria)byapreciselylocated yeIabo invisib'e c:entralcnckis a questionalMe alternative.,whichwiDbeinvestigatedindetailinthissection.Inaddition, a deterministic analysisof the propaguionofmc:ks,withdifferentlengths and locatedindifferent regions withdifferenl stresscondilions, will be analyzed.Finallywewillreviewsomebasicaspect ofdamase mechanicsand thefracture damas e intCIJIlay during theice-structure interactionprocess.Webegin our analysis fromsome basic aspects ofice fracture

2.2 lee Fracture

~described in Section2.1.liactureofice usually initiatesfroma flaw in the ice.

According 10lineat clastic &aaure mechanics (LEFM).a crack will begintopropagate when thestressintensityfactor althecracktipexceedsthefracturetoughness. An equivalentcriterionofstressintensityfactorisstrainentrIY release rate.The fracture tou ghnessof freshwalerice Wlgesfrom0.1to 0.14MPa111111_andtheCOrrespondinll criticalstrainenergyrelease rate 1'&1\8" from I to 2JIm!(Timco and Frederlcing.1916;

Dempseyee&I.•1989 ).

Once thefhcrureisinitialed.,ils subsequentpropagationdependsonitssubility.If thefracture continues10 propague.lhen thecrackisunstable. Ifadditionalforceis needed for continuJ.!crackarowth,the cnck isstable.Thestabilityof Icrackcanbe anaJyzedbythedlanse of stninenergyrelease meGwithrespecttocrack lengthQ,~^•

The CBdc:isunstab4ewhentheratio is graterthan zero.In1ftice-struaweinteraction.

1ftunstable cnck maypropagate intoIcompreuiYeroMandbecome stable andl'IOf:cause anyeu.utrophic:failw-e

AsalreadydiscussedinScaion 2.1, acradc may propagate in atensile mode. a shearmode or. mixed mode.Themixedmodefracture hasbeenstudiedertensively,eg.•

by Sih(1913),PalaniswamyandKnauss (1914).Conrad(1916),Cotterell andRice (1980).SihandTzou (1983).Hutchinsonand Suo (1992).There are threeprincipal theo- ries:first.that !he craclt will propagate Itrightanglesto!he muimumlensilestress.sec- ond.!hatiI wiDpropagateinthe dircaionwhich~tothemuimwn strainen- ergyrelease rate(SEIlR).andthird.theaackdirectionisthatwhidl correspondstothe strain enetiYdensity.The moscfundamental oftheseisjudged 10 be !he awcimum SERR. [ndeed.Conrad(1916)quotesfromGriffith:'"thecrack willgrowinthedirection alongwhichtheelasticenergy release per unitcrackextensionwillbe lheII'\I.Irimumand Ihecrack willSlUt togrowwhenthisenergy reaches10acritical value".For prlctical.

purposes.thereis linledifferencebetween thefintandthesecond criteria.Thisagrees withtheresuhs ofHulchinsonand Suo(1992 )whofound nodiscinction between acrite- rionforcracklrinlcingbasedonnwtirnizingstrainenergyrelease rateorbuedon propa-

10

propagation in thedirectioninwhich

x..

O.Figure2_2show1thatthe&ripof crack.

propagationcorresponds tothemaximumSERRwithrespect tothe ratio of K;Xn.where K{andKrtarestress intensily factors of tensileandshearmode respectively.Figure2.3 shows criticalvaluesofK1andKuItwhich themaximumSERRIt the direction of ClJ;ck.

propagation rachesthemateri&lfracturetoughness. Values ofKJandICDarenonnaIizcd withIVcandplottedtogetherwith the results ofmixedmodefracturetestSonicebyShea and Lin(1916). Thedosed formf~ohhe rebtionshipsinFigure 2..2and 2..3Me derived andF-abelowforthecom.'Cnience ofanalySs·

"&'=[-o.OO737l<..

&i

-O.6642 "&" + O.671r-: , (2.1)

Kit: Kit';

« ;

-fJ=exP[-o. OOOOJJ I8(& )J+0.01665(& )1-0.319 1'& +4.309 7]. (2.2)

KII Kif

«,

Acrack.mayalso propagate when the crack tipisunderIshearstress and I con- finingpressure.Thepropagation in this cue is more difficult t!wlforthe case of milled modetensileand shearcracksuindared bythe studies of Hallam (1986).Kadwtov. (199) andbySmithandSclluison(199 1).

2.3 A nalysis ofKendall's Double Cantilev., Seam Theory

KendaJI'sdouble cantileverbeamis showninFigure2.4.Thebeamis filledII one end and free It theOther.Acentrally10000edcrackatthefreeend divides the beaminlo twostruts.ApunchII thefreeendcausesthe stl'uts to'bendandshearoutward'.

II

80,:"-(-...

-=---) '-- - - -- - - - -- -

60

!

'

9:angleofaxkpropI8Mion

20

15 10

,

20 r

0 0-,-1

---.,...----,,.---.,,.--~

Fipn1.1A.ng/~o/Crac*PropagruiM(pamw-yandXnmill. /97.1)

1r,- - - - -- - - -- -- - - -

08

'~ .

^•LiaoleRMtMlloldt,.SIlt_-SLillo.I 916

, (1.owo:ru.uT-U3K)

06: _."

04~ ,

0.2

t

0.5 1.5

o~~ ----=---'-'---~---:_'

Figure1.jDataofShtnandlin(/986)Filled10the MartmllMSE.RR Analysisof Pa/aniswamy and Knartss(l9U).DataNonna/iudw,;,hKt-O./01MPa1fIlt2

u

Kendal!simplifiedtheforce ofthepunchastwoconcentra!ed~on the freeend{see Figure2_4)

Accof"ding to the Iawo(enugyconservation.thetotalRn.in energyofthesystem(

Ur)doesnotdwlge with theaack lengthcfor..st.tblecrackgrowth.

dUtdc==O (2.3)

Thestrain energy duetothepunchh&.stwo majorcomponents:compression.corre- spondingto forcesFI2applieda10nstheaxes ofthestruts,andabendingITM)mentcaused bylheeccentricityof !heforceFI2. The compressivecomponent isassumed not to

IJ

chmge withthe crack lengthand lha-efore disap pearsfromequ~lion(2-3)Thebending componer1lbthe simplebeamgeometrycanbe derivedas·

(1.4)

andthe total energy of theIYstem (excJudinS the compreuive component) is given by:

(2.5)

whereRis the surface energy.Applying theaboveequarion to eqIWion (2.3) Kendallde- rivedthefracturedrivingforcefor"astablt:crICk:prop agati on:

(1.6)

Withthesameprincipledescribedabove., Kendallalsoderivedtheforcerequiredto propagateIend:whichis norb:atedItthecenterofthebeam(seeFigure2.Sa)result sho ws that the force required topropagate the crackisminimum whenthe crackislocated attheeentC!'(see figure2.5b).HenceItt:conclud edthat"therewillbeapreferencefor crackstotravelonthecenaaIplmc".

SomeofKendaB'susumptionsare nowdiscussed.FIfSt,inKendall'smodel,there isnolateral.restninton thefreeendof thestruts.Thismeans thatthestrutsarefree10 run intoeach othe r asshownin figure 26,which doesnotcorrnpondtotheintended idealizati onin Figure 2.4.In reality,thereis a reactionontheendofeaen SIN!causingan

"

F~

(.)

0.50

(b)

additional bendingonthebam.Assumingttw the.freeends'are completelyrestrained, DeFrancoandDempsey (1990) derivedthe valueoffracturedriving force"

"

(2.7)

M M

rn

Figun 2.6S,", u wit" no constrains at freeend t

which is closeto three timesthevaluein Kendall'slheoc'y(seeFigure2.7) In apractical case,theendconditionmaybe bcrwcenfree andcompletely~raineddepending on the

pressure melting andsintai ng.Second.thesimplificationofthedeflectionofthestrutsas purebendingisno(appcopri&l:eforthecaseofsmallcracklengths.fnthis case~

denIO("wIleRcornpressi\'estresscIominaIes..Infact thishighcompressivestressmay cause thecrack:10dose wben the crackisveryshort.To demonstratethis.thefollowinj;

numerical analysison • doublecantileverbeam iscarriedout using.finite elementmod- elling package ABAQUS.

Figure2.8shoM an icebeamwithacentral crack IIthe free end,subjectedto an indentor of onemeter width.The indentation speedin thisca.seis aMWnedhighenough 50 thatteecan be trealedasanc!asri<:material.

16

""""\

'" I

I'- ~

(a)

-- _• .. 1

Figure 2. 7Doub/~Conti/ew r Beam wilhrestrained endsfrom DeFrancoandDem~y (/990)

Thesimplificationofindentorforceas two concentratedforcesin Kendall' stheory isnot accurate fortheanalysis ofsmaU crack lengthsandisnot appliedhere.For thelee- snucru reinteraction. the pressure distributiononthe interfaceis complicated.A damage analysisby Xiao and lordaan (1996) sho_thatthe distribution isan inverseparabolain shape when ice isinitiallyinan elastic contact, then it changes to. uniformand • parabolic shape as the icedamagesnear the interface.Thedistributionisfurthercomplicatedby spallsandthe formationof criticalzones. Forthe purpose of comparison, a uniform pressure distributionis used inthisanalysis.Values ofstrainenergyreleaserate

17

f

Figlln1.tJAnIc~.~tw;11Ia«"trottTOCk.lootMdbyQIflA:hntcr

Gatcrack lipsof differentcrack lengthswereevaluated.The (rackwill propagate when GreachesacriticalvalueG•.ThevalueofG.rocice is inthe r&ngeof 1-2J,mJ(TllI'ICO and Frederking(1986).Inthisstudy.valueofG.uIJI",Jisused.The resul tsarepre- sentedinFigure2.9Ca)toget herwithvaluesobtainedfromKtndall'sthe<xyand De- FrancoandDempsey(1990),wIleRthec:rack:lengthis .,..esentcdin •norMfunensioiW formwithrespeettc theicethicknessa'D.Figure2.9Ca)shows thatGincreaseswlth cracklength.Therueofincrease diminisheswhen the cradt:lenilhQlDis0.8andG graduallyreachesaconstanl:valuewhichcom:sponds10•5Ublcaxkgrowth-Thecon-

Rantisdoseto thevaluepredicted byDeFrancoandDempwy(1990)andoneeighthof thevalueinKendaU'stheory.Amore detailedplot(Frgw-e2.9(b» shows thatGisequal tozero for cracklengthsaiDlessthan0.22.Thisis in Igreement withthestress analysis whichshowsthatthecracklip isundet"high compressivestress.Figure 2.9(b)also shows thatGreachesG.whenthecracklengthaiDis0.3,whichcorresponds10I 60 emcrickin

I2:meterthickice sheet.This is • long flawand isunlikelytobefound.

\I

Tblrdly,theex1ensionoftheanmilylocatedcndcmodelto theIIIOI't-CenU&ljc- wedaxkmodelpresentsdifficulties.Thisisbecausein.thefinIcase me sheustrain.

enetgycomponentis not conJidered, whtcbmaybepRdominanain.the secondcase.To investigatethisfurtha",

me

samedoublecantileverbeamisan.afyzedwiththecracklocated indifferent lateral positions (seeFigure2.10 ).The crack lengthis fixed uO.S",and values ofGofcrKk:at differtn llocationswereevaluated.The resulu are presemedin Figure2.11together with Kendall'sprediction.TheresultsskewthatGincreases when thecrackis off the centralplaneincontrast to the Kendall's conclusio n

Inconclusion,Kendall' smodelis onlyvalidfOC"longcracks.Themodelumodi.

fledbyDeFrancoandOcrnpsey(1990)givesI.goodprcdH;tionof G

ror

lugecrack len gths.Theextensionofthemodel withI.centraIJyIoatedcrack 10 one with^I.nee- cerunlly locatedcndc pl"e5Clds difficulties.Thedouble canulewrbeamtheoryhasbeen I.ppIiedtothel.naIysisoficespaffinj:byanumber"ofresearchen.TheI.ppIiarion maybe suitl.blcfortheanalysisofI.lugesplittingicefeaturebutnotIUitablefor the analysis of icespalling,sinceinI.raJ6eIdsituationspalIingmayresutlfromthe propagationof CTacksofvariouslocationJ.AnahemativcbeammodelwasproposedbyHutchinsonand Suo (1992) whichconsidenI.mhc.edmodecrack.Thisapproach mayprovideI.good ap- proJOlTII.tiontoicespallingand isgiven in next section.

19

Kendall(1978)

1200 O,,--,-(J1:::m.::.'!...)

-c---,---- - -- - -- --

--Numericalresulu

20 10aID 15 (. )

~rancoandDempsey(1990) 1000 ~

800i~

:r

₂₀₀

_f

i

or l....-= = "' -= _ - _- --.-:.----'-.:e:.-e:.-- o

Kendall 1971 10'

Defranco andDempsey(1990);

1

0.4 0.6 0.8

aID (b)

~ ^o, u

1

0_2 10'~!

i

10'^ri

- - -+ - - - " ' - - - --i

i

10'

r

10·IL - _-:-_--,, ---,-,-_ ----J

o

Figure2.9(a) Resu/uofstrain energyrele~role,(b)detailoffigure(a)

20

Fiprw1.10 Ani~es_~t....ithcrack indiffirwn,~nico/locations

G(Jlm~

600 ,--- - - - - - - -- -- - -

S<Xl>

; ^- Kendall 1971

---NumericalResults

02 0.15 0.1

~ Wli"'

/ '

0.05 i 300~

200 ~

I

100

t

D o :... L--,~_~c=_-___:=--=---­

Distance fremthecentral planeVD FigJI"1.I IG'oI(J/wsforcracksQtdif/,,,,,'locations

21

].4 Analysis ofBeam Model By Hutchinson and Suo

Hutchin sonand Suo (1991)deIcribedabeammodelorigi nal lydevelopedbySuo (1990),whichissimilartothatofKendallbutinclud estheeffect of compressivestress (seeFigure12).Thestrainenergyreleaserateatthecrack.lip, G.was derived as:

G =21[f+ 12¥f+!# +12~--!b+12(1t~~,J ^(2.1)

when!

E

istbe eff'ecti1oe Young'lmodules.,PhP:.PJoM\oMloMIoIt ~ Hare defined in Figw-e2.12.

ThestrainenefgyreleaserateinEquation (2.8 ) wastim ber separatedint oopening andshearingcomponents byHutchinsonand Suo(1992)usinglinearityanddimensional- ity.Conseq uen tly.the stressintensityfactors take theConn:

K, 1f!;uCOSCIJ +Jf1:v sinC4I"z),

1f!;usjnt» +~cos(OJ +Y).

(2.9)

wheuPand M arcIineucombinationsoftheappliedIo.ds

p""P.-C₁P,- C/"/I'h. M-M,-C1M,• (2.10)

andU.Vandraregeometricfactorsdescribedas below:

"

F;p~2.12A Be_ ModelbySIlO(1990)

A~r.ledetermination ofaJofEqu.tion (2.9)isvery complicated.Theelasticity Pfoblem wassolved rigorouslyv.iththe hel.p of numerica.l solutionsof an inlegnJ equationby HUlchinsonandSuo and theresults are presenledinan approllimatefonruIa:

41=52-1"-3"". (2.13)

Further,HutchinsonandSuopresented • criterionfor","edmodecrackpropaga- tionby:

(2.1.)

whereGaois the criticalenergy releue rate,

"is

^1Mfactor depending on theralio of KilO Kg.InEquation(2.14), IVisthe direction ofcrackpropagalion, :is.parameler relaled to traction Itcracklip and

r

is Ihefracturetoughnns.FinEquation(2.14)isequalor less than I,which means the mixed mode crack:willpropagate IIan"apparenlstrainen-

energy release rate"lessthan thefracturetoughness.This isinagreement withtheresu lts ofPalaniswamyandKnauss (1974).

Thepreced ingapproach by Hutchinsonand Suo provides a better treatmentof beamchan Kendall by accounting for the compressivecomponentoCthestrainenergy.rn the following,wewin use this modelto investigatethe fracturestrengthof an ice sheet shown inFigure2.13 .We assumethat a longcraclcexists andis parallel to theice sheet.

The end of tileice sheet isloadedby a patch load. with a widthof w.andhasa parabolic pressu re distribution. This patchIaadis similar to a critical zonalforce.We define an equivalent fracturestrength of the ice sheet:as the meanpressure over the thicknessof the iceat which the crackpropa gate:

J

p(rjdr

P-r=~' ^(2.lS)

wherep(x)is thepressur e distributioncorrespondingto the propagation of the crack.

Tentative ly,we assume it has theform:

P(x)=Po(1-(; ..,-,

i)~~) ,

wherepoisdefinedinFigure 2.13.

(2.16 )

Factors affecting the fracture strengthincludethe positionof the crackrelative to the centerof the icesheet.I.the widthof thepatch load.If',andthe locationoftheload^Xo.

(see Figure 2.13).In thefollowing we analyze thesefactors.

~ . .

Toinvestigate theeffectofI,we examine thecase whenw..D.x~..0andIvaries between0 toDI2. For eachvalueoff.Equation s 2.9102.13 are usedtocalculaleK{

andKufortheeasewhenPu-I. Theamplitudeofpowhichcausescrackpropagationis thenderivedbasedon minimumSERRcriterion(Equation(2.1)).Thefracturesr:mlgt his IbmCAkulatedfromEquation (2.15).The resultsue presentedFigure2.14.TheSlfength isoormafizedwith

p ./.

whichistbefracture5l:ren5thwhenI•O.Noteth.tthefracture strengt his lowerwhenthecrackisofrthe center.ThisisQ)ftSiSZmlwiththeresultfrom ourfinitedement anafysis(seeFigure2.11).

Next,weinvestiglletheeffectofttlewidthaCmeloadedarea,...Weexaminethe case whenJ..O.%ll-0and...varies between0.2DtoD.Thefracture strengthfor eachw isderivedfromthesamemtt hod usedin analyzingthe effect ofI.The strengthisnor.

malizedwithrespectto

p ./

andispcesemed in Figure2.1S.Notethatthestren'!thde- creases with lheloadwidth,implyingthatthemoreconcentratedloadsmakethe fracture propagationeasier.

Fipn2.1-1A,ralysison litetffee,o/ locaJionof1M crack FuWly.weeumine the effectoh..We varyXobetween0tof),4fon lle casethat

Strengthagainst.Etue presentedinFigure2_16intermsofnonnaIized form.Notethat

NOie thatintheaboveanaly1isweonly dealt withsome special casesofa compli- caredcombinationbetweenI. ..andrfl.In reality.this combinationcouldDerandom, which resultsin therandomnessorlhefracture strength.To investigalethis, we perform thefollo wing Monte Carlo simulations

,.

1

p.,p./

0

.e

weD 0.8

0.'

;

0.i5 ~

,.,:.zs _, -:::;;;;::;;:;' _{~ D.2. _}

- :/ '

.

0.'

f

P< //

r >:

0."

f

e.s ! !

O"

0.2

V

Figun 1.IJ AItalysis on rtf"tojw

I 0.2 0.25 0.15 , ..D 0.1

.. "-

<,

0.05

\

\ _-,

1 P#fP/

, - - - -

.\

0.9~

i

0_8~

! 0.7

~

j o.e r

05

o,....----;;:os--o:;-~::::=-

1

Figurr1./6:Analysis ontJwrtfectojro

"

IneachsimuWion.werandomly

seeee

wbetwftn0andD.Then..werudomIy sdect~bdweerl0and(L)..w).We alsorandomly chooseIbetween0mel00.Forthe sdectedcombinarionoft,...and.r.t,wecalculAtethe5trengdt AD thesepanmer:en are selectedfollowing a uniformdi5tribution.Atotalof5000simulationswerepetformed.

Theresults of p., arerankedandpreserucdintermsof probabilityofaccedanceinFigure 2.17.ThesinKJ.lated resultsindicale thatp.,is scatteredwithin therangefrom165Pa[0 3SMPawithameanvalueofO.ZMPa.Theresultsindicate the factthaiicefailureby crackpropagationcanoccur IIany loadlevel dependingontheload configuration and the location ofcrack-Itshould be realized[hat only fraaurefailureis considered inthe simulation.Theicesheetmayfail byothermechanism such as damage

Theprecedinganalysis shows that an open crack pualiel10the icesheetmay propagate at a randomloadtevd depending on thelocationof[hecrackandthe loadpr0- file.[nreality,thefi'acturesuengthofthe iceis even morecomplicatedsinceaacksin l'WUteare usuaIIysmaJlerandlheitpro~ionismorecomplicated.Theycan belocated in a rudorn.locationwitha randomorientation.The propagationoflhese cracksis J1)()f"e difficult topredK:t.Thisisillustrated byadeterministicanalysisof closefonn cracks given inthefollowingsection.

2.5 Analysis 01Small Cracks at Different Locations

The1¥ge opencracksofKendall'smodelare rarelyfoundin ice fields.Instead, small cracks haveahighprobability[0exist.WithIfavorablelocalionandorientation.

thesecracksmaypropagateandresult indiscreteicepieces spallingoff.

"

Figtlrt2./1 Rem lu ofMonteCarloSiMulatiOiIS

Inthefollowing.weshallinvestigate these cracks atdifferent locations in anice sheet oflWO metm thicknessloadedbyan indentor&Iitsend (sec Figure 2.18).Thein- deecrforteis assumedto have •panbcMic:distributionrol\owing adamageanalysis by Xiaoand Sorda&n(1991).Theinteractionruec:onsideredhereishighenoughthatdam- ageto the

a

^onlyoc:c:ursneartheinrerfau and theresponseoftheres!:oftheice sheetis

TheSlI'eSIdistribution in theicesheethasbeen analyud A tensilezonehasbeen found nearthecenterof theicesheet (seeFigure 2.18).Thedirect ion of the tensile stress ismainlypcrpcndicu.Iartotheicesheet.Thissuggests that the cracksparallel(orclose to paralld) totheicesheetare more likelyto propagate.Cracks with other orientations may

be subjected tocompressive stressandare moredifficult togo"",.Theshear SIms paral.

Id10thecrKk plane will alsoC&II;SCthecradt topropapte.Zones of 5UdIshearstress panlldto theicesheet areidenlified and are plottedinFigure2.18.

CDidcsAtIhreediffcmll:Iocal:ionsare invesligated.Thecracks arewumedtobe

~to theiceshed forsimplicity.Cncbofdifferentorimurions can beconsidered Wes-.Cracks&IJocarioD1aremainlysubjeeledto shear stress.,aaduatIocabon1may causemiud modefrIaure and endsat1oation ]Wil lcausetensilefracture.Valuesof Slrainenergyrdeue rateha~beenevaIuaIedfewdi~craclc.lengths andarepk)nedin Figln2.19.Theresultshowsthat0inc:reaseswithcrack Icnlfh-OleiU)(fOtICarec:rilical straineneriY Dilesforlensileandshear aaclcmodes respectively,which arederived from K,andKudiscussedinFigure2.3.Ooc-O.6GICisusedin this study.Amixedmodecrack willpropagatewith IhevalueofGbetweenOleandOtICdependingon therlliooftensile andshear5lressintensity facton u di5CUS.Sedearlier.WhileFigure 2_19shows that the mixed modecrackAtlocation2hasIbe highesl: Gvalue.italsoshows that cracks&Iail locations can propagateforvaysmall crxk Ienllhs. Suggestedcraclttrajectories followingCornd(1976) are aI50ploaedin.Figure1.18.Craclcsu locationIand 2 may resultindiscreteicepiecesspaIlinll off.ClUb atlocalion3 will causesplittingofthetee feature.Such asplininghasbeenreponedbyKimI et&I.(1990 ).Itis also notedthat dependingonthelocationofthef;rKk,Ihe sizeofthesp&Ilcd piece isdifferenl;scbse- qucnt1y,lhesize of critica1zones (remainingcontactareas)is also different.Since

J.

Loc:ation I

_·-Suggested c:radt Injector)'

the location,sizesandorientationsofflaws in mlturcare random,lhetrajectories of !fac- lurepropagation arealso random.Thisleadsto the fact lhatlocations,sizes and imensi- tiesof localizedhighpressure zonesare alsonndom.

Thepreceding example demonstrates howaspallcan be initialedfromaflawin III icesheet.Thespallintensifies the preuureintheremainingcontact area. The intensified pressurewillformI luger- shearzone.hence causing subsequen1spalling.Inthemean

damage.Somebasics oficedamqemedwIia are describedinthenextsection.

1.6 lee Damage

Asspalling

cx:cun.

the remaininscontact area is reduced.This

win

causethehigh stress concentrationand severe ice damage.Damage mechanicsmayoffer theinsightlook al the failure processand..methodto estimateof theforces onthestructure

J.

Most oflhe early work on damage mechanicswasbased on the idea thas the dam- age to a structure can be measuredby a scalar factor.which equals either the rllio of the

004 0.01 0.03

.... Iocation1

aL I ..z:... ---'

o

4f-locatlon3 linregral(l/m^l)

8

I

^{r - - - - - - - - - - - -}

!

6

1 -

^{location 2}

2 ~

Figure1.19GVQIII~SofDiff~rentCTtKk Lengths

areaofvoids to the whole cross section. orIfunction of the density of microcracksand voids which would permanently affect either the elastic modulus or shear modules.The importance of thiskind of modd is lhe establidlment of a rationaldamage law which de- fines the rate of damage accumulation in terms of current values of stalevariables and internalvariables.

"

Dam&8emechanic;shu beenappliedtoicebylordaanand McKmn&(1981).

McKennaet aI.(1989).KarrandChoi(1989)andotbers. Anisouopi<:damage modd witha singlescalardamagepanmelefhasbeendeveloped.bylordaanandMcKenna (1988)basedonrate lbeory.andIw thefonn:

where~is!he thrC5holdsuess.Gtis a unit SUCSI.f/IfisaconstantandfiGis. reference rate.Thedamage.D.\;.due10mia'OCfaClcingis definedin Ihe form:

D..,=aIN whereQis lheradiusofcrack.

(2.18)

[tshouldbenotedhere!hatitisnotappropriate10usecrack density as lheonly measureforthedamage.ForewnpIe.inthe casesofaushedicein!hecritialzones.the crysaI stNetureofimacticehasbeen brokendownto fine

P ns .

UrJ:Ierhighconfining

massdue 10pressure meltingor reaysWlizalion.

Theapproach lakenbySchapery(1981.1991)offersarigorous solutiontoa class of p!"oblems involv;ngcracking and damagingv;scoelasriemai NS.IIincludesaproper treatmentofenergyftUllimo theerGlipzone.athin layerof damage maleria!inthere-

JJ

region:ofthemektip,and4ama&einthepamumaterial_Thedarrusemeasure givenby Schapery is:

S=[~dr,

whereqis aconstantand SislhedamagepaRmelei'.

(2.19 )

Fromexperiment. especiallycompressivecreeptests.ithasbeenfound thatthe presenceofcracks and cbmaaesianificantly enhancesthecreepstrain.Thecreepstrainof damaged.iceis5 1010timesthatofintaetice.AneltpOnentiaJfactorforcreep strain rate was introducedto capturethe behavior fOf" both lowandhighcrackdensities.,whichhas the form:ap(BS),whereB is a damageenhancementpanmcter.

2.7 Fracture and Damage Interplay in lce-Structer e Interaction

Aswedescribed insectton2.1.fJ.llureofadurirlg theice-struaureinteractionis e;kanaerizcdby fraaure and damage precess.Thefracture usually causes pieces ofice spallingolf and thereduaion of thecontactarea.Extensivedamageoficetakes placein thereducedareaandmullSinthereductionofthetotaJindentationforce.Thisinterplay processplaysa key role in the appearinganddisappearingofcrilical zones.Followingwe illustrate thisprocess byanumericalexamplegivenin lordaan.Xiaoandlou(1993).

InFJW't:2.20(A),anjetsheet:2m thickis Ioadec:l byIrigidindentoral itsendat

"fIIttof 100mmls.For illustrativepurpose,twol1aws are assumedtoexistinlheice shed at the kxations showninFigure2.20(A) The propagationoft hne twocracksare

modelledbyApplyin grnaxirRunSERAprincipleandbyusins finiteeIemerI:package ABAQUS.Thepropagation.oftheCRCks evmtu&llycausesspallsatimtanlBshownin Figure2.20 (8).Thespalls resultintbe reductionof l;ontl.Clarea and pressure redistribu- tion.figures2_20(8)to(F)showthe pressureredillributionprocess within remaining contxt area,The pressure inthe remainingareais very high initWly.andthe distribution quicldychangesfromI.I"C'\'e1'WdpanboIic:10I.paraboIM:shape.The amp{itude ofthe

-

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p"JOMP1I~ ~ _B

^_

p~~_ c ^_

~

_~--

D

p~~<

_~---^E

P~IC

C , Illlkmalion Di5llUll;c

.loBlDI F

.

'~^~-

Figurt1.20 $elwmalie lI/lISIrationofPnSSlJr~Van alioll DurIng 'Mtl1leract;o" Process

J6

2O,~,L_oad--..:(_M...:N)--..: ^_

0.2 0.4

Time(second) 0.6

Fig,," 2.21 EffeclojSpaJts onTotalForce

pressure decreases as the indentation proceeds.The decrease is causedbythedamageof theice neartheice-indentorinterface.Thepressurewilleventuallydecrease to a very smallvaluewhen the ice is completely damagedandextruded.The whole process corre- spondsto the fonnationand disappeann« ofa critical zone.Figure2.21shows the fon:c -time curve;thepeakobtainedandsubsequent declinein load results from the damage processinice.Thepeakload in Figure 2_21should be contrasted with the value about 40 MN thatoccursinlheabsenceofspalling.

J7

2.8 Conclusions

lee- structure interact ionwasanalyzedintermsof ice fracture and icedamage processes,Thelb.au recausespieces ofice spallingoft'andformationofloc&Iizedhigh pl'tS5Uf'e regions(criticalzones).Intheseregionsiceis subjectedto sever damageand resuItJin thedeclineoftotalindenurion forte.Criticalzones are keydementsinesti- mationof'ocalicepreuureand lTacture ttaj«tory governsthesizes.loationJ and

wen-

sitiesof these zones.

TwobeammodelslOr fracture.namdyKendall's doutMecanrilevubeamandthe model ofHutchinsonandSuo,wereanalyzed.Both models are limited 10 the cueoflo ng opencrac:k.s.Themodel ofHutchinsonand Suoprov\des a better altenlalive which also considersthecompressivecomponentof strain energyandcan be usedformilledmode fracture.Thismodelwassubsequentlyusedinanalyzinglhefr.cturestrength of anice sheawithan opencrack.MoneeCarlosimulationswere carriedout.inwhKhlKton suchthe~of tlw:cndt:andthemetconfigurationwerechosennndomIy.Results showthatuncertaintiesinthesefactoncausesigni6cantvariationsinfracture strength

InitialanalysisofsmalldosedCfl(;ks at three differentlocations shoWl lhat shear cracks and mixedmodecracksare

ee

likely candidatesfor spalldevelopment.Thejoca- lionand theorientationor lhecrack didate thetrajectoryof crack propag ationhence also governthesizeandlocationofcriti<alzones.Bec.auseoftherandomnessof flaws inna·

ture, lhecriticalzonesan: also random. Aprob abilistic approach to lhaccritical zones andice load,is necessary.whichisinvesrigateclinthenextchapter.

"

ChapterJ

Probabilistic Analysis of Ice Loads

3.l ln t, oduetlon

As discussed inChapter2.ice- st ructure interactionischaracterizedbyspalls and critical zones as lhe result of fractureanddamage process.This affectsthree distinct re- gionsof pressure ina design area.The first regio nisthecriticalzonewhere intense local pressuresandpressure gradientsexist.These arecausedbythespallsandmay alsobe attributedto the forced ecrusic nofdamaged.iceina "cry narrowlayer betweensolidice and the structure.Measurementsin the medium scale indentation tests (Frederlcingetal., 1990)andin ship trials (Glenand Blount(9&4)indicat e lhatthe pressure inthis region may reachupto70 MP. overafairlysmallarea. Inthesecondregion, lowerpressures arepresent.Thisregion maybe likenecllo an areaof~backgroundpressure".Such pres-- sureisassociatedwiththe ejectionof granulariceinwidespacesandismuchlowerthan those incritical zoncs.Thethird regionisone inwhich pressureis approximatedbyzero.

Thisregion is associatedwithareas of spaI1s where iceis no longerincontactwiththe structure.These three regions are shown schematicallyin Figure 3.1. Among thethree regions, the criticalzonesaremostimponantin estimatingtheiceload sandarethe key elementsinthe approachpresentedinthischapter.

"

! ^cmra

AH'

I

A, I

I ~

^A,

^I

i .

I

At!: Critica1Zorw: of High Prnsun=

, ,: AR:aofLow~s:sun:

A.,:. SpaDArelI

DesignWirWw

FipreJ.J&ht-malic Vi_ of11lne Regions ofPressurewithina Design Window.

figure3.2shows pressure measurements takenonboard CCGS Louis St Laurent duringaramming test (BlountetaI.•198 1).Eachframeinthe figurerepresents thepres- suredistnbutionon theinstrumented panelatapointintime. The transducermarkedwith the dark coloris the onewiththe maximumpressure whilethe onesmarkedbylightcolor are active transducen.Indicatedatthe lower rightcomerof eachframeis thevalueofthe maximumpressure.The maximumpressure duringthe ramreached S I MPa.Theshaded areas in the figure approlrimatethe criticalzones. As indicatedin the figure.these critical zones appear tobertndom,move from place to place. and change in intensityand

J'

"

1l I 7,8,9.IOll ,12

IIII

2

'f l \

time I I I I

U20mm

.

c0

, ;

0 0 ⁰

, . .

⁰ 0^c 0

,

^o

^,

^.. .; 0^·:;0 0

^{, ,}

⁰

^{, ,}

·

⁰

0 0

I ⁰ 2

, .

7.605-= 51.SMPa 7.61soc 28.9MPa7.7I,*" i7.SMPa1.123teC 1I6MPa

0

. _·

^{0 0 0}

~ ⁰

. : :

⁰⁰

..

^c ~

: .

⁰

_{· ·} ^;

^{0 0}0 e

_· · _·

~ e

S 6 1

.

7.738scc 12.67 MPa7.7n!lt:f: '-S8Mra7,841s«: i7.86MPa7,842s«: 21.18MP a

e

, , , , ,

c 0

, , , . ^, .

· ^.

.".; '-C ^, .. · ^, . · ^, ·· ^{, .}

s

'0 "

¹²

7.843scc 18-10MPa1,856sec 17-,~9MPa7.874sec: 1l.9olMPa 7.891SllC: 5.53MPa

:

^{c 0 0}

0 c

; , . _: ^{, ,}

,

00

.

c o0 0 0

. ^{. ,} .

1l

.

"

^IS

^,

'''''''

^{4.'J6MPa8.101sec} 9.88 MPa 8.10Zscc 14,2MPa

• indiclt Clitransd ucer o ( Maxlmurn f'res:sI.R . indic_ .,tivelnlWluccr

shadcdarcaappro:<im8leS 1bcai tiQIa>na inSlllllancous pcu pl'e$SllRoolclinlowcrris!lt eomcr

FigureJ.2Criticall~ActivityWithin /M ContoetAnI>,(bawdonBlaunfdal..1981, CaMII