ICE FORCES ON A MULTIFACETED CONICAL STRUCTURE
<I:>Zbiguo Wang , R.E., M.E.
Athesissubmitted to theSchoolof Graduate Studies in partial fulfilment of the
requirements fol' thedegree of Doctor of Pbilosopby
Faculty of Engineering&Applied Science Memorial University of NewfOUDdland
JUDe1997
St. John's, NewfoundlaDd, Canada
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Acknowledgements
[owe a great dealtomany individuaJs who madethiswork possible. My most heartfehthanks gotomy supervisorDr. Derek: Muggeridge who introduced me intothefaceted conetest programandbas financiallyandacademically supported meduringmy smdy. His friendly and thoughtful advice and guidance have benefited me not only forthisstUdy but also for many aspects of my life.
I wish to express my gratitude to my co-supervisor Dr. A.S.l. Swamidas. His encouragement played a major roleinlhcprogress ofthiswork:: his careful reading and correcting ofthemanuscript significantly polished it. Dr. Swamidas' suppon for printingall copies ofthisthesis and related materials are also gratefully appreciated.
Theauthor wishes[0extendhis sincere gratitude to Professor Ken CroasdaJe,andDr.
Richard McKenna, members ofthesupervisory committee, for their encouragementandhelps invarious aspects. Professor Croasdale offered his experience to guide this researchandbe provided support forthelastsemester of my srudy. Dr. McKenna helped to obtainthe permission for use of the discrete element code. DECICE, and his iIuellecruai support bas helped theprogress oftheresearch.
Special thanksareaddressed to Dr.I.J.Sbarp, Associate
DeaD
of Engineering, for- hiseDCOUragement for completion ofthisprogramandhelp withrespecttofmancw supponand teaching assistantships which panty ensuredthecompletion of this program. Sincere appreciation is extended[0theSchool of GradualC Srudies formefellowships awarded tllroughout this program.
Theauthor wishes to expresshisgratirudetotheInstitute for Marine Dynamics (IMD) oftheNational Research Council ofCanadafor permission(0usetheDECreEcode,andfor dIeuse of computing facilities.Deepthanks go to Dr. Stephen Jones andMr. Donald Spencer, researchofficers of IMD,andMr.L.Bruce Schooley, system manager of IMD's computer system, for their assistance, patience, and helpinwingthesoftware and facUities.
Sincere thanks go toallteam members ofthemultifacetedCODetest program for their effontomake the dataaccessible.
Last, butDO(leas(,my unbounded thanks are expressedtomy wife Wei-Zhong Zbeng andmy daughterZhenChao for their understanding, love,andsuppon throughoutthisprogram.
Abstract
To simplify fabricationandreduce costs of conical structures for arctic offshore development, a multifaceted conical shapewasproposed to replacetheconventional smoothCODe.Thisraised a number of concerns aboutthemechanisms for ice interaction withthismultifaceted conical structure(Mes)and thevalidity of analytical models whicb were developed forthesmooth conical structure(SCS)..A venical neck at the top oftheMeSwas proposed for a protorypeand industry bas desired a large siu forthisneck. Le .• its diameter to be only slightly smallerthan water·line diameter.Thisraisedanother coocem; what wastheeffect ofthisvertical neck OD iceloads?
To addresstheseconcerns. a university-industry joint program (NSERC file # 661- 119188)wasinitiatedto cartyOUt a series oftestprogram.1beprograminvolvedthreeseries oftestscarried outinthree Canadiantestfacilities(ESSOResourtts Canada. Calgary; NRCC's Institute for Mechanical Engineering, Ottawa; and NRCC's Institute for Marine Dynamics. St.
John's) with structural modelsalscales of 1:50to1:10 and at a cost about 1.3 million Canadian dollars.Theresults oftheseteStSwere presentedintest repons published by each facility; while presenting thesetestresultsDOdetailedanalysis was carriedOUItounderstaDdtheicelstruemte interactioninacomprehensivemanner.TI)tdata containedin thesetestreportshave beenused in this study to understandindepththevarious interaction scenarios possible betweenamulti- year ice ridgeand theMeS.
iii
1bedirect analysis of thetestdata. presentedin thisstudy. covers answers to most of theconcerns raised bytheoffshore industry but isnotlimited to them.Besidestheice failure mechanisms involvedinthe process of ice interaction withtheMCS models.theparamelers analyzed include neck size. sttUcturaJ orientation. ridge width.and theevents that causedthe maximum ridge loads.Inthe analysis ofthe icefailure mce:banisms.threeridge failure patterns are identified. Both ridge crackingandridge segment ride up processes are recognized tobe events causing the maximum ridge loads. The i.nfluence of a number of factors on ice cracking panemandice loads exerted ontheMCSs are consideredinthedataanalysis.
To provide an insight intotheinteraction processand theice failure mce:hanisms. a series of numerical simulations are carried out using a commercial discrele element code (DECICE).
DEOCE is capable of realistically simulatingtheice breaking processes accompanied by broken ice pieces riding up onthestructural surface. Thisovercomesthedisadvantage ofthe conventional Hnite element analysisinwhich the ride-up forces are to be approximately computed under an unrealistic assumption that only one layer of ice rides up.Thesimulations using DECICE show the brokenicepieces to be actively involvedinthebreaking process of impinging ice. The effect of neck size on ridgeandsheet ice loadsisalso studied using DECICE.
Ananalytical modelisdeveloped whichtakes thepanicular feature oftheMCSs and ridge length into account; this model should provide designers with a simple estimation of ridge cracking loads. This analytical modelisgiveninthe form of a set of equations coveringthe
iv
initialcrack: eventandhinge crack event for both finite length ($bon) and infinite length (long) ridges. Three loading conditiom for hinge cracksinan infmite ridge are consideredinthe equations. The most conservative loading condition for the hinge cracksischosen for shon ridgestogive a cooservative estimation of the maximum ridge loads. The equations for long ridges are expressed in a general form whh differelll coefficienlS for various crack events and loading conditions.
Anextensivecomparisonoflheexperimental results givenin thisthesis,for level ice fields, has beenmadewilhWeanalyticalmodels mat were develped for prediction of levelice loads on SCSs.'Theresults show Nevel's analytical model forsheetice load estimationtobe fairly valid for useinestimation of sheet ice loads on MCSs mough it was developed for smooth cones. Ralston's model is also acceptable for MCSs if approprialC: parameters are chosen for inputstothismodel.
Of the various analytical models available for ridge load estimation, the model developed inthisthesisgivesthebest prediction(closestto themeasuredloads).Asa second choice, Wang's plasticity model which has been widely accepted for smoolh cones is also applicable to the case of MeSs.
Contents
Aclmowled.gemets AbsIract Contents ListofFiguces List oCTables Nomeudatun
iii .; xi xiv
lntroductioD ••.•...•...•.•..•...•...•... 1
1.1 Baclcgrouod of theTestProgram . 1
1.2 Backgroundof ThisStudy 3
1.3 Objectives 4
1.4 Organization ofmeThesis . 6
LiteratureReview... ....•..••... ...•... ..•... 8
2.1 ExperimentalStudies of lee Ridge Forces ... 8
2.1.1 Failure ProcessandForces of Broadside Ridges.. 10 2.1.2 EffeaofRidgc Orientation on FailureProcess andPeakLoads. 11 2.1.3 Effects of Sheet TbiclmcssaDdStteagth
on Failure ProcessandPeakLoads .. 13
2.1.4Ratio ofHorizontaltoVertical Forces .. 13
2.1.5 Effect of Ridge Length00Peak Forces . 14
2.2 AnalyticalModels for Ridge Force Estimation .. IS
2.2.1 Croasdale ModelandAbdelnour Model.... 15
2.2.2 Kim andKattas Model.. 17
2.2.3 Ride-up Model.. 18
2.2.4 PLasticilY Method.. . 19
2.2.5 Comparison of ModelsandDiscussioDS _ 20
2.3 Ice Sbcet Intc:nctionwitha SCS .. 21
2.4 AnalyticalModelsfor Ice Sheet and SCS Interaction .. 22
2.4.1 RalSlOo Model . . 23
2.4.2 Croasdale Model. . 23
2.4.3 Nevel Model... . . 24
2.4.4 Comparison ofModelsandDiscussions 2S
vi
2.5 Numerical Analysis 2.5.1 Finite Element Analysis . 2.5.2 Discrete Elemem Analysis.
_________ 26 26 28 FacetedCoDeTestProgram •••••• ••.•••.••••..•..••. .•••. .•••••••••. .••. ••..••••••. •••••• .••33
3.1 TestFacilities .... .. 33
3.1.1 ERC'sIceBasin 33
3.1.2 IMD's and IME's Ice Tanks.. 34
3.2 StrUctures andInstrumentation . 35
3.2.1 PrototypeStructures and Test Models 3.5
3.2.2 Instrumentation.. . 38
3.2.3 CoordinateSystem •.• •••...•..•.•...•...•...•.•...39
3.3 Test Matrices . 39
3.3.1 Overall Scope .. . 39
3.3.2 Test Matrices 41
3.4 TestedIce.. . 50
3.4.1 1belceforERC'sTests. 50
3.4.2 TheIce for IME's and. IMD's Tests 52
3.5 Test Results . 54
AnalysisoftheT 60
4.1 Typical Interaction Scenario . 60
4.1.1 The Process of Sbeet Ice and MCS Interactioo 61
4.1.2 Ridge Failure Pattern I .. . ... 62
4.1.3 RidgeFailurePatternn.. .66
4.1.4 Ridge Failure Pattem
rn . ..
674.2 Ridge CrackLoadsandMaximum Loads. 68
4.2.1 WhatCausestheMaximum Loads 1 69
4.2.2 Horizontal and Vertical Ridge Forces... . 72 4.3 Influence of Various Paramelers00Ridge Failure ProcessandForces. 74
4.3.1 EffectofRidgeWidth.. . 75
4.3.2 Effect ofStructuralOrientation 80
4.3.3 Effect of Neck Size . 8S
4.4 Analysis of Sheet Ice Forces.. . . 91
4.4. 1 Approach fortheAnalysis 91
4.4.2 Effect of Strucmral Orientation on Sheet Ice Forces 94 4.4.3 Effect of Neck SizeOD.Sheet Ice Forces. . 96
vii
NlIJbet'ic:al Simulatioo •••••••••••••.•••.•••••••••••••••••••••••••.••••.••••••••••..••••••••••...100
5.1 TheApproachforNumerica1Simulation 101
5.1.1 DECICE Program and tbeProctdures for Problem Solving 101
5.1.2 StructureandIce Modelling . 103
5.1.3 Failure CriteriaandIce Strengths ... 106
5.2 Simulation ofSbec:c Ice and Structure Interaction 109
5.2.1 IceConfigurationaodElemencs.. . 109
5.2.2 Overview of Simulation Results 111
5.2.3 EffeccofElememSize . 113
5.2.4 Interaction of Sheet with Sma.ll Neck Structure 118
5.3 Simulation of RidgeandStructure Interaction 126
5.3.1 The Ridge, Sheet. and Their Discretization ... 126
5.3.2 Comparison of Simulation with Test ... 128
5.3.3 RelationoflnteractionProcessaodGlobalForces . 131
5.4 Numerical Study on
me
Effect of Neck Size 1375.4.1 Ice Sbeet Interaction witb Large Neck:Strucrure . 139 5.4.2 Ice Ridge Interaction with large Neck: Structure.. 141
5.4.3 Discussions of Neck: Size Effect 144
AnalytkalStudies .•.•..•...••...•...•...•..•..•.•..•..•....•....•.•..••••••..•...••..•.146
6.1 TheProblem and Its Simplification.. . 146
6.2 LoadingConditions 151
6.3 BeDding MomentandCrack: Locations for Infmite Ridges.... 155 6.3.1 Bending Moment and Creak: Location for Initial Crack: .... 155 6.3.2 Bending Moment and Crack Location for Hinge Crack:
under Uniformly Distributed Load CoDdition.. 158 6.3.3 Bending MomentandCrack Location for Hinge Crack:
under ConcentratedLoadCondition 159
6.3.4 Bending Momem and Crack Location for Hinge Crack:
under TriangularLoadCondition 162
6.4 Fonnulae for Estimation oftheLoadsExened by InfiniteRidges 164
6.5 Consideration of RidgeLengthEffect. .... 168
6.5.1 Initial Crack Load ora Finite Length Ridge .. 169 6.5.2 Hinge Crack Load of a FiniteLengthRidge
under a ConcentratedLoad .171
6.6 Discussion abouctbeAnalyticalModel 173
6.6.1 Effect of Facet Length on theLoadsand viii
Crack: Locations of infInite Ridges ...
6.6.2 Effect of Ridge Length on Crack:Loads ....
6.6.3 Shon. Finite. and Long Ridges ...
6.6.4 The Maximum Ridge Crack:Loads ..
6.7 Ride-up ForcesandTotal Forces ....
11.
m
179
. 180
. 181
Validation of AoalyticalModeis •••••.•.••.••••••••••.•••••.•....••••••.•••••••.••••••••••••• 184
7.1 VerificationofthePresenr:AnalyticaJ.Model. 184
7.1.1 ComparisonofComputedandMea.sured Loads.. 185
7.1.2 AnalysisofthePrcdiction... 189
7.2 Validation of Other AnalyticalModels for Ridge Load Estimation 196
7.2.1 TheLoadPrediction.. . 197
7.2.2 Evaluation oftheAnalyticalModels .. . 201
7.3 Validation of the Theoretical Models for Sheet Ice Load prediction.. 206
7.3.1 TheModelsand "'"Inputs . ... 206
7.3.2 ComputationResu1ts. . 208
7.3.3 Analysis ofPrediction 213
Conclusions and RecollllDelldadons •••••••••••••••••••••••••.•••••••••••••••.••••••...•••.. 220 8.1 Conclusions Regarding Ice Failure MechanismsandMaximum Loads.. 220
8.1.1 Ice RidgeandSbeetCrackpattems 221
8.1.2 1beEvents GeoeratingMaximum Loads.. ... 221
8.1.3 Effect ofSuucturalOrientatioo .. . nl
8.2 Conclusions RegardingtheEffect of Neck Size 223
8.2.1 Effect of Neck Size on Ice Ridge Loads 223
8.2.2 EffectofNeckSizeonlceSheetLoads. 223
8.3 ConclusionRegardingValidation of Load Equations.... 224 8.3.1 Validation of Ridge Ice Load Equations.. . 224
8.3.2 Validation of Sbeet IceLoadEquaons . 225
8.4 Contribution ofThisWott: 225
8.5 RecommeDdationsforFurweWott:... ... 227
References 229
Appendices ••••••.•.•..••••••••••••••.•.•••..••...•••.••••••••••••.•••.•••••.•.••••••.•••••••••••••••••••• 236
AppendixA Assumption for Ice Behaviour... . 236
AppendixB Estimate of Parameters for Mohr-Coulomb Criterion 242 ix
Appeodix C Simplification ofRidge Crack Problem ..
Appendix 0 Functions A(y). B(y). C(y). O(y)andTheir Operations ..
Appendix E Multi-Year Ice Characteristics for Beaufort and Chukchi Seas
. 241
256 260
List of Figures
3.1 ThePrototypeSuueture with Small Neck ..
3.2 The PrototypeStructurewithLarge Neck ..
4.1 Vertical Ridge Forces on Urge Neck SlnlCb1leS . 4.2 Horizomal Ridge Forces 00 Large Neck Structures . 4.3 Vertical Ridge Forces aD Small Neck Structures . 4.4 Horizontal Ridge Forces OD Small Neck Suuetures 4.5 Vertical Ridge Forces on Face--on Sttuctures ._. . ...•..
4.6 Horizontal Ridge Forces on Face-on Sb'UCtures . 4.7 Vertical Ridge Forces on Edge-on SttUCtures 4.8 Horizontal Ridge Forces on Edge-on Structures 4.9 Effectof Struetural Orientation on Horizontal Sheet Forces . 4.10 Effect of Structura.I Orientation aD Ven:icaJ Sbec:t Forces . 4.11 Effect of Neck Size aD Vertical Sheet Ice Forces _
4.12 Effect of Neck: Size on Horizontal Sheet Ice Forces ...•
4.13 ZoomedPlotting of Vertical Forces against
c; ..
36 36 ... 78 78 79 79 87 88 89 90 9S 96 98 98 99
5.1 Simulated Small Neck MCSSUucture ..•.•.•.•.103
5.2 Simulated Ice.BasinWaIlsandtheS~. .. . ... ...• 104
5.3 Ice Sheet:aDdElements.. . 110
5.4 SimuIaledandMeasured Global Sheet Loads.. . III
5.5 Ice Sheet/MeS Interaction Scenario atthe78th Second... 112 5.6 Interaction of Structure with Fine Meshed lee Sheet atthe78th Second .. 113
5.7 Effect of Element Mesh on Global SheetLoads . 114
5.8 Musured SheetLoads and theSimulation with Fine Mesh .. 115
5.9A DispiacementsoflceSheetElement27 119
5.98 RotationsoflceSbeetElement27. . 120
5.10 Crac.ksofFrontElernems... . 121
5.11 Side View of lee Sbeetl MeS Interaction Situation atthe9thSecoDd . 121 5.12 Side View of Ice SbeetIMCS Interaction Situation atthe22.$th Second.. 122 5.13 Side View of Ice SheetIMCS IntenctionScenario atthe48th Second.. 124 5.14 Side View of Ice SbeetlMCS Iorenction Scenario atthe78th Second.. 124 5.15 Time History of SimulatedandMeasured Global RidgeLoads ..•. 128
5.16 Measured and Simulated Ridge Crack Paaerns .. 129
5.17 Simulated RidgeIMCS Interaction Scenario atthe116mSecood.. 129
5.18 Ridge Crack PaaernofYIT1R2 . 130
5.19 Ridge!MCS Interaction Scenario atthe720d Second. 132
5.20 Ridge/MCS Intenction Scenario at the 8200 Second 133
5.21 Crack Pattern immediately after Event "d" .. 134
5.22 Crack: Pattern during Event "e" .. .. 135
xi
5.23 TbeRidge-SbeetlceClearingProc:ess... 131 5.24 Simulated SheetLoadsfor Large and SmaIl Neck StrUCtures ... 139 5.25 A Scenario of Sheet Ice Interaction withtheLarge Neck structure. 140 5.26 Simulated Ridge IceLoadson
me
LargeandSmall Neck Str\JClUres .. 142 5.21 An[nteraction Scenario of me Ridge Inleracting withtheLarge Neck Structure.. 142 5.28 Side View of a Scenario of Ridge ClearingProcess . 143 6.1 Cross Sec:tion of RidgeBeamwith Ice Sbeet: Ranges . 148 6.2A COOlaCt Condition for Initial Crack.. ...•... 1526.28 Loading Condition forlnitial Crack . 152
6.3A Corner Contact for Hinge Crack .. . 153
6.38 ConcentratedLoads for Hinge Crack. . 154
6.4 TriangularLoads for Hinge Crack. . .. 154
6.5 Nonnalized ClaCk Location of InitialandHinge Cracks.. 157
6.6 LoadFunctions oflnfinite Ridges. . 166
6.7 Contaetand Loading Conditions for Hinge Cracksina Finite Ridge.. 169 6.8 Load Function for
me
Cenb'al Crackina FinilC Length Ridge 170 6.9 LoadFunction for a Hinge Cracksina Fi.nilC Length Ridge.. 1737.1 VerticalPredictedandMeasured RidgeLoads .. 186
7.2 HorizontalPredictedand Measured Ridge Loads .. 186
1.3 Vertical Ridge loads of the ERC Tests . 190
7.4 Horizontal RidgeLoadsoftbe ERC Tests.. 190
7.5 Vertical Ridge Loads ofIMD Tesu . . . 191
7.6 Horizontal RidgeLoadsofIMD TestS .. . 191
1.7 Vertical RidgeLoads oftbe IMETests .. . 192
1.8 Horizontal RidgeLoadsoflhe IMETcsts ... 192
7.9 VerticalLoadsfrom Three Models fortheERC TeslS . 198 7.10 HorizontalLoads from Three Models fortheERC TeslS . 198
1.11 VerticalLoadsfrom Three Models fortheIMD TeslS 199
7.12 HorizontalLoadsfromThree Models fortheIMD Tests 199
7.13 VerticalLoadsfrom Three Models forlhe[METeslS 200
7.14 Horizontal Loads from Three Models for the[METests .. 200 7.15 Vertical Sbeet iceLoads,NIL. RCL, andCCL.. ... 210
7.16 Horizontal Sheet iceLoads.NIL. RCL. andCCL. . 210
7.17 Vertical Sbeet iceLoads, NIL.Rll..andCIL.. .. 211
7.18 Horizontal Sbec:ticeLoads. NIL.Rll..and CIL ... 211 7.19 Vertical SheeticeLoads,NIL. RCN.andCCN.. ... 212
7.20 Horizontal SbeeticeLoads, NIL. RCN. andCCN... 212
7.21 Predicted Vertical Sheet ice Loads with NNAandNNP .. 217 1.22 PrediclCd Horizonal SbeeticeLoadswith NNAand NNP.. 217 A.I Strains for ERCtestYITIRI
A.2 Strains for ERC test YITIR2.
xii
... 239 ... 239
C.l Forces00a Ridge . C.2 Equivalent Forces ontheRidge C.3 Idealized Geometry of Multi-year Ridges
xiii
..248 ... 250 ... 251
List of Tables
3.1 OverallScopeofTbeTestProgram. 40
3.2 TestMatrix forERe's Year-Qne Tests .. . 42
3.3 Test Matrix of ERe's Yeac·Two Tests .. 43
3.4 Test Matrix for IME's Ice Sheet Tests. . .. 46
3.5 Test Matrix orIME's Ridge Tests . . , 41
3.6 Test Matrix for [MD's Tests wilb. 1:25 Scale Large Neck Model. _ 48 3.' Test Matrix oflMD'sTestswith1:25 Scale Small Neck: Model
and1:50Scale large Neck Model. 49
3.8 IcePropertiesfortheEReTests. 51
3.9IcePropeniesofIMDTests. 53
3.10 EReTestResults , . . S6
3.11 IME TestResults 57
3.12 IMD TestResults 59
4.1 Crack LoadsandMaximum Load for theERetests 70
4.2 Ridge CrackLoads andMaximum.LoadsfortheIMD Tests .. 71 4.3 HorizontalandVenica1 Ridge Forces forall theTests . 73
4.4 Crack Location oftheERC Ridges 82
4.5 Crack Locationoftbe lMERidges . 83
4.6 Statistical Measurements of the Neck Size Effect ... .. ...•.... 86 6.1 CoeftlCients ofF(211LJ .
7.1 Statistical Measures ofthePredicted RidgeLoads ..•.•.
7.2 Statistical Measures of Vertical Loads fortheThree Models ..
7.3 Statistical Measures of Horizontal Loads for the Three Models.
7.4 Overall Statistical Measures of Prediction ofthe'ThreeModels . 7.5 Overall Statistical Measures of sheetIceLoadPrediction ...
7.6 Statistical Measures for Vertical SheetLoadPrediction 7.7 Statistical Measures for Horizontal SheetLoadPrediction ..
7.8 Statistical Measures ofNNAand NNPPredictions.
. .... 167 188 201 202 20S 213 214 214 216
A.l ParametersCorSinba'sModel ... 238
A.2 Strains forYITlRlandYITlR2 at 20th Second ofLoadiDg 240
B.l EstimatedCompressive and Temile Strengths 244
C.l Ridge Dimemion . . 249
E.l Multi-Year Ice Characteristics ...•... 260
E.2 Ridge Characteristic Length 262
xiv
Nomenclature
B, B, B,
ca..
CCH. CIL C, DECICE DEM Dr D.edge..an ERC E, E, raccoOn FEM Fcf2//LJ
F,(2IILJ F,IL•.IJ F.IL••IJ F.s F.
effective width of ice sheet attached to a ridge slope of best fitting line for predicted vs. measured forces ridgetopwidth
Refer to section 7.3.2
=
D.}PIg I (eT,h) (refer to Equation (4.3»the name of a discrete element computer program Discrete Element Method
cone top diameterfOfSCSs. circumscribed neck diameter for MeSs waterline (circumscribed. for MCSs) diameter
referto Section3.3.1 Esso Resou=sCaJJada Ltd.
Young's modulus for ridgeice Young's modulus for sheet ice refcrtoSection3.3.1 Finite Element Method
load function forthehinge crack of an infinite length ridge under concentrated loads (MCS).
load function for the hinge crack of an infmite length ridge under uniform loads(MeS).
load function forthebinge crack: of an infInite length ridge under triangular loads (MCS).
load function fortheinitialcrack: of an infinitelength ridge against aMeS.
load function fortheinitial crack: of a finite length ridge againstaMes.
load function for the hinge crack of a fmite length ridge againstaMes.
load function forthehinge crack: of a(mile length ice ridge against a SCS.
load. function fortheinitial (<:enual)crack.ofafmile lengthiceridge against a SCS.
X component ofthemeasured maximum ice load on a MCS Y component ofthemeasured maximum ice load. on a MCS Z component ofthemeasured maximum ice load on a MCS general symbol forthe X component oftheice load onaMeS general symbol fortheY component oftheice load onaMeS acceleration due togravity
H.
[ [, [.
IMD
!ME k L I L, I, L, I, Mes M(y) M_
Mi'M~.Me. M,
M,IL,.IJ NfL NNA. NNP P, Po PH'p~
P;". p..
P, • PD' PC' PT
thickness oficesheet ice ridgekeel depth
momeDl of inertia of an ice ridgeandaaacbed ice sheet moment of inertia of the ice sheet attached(0ice ridge moment of inertia an ice ridge without ice sheet attached
Institute forMarineDynamics of National Reseacc:h Council ofCanada(in St.John's,Newfouodland)
lostimte for Mechanical Engineering of National Research Council of Canada(inOttawa. Ontario)
foundation modulus. see Equation(6.1) ahalflength of an ice ridge
ahalfof facet width of a MCS at waterline
characteristic leagtb. of aniceridge includingthe attaebed ice sheet characteristic length of anicesheet
=L/L,
=IlL,
Multi·facelCd Conical Snucture bendingmoment along theYaxis
general symbol for the maximumbeDdingmoment
themaximum beading momentsinan infinite length ridge fortheinitial cnck:(MJandhinge cracks under uniform(M,J.CODCCotrated(M,),and triangular(M,)loads. respectively
bendingmomem at the center line (perpendicular to Y axis) of a finite length ridge
refertoSection7.3.2
Nevel model (sheet ice) considering "active action"and"passive action".
respectively. refer lO Scction7.3.3
concentrated load forthehinge crack ofan innoire length ridge concentrated load for the hinge crack of a finite length ridge geoerai symbols forthehorizontalandvertical forces
venica1 ridge forces fortheinitial crackandhingecrack,respectively themaximum crack forces of an infmire length ridge fortheinitial crack (P,) andhinge cracks under uniform(Pr). concentrated(Pd. and triangularPT)loads, respectively
theinitial crack:andhinge crack: forces of a finite length ridge intensity of uniform load for binge crack ofan infinite length ridge
xvi
q, q.
q, R Ra.. RCN. RlL R, RMS SCS S, XI.XI{
z,. z.
".~
P,.p.
",
",
"f
intensity of uniformloadfor central crack of aninfinitelength ridge intensityof Wlifonnloadfor centtal crack of afinitelength ridge maximum value oftheincensi[y of triangular load for hinge crack of an infinite length ridge
correlation coefficient of measuredandpredicted ice forces refcrtoSection7.3.2
mean ratio of predicted to measurediceforces Root Mean Square of relative error of force prediction Smoothly..eurved Conica.l Srructure (i.e.• smooth cone) standard deviation of force ratio.R,
horizontal forces forinitial and hinge cracks. respectively vertical forces forinitialandbinge cracks. respectively
thedistancefromthecenuoid of aridgecross sectiontoits top fibre and its boaom fibre, respectively
freeboard of aSCS for Equation (2.8) slope angle ofmain cone (from borizontal) internal friction angle
friction coefficient betweeniceandstrueD1Ialsurface internalfriction coefficient of ice. 1J.o=fanII' ice and water densities. respectively density of ice ridgeandice sheet. respectively buoyancy of ice sheetandice ridge. respectively oormal stress
maximum and minimumpriJxipalstresses, respectively totalbeDdingsuess
compressivestress flexural strength of ice
flexural suength of ice ridgewith bottom or topin[ension. respectively flexural strength of ice sheet with bottom or topin[ension, respectively shearstressand shear strength, respectively
Poisson's ratio
xvii
Chapter 1 Introduction
1.1 Background of the Test Program
Upto lhc:early 1990's, many significant geological strueD.1reSin theCanadianfronticrarea5 have been drilledandtestedfor oilandgasata row cost of overIS billion CanadiandoUars.
Discoveries have been significant astheoil reserves (including discoveredand po[C:otial)in the Grand Banks and Beaufort Sea areas alone are about 8 billion barrels (Croasdale, 1991).
However. HiberniaandTerra Nova arelhc:only froD!ier oil projectsbeingor [0be developed to date. 1behighcost for safe exploration and productionisthemainreason for slow progress withthefrontier oil developments.
ConicalshapedstruCtl1tt$can induce icebeDdingfailureandthismodewillexert much lower loads onthestrue:ture compared to ice loads from a crushing failure mode. Therefore conical shaped structures are preferred for arctic oil and gas exploration/production operations.
The conical structures designedtillthe1990's have been of smoothly curved surfacesandbave assumed steel coDStI'UCtion.ThedifficultiesellCOWlleredinmanufacauing a smOOth surface lead to a higber cost of consauetion, consequently makingthetotal cost of oil and gas development projects h.igber. For ease of fabricationandsavingsinthe cost of construction, Exxon ProductionResearch Company proposed the developmem of a multifaceted surface to approximate t:be smooth surface (Weiss, 1988).This newly proposed configuration ofthe
SUUeture will be referred(0as the muIrifaceted conical strucrun (MCS)intherestofdlisthesis, andtl1e conventionalsmoothly curved conical structure will be referred toas SCS.
Utilization of such a SUUCUlre raised severalDeWconcerns abouticeload estimation.'The mainconcernsare described as foUows:
1. Themechagismoficefailure _The multifaceted surface may affect the ice failure process aDdmake theprocess quite different fromthatfor a smoothly<WVed conical suueQlre (SCS);beocelbeiceloads onlbemultifacetedsurfacemaybe different.
2. Theeffect of ice interactiog with the vertical neck (refer to Figures 3.1and3.2).
Designerspreferredthediameter oftheverocal neck (() be only slightly smallerthandie water·linediameter(Weiss 1988) but were afnid a large neck could leadtoa higherice load.Theice load formulae aDd procedures giveninthedesigncodesup to that time did not account for ice interaction with a normal veroca1 neck. let alonethislargeneck.
3_ The
"£hods
orPros;edures for estimation of iceloads onthistypeof MCSs.Allthe existing formulaeaB:1 procedures for ice load estimationindesign codes have been supponed by andIorbasedontestswith SCSs; hence it was questionable whether these formulae and procedures could still beusedfor MCSs.To stUdythenew featureS of ice interaction with a MCS and help understand the ice failure mechanisms and develop proper ice load estimation formulae, a NSERC University·lndustty coUaborative researcbprogram (NSERC fIle#661·119/88) was initiated.
Ibisprogram.withafundingof1.3millionCanadian doUan wascarriedoutby Memorial
University of Newfoundland (MUN). FSSOResourcesCanadaLtd.(ERC) (on behalf of Imperial Oil Resources andits industry panners including Exxon Production Research and Mobil OilLtd.). and National Researcb Council ofCanada(NRCC).Theprogram involved lhreeseries oftestscarriedoutinthethreefacilities: ERC's outdooricebasin at Calgary and the indoor icetanksof NRCC's [mtiture for Marine Dynamics(IMD) at St. John's, Newfoundland. and Institute for Mechanical Engineering(IME)in Onawa.
ERC's tests wete done duringthewimer of 1988-1989 (to be referred to asYear One Tests)andthewioterof 1989-1990 (tobereferred to asYearTwoTests). respectively. The 1MB and IMD tests were completed duringthespring and the summer of 1992. respectively.
1.2 Background of This Study
Eacb ofthe test teamsdocwnented tlleir resultsinseparate~treports (Metge and Weiss 1989.
MetgeandTucker 1990, Irani et al 1992. Lau et al 1993). These repons mainly recorded the test conditionsandthe physical measurements for each individual tests. No theoretical analysis was done during presentation of these test reports; tlle present researcb work:is the
rlrSf.
comprehensive study carried out ontheexperimental results documented in these test: reports.
Since concerns 1and2 presentedinthelast section could notbeanswered without an overall analysis of test results, sucb an analysis of these[est.resultsbecamevitalandimporum.
Moreover widely usedanalyticalmodels for ice load estimation. available earlier, were based
on test conducted with SCSs: hence concern 3 required an eXlensive evaluadon of the validity ofthesesmodels forthenewly proposed MCS. Consideringthedifferenceinme loading cooditions between a SCSanda MCS.DeWanalyticalmodelsaccounting forthecharacleristic interaction of ice ridge with MCSs were found to be desirable for estimating ice ridge loads on MCSs. Another concern, Le.•lbeeffect of neck size, could have been bener addressed if me conditions of twoleStSwere keptthe same except for strueturc's neck size. Unfonunalely, no single pair of suchtestscould be foundin allthetest series. Therefore. a set of numerical simulations withthesame paramelers were undertaken for this purpose. Numerical simulations were belpfulinunderstandingthemechanism of ice failure (concern I). All studies carried out to address these aspectsandtheconclusionsobtainedfrom these stUdies are presented in this thesis. Except forthetest results obtained from the test reports. aU the grapbical plots. analysis and conclusions presentedinthisthesis wereobtainedas apan oftheinvestigationcarried OUt for this thesis work:.
1.3 Objectives
Theprincipal objectives ofthepresent study are to get an insightinto theiceJMCS interaction and to provide theoretical and ptaCtical~Itsfor designerstoconsiderintheir struCtural design or for researchers' further study. The study will focus ontheconcerns raised by industry. [t is divided intothefollowingtaslcs:
I. Identification qftherelationship betweentheice loadsand
me
ice cAC!c.ing Process under lest COnditions. The task willbefulftlled by thoroughly analyzing allthetest dataincludingboth theload recordsandthevideo records. A numerical analysis will also be perfonnedtoassistin thecompletion ofthistask.Thisis expectedtohelp inthefurther understanding of ice-structure interactionandtoaidin thedevelopment of theoretical models for ice cracking load estimation.
2. A study oftheeffects of sUYeturalparametersandorientations ontheicecrackpattern andlbejce loads on thestructure.Theseincludeoecksize (one ofmefactors of concern, toindustry). therelative orientation between a suuetuea1 facet faceandsheet ice motion.
theridge orientation. etc.Thistask.willbecompletedbymeansof analysis ofthetests andnumerical simulation.
3. Development ofatheogtjg'model for easy estimatioQ of ice ridge cracking loads on
i...MCS.,
Ibis isconsideredas aseparateitembecause theice ridge cracking load is the most imponant consideration for structural designers andno analytical or semi-empirical modelsareavailable foraMCS.4. Evaluation ofthesuitability of exjsting analytjcal models for estimation of ice loads on
~.Due to the reasons describedinSection1.2.anevaluation of the validity of existing SCS models fOl" a Mes became a necessity. Since the MCS bas[wodiameters (inscribedandcircumscribed)anda verticalneck which are not accounted forinthese existinganalyticalmodels. determination of which geometrical dimension(s)is(ace) appropriateto beused asinputstothese existing models is another work thathadbe done.
1.4 Organization of the Thesis
Thisthesis consists of eight chaptersanditsmain coments can be divided into four partS.The firstpart thatfoUowsthisinttoductionisa literature review giveninChapter 2.Thereview focuses on che ridgeteStswithSCSs that canbeconsidered as a counterpan of the present tests.
Anodler area of literature reviewedison typical analytical models developed earlier by adler researchers.
The second pan is a single chapter. Chapter 3. which presents a summary of the tests and their results. tbe materials giveninthischapter provide adatabase fortheanalysisin the chapters that follow.
The third part consists of two chapters: Chapter 4 and ChapterS.1be nest portion of Chapter 4summarizesthekeyscenarios oftheice-structure interaction process. whichis followedbyan analysis oftheeffect of neck size andthestructural orientation onthesheet ice loads and. on the ridge ice loads. ChapterSpresentS a series of numerical simulatioDS carried out using a discrete element code.Thesimulation mainly focuses on the identiftcation ofthe relationship betweeniceloadsandicecracking process.Theeffect of neck sizeisalso analyzed bythenumerical studies presemedinChapter 5.This part directly addresses concerns 1 and 2 ortaSks 1 and 2 given earlier.
O!apters 6and7 contribute me founb part of litis thesis. Chapter 6isdedicaled [0the
presentation of lbe Dewly developed theoretical model fortheestimation of ice ridge cracking loads on MeSs. Irs verification using test datais giveninChapter 7. Chapter 7 also contains (he examination of other earliert:heoreticaJmodels available. 1bese modelsweredeveloped for estimationof eilber ridge ice loads or sbeet ice loads on SCSs. Thispartisexpectedtoaddress coocem 3 or tasks 3and4given earlier.
Finally, an additional but moreimportantchapter, Chapter 8,isarrangedtosummarize thecoaclwions obtained and contributionsmadein me course of(hisstudyandtogive recommendations for further srudiesinthis area.
Chapter 2 Literature Review
Beforethepresent research program. there have been few theoretical andIor experimental studies onMeSreportedintheopen literature.Theliteraturethatisreviewedinthischapterispart of thelarge literature available on ice interactionwith SCSs.Inaddition.thisreview willalsocovcr some impona.nt developmentsandconclusions arrived from earlier research on ice interaction wilhSCSs.
Duringthepast twodecades, many excellent review papers and reports (Chao 1992a&
1mb.WesselsandKato 1989. Marcellus etaJ1988. Sodhi 1987. Nessim et al1987. K.rankkaJ.a andMaananen 1984. CroasdaJe 1975&1980, CammaertandMuggeridge 1988) have been published on ice-structure interaction.Inthesepublications. theresults and progressinthe studies of ice sheet loads on SCSs were extensively reviewed. However,theSCSand ice ridge interaction have received lesser attention. Therefore.theemphasisinthischapter willbe given to reviewthestudies of ridgeiSCS interaction.
2.1 Experimental Studies of Ice Ridge Forces
So far, only a fewrestdatafor ice ridge forces existin theopen literature.Inthefollowing, severaltypicalmodelleStprograms are reviewed. A brief introductiontothesetestprograms willbe followed by a summary ofthetestresults which are organized into five subsections.
LewisandCroasdale (1978) reported one of che earlier test programs on ridge-eone interaction.1betestswere conducted with a 45° conicalsuuctutemodelandsalineice ridges at atest scale of about 1:50. Eleven ridges were successfullytestedfor strucrurelridge interaction. The ridges were built from ice sheetsandcouldbeconsideredaspressure ridges or layer ridges.Theresults have been usedtosupport analytical models (Croasdale 1975&1980.
Kim. andKotr'aS 1973).
KamesakiandYoshimura (1988) conducted a new series oftestswith two cone models at a scale of 1:100. The slope anglesatwaterline for chese (wo models were 45°and40.7°, respectively.Theratioof ridge keel depthand icesheet lhickoess, ridge length.andridge orientation were changed to investigate their effects.
Abdelnour (1988) presented a summary of two extensivetestprograms.basedonthe work: carried out by AbdeLnourandTeh (1976)andEdwardsandAbdelnour (1977). A total of sixty ridges were tested against a 45° cone with a waterline diameter of 0.61 meters. The ridges andlhesurrouoding sheeticewere modeled using a synthetic materialtosimulate natural ice at scales between 1:50and1:75. Besidesthebroadsideand 45° skewed orientation, an end·on orientation of the ridges (the ridgeaxiswas paralleltoits moving direction) was also tested.
Ridge length variedfrom 0.38 meters.tosimulate very short ridges.[04.1 meters, to simulate inflnite ridges.Theexperimental data from these tests have beenused[0developandverify analyticalmodels (Wang 1984. Abdelnour 1988).
10
2.1.1 Failure Process and Forces of Broadside Ridges
Thecypicalridge Failure sequence observedanddescribed by Lewisand Croasdale (1978) can bepresentedinfour steps as follows:
I. Whentheridgeisinitially approachingtheconethe icesheet betweentheridgeandlhc:
conebreaks.Thecorresponding forceisquite low (comparedtothe maximum force), and is at the level oftheice sheet force.
2. As dieridge moves funber forwards.thecone encounterstheunderwater leading edge of me ridgeandbeginslO lifttberidge slightly. causing an initial crackinthe ridge.
usuallyatthecenter of the ridge. often referredtoas initial crack or center crack;it bas also been observedthatthecrack could extend throughtheridge into the ice sheet.1be magnilUde of force increases sharply untilthecrack formsand then levels off.The magnitude oftheforce atthisinstant may not beatits maximum but itismuch higher thantheearlierpeaks associated withthebreaking ofthetee sheet.
3. Asche motion continues.theice sheetisseparated frommeridgebya tensile failure.
The ridge is now noticeably deflected upwards and the initial crack is widenedand extends furtherinto
me
icesheet.Themagnitude oftheforce continuestoincreasebut has not rucheditsmaximum.4. Theridge continues tobe deflected upwards until a second crack (hinge crack:) occurs at some distance away fromthecenter crack. Then, the ridgeand ice sheet fail simultaneously,andthe surrounding sheeticewhich have been deflected considerably upwardsbeginstosettle back:intothewater. The forceisatitspeakmagniwde.
11 Theabove failuresequenceistypicalonly for relatively longandbroadside ridges surrounded by a moderately thick: ice sheet.Infact. the mode of ridge failureis depeodcOl 00 the type of interaction. ridge length, sheet thickness, and many other factors. Abdelnour (1988) summarized four distinct failure processes observed forthebroadside ridges of various lengths.
1. Complete separation oftheridge from the ice sheet followedbyinteraction ofthe advancing ice cover with the ridge
2. Complete separation of the ridge from the ice sheet followed by a central crackinthe ridgeandclearing oftheridge aroundtheCODe.
3. Separation oftheridge fromtheicesheetaheadoftheridge (side of ridge nearest to the cone)andattheridge ends followed by central crn:ldng of ridge and occasiooally by hinge cracks.
4. Ridge failure atthecenter followed by hinge cracks. No apparent ridge/sheet separation;
either orbothcads of ridges still fumly embeddedinicesheet.
Theaverage ratio of hiDge crack forcetoinitial crack force was 1.73 on average for Lewis and CroasdaJc's tests (1978).Thisratio for Abdelnour's results was estimatedtobe close tal.
2.1.2 Effect oC Ridge Orientation on Failure Process and Peak Loads
KamesakiandYoshimura (1988) observed lbattheeod-on ridges were broken like a semi-infmite beam loaded attheend. The broken beams. approximatelythesize oftheridge width. frequently
12 piled upinfront oftheCODe.
Abdelnour (1988) reported two distinct failure processes observed for lhe interaction of end-on ridges with a SCS.
Complete separation of me ridge from theicesheetfollowed by interaction oftheridge withtheadvancing ice sheet.
Separation oftheridge from the ice sheet atbothsides with a sequential hinge failure.
The failure process forthe30"and45° skewed ridges was observed[0besimilar to the ones for broadside interaction scenario. However. aftertheoc:c:umncc of the center crackand.
hinge crack. the ridge could comeinconlaCt withthecone once moreandcould produce another hinge crack (Abdelnour 1988.KamesaJciand Yoshimura 1988).KamesakiandYoshimura's tests also showed
mat
the«1' skewed ridges failedina quite different way:theponinD of lbe ridge beI:Ween its leading edgeandme
center crack wasDOtbroken. andtheponico between ilS nailing edgeandme center crack was completely cracked alongthemoving direction.Abdelnour's (1988) results showed lhattbebroadside orientation yielded an average load thatwas atleasttwice as large asthatfortheeod-on orientation. However.K.amesakiand Yoshimura's results (1988) indicated thattheloads forthesetwo orientations were roughly at the same level.
13
2.1.3 Effects of Sheet Thickness and Strength
on Failure Process and Peak Loads
Thickness of the ice sheet strongly affects the failure process,andbence the ice loads (Abdelnouc. 1988).Iftheicesbeet was sufficientlylb.i.n(compared totheridge kccl depth),the ridge teoded torotateinitsplane after a center crack: developed.[fthesurrounding icesheetwas sufficiently thick, a local bending failure or a circumferential crack was liJcely to occurinthe centre ofmeridge because ofthehighconfinement effect ofthesurroundingiccsheet(Kamesaki aDdYoshimura, 1988). Abdelnour (1988) pointed out that an increaseinice thicknessbya factor of two resultedinan increaseinthe force by at least two to four times for most cases of his tests.
Another important effect oftheice sheet wastoincrease the global force through the ride·up sceoario. Wang (1979)sum.ma.rizedthepeakforces oftheridges with and wimout ice sbeet ride-up(thedatawerequotedfrom EdwardsandAbdelnour'slCStS(1977». The results showed that the sheet iceride~upaction increasedtheaverage verticalandhorizontalpeakforces by 31%andby 29%. respectively.
2.1.4 Ratio of Horizontal to Vertical Forces
Themean ratio oftheborizontaltovenica1peak.forces forthe27 tested ridges,swnnwized by Abdelnour (1988), was 1.18.Thecorresponding value for LewisandCroasdale's tests was 1.66,
14 andforKamesakiandYoshimura'stestswas 1.97. All thesedatawere for 45" cones.
Ther.il.tio ofborizomal andvertical forces on a cone canbetheoretically ex:pr-essed as (Croa.s<We. 1975. 1980),
PIP "" SinCl+~COSCl
H V" COSU-lJosinu (2.1)
wherePHandPvatethe horizontalandvertical forces. respc:c:tively, aisthecone slope angle fromtheborizomal,andIlis theice/CODesurface friction coefficient.
While applying equation (2.1) totheabovetesIS.one willfindtheratio should vary from 1.15to1.56 as coefticicnr of frictionIJ.varies from0.1to0.2. Itisobvious thatK.am.esakiand Yoshimura'steStsyield a ratio much higher thantheone predicled by equation (2.1).Thesame conclusion CQuid alsobedrawn fromtheresults of other test programs. This difference could bedue tothefactthatlhisfonnulaisvalid only for two-dimensional casesandalso may be due [0theerrorincoefficient of friction measurement aspointedOUt byAbdeInour(1988).
2.1.5 Effect of Ridge
Lengthon Peak Forces
Abdelnour (1988)usedadimensionless ridge length2LIL~(0measure the effect of the ridge length. whereLis thebalf ridge length, andLcis the characteristic leoith of a ridgeinwater.
He concludedthata ridgewiththedimensionless length between 1and1.5 exerted a higber vertical forcethana ridge with a dimensionless length below or abovethisrange. These
15 relatively short ridges may exhibit forces twice ashighas an infinite ridge.
Kamesaki andYoshimwa (1988) ploaedthepeak.: forces against a ratio of2U1:4:.where Htis ridge keel depth.Theplot showedthattheforce increased withtheincrease of 2UHtuntil 2URk reached a value of 20; when 2Ul4. ratio increased beyond 20 (wheretheridge might beregarded as infinite)thepeakforce became almost a constant.
2.2 Analytical Models for Ridge Force Estimation
2.2.1 CroasdaJe Model and Abdelnour Model
Croasdale (l975&.1980) appliedthelbeoryof an beam on an elastic foundation. developedby Hetenyi (1946),toestimate the maximum force of a ridge on a CODe.Itwas assumedthat ice ridge will crack wbentherensile stress at its outer fibreequalstheiceflexunJ strength. The formulae for venical forces were derivedandgivenintheform:
(2.2)
wherePI~andp~.are vertical forces for centerandbinge cn.cks. respectively;Zc andZt.are the distance from centroidalaxisoftheridge to its top and bottom layers;C7rIand(1,~are ridge flexural strength for top and bottomintension, respectively;Lc;ischaracteristic length ofthe
16 ridgeandattachedicesheersandI ismoment ofiDeniaof ridge cross section. The horizontal forces canbecalculated using Equation (2.1).
In thismodel.theridgewasassumedco beinfini~.andtheeffect oftheauached sheet ice was not taken into consideration.Moreover.a concentraced load acting at the ridge/cone contactpointwas assumed. that is.theeffect oftheload distribution along the contact edge was notrakenintoaccount.
Abdelnour (1981, 1988) also applied Hetenyi's theoryto theridge/cone problem. His expression of load formula includingtheeffect of ridge lengthandattached sheet ice was considered,isrewritten wilhtheootatiOlJSusedinthisthesis as foUaws:
(2.3)
whereFrsandFHSare load functions for initial (cectal)andbinge cracks, respectively,andthey canbeexpressed as
(2.4)
17
where2Lrepresents full ridge length.Y is thelocation where the maximum moment occurs or where ridge failurebappe~andit can be obtaiDed by differentiatingthemoment equationand equatingit to zero.'The beDdingmomem for a hinge crack canbewritten as follows:
For convenience. Equation (2.2) rogetber with Equation (2.3) willbereferredto as the CroasdaIe-Abdelnour modelinthislhesis.
2.2.2
Kimand Kotras Model
Kim.andKocras (1973) developed a sequentially straighlforward approach. also based on the LewisandCroasdale's observation and Hcrenyi's theory.lberidge andthesu.rroundingice sheet were treated as an elasticbeam.andplate on an elastic foundation. respectively. Their approachusedindeterminingthefailure sequeoce can besum.m.arized inseven steps. which was latercoded intoa computer program by Semeniuk (1975).lbefirst four stepS are forinitial(or cenrer) crack andtherest arc for analysis ofthehinge cracks.
18 1. Aftertheridge contactsthecone,theridge's upwards deflection,Woo atthecontactpoint can be calculated for a given penetration distance X. ForthisWoothe ridgeandsheet deflection W(x,y)isapproximately derermiJ:led usingbeamandplate theory.
2. Determinethevertical forcerequiredtolift theice tothedeflectionW(x.y).
3. Check: both shearand bendingstresses attheinterface between the ridgeand theattached ice sheettosee iftheridgeisseparated fromthesheet.
4. ChecIcto seeifthecenter crack occurs.If theicesheetwas notseparaled fromtheridge.
theridge/sheet combination wasidealizedas abeamwithanacbed flanges. Comparethe stresses atthecenter oftheridgewithridge flexunl screngthtoseeiffailure (center crack) occurs.Ifno failure occurs, i.Jx:reasethepenetration andrepeatstepS 1 through 4until the initialcrade occurs.
5. Astheridge(andsheet.ifit was DOt separaltd fromtheridge) moves funher forwards.
update its deflectionandtherequired forces.
6. Check:theseparation at sbectlridge interface again. Aftertheinitial(or center) crack. the sheet.ifnotseparated fromtheridge beforetheinitialcrack. could bedetaChedfromthe ridge just before hinge cracks.
7. Checkthestresstoseeifthehinge cracks occur (similar to Step 4).
2.2.3 Ride-up Model
!beCroasdale-Abdelnour modelandKim andKottas model are only (orinfIniteridgeswhich do DOt account forthepossibleride-up process. Winkler and. Nordgren (1986) developed a
19 model for calculation oftheridge force duringtheridc-up process withtheassumptionthat the ridge is free-floating within a surrounding ice floc.
TIleride-up problem of a ridge was analyzedintwO steps.Theridge ftrst was modeled as a rigid body undergoing lacge rotationandtranslationinirs cross-sectional plane. The forces acting00theridge consist oftheforce exertedbythe cooe, buoyancy force, gravity load,and a forcettaDSmitted fromtheice floebehind.For each stage oftheride.-up process (Le. for a cenain rotation angle oftheridge).theridge force onthecone canbe ca.lculared by solving the equilibrium equation oftheforce system. Thenthe ridge was treated. as an elastic beam onthe cone.Amaximum ridge force forflexunlfailure canbedetermined at each stage oftheride-up process. The maximwn force over the entire ride-up process gives the overall maximum ridge force for a given ridge cross section.
Theapproach was also extended to include the effects of dynamicsandlocal crushing (Nordgrenand Winkler 1989), andtoprobabilistic analysis (WinklerandReece1986).
2.2.4 Plasticity Method
Alltheabove models arebasedon elasticity theory. and are likely(0uoder~timatetheactual forces. To estimate an upper bound of ridge forces. Wang (1979&1984) developed a model basedonplasticity theQry.
20 Inthismodel.theice ridge and ice sheet wereassumedtobeelastic-perfectly plasticand resting on an elastic-perfectly plastic foundation. The ice sheetinfront of the leading edge of theridgewas assumed tobeseparated fromtheridge before the ridge cracked. lben.theupper bound theorem was appUed tothissbeeHidge~onesystem. Five components oflherale of energy dissipation were considered. viz.•therates of energy dissipation due to ice sheetand ridge beDding, ice sheetandridge weight (or buoyancy)andfriction between the ridgeandthe cone. Fivetypesof admissible velocity fields were considered.. two of which were designed for long ridges with centerandhinge cracks. another two for sOOrt ridges with a center crack only, andone for very short ridges without cnck at all. Eacb. of these five velocity fields gave an upper bound fortheridge force.Amongthefive bounds.thesmallest was selected as the calculated value.
This model has been widelyusedinridge force estimationandanalysis (Schreiber~lat (989). Nevel(1991)simplified the force equation forthelong ridgetypeI velocity field which isthe most likely breaking pattern for long ridges.
2.2.5 Comparison of Models and Discussions
Comparison of these analytical models with experimental data has been carried out by many researchers (Wang 1979, MacceUuset al 1988.KamesaJdand Yoshimura 1988.andChao 1mb. etc).The latestand themost extensiveODewasdODe by Chao (1mb).These comparisonssharea common conclusion:theelasticity~thodsgenerally unduestimalt! the
21 ridge loads on a cone, while the plasticity methodsmay oW!r-prediet the loads.
!beplastici[)' modeland theKimandKottas model are theoreticallythemost elegant ones because
mey
simulatetherealsituations more completely than other models. Compared with the Kim andKotras model. Wang's plasticity model covers more situationsinterms of ridge length andpossible crack: patterns (velocity fields). Wang (1979)didan extenSive comparison ofthese [wo models usingthe results offifty ridgetestsandshowedtheplasticity mOOeL predictedthe loads beuer. whileKim andKotras model under-predictedtheloads.TheCroasdale-Abdelnour mcxlelisquite simple and easytoapply for ridge load estimation. This model does not include the forces duetothesheet ice pieces riding up. neither doestheWinklerandNordgren model (1986).
2.3 Ice Sheet Interaction with a SCS
Numeroustestprograms have beencarriedouttoslUdytheice sheet/cone interaction (see the reviews: Croasdale 1980. Sodhi 1987. Wessels and Kata 1989).Theobserved failure process andmodesaresummarizedas follows.
Astheice sheet first encounters aCODe,localcrushing occurs on the underside edge of theicesheet, which causes an interaction force normaltothesurface ofthesaucture.Theforce.
which increases asthe crushing area increases, will deflecttheice sheet.Ifthe ice speed is low
22 andme cone diameteris smallcompared(Qthethickness of me ice, radial crackswillinitiate the ice·sbeet failure. Peak::interaction force. however, occurs when circumferential cracks develop aroundthecone, leading totheformation of wedge-shaped broken ice pieces.(fthe cone diamecerisrelatively large.the maximum tensilestresseSoftheice cover change fTomthe circumferential direction(0theradial direction.Thisprocess causes anicesheet tofail fIrSt circumfereotially and thereafter radially. The cracked ice pieces willbepushed up onthesurface ofthestructure, which basbeentermedritk-up, thenwillslide over the surface and downinto water or ontheicecover.
Many factors could affectlheice failure mode. lncreasing roughness ofthecone surface, or increasingicethickDes.scouldgraduallyalterthefailuremode from beDdingtoshear.With increasingspeedof iceJsttuetute interaction,thedistance between r.be circumferential cracks would decrease. andfInally, theice-sheet failure would change abruptly from beDding to shear.
resultingina lower peak force due tothedynamic effect.
2.4 Analytical Models for Ice Sheet and SCS Interaction
There exist many analytical models m:1 empirical (or semi-em.pirical) equations developed for estimation of sheet ice forces on SCSs (Chao 1992a).Intenns ofthetheorythemodels were based on,theycan be divided into two categories: elasticity models and plasticity models. This section reviews two typical elasticity modelsandODe plasticity model.
n 2.4.1 RaIstoo Model
Ralston(1978&1980)applied the technique of plastic limit analysistothe case of ice/cone interactionanddeveloped an analytical model to estimate
me
maximum ice sheet fortes on a CODe.1bederived formulae for horizontal forcePHandvertical forcePvan givenby:PH'" A.. [Ai
0/tl
+~p..ghD~+A,p,Jh(D;-D:'>JPy'"8tPH+81p",gh{D; - D~)
(2.7)
where Or and h areflexuralstrength and thickness oficesheet,respectively;DrandD. are top andwaterline diameters of a cone, respectively; A,. At. A].
A..
8" and B1are the coefficients determined by solving complete elliptic integral equationsandby optimizingmebound for lhe failure force (refer(0Ralston1978).2.4.2 Croasdale Model
Croasdale (1980) presented a simple elasticity analysis model.Theice sheet wastreatedas a semi·inftnite elasticbeamon an elastic foundation subjectedtoa vertical load Pvand a borizomaJ loadPHatODeeod.Theice forces on the structure were givenby:
(2.8)
when:
24 (2.9)
r . I . - - 'x'L 4D
ris a modification coefficient «(or a 20 structlire, r
=
I),L.is characteristic length of sheet ice.Eisa function of slopeangle ofthecone (a)andfriction coefficienr:(,u.) andis equaltoPo/PH as giveninequation (2.1).Pvcallbedeterminedusing equation (2.1).R.ecemly, Croasdaleand his associates have modified Utis model to includetheeffect of ice rubbleinfront of a cone (Croasdaleetal.1994, CroasdaleandCammaert. 1993).
2.4.3 Nevel Model
Nevel (l992) presented a rigorous modelbasedon elasticity theory andhis earlierlheoretical studies. The model treated the ice floe as a series of truncated wedges which were formed as a result of radial cracking. Itwasbasedonthefollowing observation from physicaltests:asthe wedges move againstthecone,they maybreakduetothebending failure atthebottom ofthe wedges;inthe mean time the smaller ice pieces broken from the wedges during the preceding interaction process arepushedfunher up onthecone surface. The model assumesthattheice pieces completely coverthefront balf ofthecone.Theimpinging wedges subjected[Qboth verticalandhorizontal(inplane) loads may break simultaneously or sequentially. For the sequential break.themodelassumed thatthemaximum. load occurs whenthecenter wedge breaks.
25 'Thegreatestcontribution oflb:ismodelisitsformulation of me forces due to iceriding up onthecone swface. The modeliscapable of dealing withlite computation of sheet ice loads on aSCS with a number of conical sections, including a vertical neck. Two action conditions were consideredinthemodel: passive actionandactive action.Astheauthorstatedinhis paper (Nevel. 1992), "active ice action is defined when the broken ice pieces Onthesurface of the cone slideintothesection above".and"passiveiceactionisdefinedwhenthebroken ice pieces doDOl:slide intothesection above".Inan application,wenofthismodel can cboose eilhc:r of these two action conditions.
2.4.4 Comparison of Models and Discussions
Chao (1992a)andMarcellus~taJ(1988) comparedthevariousanalytical models and empirical formulae. A genenl cooclusion from the comparisonislhat Ralston's model which was based on plastidcy theory overestimatesthefailure loads whilethemodels based on elasticity theory.
includingtheCroasdaIe model,underestimatetheload.Thesecomparisonsandconclusionsdo not covertheNevel model because it was published later.
Chao(l992a)andMacellust!tal(1988) also analyzedthe crackandride-up components ofthe predicted failure load.!beystatedthatthedifferencebetweenthepredicted loadsfrom the plasticity model (Ralston's model) and elasticity modelswas mainly due to the differencein predicted crack loads.The crack loads predicted from Ralston'smodelismucb largerthanthose from elasticity models, whiletheride*up loads fromallthemodels are relatively close to each
26 other. This might be becausetheice sheet under plasticity theory could stand larger forces.
Manyoftheoffshore drillingstructUreS,proposedfor useintheArctic. have sides with multiple slopes or at least venical upper walls(liketheneckintheMeStobesbowninlhe next chapter)to reducethecbaDce ofhigh iceridc:-upandtomaximizethe working surface with respect tothebase diameter. Whenthebroken ice pieces ride up to the corner of [wo slopes the leading ice piece cannot go further.Thisleading piece could either be crushed or lifted. This.
if itlXCUI'S.could increasetheload ontheupper Slope or upper verticalwallaDdalsoincrease the total load. Coonet of(1985)andImmiyamael of(1994) srudiedthisaspectandgave a set of formulae accounting forlhisadditional load. Ofthethree models reviewed above,theNevel modelistheonly ODeaccountingforthiseffect.
2.5 Numerical Analysis
2.5.1 Finite Element Analysis
Bertha (1973. APOA # 57) carried out one oftheearliest fInite element analysis(FEA)of an ice ridge wilh attachedicesheet against aCODeusing a commercialcodeANSYSintheearly 1970s.Theice wasassumed(0bea fast brittle, isotropic. homogeneous. linear elastic material.
Thesimulation for a long ice ridge (4000 feet long) sbowed a crack pattern similar totheone observedbyLewisand Croasdale (1918),and thepeakloadwasalsoreachedduringthebinge crack process. His simulation also showed thalthemaximum force for the short ridge was about
27 30% lowerthanthatfortheloog ridge.
Maattanenand Hoikkanen(l990) appliedthefiniteelemenr: methodtodetermincicesheet loads on aCODe.Theice sheet was subjectedtoedge load due totheresistance of me coneand disaibuted loads on the upper surface oftheice cover duetotheweight ofthepiled-up ice pieces.1beicesheetwastteatedas an elastic wedge on an elastic foundation.Theycompared thepredictionswiththeirfull·sca1e measurements (Maattanen and Muswnaki 1985)andthe predictions from Ralston's model. The resultsshowed that their model yielded a better agreement. Maananen (1986) also appliedlhisapproach tothecase of sloping walls.
Derradji-Aouat (l994a&: 1994b) implememeda nonlinearandtime-dependcntconstitutive model. Le. Sinha's model (Sinha 1984&:1988). into a finite clement progr;untocompute sheet iceloads on aCODe.Hetook. theride-up iceintoaccount,butassumedthethickDess of ride-up ice[0bethe same as lhe pareDt ice floe. It has been recognized thatthe[olal thickness of lhe ride-up ice (morethanone layer) could be much bigger (McKennaandSpeocer 1994).
The aboveFEAsare based on a number of assumpations some of which are not fully realistic.For example.theassumption oftightcontact alongtheice/CODecoD1act line maybe valid only fortheverysmallstruClUrC:andrelatively soft ice (Sanderson 1988). For a large strUcture, wsassumption mayresultinanoverestimation oftheice crackload.Theassumption isnot realistic even for smallstructuresif theiceisquite brinte. As manytestshave shown.the cracks of brittle ice usually form a front suchthat.only pan of it cancontaCtme cone forthe
28 next crack. Another exampleislhatmost of FEAs consider !:be effect of the ice rubble on the cone and. on the top of the ice sheet by adding their force (duetotheir gravity loads)tothetotal ice loads.As pointedoutbysome researchers (McKennaandSpencer 1994),therubble. besides theirpositive contribution tothelOWloads, couldalsoassistinthe failure of the ice sheet.
2.5.2
DiscreteElemeot Analysis
The discrete element techniqueis a powerful toolthatbasbeen widely usedinrock mechanics andmany other areas including ice mechanics (Mustoeuo[1989,WilliamsandMustoe 1993).
]betheory ofthistechnique was given by Williams (Williamsel at1985, Pande n011990).A distinct feature of me Discrete Element Method(OEM) isthateach element is considered as a distinctbody which communicateswith itssurrounding elements via face. edge. and comer interaction forces that change aslhebodies move and/or deform.
Compared withthefinite element technique,thediscrete element techniqueis more suitable fortheanalysis of multiple, interacting, deformable, discontinuous or- fraccured bodies undergoing largemotioDSandrotations. which isthecase of ice interaction with conical shaped strUCture.Inaddition.theanalysiswithOEMcanrealistically and fully account fortheeffect of rubble ice wbichFEMcan only paniaJly take into account.
There are manyItinds(althoughsimilar) of discrete element approaches availableinthe literaDJre and many computer codes have been developed. EvginandSun (1990) gave an
29 extensive review of these approaches. The most elegant one was developedbyHockingand his co-workers (Hockingn aJ1985a, 1985b. 198.5<:)andcodedina computer programflI'St named CICEandlater on changed(0DECICE.
OECICE formulationisbasedupon aninternaldiscretization of Simply Deformable Finite Elements (SDFE).Inother words. the linear shape functionis implememed forthe elementsinDECICE.Thedetailed formulation of OEMisgiveninDECICE Theoretical Manual (bylntera Information Tccboologies).Anoverview of DECICEwill bepresentedinChapterS.
Only a few applications of OEMtoice/sloping sttueture interactionwillbe briefly reviewedin thissection.
Rigid elements wereusedinearly development of discrete clement technique.The typical approach using a rigid element was proposed by Kawai (1977& 1979),termedas Rigid Body-Spring Model(RBSM).Thismodel consists of afmite number of small rigid bodies (elements) connectedwithsprings distributed over the contact area of neighbouring bodies.
Displacement components of anarbitrarypoint:inthatrigid clemeD! are expressedintenns of the displacement components of the element center of gravicy. The problem is reduced to solving aset of simultaneous linear equations similar to FEM butinterms of displacements ofthecenter of gravity ofallelements ateachload incrementstep.
WatanabeandKawai (1980)first appliedthisapproachtoanalyzethebendingcollapse problem of level ice against an ice-breaker bow model with emphasis on the prediction of ice
30 crack pattern. The stress-strain lawintheir analysis was elastic-perfectly plastic. The results showedthatthecalculated andexperimental crack patterns coincided with each other weU.
Later. YoshimuraandKamesaJd(1981) adoptedthesame methodtoanalyzethecrack panern of the ice sheetinfront of a cone, but they consideredtheStreSSrelicf accompaniedwiththe initiation of cracks. Shibue andhisassociates (ShibueandKata 1988. Shibuc:~taI 1994) introduced a thick-walled shell element intotheRBSM. Theyanalyzed the failure process of ice sheets as well as ice ridges against conicalstructuresandincliDcd indenters.Thestress-strain relationshipusedintheir analysiswas idc:ntified by simulation oficeproperty tests.
Although lbc: predictiocsfromRBSM were claimedtogive good agreement with experimentalresults.thedisadvantage oflhisapproachisobvious.Firstly.itisassumedthatthe elementusedinRBSMis rigidandelement deformabilicyisDOt considered; thus,thisapproach isonly appropriate for stUdyingthebrittle behaviour of ice.1becreep and ductile behaviour cannotbe consideredinthisapproach.Thereasonthatgood agreement was obtained berween the predictionandexperimental results couldbethattheevents studied involved mainly brittle behaviour of ice. Secolldly, generation oftheelement mesh largely depends on prior analysis experience. Ithas a great influence onthe ice collapse pattern since failureoccurs only at element edges which are linlc:ed withspringstothesurrounding elements. Thus. a flne meshis requiredinthefailure zoneinordertogettypicalfailure patterns.
IntheCICEor DECICE program,theOEMbasbeen generalizedto thecase of elemem deformability, i.e., SDFEs areused.Depending ontheconstiwtive behaviour applied to theice,
