oe4680 2015 - lecture 15 - discussion exercise & exam questions
DESCRIPTION
exerciseTRANSCRIPT
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MScOffshore&DredgingEngineeringFacultyCEG,DepartmentHydraulicEngineeringFaculty3mE,DepartmentMaritime&TransportTechnology
116June,2015
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
BonusExerciseSummaryAim:
Determinetheglobaliceloadsfor2differentsubstructuredesignsofaGBSintheKaraSea
Stepstobetaken: Reviewoficeconditionsandproperties; Reviewoflimitingmechanisms; Crushingversusbending; Reviewofthestructuralconfiguration;Forthisexercise,youneed: Theexercisehandout; Thematerialgiventoyouduringthelectures; ExcerptfromISO19906(onBlackboard)
16June,2015 2
Figure1:Mapof1)Southwestand2)NortheastKaraSea
Rusanovskoye
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
BonusExerciseSummaryNoteherethat: Rusanovskoye islocatedinBaidaratskaya Bay
inthesouthwesternpartoftheKaraSea ThelocationoftheGBSisdefinitelyoffshore
16June,2015 3
Figure1:Mapof1)Southwestand2)NortheastKaraSea
Rusanovskoye
Parameter AverageAnnualValuesOccurrence,firstice October
Occurrence,lastice July
FYlevellandfastice,thickness 1,6m
FYlevelicefloes,thickness 1,4 1,8m
FYlevelicefloes,eq.diameter 4,5km
MYlevelicefloes,thickness
FYridges,keeldepth 6,5 7,5m
MYridges,keeldepth
Icemovement,nearshore 0,4m/s
Icemovement,offshore 0,3m/s
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Structuralconfiguration
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Figure2:SketchofPlatformDesignOptionsfortheKaraSeaGBS
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Givenparameters
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Parameters Symbol Value UnitAirDensity(at19C) a 1,37 kg/m3
Windvelocity Va 21 m/sDensityseawater w 1027 kg/m3
Currentvelocity Vw 3,4 m/sSalinityseawater S 31 Densityseaice ice 910 kg/m3
Youngsmodulusseaice E 5,0 GPaPoisson'sratio 0,3 Rubbleheight hr 5 mIcetoicefrictioncoefficient i 0,05 Porosityicerubble e 0,35 Rubbleangleofrepose A10 Cohesionoficerubble c 1,7 kPaInternalfrictionangleicerubble 40
VariableParameters Symbol Unit Value Value ValueExtremeicefloethickness H m H1=1,6 H2=1,9 H3=2,2Icestructurefrictioncoefficient C C1=0,01 C2=0,02 C3=0,03
A1=40 A4=49 A7=58Coneangle A A2=43 A5=52 A8=61
A3=46 A6=55 A9=64
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
OverviewExerciseScoring Answeringallproblemscorrectly,yieldsa0,75 bonustoyourexamgrade. Thisbonusisvalidfor:
TheexaminQ4,onWednesday24June2015,09:0012:00,and TheretakeinQ5,onThursday13August2015,09:0012:00. Ergo:doingtheexamnextyear,meansredoingthebonusassignment!
Intotal,therewere32pointstobeearned,dividedamongthe4problemsas:1a. [2] 2a. [2] 3a. [1] 4a. [1]1b. [2] 2b. [2] 3b. [4] 4b. [8]
2c. [3] 3c. [1] 4c. [3]2d. [1]
1. [4] 2. [8] 3. [6] 4. [12]
Thus,everysinglepointequalsa(0,75/30=)0,025bonustoyourexam.16June,2015 6
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
ProblemStatement1[4pts]Inthewinter20142015,themeandailyairtemperatureattheconsideredlocationintheKaraSeawasbelowtheseawaterfreezingpointfrom16September2014untilandincluding18April2015.Theaveragemeandailyairtemperatureduringthisperiodwas17,1C.
Forthecalculationoficethickness,theKaraandChukchiSeashavethesamesitespecificconstants:intheChukchiSea4096freezingdegreedaysyieldanicethicknessof2,24m.
1. Forthegivenweatherconditionsinthewinter20142015,a. Calculatethenumberofaccumulatedfreezingdegreedaysin
theKaraSea.b. DeterminethemaximumundisturbedicethicknessintheKaraSea
assuminglinearheatconduction.
16June,2015 7
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Problem1aForthegivenconditionsinthewinter20142015:a. calculatethenumberofaccumulatedfreezingdegreedaysintheKaraSea.
Thenumberofaccumulateddegreedaysisfoundas:
meandailyairtemperatureattheconsideredlocationintheKaraSeawasbelowtheseawaterfreezingpointfrom16September2014untilandincluding18April2015.Theperiodfrom16September2014until18April2015yieldsatotalof:
15+31+30+31+31+28+31+18=215days.
Theaveragemeandailyairtemperatureduringthisperiodwas17,1C.Ta isgivenas17,1C.Theseawatersalinityis31,andthus(fromthelectureslideswefindthat)thefreezingpointoftheseawaterTbis1,705C.
Andthus:
16June,2015 8
a b a bFDD daysC T T avg T T n
17,1 1,705 215 3310FDDC
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Problem1bForthegivenweatherconditionsinthewinter20112012:b. DeterminethemaximumundisturbedicethicknessintheChukchiSea
assuminglinearheatconduction.
Themaximumundisturbedicethicknessisfoundas:
Forthecalculationoficethickness,theKaraandChukchiSeashavethesamesitespecificconstants; intheChukchiSea4096freezingdegreedaysyieldanicethicknessof2,24m.Assuminglinearheatconductionitfollowsthatb=0,5,fromthedatafortheBeaufortSea,wethusfind:
WepreviouslyfoundthatCFDD =3310,thuswefindtheicethicknessfortheChukchiSeaas:
16June,2015 9
bFDDh aC
;;
2,240,035
4096b Chukchi
Chukchi FDD Chukchi bFDD Chukchi
hh aC aC
0,035 3310 2,014bFDDh aC m
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Insteadoftheundisturbedicethickness,extremeicefloethicknessesshouldbeusedforthedesignloads.Inotherwords,fromthispointonwardsusetheextremeicefloethicknessvaluespecificallygiventoyourgroup.
AssumethatforextremeicefloethicknessesintheKaraSea,theicetemperatureatthefloesurfaceis19C.
2. ForsubstructureA,thusforthesubstructurethatiscylindrical atthewaterline,a. Determinetheiceactionforanaveragesizedisolatedicefloeforlimitforce;b. CalculatethedesignactionforicecrushingfailureaccordingtoISO19906;
ProblemStatement2[8pts]
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SubstructureA
50m24m
18m
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
ForsubstructureA,thusforthesubstructurethatiscylindrical atthewaterline,a. Determinetheiceactionforanaveragesizedisolatedicefloeforlimitforce;Foranisolatedicefloe,wheretheicefloeisdescribedasanequivalentcircularfloewithadiameterDeq,wehavenoiceiceinteractionandthethermalexpansiondoesnotleadtoadditionalforces.Thus,thelimitforceactioncanbedescribedas:
Fromthelectureonicemechanics,wefindthatCd,a =0,025andCd,w =0,002. Andfromtable1:a =1,37kg/m3,Va =21m/s,w =1027kg/m3,Vw =3,4m/s. Additionally,table1givesanaverageannualvalueforthediameterofaFYlevel
icefloeasDeq =4,5km.
Thus: 2 22 3 2 3, 8 8,
0,025 1,37 21 4,5 10 0,002 1027 3,4 4,5 10
120,11 188,82 308,9LF floe
LF floe
F
F MN
Problem2a
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2 2 2 2 2, , ,4 8 8floe eq LF floe d a a a eq d w w w eqA D F C V D C V D
Isthisconservativeornot?
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Problem2bb. CalculatethedesignactionforicecrushingfailureaccordingtoISO19906;
AccordingtoISO19906,wefindtheicecrushingloadthroughtheglobalicepressureduetocrushing(eqs.A.820andA.821)as:
TheicestrengthcoefficientforArcticareasisequalto:CR =2,8MPa. mandnareempiricalcoefficientsthatdependontheicethickness,butforthe
possiblethicknessesarealwaysfoundas:m=0,16,n=0,3. Thewidthofthestructureis:w=24mandh1isaunitvariable:h1=1m.
Withh=H2=1,9m,wefind:
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1 1
, n nm m
G G G R G Rh w h wF p hw p C F C hwh h h h
0,160,31,9 242,8 1,9 24 70,2 1,539
1 1,9G GF MN p MPa
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Insteadoftheundisturbedicethickness,extremeicefloethicknessesshouldbeusedforthedesignloads.Inotherwords,fromthispointonwardsusetheextremeicefloethicknessvaluespecificallygiventoyourgroup.
AssumethatforextremeicefloethicknessesintheKaraSea,theicetemperatureatthefloesurfaceis19C.
2. ForsubstructureA,thusforthesubstructurethatiscylindrical atthewaterline,c. Determinethepenetrationofthestructureintoanaveragesizedisolatedicefloefor
alimitenergyeventanddeterminethecorrespondinglimitenergyiceaction;d. Concludewhichlimitingmechanismgovernstheiceactionandexplainwhy.
ProblemStatement2[8pts]
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SubstructureA
50m24m
18m
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Problem2c(1)c. Determinethepenetrationofthestructureintoanaveragesizedisolatedice
floeforalimitenergyeventanddeterminethecorrespondinglimitenergyiceaction;
Theiceactionforlimitenergyisdeterminedfromtheworkenergyprincipal:
Anaveragesizedicefloehasadiameterof4,5km.Thus,withice=910kg/m3 andh=H2=1,9m,themassoftheicefloebecomes:
Thestructureisoffshore,sofromtable1:vbeg =0,3m/s.Obviously,vend =0m/s.
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2 21 12 2beg endF x dx p x w x h x dx mv mv
22 34 4910 4,5 10 1,9 27,5ice eqm D h Gkg Somehavechosenvbeg =0,4m/sandclaimedthistobeconservative.Isthiscorrect?
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
IceFloe
Recap RoadmapforLimitEnergyIceAction
Fromtheworkenergyprinciplewefound:
Astheanalyticalintegrationoverxisnotalwayseasytoapply,theiceactionforlimitenergycanbeapproximatedusingthefollowingroadmap:1. Increasethepenetrationx usingsmallincrementsx,2. Ateachpenetrationxi determineicepressure,interactionwidthand
icethickness,aswellasthecorrespondingiceaction.3. Perincrementassumethattheicepressure,interactionwidthandice
thicknessareconstantsothatthevelocityattheendofeachincrementcanbedeterminedusing:.
4. Repeatuntil,theiceactionforlimitenergyis:.16June,2015 15
RigidStructure 2 21 12 2beg endF x dx p x w x h x dx mv mv
2 21 1 12 2i i i i ipw h x mv mv 1 0iv ,maxLE iF F
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Problem2c(2)c. Determinethepenetrationofthestructureintoanaveragesizedisolatedice
floeforalimitenergyeventanddeterminethecorrespondinglimitenergyiceaction;
Theiceactionforlimitenergyisdeterminedfromtheworkenergyprincipal:
Anaveragesizedicefloehasadiameterof4,5km.Thus,withice=910kg/m3 andh=H2=1,9m,themassoftheicefloebecomes:
Thestructureisoffshore,sofromtable1:vbeg =0,3m/s.Obviously,vend =0m/s. Usingtheroadmap:
Forh=H1=1,6m,wefindtheexactpenetrationas:19,48m.Forh=H2=1,9m,wefindtheexactpenetrationas:19,90m.Forh=H3=2,2m,wefindtheexactpenetrationas:20,27m.
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2 21 12 2beg endF x dx p x w x h x dx mv mv
22 34 4910 4,5 10 1,9 27,5ice eqm D h Gkg
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Problem2c(3) FastApproximationc. Determinethepenetrationofthestructureintoanaveragesizedisolatedice
floeforalimitenergyeventanddeterminethecorrespondinglimitenergyiceaction;
Theiceactionforlimitenergyisdeterminedfromtheworkenergyprincipal:
Anaveragesizedicefloehasadiameterof4,5km.Thus,withice=910kg/m3andh=H2=1,9m,themassoftheicefloewasfoundas27,5Gkg.
Againfromtable1wehave:vbeg =0,3m/s.Obviously,vend =0m/s. Now,asafirstestimateletusassumethatF(x)=FG isconstant.Thepenetrationmaythenbeapproximatedas:
Solvingtheproblemusingtheroadmap,yieldedapenetrationof19,90m.
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2 21 12 2beg endF x dx p x w x h x dx mv mv
2 9 2212 627,5 10 0,3 17,632 2 70,2 10begG beg Gmv
F x dx F x mv x mF
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Problems2c(4)and2dc. Determinethepenetrationofthestructureintoanaveragesizedisolatedicefloe
foralimitenergyeventanddeterminethecorresponding limitenergyiceaction; Usingtheroadmap,wefoundanexactpenetrationof19,90m,
whileafastapproximationyieldedapenetrationof17,63m. Withadiameterof24m,thestructureisfullyenveloped atapenetrationof12m. Thelimitenergyiceactionisthusequaltothelimitstressload:
d. Concludewhichlimitingmechanismgovernstheiceactionandexplainwhy. Fromquestionsa.andb.wefind:FLS
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
ProblemStatement33. UsingtheISO19906provisions:
a. Calculatetheaverageicesalinityfordesignconditions;b. Calculatethecorrespondingbrinevolumeandtotalporosity;c. Determinetheflexuralstrengthoftheiceforpreliminarydesign.
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Problem3aUsingtheISO19906provisions:a. Calculatetheapproximateicesalinityfordesignconditions;TheAVERAGEicesalinityofagrowingfirstyearlevelicesheetisfoundaccordingtotheISO19906provisionsbythefollowingequation:
Clearlyallgivenextremeicethicknessesare>0,34mandthus,substitutingthepossiblevaluesgivesasalinity(inppt)as:
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13,4 17,4 for 0,348,0 1,62 for 0,34
h h mS
h h m
1 1,6: 5,4088,0 1,62 2 1,9: 4,922
3 2,2: 4,436
H SS h H S
H S
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Problem3b(1)UsingtheISO19906provisions:b. Calculatethecorrespondingbrinevolumeandtotalporosity;
ThecorrespondingbrinevolumefollowsfromISO19906as:
Forthecalculationofthebrinevolumethatcorrespondstotheaverage salinitySoveranicesheet,wemustalsousetheaverage temperatureovertheicesheet.
AssumethatforextremeicefloethicknessesintheKaraSea,theicetemperatureatthefloesurfaceis19C.Inthelectureonicemechanics,itwasexplainedthatthetemperatureinanicefloebyapproximationchangeslinearlyovertheheight: atthefloesurfacethetemperatureisgivenas19C. Lookingattheheatfluxthroughtheice,thetemperatureatthebottomofthe
icesheetmustbeequaltothefreezingpoint,i.e.1,705C.
Andthuswefindthat:
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49,18 0,53brineV S T
19 1,705 2 10,3525avgT T C
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Problem3b(2)UsingtheISO19906provisions:b. Calculatethecorrespondingbrinevolumeandtotalporosity;SubstitutingtheaveragesalinitySandtheaveragetemperatureTyields:
Accordingtotheicemechanicslecture,theairvolume(inppt)maybeapproximated as:
Andthustheporosityisfound(inppt)as:
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1: 28,5649,18 0,53 5,28 2: 25,99
10,35253: 23,42
brine
brine brine
brine
H VV S S H V
H V
9101 1 1 8,76
918,05bulk sea ice
airparticles pure ice i
VT
1: 28,56 8,76 37,322: 25,99 8,76 34,753: 23,42 8,76 32,18
brine air
HV V H
H
916,7 0,13pure ice i iT T
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Problem3cUsingtheISO19906provisions:c. Determinetheflexuralstrengthoftheiceforpreliminarydesign;
TheflexuralstrengthoftheiceisdefinedinISO19906as:
Here,thebrinevolumeshouldbesubstitutedasthebrinevolumefraction,thusabrinevolumeof34,75(inppt)correspondstoabrinevolumefraction0,03475.
Thus,theflexuralstrengthscorrespondingtothedifferenticethicknessesare:
NotethatthesevaluesarehigherthanwhatISO19906notesreasonable!
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5,881,76 bVf MP ea
5,88
1: 0,6521,76 2: 0,682
3: 0,716
b
fV
f f
f
H MPae H MPa
H MPa
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Withtheaimtoreducetheiceaction,thestructureisredesignedandequippedwithaconeatthewaterline.
4. ForsubstructureB,thusforthesubstructurethatisconical atthewaterline,andforthespecificcombinationofparametersspecifiedforyourgroup,a. Determinethediameteroftheconeatthestillwaterlevel;b. Calculatethetotalhorizontal andverticaldesignloadforbendingfailure
accordingtoISO19906(wehereactuallyassumethatthecodeprovisionsforslopedsurfacesalsoholdforconicalcollars);
c. Determinethereductionofthetotalhorizontaldesignloadbyapplyingadownwardconewiththesamewaterlinediameterastheupwardcone.
ProblemStatement4.[12pts.]
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SubstructureB
50m
A
18m6m24m
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Problem4aForsubstructureB,thusforthesubstructurethatisconical atthewaterline,andforthespecificcombinationofparametersspecifiedforyourgroup,a. Determinethediameteroftheconeatthestillwaterlevel;Thetopoftheconeislocated6mabovethewaterline(MSL)asshowninFigure2,andthediameterofthetopoftheconeis24m.Thediameteroftheconeatthewaterlineisthusfoundas:
Consequently,thediameteroftheconeatthestillwaterlevelisfoundas:
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,
1: 7,15 4 : 5,22 7: 3,756
2: 6,43 5: 4,69 8: 3,33tan tan
3: 5,79 6: 4,20 9: 2,93
add add addtop cone
add add add add
add add add
A r A r A rh
r A r A r A rA A
A r A r A r
bot,
1: 38,30 4 : 34,43 7: 31,502 2: 36,87 5: 33,38 8: 30,65
3: 35,59 6: 32,40 9: 29,85c c add
A w A w A ww b r A w A w A w
A w A w A w
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Problem4b(1)b. Calculatethetotalhorizontal andverticaldesignloadforbendingfailure
accordingtoISO19906;
ThetotalhorizontaldesignloadforbendingfailureisfoundaccordingtoISO19906as:
IngeneralthebreakingcomponentHB isthemaincomponent,whichisfoundas:
Here,theflexuralstrengthf istheresultofquestion3c.16June,2015 26
1
B P R L TH
B
f c
H H H H HF Hh
: Loadrequiredtobreaktheiceblocksagainsttheslope: Loadrequiredtopushtheiceblocksuptheslope: Loadrequiredtoturntheiceblockatthetopoftheslope: Loadrequiredtopushthe
B
R
T
P
HHHH sheeticethroughtherubble
: LoadrequiredtolifttheicerubblewiththeunbrokenicefloeLH
0,25
2 3
0,255 2with:
4 12 10,68sin coscos sin
C C Cw w
B f C
Ehw L Lgh g vHE
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Problem4b(2)b. Calculatethetotalhorizontal andverticaldesignloadforbendingfailure
accordingtoISO19906;
Wefind:
Where:
Thisyields:
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0,25
2 3
0,255 2with:
4 12 10,68sin coscos sin
C C Cw w
B f C
Ehw L Lgh g vHE
sin cos sin 5 2cos 5: 1,334cos sin cos 5 2sin 5
A C AA C A
C2 = 0.02,A5 = 52
0,25
9 3
2
1: 20,77 89,555 10
2: 23,63 91,6812 1027 9,81 1 0,3
3: 26,38 94,93
C C
C C C
C C
H L m mHL H L m m
H L m m
0,2551, 1, 1: 2,30
0,68 2, 2, 5: 4,773, 3, 9: 10,34
Bw
B f C B
B
H C A H MNghH H C A H MNE
H C A H MN
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Problem4b(3)b. Calculatethetotalhorizontal andverticaldesignloadforbendingfailure
accordingtoISO19906;
ThetotalhorizontaldesignloadforbendingfailureisfoundaccordingtoISO19906as:
Theremainingloadcomponentscanbewrittenas:
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1
B P R L TH
B
f c
H H H H HFH
h
: Loadrequiredtobreaktheiceblocksagainsttheslope: Loadrequiredtopushtheiceblocksuptheslope: Loadrequiredtoturntheiceblockatthetopoftheslope: Loadrequiredtopushthe
B
R
T
P
HHHH sheeticethroughtherubble
: LoadrequiredtolifttheicerubblewiththeunbrokenicefloeLH
22 tan 11 1
tan 2tan
sin cos tan sin cos0,5 1 cos 1cos sin tan tan tan sin
tan 1 1 tan1 0,5 1 tan 1tan tan tan t
P r i i
i rR i r i
L r r i
H wh g e
w ghH e h h
H wh h g e
2
ancos1,5 0
sin cosT i
c
H wh g
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Problem4b(4)b. Calculatethetotalhorizontal andverticaldesignloadforbendingfailure
accordingtoISO19906;ThehorizontalbreakingloadHB ,aswellastheothercomponentsarenowfoundbysimplysubstitutingthecalculatedvaluesintotheISO19906equations.
ForexampleusingH2,C2&A5,wefind:(i.e.h=1,9m; =0,02; =52)
Andthetotalhorizontalandverticalforcesbecomes:
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4,77 0,01 4,83 0,67 1,28 12,04 9,034,771 10,682 91,68 1,9
B P R L T HH V
B
f c
H H H H H FF MN F MNHh
4,7711,84,830,671,28
B
P
R
L
T
H MNH kNH MNH MNH MN
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
UpwardBendingHorizontalActionFH(angle)
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6,0
10,0
14,0
18,0
22,0
20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64
H1.6C0.01H1.6C0.02H1.6C0.03H1.9C0.01H1.9C0.02H1.9C0.03H2.2C0.01H2.2C0.02H2.2C0.03
angle
MN
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Problem4c(1)c. Determinethereductionofthetotalhorizontaldesignloadbyapplyinga
downwardconewiththesamewaterlinediameterastheupwardcone.
Upwardconespushtheiceup,whereasdownwardconespushtheicedown.
Thus,onanupwardcone:1. Therewillberubblepileup,asaconsequence
a. operationsarenegativelyinfluencedbyrubblegettingintheway,andb. iceactionsincreaseastheicerubbleblockstheslope.
2. Lowericeactionsduetoalowerflexuralstrengthoftheice3. Highericeactionsaswehavetotakeintoaccounttheweightofice,
insteadofitsbuoyancyonadownwardslope.4. Highericeactionsasthefrictioncoefficientishigheronanupwardslope;
downwardslopesarelubricatedduetowaterinbetweentheslopeandtheice.
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Problem4c(2)Onanupwardcone:1. Therewillberubblepileup,asaconsequence
a. operationsarenegativelyinfluencedbyrubblegettingintheway,andb. iceactionsincreaseastheicerubbleblockstheslope.
2. Lowericeactionsduetoalowerflexuralstrengthoftheice3. Highericeactionsaswehavetotakeintoaccounttheweightofice,
insteadofitsbuoyancyonadownwardslope.4. Highericeactionsasthefrictioncoefficientishigheronanupwardslope;
downwardslopesarelubricatedduetowaterinbetweentheslopeandtheice.
InISO19906,theflexuralstrengthiscalculatedasanaverageflexuralstrengthandthereforecannotdistinguishbetweenup/downwardbending!
Furthermore,ISO19906considersonlyoneicestructurefrictioncoefficient,anddoesnotdistinguishbetweenfrictionaboveandunderwater!
16June,2015 32
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Problem4c(3)UpwardversusDownwardbending:
Theremainingdifferencesbetweenupwardanddownwardbending: Theweightoftheiceonanupwardslopeshouldbereplacedbyitsbuoyancy
foradownwardslope,i.e.theicedensityshouldbereplacedbythesubmergeddensity.(i wi ;alsoseethelecturesonIceActions)
Differenceiceactionsduetodryandwetrubblepileup
So: Forupwardanddownwardbendingthehorizontalbreakingload HB isthesame. Forupwardbending,wecalculateHP,HR,andHT withtheicedensityi. Fordownwardbending,HT =0,butallothercomponentsthatareafunctionof
theicedensity,i.e.HP,HR,HLarecalculatedwiththesubmergeddensitywi.
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Problem4c(3)c. Determinethereductionofthetotalhorizontaldesignloadbyapplyinga
downwardconewiththesamewaterlinediameterastheupwardcone.
ThetotalhorizontaldesignloadforbendingfailureisfoundaccordingtoISO19906as:
Theremainingloadcomponentscanbewrittenas:
16June,2015 34
1
B P R L TH
B
f c
H H H H HFH
h
: Loadrequiredtobreaktheiceblocksagainsttheslope: Loadrequiredtopushtheiceblocksuptheslope: Loadrequiredtoturntheiceblockatthetopoftheslope: Loadrequiredtopushthe
B
R
T
P
HHHH sheeticethroughtherubble
: LoadrequiredtolifttheicerubblewiththeunbrokenicefloeLH
22 tan 11 1
tan 2tan
sin cos tan sin cos0,5 1 cos 1cos sin tan tan tan sin
tan 1 1 tan1 0,5 1 tan 1tan tan tan t
P r i i
i rR i r i
L r r i
H wh g e
w ghH e h h
H wh h g e
2
ancos1,5 0
sin cosT i
c
H wh g
3with 117i w i kg m
NotethatthecomponentHT maybeneglectedcompletely,asasubmergediceblockwillturnbeforetheendoftheslope.
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Problem4c(4)c. Determinethereductionofthetotalhorizontaldesignloadbyapplyinga
downwardconewiththesamewaterlinediameterastheupwardcone.ThehorizontalbreakingloadHB remainsthesameandtheothercomponentsarefoundfromtheISO19906equations.
ForexampleusingH2,C2&A5,wefind:(i.e.h=1,9m; =0,02; =52)
Andthetotalhorizontalandverticalforcesbecomes:
16June,2015 35
,4,77 0,00 0,62 0,18 1,28 5,81 6,244,771 1
0,682 91,68 1,9
B P R L TH H red
B
f c
H H H H HF MN F MNHh
4,771,520,620,180,00
B
P
R
L
T
H MNH kNH MNH MNH MN
4,7711,84,830,671,28
B
P
R
L
T
H MNH kNH MNH MNH MN
12,04HF MN
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
DownwardBendingHor.ActionFH(angle)
16June,2015 36
2,0
3,0
4,0
5,0
6,0
7,0
8,0
9,0
10,0
11,0
12,0
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64
H1.6C0.01H1.6C0.02H1.6C0.03H1.9C0.01H1.9C0.02H1.9C0.03H2.2C0.01H2.2C0.02H2.2C0.03
MN
angle
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Commonerrors Insertingthewrongunitsintheequations,forexample:
cohesionc=1,7kPa,sointheequations,thevalueofc=1700,not1,7.
Forexample,inexcel,trigonometricfunctionsarecalculatedusinganglesinradians,notdegrees.
Calculatetheaveragetemperatureas:
Usetherightequation,usingtherightvaluesforallofthevariablesandthensomehowmessupthecalculationandendupwiththewronganswer.
Usethenearshoreicevelocityof0,4m/s,insteadoftheoffshoreicefloevelocityof0,3m/sforastructurethatisapproximately200kmoffshore.
Forgettingpartsofequations
16June,2015 37
21 1,595 9,72avg
T C 21 1,595 11,3
2avgT T C
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Generalremarks 1groupmanagedtogettheirgroupnumberwrong,andthereforeused
differentparametersthangiven.
2groupsmanagedtonotregisteratallandusedselfchosenparameters.(butdidnotdoatallbad!)
Multiplegroupsforgottoincludeasinglepageoverviewoftheanswers Quiteafewmanagedtopresent,forexample,aresultingiceforceof
22658254,86NPleasewritethisas:22,66MN(!)
Pleaseproperlyincludethecorrectunits,sometimesIcantevendistinguishwhetherIamlookingatN,kN orMN!
1groupmanagedtoproperlycopyallthecorrectequations,butwithoutgivingtheresultinganswers
Noneedtorepresentthewholeexercise.Especially,ifyoudonotintendtogivepartialanswers
16June,2015 38
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Overviewexerciseresults
Therewere55groups,ofthese2groupsfailedtodelivertheiranswers Theaveragescoreofall106 participantswas 22,0 points;
16June,2015 39
0
1
2
3
4
5
6
7
8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
BonusExerciseResults
16June,2015 40
Grp Score Bonus Grp Score Bonus Grp Score Bonus
1 23 0,575 20 29 0,725 39 14 0,350
2 25 0,625 21 30 0,750 40 13 0,325
3 29 0,725 22 26 0,650 41 20 0,500
4 25 0,625 23 42 22 0,550
5 26 0,650 24 43 28 0,700
6 29 0,725 25 10 0,250 44 21 0,525
7 12 0,300 26 18 0,450 45 17 0,425
8 26 0,650 27 27 0,675 46 17 0,425
9 19 0,475 28 28 0,700 47 28 0,700
10 24 0,600 29 30 0,750 48 14 0,350
11 27 0,675 30 10 0,250 49 25 0,625
12 18 0,450 31 9 0,225 50 13 0,325
13 30 0,750 32 25 0,625 51 16 0,400
14 26 0,650 33 28 0,700 52 14 0,350
15 14 0,350 34 24 0,600 53 14 0,350
16 21 0,525 35 28 0,700 54 18 0,450
17 23 0,575 36 28 0,700 55 24 0,600
18 29 0,725 37 27 0,675
19 28 0,700 38 15 0,375
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MScOffshore&DredgingEngineeringFacultyCEG,DepartmentHydraulicEngineeringFaculty3mE,DepartmentMaritime&TransportTechnology
4116June,2015
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
16June,2015 42
Examdates&ConfigurationoftopicsExamdates
Exam: Wednesday24June, 09:00 12:00, 2Czaal2Reexam: Thursday13August, 09:00 12:00, t.b.a.
Theexamroughlyfollowsthesetupofthecourseschedule:
GeneralArcticEngineering: 7080% Arcticregions,Arcticstructuresandicefeatures; Icephysicsand/oricemechanics; Iceactionsandicestructureinteraction; Icemanagementand/orISO19906; ScalemodellingandArcticOceanography.
Dynamicsoficestructureinteraction: 2030% Frequencylockinandiceinducedvibrations; Physicsbasedandnumericalmodelling; Industryexperience;
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
1
2
16June,2015 43
Arcticregionsandicefeatures
Q: Nametheseas/areasoftheselocationsanddescribetheicefeaturesthatyouexpecttoencounterhere.
1. BaffinBay Firstyearlevelicefloes, Firstyeariceridges, Multiyearlevelice floes,and (Many)Icebergs.
2. (Southwestern)KaraSea Firstyearlevelicefloes, Firstyeariceridges,and (Rarely)Multiyeariceridges.
Atthelocationsgiveninthefigurebelow,offshorehydrocarbonfieldsarebeingdevelopedorwillbedevelopedinthenextfewyears.
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
16June,2015 44
ArcticconceptsQ: Discusstheadvantages(pros)andlimitations(cons)ofthefollowing
hydrocarbonproductionconceptsforuseintheArctic: GravityBasedStructure ShipshapedFloatingProduction,StorageandOffloadingunit(FPSO) ArcticTLP
LetsdiscusstheShipshapedFPSOunit(pros &cons): FPSOscommonlyusedfordeeporverydeepwaters. Goodrubbleclearing Canbedisconnectedforpossiblecollisionswithseverefeaturessuchasicebergs. Canbereused. Largedeckspaceavailable. Requiresnooffshoretopsideinstallation. Reliesforabigpartonicevaning capability Canonlyresistfirstyearicefeaturesandoftenrequiresicemanagement. SmalloperationalweatherwindowcomparedtoaGBSoranArtificialisland. Relativelyexpensivetomake. Theriserandmooringsystemsmaybeexposedtobrokenice.
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
2
16June,2015 45
Arcticregions/conceptsandicefeaturesQ: Whichofthegivenconceptswouldyouchoose
foreachlocationandexplainwhy.
1. BaffinBay GBS:Toodeep(200300m) FPSO:Goodopenwaterbehaviourandassumingitsdisconnectablemakesthisaviableoption.
ArcticTLP:perfectforopenwaterbehaviour,butitcannotbedisconnectedforicebergs.
Bestoption:FPSO(disconnection,openwater)
2. (Southwestern)KaraSea GBS:Viableoptionespeciallyintheshallowparts FPSO:Notaviableoptionastheoccurringiceloadsaretoohigh,evenwithicemanagement.
ArcticTLP:Probablytooshallow.Bestoption:GBS(ifwaterdepthallows)
GBS, Ship-shaped FPSO or Arctic TLP?
1
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
16June,2015 46
Arcticregions/structuresandicefeatures
Q: Name2(3)areaswhereoffshoreplatformsmustbedesignedforbothiceandseismicloads?
SeaofOkhotsk(Sakhalin), CookInlet(Alaska),or Bohai Bay(China)
Notehere:theCaspianSeaisawronganswer: ThereareearthquakesinthesouthernpartoftheCaspianSea,but
thereisnoseaicethere. InthenorthoftheCaspianSeathereisseaiceduringthewinters,
buttherearenoearthquakes.
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
16June,2015 47
IceactionsQ: Whatarethemechanismsthatlimittheiceloadonastructureduringice
structureinteraction? LimitEnergy LimitStress LimitForce
Q: Explainbrieflywhatismeantbyeachoftheselimitingmechanisms.
LimitEnergy:Themechanismthatoccurswhentheactionislimitedbythe(relative)kineticenergyormomentumoftheicefeature.ThismechanismisalsoreferredtoasLimitMomentum.
LimitStress:Themechanismthatoccurswhenthedrivingforcesworkingontheicefeaturearesufficientfortheicetofailasitinteractswiththestructure.
LimitForce:Themechanismthatoccurswhenanicefeatureisdrivenagainstthestructureandthedrivingforcesareinsufficientfortheicetofailandenvelopthestructure.
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
16June,2015 48
IceactionsQ: Theiceloadsexertedonaslopingstructurearedifferentfromtheiceloads
exertedonaverticalstructure.Explainonwhichofthestructurestheicefloeexertsthelowestloads,explainwhy,andnamethecorrespondingfailuremodes.Againstslopingstructurestheicefailsthrough(ice) bending,whileonaverticalstructuretheicefailsthrough(ice) crushing.
Theiceactionbybendingdependsmainlyontheflexuralstrengthofice,whilecrushingactionmainlydependsonthecompressivestrengthofice.Theflexuralstrengthoficeismuchlowerthenthecompressivestrengthoficeandthereforebendingexertslowerloadsonastructurethancrushing.
Ergo,theloadswillbelowestonslopingstructures.Notehoweverthatrubblepilingupand/oradfreeze maydiminishtheadvantagesofslopingstructures
Tocalculatestaticiceactions,weprincipallyapplytheISO19906,butwehaveextensivelydiscussedthisduringthefirstpartofthislecture.
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Adfreeze theformationoficebustles
Tidescausewatervariationsandwhenthewaterlowers:thewaterfilmleftonthepilewillfreezeandaccumulate
16June,2015 49
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
IceactionsQ: IntheArctic,offshorestructuresarevulnerabletomanydifferent
environmentalloads.Someoftheseenvironmentalloadswilloccuratthesametime.Forthegivencombinationsofenvironmentalloadsexplainwhetherornotyouwouldchoosetoconsiderthemsimultaneouslyandexplainwhy:
MaximumwaveandiceloadsWaveandIceloadswillnormallynotoccurtogether,sincewavesareattenuatedbythepresenceofseaice.Therefore,thecombinationofthesetwoloadsIsnotaviableloadcombination.
MaximumwaveandmaximumwindloadsUsuallywavesareatitshighestwhenthewindloadsarehighest,thereforetheloadcombinationofmaxwaveandmaxwindisveryviable.
LeveliceandicebergcollisionloadsLeveliceandicebergcollisionloadswillcausefailureagainstastructureusingacompletelydifferentlimitingmechanism.Leveliceisusuallylimitstress,whileicebergcollisionsarelimitenergy.Althoughtheoccurrenceofbothphenomenonatthesametimeispossible,designingforthecombinationofthetwotogetherisirrelevant,duetotheirdifferenceinloadingmechanism.
16June,2015 50
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Crystallography:BernalFowler/icerulesQ: TheBernalFowlerrulesdescribethearrangementofwatermoleculesand
hydrogenatomsintheidealcrystallinestructureofice.Givethe4BernalFowlerrules.
1. Thewatermoleculeispreservedintheicelattice.Ergo,1Oatomwith2Hatoms.
2. Eachwatermoleculeistetrahedrically bondedto4adjacentwatermolecules.
3. Thereisonly1hydrogenatomperoxygenoxygenbond.4. Thehydrogenatomsaremobilesorules13maybesatisfiedinany
configuration.
16June,2015 51
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
IcegrowthQ: Whenseaiceformsandgrowsitobtainsdifferentformsandshapeswhile
goingthroughthedifferentstagesofitslife.Withrespecttothis,explainthefollowingterms:
FrazilIceFinespiculesorplatesofice,suspendedinwater.
CongelationiceCongelationiceisalsoknownassecondaryiceandthisisthepartofanicelayerthatisgrowninadditiontotheprimaryice.Congelationiceconsistsofthetransitionzone,thecolumnarzoneandtheskeletonlayer.
BrineBrineiswaterthatissupersaturatedwithsaltthatisenclosedinseaice;Assaltisexpelledfromthefirsticeplateletsthatform,thesalinityofthesurroundingwaterincreases.Duringgrowth,theiceplateletstakeinwaterfromthesurroundingseawater,increasingthesalinityofsurroundingwaterfurther.Duringfurthericegrowththehighsalinitywaterisincludedalongtheplateletboundariesintheformofliquidorsolidinclusions.Thenowisolatedbrineinclusionsarecalledbrinepockets.
16June,2015 52
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
IceMechanicsQ: Whatarethe4physicalicepropertiesthatinfluencethestrengthofice? Temperature Porosity Salinity Crystallography
Q: Howdoestherelativevelocitybetweenastructureandanicefloeinfluencetheloadsonthatoffshorestructureduringicestructureinteraction? Lowvelocity ductilefailure High(er)velocity brittlefailure
16June,2015 53
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
DynamicsoficestructureinteractionQ: Whatarethe3maintypesofmodelsthatareavailabletomodeldynamic
interactionbetweenseaiceandoffshorestructures?Giveashortexplanationofeachtypeofmodel. Physicsbased models
Thistypeofmodelling triestoapproachrealityasmuchaspossiblebytakingintoaccountthefundamentalphysical(micro)propertiesofthephenomenontobemodelled.
Empirical modelsModelsbasedondata.
Phenomenological modelsModelsthattrytomimicthebehaviour ofacertainphenomenonratherthanlookingintothesourceofthisbehaviour.
16June,2015 54
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
IcestructureinteractionQ: Theinteractionbetweenanicefloeandaslopingstructureisdescribedbya
loadingcyclein2alternatingphases.Describethisloadingcycleandidentifyits2phases.
1. Uponinitialcontactoftheicefloewiththehulloftheslopingstructure,thetipoftheicefloeispusheddownwardsandtheicefloestartsbendingdownwardsuptothepointwheretheicefloe,heremodelledasabeam,breaksinbendingatacertaindistancefromtheinteractionpointatthetipoftheicefloe.Thisisthefirstphasecommonlydescribedas:Bendinguptofailure.
2. Onceapieceoftheicefloe(beam)breaksofffromtheicefloe,thispiece(orpiecesofrubble)ispusheddowntheslopebytheremainingicefloe,untilthetipoftheremainingicefloehitsthehulloftheslopingstructure.Thisisknownasthesecondphase.Oncethetipoftheremainingicefloehitsthestructuretheicefloeisonceagainapplyingadirectloadtothestructure,andwethuscommonlydescribethisphaseas:Pushingrubble(down)untilreloading.
16June,2015 55
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
IcestructureinteractionQ: Whichbeamtheorywouldyouusetomodeltheinteractionbetweentheice
andthedownwardslopingstructureand why? EulerBernoullibeamtheory,alsocommonlyknownastheclassicalbeam
theory.
Whenmodellingtheiceasabeam,thebeamrepresentingtheicecanalwaysbeconsideredtobelongorslender;Whenbeamsarelong/slender,sheardeformationsandrotationalinertiamaybedisregardedasisassumedfortheEulerBernoullibeamtheory.
AdditionalNote: Whenconsideringshortbeams,sheardeformationsandrotationalinertia
shouldbetakenintoaccountaccordingtoTimoshenkoRayleighbeamtheory.
16June,2015 56
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
DynamicicestructureinteractionBecausetheicesheetismoving,thedisplacementoftheicesheetdoesnotonlydependontimebutalsodependsonitspositionintime.Themovingicefloe,modelledasabeamonanelasticfoundationisthereforeknownasaconvectivesystem.Consequently,itsverticalaccelerationisfoundasafunctionoficefloevelocityandaccelerationas:
Q: Assumingthatthevelocityoftheicesheetisconstant,givetheequationofmotionforthebendingofamovingicesheetonanelasticfoundationusingEulerBernoullibeamtheory.Here,theaxialcompressionalongtheicesheetandthecorrespondingdampingmaybeneglected.
Assumingthattheicefloevelocityisconstant,wecanwritetheverticalaccelerationoftheicesheetas:
Consequently,wefindtheequationofmotionas:
16June,2015 57
2 2 2 222 2 22 z z z z zD u u u u uv t v t a tDt t x t x x
2 2 22
2 2
2
2 2
z z z zu u u uv vt xD tt x
D
2 2 2 4
22 2 42 0 z z z z
zfoundation
bendingconvective inertia
u u u uA v v EI kut x t x x
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
Dynamicicestructureinteraction
16June,2015 58
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
DynamicsoficestructureinteractionDuringastructuresfirstoperationsintheChukchiSea,theicefloevelocityintheChukchiSeavariesisobservedtobebetween0,04and0,08m/sandthebreakinglengthoftheicethatfailsagainstthestructureinbending rangesfrom10to14m.Thenaturalfrequencyofthestructureis0,195rad/s.Q: Determinethefrequencyrangeoficefailureagainsttheslopingstructureandexplain
whetherfrequencylockinmayoccurwhileoperatingthisstructureintheChukchiSea.Thelowesticefailurefrequencyisfoundforacombinationofthebiggestbreakinglengthandthelowesticefloevelocity:
Accordingly,thehighesticefailurefrequencyisfoundforacombinationofthesmallestbreakinglengthandthehighesticefloevelocity:
Previously,wefoundanaturalfrequencyof0,195rad/s,whichis4timesbiggerthanthehighesticefailurefrequency.Duetothebigdifference,wemayexpectthattheicefailurefrequencyandthestructuresnaturalrollingfrequencywillnotsynchronize.Thus,wedonotexpectfrequencylockintooccurhere.16June,2015 59
min
max
2 2 0,04 0,01814
lowv rad s
max
min
2 2 0,08 0,05010
highv rad s
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
BeforeIgo
Doyouhaveanyquestions?
or
Isanythingunclearthatyouwouldliketoseefurtherexplained?
IfyouthinkofsomethinglatercometomyofficethisThursdayorthisFriday
16June,2015 60
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DiscussionExercise&ExamQuestionsOE4680ArcticEngineeringMScOffshore&DredgingEngineering
16June,2015 61
Good luck with the examon Wednesday 24 June,
and enjoy the summer holiday!