Design of Ships and Offshore Structures: A Probabilistic Approach for Multi-Year Ice and Iceberg Impact Loads for Decision-making with Uncertainty

Des ign of Sh ips and Offshore S truc tures:

A Probab i l is t ic Approach for Mu l t i-Year Ice and Iceberg Impac t Loads for Dec is ion-mak ing w i th Uncer ta in ty

By

©Freeman E. Ra lph P .Eng . M .Eng .

A Thes is

subm i t ted to the Schoo l o f Gradua te S tud ies in par t ia l fu lf i l lmen t of the requ iremen ts for the

degree of Doc tor of Ph i losophy

Facu l ty of Eng ineer ing and App l ied Sc ience Memor ia l Un ivers i ty

S t . John’s , NL

Oc tober 2016

Th is page is in ten t iona l ly lef t b lank

Abstract

Ice is a comp lex ma ter ia l tha t exh ib i ts d ifferen t fa i lure proper t ies depend ing on the load ing ra te , tempera ture and sa l in i ty . Under fas t load ing ra tes such as a sh ip ramm ing a mu l t i-year (MY) ice , i t fa i ls as a br i t t le frac tur ing ma ter ia l . Frac ture and spa l l ing processes non- s imu l taneous ly reshape the con tac t zone resu l t ing in concen tra ted forces on loca l ized con tac t areas . These loca l ized H igh Pressure Zones (HPZs) are h igh ly var iab le in t ime and space . The re la t ionsh ip be tween loca l and g loba l processes is tha t the sum o f n HPZs forces transferred in to the s truc ture a t any po in t in t ime is the to ta l g loba l force transm i t ted to the s truc ture . As w i th o ther frac tur ing ma ter ia ls , an inheren t sca le effec t ex is ts.

G loba l pressures resu l t from the sum of n HPZ forces averaged over the nom ina l con tac t area (e .g . the impr in t of a sh ip’s bow in to the ice w i thou t correc t ion for spa l l ing effec ts) . The max imum g loba l force w i l l genera l ly occur a t the end of a ram a t the max imum nom ina l con tac t area . Due to the random occurrence of na tura l f laws in the ice , pressures w i l l vary as frac tures occur , con t inua l ly chang ing the con tac t face . A g loba l sca le effec t ex is ts such tha t pressures on larger con tac t areas , inc lud ing zones of low and zero pressure , average ou t to be sma l ler .

Un l ike g loba l pressures , max imum loca l pressures may occur on any pane l and a t any po in t

through the ram dura t ion . Mode l ing exposure is impor ta n t as des ign pressures w i l l increase

for increas ing number of in terac t ion even ts as we l l as increased pene tra t ion or dura t ion . The

sca le effec t for loca l pressures w i th in the nom ina l con tac t area is more demand ing than for

g loba l pressures such tha t pressures on sma l ler areas are cons iderab ly h igher . Wh i le th is is

expec ted, g iven conf inemen t can suppress damage and l im i t frac tur ing even ts , a force l im i t

ex is ts where m icros truc tura l damage occurs, sof ten ing the ice and caus ing HPZs to fa i l .

Loca l pressures on vary ing pane l areas were s tud ied based on spa t ia l HPZ dens i ty and HPZ

force . Bu i ld ing on ear l ier HPZ ana lys is us ing Lou is S . S t . Lauren t da ta, in th is thes is HPZ

dens i ty and forces were der ived from ana lys is of four Po lar Sea da ta se ts . The occurrence and in tens i ty of HPZs on pane l areas were s imu la ted us ing a Po isson Process and an exponen t ia l d is tr ibu t ion for HPZ force . The inf luence of mode l ing HPZ cu toff force on HPZ dens i ty , HPZ force d is tr ibu t ion as we l l as loca l pressure parame ters were s tud ied and appropr ia te comb ina t ions recommended .

Bu i ld ing on the Po lar Sea HPZ ana lys is , a new mode l was deve loped for th is thes is tha t cons iders HPZ occurrence in t ime through a ramm ing even t , mode l ing HPZ ra te. Th is was fur ther enhanced by corre la ting HPZ ra te w i th sh ip speed . Such a mode l a l lows the des igner to de term ine base l ine ‘paren t’ loca l pressure des ign parame ters based on vesse l s ize and expec ted opera t iona l speed . The fas ter a sh ip opera tes through an ice reg ime , the g rea ter the HPZ ra te . Larger and fas ter sh ips w i l l pene tra te fur ther, hav ing longer in terac t ion dura t ion s and hence a grea ter number of HPZs form ing (un less, for examp le, the sh ip passes through a r idge) . For des ign , we are in teres ted in the max imum loca l pressure on a s ing le pane l area through the ram dura t ion . Ra tes too w i l l vary a long the vesse l be ing g rea ter on the bow and leas t from m id -body to s tern . For f ixed s truc tures des igned for iceberg impac ts , ra te and dura t ion based on iceberg s ize and dr if t can be used to mode l exposure in t ime . For f loa ters , mode l ing HPZ forma t ion in t ime prov ides a means to es t ima te dynam ic g loba l forces and moor ing loads i l lus tra t ing benef i t of comp l iance effec ts . Mode l ing of HPZ occurrence over a pane l area is a lso very a t trac t ive for s truc ture response ana lys is . The random p lacemen t of n HPZs over a s truc tura l pane l g ives a be t ter bas is to mode l s tress loca l iza t ion, wh ich is very impor tan t for l im i t s ta tes des ign .

A pre l im inary rev iew of the IACS Po lar C lass ru les was carr ied ou t in th is thes is . G loba l

impac t forces are es t ima ted us ing a k ine t ic energy co l l is ion mode l . Cons idera t ion for

mode l ing ice crush ing s treng th assumes a pressure-area re la t ionsh ip tha t is propor t iona l to

A

wh ich is no t cons is ten t w i th exper imen ta l resu l ts demons tra ting a sca le effec t

propor t iona l to A

. The resu l tan t des ign formu la t ion mode ls excess ive sem i-loca l pressures

increas ing w i th increas in g sem i-loca l con tac t area . Wh i le the in ten t is to mode l increas ing

pressures loca l ly w i th increas ing vesse l d isp lacemen t and subsequen t pene tra t ion and con tac t

area , jus t if ica t ion for th is trend sugges ts tha t there is no reason for trad i t iona l pressure area

sca le effec ts to ex is t and tha t w i th conf inemen t , frac tur ing processes w i l l be l im i ted . Bu t

frac tur ing processes ex is t a t a l l sca les . The occurrence and behav ior of HPZs e i ther lead to

very large s tress loca l iza t ion tha t enhances frac ture even ts or they undergo m icros truc ture

damage tha t sof tens the ice a t the s truc ture in terface . Wh i le the des ign trend in the Po lar

C lass ru les may be okay, the backg round ice mechan ics can be improved . An a l terna t ive

co l l is ion mode l is deve loped in th is thes is w i th an ice s treng th mode l based on da ta and an

exposure a lgor i thm to mode l pressures increas ing loca l ly w i th larger d isp lacemen t vesse ls .

In the m id 1990s as par t of the Arc t ic Sh ipp ing Po l lu t ion Preven t ion Regu la t ions (ASPPR)

proposa l rev iews, a probab i l is tic t ime -s tep sh ip ram mode l was deve loped to es t ima te impac t

forces . Cons is ten t w i th the ASPPR work, exposure based on annua l number of co l l is ions

was mapped to each Po lar C lass (e .g . PC1 , PC2 , PC3 can expec t on the order of 10000 ,

1000 , 100 rams per year respec t ive ly ) . Us ing the MV Arc t ic as a tes t case and exerc is ing

ex trema l ana lys is , impac t forces were es t ima ted for each Po lar C lass . Charac ter is t ic 10

g loba l forces were compared w i th Po lar C lass ru le es t ima tes . Probab i l is t ic loca l pressures

were a lso compared w i th ru le based es t ima tes. Assum ing impac ts w i th MY ice , pre l im inary

resu l ts show tha t p la t ing des ign pressures may be reasonab le , w i th recommenda t ion for

ad jus tmen t to the Po lar C lass 1 coeff ic ien ts to reduce conserva t ism , and poss ib le increases

for lower c lasses . Ana lys is shou ld be ex tended to o ther vesse ls and opera t ing cond i t ions .

A probab i l is t ic me thodo logy for des ign of sh ips based on the pr inc ip les of safe ty and

consequences is impor tan t and necessary bo th for des ign and safe ty va l ida t ion . Such

approaches can cons ider the c lass of the vesse l on the bas is of expec ted number of annua l

in terac t ions w i th ex treme ice fea tures . An examp le i l lus tra t ion of a des ign based on an arc t ic

sh ipp ing rou te , ice cond i t ions , des ign s tra tegy , r isk m i t iga t ion v ia de tec t ion and avo idance

and resu l tan t loca l pressrues on the hu l l for s truc tura l des ign . .

Acknow ledgements

I wou ld l ike to express s incere g ra t i tude to my superv isor , Dr . Ian Jordaan , for unwaver ing comm i tmen t and suppor t through th is research journey . Your pass ion for the sub jec t made the journey en joyab le and reward ing . Your insp ira t ion and gu idance no t on ly kep t me focused , bu t has inf luenced my way of th ink ing . Thanks , too , to my superv isory comm i t tee members , Dr . Br ian Ve i tch and Dr . We i Q iu , for your suppor t and comm i tmen t to the PhD process .

I wou ld l ike to express g ra t i tude to Dr . Char les Rande l l , Pres iden t and CEO of C-CORE , for con t inued suppor t and encouragemen t through th is journey . Thanks a lso to many co l leagues and fr iends , par t icu lar ly Pau l S tuckey and Mark Fug lem , who were a lways w i l l ing to ass is t and prov ide prac t ica l gu idance when needed .

I wou ld l ike to acknow ledge HMDC , the Terra Nova Pro jec t and RDC who funded C-CORE 's Cen tre for Arc t ic Resource Deve lopmen t (CARD) , through wh ich th is work was poss ib le .

Thank you to my paren ts , B i l l and Doro thy Ra lph and in-laws , Rod and Lav in ia Jeans , for the ir cons tan t suppor t and encouragemen t .

F ina l ly , I wou ld l ike to thank my w ife , T ina , and son , Corban , for the ir unwaver ing love ,

suppor t , encouragemen t and pa t ience , w i thou t wh ich th is wou ld no t have been poss ib le .

To T ina and Corban

Tab le of Contents

CHAPTER 1 . In troduc t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1 .1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1 .2 Thes is Ou tl ine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

CHAPTER 2 . Des ign for Ice S truc ture In terac t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 .1 Re l iab i l i ty Based Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 .1 .1 Overv iew of Probab i l is t ic Me thodo logy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 .1 .2 Ice Load D is tr ibu t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 .1 .3 Ex treme Va lue Des ign Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 .1 .4 Des ign S tra tegy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2 .1 .5 S truc tura l Res is tance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2 .1 .6 Spec ify ing Safe ty Targe ts for Des ign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2 .2 Pr inc ipa l Cons idera t ions for G loba l and Loca l Des ign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2 .2 .1 Ice S truc ture In terac t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2 .2 .2 G loba l Des ign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2 .2 .3 Loca l Des ign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2 .3 G loba l and Loca l Pressure-Area Re la t ionsh ips for Des ign . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2 .3 .1 Da ta Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2 .3 .2 G loba l Forces and Pressure-area Re la t ionsh ip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2 .3 .3 Loca l Des ign Pressures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2 .3 .4 O ther Pressure-area Cons idera t ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

CHAPTER 3 . Compress ive Ice Fa i lure and Sca le Effec ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3 .1 Mechan ics of Compress ive Ice Fa i lure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3 .2 S ize and Sca le Effec ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3 .2 .1 Non-S imu l taneous Fa i lure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3 .2 .2 L ine-L ike Con tac t and HPZ Loca t ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3 .2 .3 Pressure-Averag ing Effec ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3 .2 .4 Impor tance of Frac ture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

3 .3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

CHAPTER 4 . G loba l Sh ip Ram S imu la t ion and Loca l HPZ Mode l – Base l ine Mode ls for Presen t Research 83 4 .1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4 .2 Mode l ing G loba l Forces , Hu l l Response and Nom ina l Con tac t Area from Sh ip Rams 84 4 .2 .1 Overv iew . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

4 .2 .2 Vesse l - Ice In terac t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

4 .2 .3 Mode l Va l ida t ion and S imu la t ion Resu l ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

4 .2 .4 S imu la t ion Resu l ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

4 .2 .5 App l ica t ion for Des ign - Probab i l is t ic Me thodo logy . . . . . . . . . . . . . . . . . . . 104

4 .2 .6 Ex trema l Ana lys is . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

4 .2 .7 Sens i t iv i ty to Pressure Area Cons tan t , Cp and Mode led D is tr ibu t ion111 4 .2 .8 Sens i t iv i ty to Pressure Area Cons tan t , Dp and Mode led D is tr ibu t ion119 4 .3 Probab i l is t ic Mode l ing and S imu la t ion of HPZs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

4 .3 .1 Rev iew of Zona l Force Ana lys is . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

4 .3 .2 Zona l Force Mode l ing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

4 .3 .3 Mon te Car lo S imu la t ion of HPZ Occurrence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

4 .3 .4 S imu la t ion of Loca l Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

4 .3 .5 Sens i t iv i ty of Loca l Pressure to HPZ Dens i ty and Force Parame ter γ137 4 .3 .6 Inf luence of HPZ Force Cu toff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

4 .3 .7 Po isson S imu la ted Pane l M isses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

4 .3 .8 Exposure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

4 .4 HPZ Ana lys is based on Po lar Sea Da ta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

4 .4 .1 Po lar Sea Measuremen t Sys tem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

4 .4 .2 Mode l ing HPZ Parame ters Area , Force and Dens i ty . . . . . . . . . . . . . . . . . . . 162 4 .4 .3 HPZ Force and Dens i ty based on Measured Peak Subpane l Pressures

166

4 .4 .4 S imu la t ion of Loca l Pressures from Po lar Sea HPZ Forces . . . . . . . . . 177

4 .4 .5 Mode l ing Loca l Pressure Area Da ta – S imu la ted vs Measured . . . 188

4 .4 .6 Mode l ing HPZ / Pane l H i ts or M isses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

4 .4 .7 Summary D iscuss ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

4 .5 Mode l ing HPZ Ra te . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

4 .5 .1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

4 .5 .2 Mode l ing Loca l Pressures us ing HPZ Forma t ion Ra te . . . . . . . . . . . . . . . . 200

4 .5 .3 Me thodo logy for Es t ima t ing HPZ Ra te . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

4 .5 .4 Inf luence of Cu toff Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

4 .5 .5 Re la t ionsh ip be tween HPZ ra te and Sh ip Ram (or in terac t ion) Speed 217 4 .5 .6 Examp le Ver if ica t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218

4 .5 .7 Sources of Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

4 .6 HPZ Mode l ing Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

CHAPTER 5 . Cons truc t ive Rev iew of IACS Po lar C lass Ru les . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

5 .1 Po lar C lass Ru les Deve lopmen t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

5 .1 .1 Ph i losophy and Approach (IACS , 2006) , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

5 .1 .2 In i t ia l Commen ts and Cons idera t ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228

5 .2 Energy Based Sh ip Ice Co l l is ion Mode l ing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

5 .2 .1 In terac t ion Geome try . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232

5 .2 .2 Ice Crush ing Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234

5 .2 .3 L im i t ing F lexure Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

5 .2 .4 C lass Fac tors Descr ibed for Des ign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240

5 .2 .5 Load Pa tch Def in i t ion ( i .e . Ice Con tac t Area) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

5 .2 .6 L ine Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

5 .2 .7 Effec t ive Des ign Area and Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

5 .2 .8 Peak Loca l Des ign Pressures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

5 .2 .9 Hu l l Loca t ion Fac tors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248

5 .2 .10 She l l P la t ing Th ickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248

5 .2 .11 Po lar C lass Ru le Des ign I l lus tra t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253

5 .2 .12 Sens i t iv i ty of IACS Pred ic t ion to Inc lus ion of Pressure Area Sca le

Effec ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258

5 .3 D iscuss ion of Po lar C lass Ru les . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260

5 .3 .1 Exposure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260

5 .3 .2 Mode l ing Sca le Effec t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262

5 .3 .3 C lass Dependency for Des ign Parame ters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264

5 .4 Po lar Code Compar ison w i th A l terna t ive Pressure Area Mode l . . . . . . . . . . . . . . . . . 267

5 .4 .1 Max imum G loba l Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267

5 .4 .2 Pressure Area Sca le Effec t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267

5 .4 .3 Reduced Loca l Con tac t Area from Nom ina l Load Pa tch . . . . . . . . . . . . . 268

5 .4 .4 Increased Loca l Pressures w i th Increased Exposure - Vesse l D isp lacemen t. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268

5 .4 .5 Pre l im inary Resu l ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

5 .4 .6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274

5 .5 Ex trema l-Based Po lar Code Des ign Compar ison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276

5 .5 .1 Po lar C lass , Exposure and C lass Equ iva lence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276

5 .5 .2 Ex trema l Mode l ing of G loba l Impac t Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277

5 .5 .3 Po lar Code De term in is t ic Mode l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279

5 .5 .4 Vesse l Par t icu lars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279

5 .5 .5 Resu l ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280

5 .5 .6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282

5 .6 Compar ison of IACS Pressures w i th ISO Loca l Pressure Mode l . . . . . . . . . . . . . . . 284

5 .6 .1 Des ign Parame ters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284

5 .6 .2 Resu l ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285

5 .6 .3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286

5 .7 Pre l im inary Coeff ic ien t Ver if ica t ion Recommenda t ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292

5 .7 .1 Ex trema l Probab i l is t ic Mode l ing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292

5 .7 .2 Resu l ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293

5 .8 Cons idera t ion for Icebreaker Des ign and Concen tr ic Bow Impac ts . . . . . . . . . . . 298

CHAPTER 6 . I l lus tra t ive Des ign Examp les . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299

6 .1 Arc t ic Sh ipp ing Type I l lus tra t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299

6 .1 .1 Overv iew . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299

6 .1 .2 Co l l is ion Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299

6 .1 .3 G loba l Force Es t ima t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301

6 .1 .4 Loca l Pressures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302

6 .1 .5 C lass if ica t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302

CHAPTER 7 . Thes is Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306

CHAPTER 8 . Recommenda t ions for Fu ture Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313

CHAPTER 9 . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315

CHAPTER 10 . B ib l iog raphy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328

LIST OF TABLES

Tab le 1 Re l iab i l i ty targe ts based on r isk to personne l and consequence of fa i lure (ISO , 2010)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Tab le 2 Targe t safe ty leve l and load fac tors based on ice load even t type (ISO 2010) . . . . . . . . . 16

Tab le 3 Inpu t parame ters for g loba l force s imu la t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

Tab le 4 I l lus tra t ion of ASPPR c lass fac tors , es t ima te for annua l number of rams , es t ima ted and norma l ized force for MV Arc t ic type vesse l and 10

annua l exceedance probab i l i ty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Tab le 5 Ana lys is ma tr ix for ca l ibra t ing F

des ign equa t ion (af ter Car ter e t a l ., 1996) . . . 107

Tab le 6 Probab i l is t ic des ign loads based on Cp = 3 ±1 .5 and Dp = -0 .4 ±0 .2 for des ign s tra tegy correspond ing to 1% probab i l i ty of exceedence (af ter Car ter e t a l ., 1996) . . . . 107

Tab le 7 Compar ison of max imum ver t ica l bow force Fv for se lec t vesse ls us ing Eq . ( 19 ) fo l low ing the ASPPR rev is ion ana lys is (af ter Car ter e t a l ., 1996) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

Tab le 8 Spa t ia l dens i ty and mean HPZ area from Lou is S . S t . Lauren t da ta (Zou , 1996) . . . 126

Tab le 9 Inf luence of HPZ force cu toff on HPZ dens i ty , area , and force mode l parame ters 141 Tab le 10 Propor t ion of s imu la ted HPZ occurrences ( i .e . [1 – m isses ]) based on Po isson samp l ing – γ = 0 .78 MN , ρ = 0 .89zones /m

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

Tab le 11 Hu l l Areas and correspond ing Hu l l Area Fac tors in F igure 122 (IACS , 2010) . . . 157

Tab le 12 Summary of exponen t ia l f i t parame ters for HPZ force and correspond ing HPZ dens i ty for d ifferen t Po lar Sea tr ia ls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

Tab le 13 HPZ force correc t ion fac tor app l ied to s imu la t ions for a range of pane l areas . . . . 178

Tab le 14 Summary of exponen t ia l f i t parame ters for HPZ force and correspond ing HPZ dens i ty for d ifferen t Po lar Sea tr ia ls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

Tab le 15 Sh ip ram par t icu lars inc lud ing 0 .1 MN pressure cu toff on da ta process ing . . . . . . . . . 203

Tab le 16 K igor iak 1982 impac t cond i t ions and parame ters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

Tab le 17 Po lar Sea Beaufor t 1982 impac t cond i t ions and parame ters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220

Tab le 18 Range of f

for icebreak ing vesse ls for shou lder (g lanc ing ) and concen tr ic h i ts . . 239 Tab le 19 C lass fac tors in IACS ru les and govern ing parame ters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 Tab le 20 Peak Pressure Fac tors (PPF) for sca l ing loca l pressures for reduced con tac t areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 Tab le 21 Vesse l Par t icu lars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 Tab le 22 Po lar C lass pressure-area resu l ts from i l lus tra t ive examp les . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 Tab le 23 Po lar C lass 1 max imum bow force , des ign pressure and p la te th ickness for

d ifferen t d isp lacemen t vesse ls hav ing ma in frame spac ing of 0 .5m mode led w ith pressure area exponen t e

= -0 .1 and des ign area ad jus tmen t exponen t g iven as w

= 0 .7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 Tab le 24 Po lar C lass 1 max imum bow force , des ign pressure and p la te th ickness for d ifferen t d isp lacemen t vesse ls hav ing ma in frame spac ing of 0 .5m mode led w i th pressure area exponen t e

= -0 .4 and des ign area ad jus tmen t exponen t g iven as w

= 0 .7 . . . . . . . . . . . . . . . . 259 Tab le 25 Compar ison of inf luence of pressure area coeff ic ien t ex ( i .e . A

) on es t ima tes of g loba l ver t ica l forces us ing Po lar C lass ru les for MV Arc t ic type sh ip . . . . . . . . . . . . . . . . . . . . . . . . 272 Tab le 26 Compar ison of Popov added mass coeff ic ien ts w i th MAPS0 es t ima tes . . . . . . . . . . . . . . . 273 Tab le 27 Es t ima tes of g loba l ver t ica l forces for MV Arc t ic type sh ip for a l terna t ive pressure

area mode l ( i .e . ex = -0 .4) w i th ad jus ted C lass coeff ic ien ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

Tab le 28 C lass equ iva lenc ies and pre l im inary compar ison to annua l number of impac ts . . 277

Tab le 29 Compar ison of ex trema l based ver t ica l g loba l forces w i th Po lar C lass es t ima tes . 281

Tab le 30 Rev ised Po lar C lass ru le ice parame ters and g loba l force es t ima tes . . . . . . . . . . . . . . . . . . . . 294

List of F igu res

F igure 1 Pressure-area da ta and h igh l igh ted da ta gap (Mas terson and Frederk ing , 1993) . . . . . . 6 F igure 2 I l lus tra t ion of con tac t geome try and coord ina tes for sh ip ramm ing in to a f loe . . . . . . . . 6 F igure 3 Impr in t of sh ip bow in to ice , i l lus tra t ing the d is tr ibu t ion of HPZs re la t ive to the

nom ina l con tac t area and the measuremen t area a t a spec if ic po in t in t ime dur ing a sh ip ram . (No te tha t areas o f spa l l ing near the edge o f the f loe are inc luded in the nom ina l area.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 F igure 4 Examp le f low char t for probab i l is t ic mode l deve lopmen t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 F igure 5 H is tog ram of ice ram forces measured dur ing ram tr ia ls on board the MV Arc t ic off Co lburg Is land in May 1984 (Car ter e t a l ., 1992) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 F igure 6 I l lus tra t ion of the re la t ionsh ip be tween rare ( i .e . years be tween in terac t ions) and frequen t ( i .e . many in terac t ion per year) d is tr ibu t ions and the gener ic paren t d is tr ibu t ion for an env ironmen ta l process (Jordaan , 2005a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 F igure 7 Def in i t ion of exceedence probab i l i ty , p

wh ich def ines a spec if ic des ign s tra tegy

where the g rey dens i ty represen ts the exceedence probab i l i ty (e .g . 10% , 1% , 0 .1%

exceedence) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 F igure 8 I l lus tra t ion of the app l ica t ion of the probab i l is t ic des ign approach from rou te se lec t ion through des ign loads based on des ign s tra tegy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 F igure 9 Probab i l is t ic trea tmen t of load and res is tance (No te tha t the probab i l i ty o f fa i lure is

no t the area o f the shaded reg ion bu t a convo lu t ion) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

F igure 10 I l lus tra t ion of safe , unsafe and over ly safe des ign based on fa i lure probab i l i ty (see

no te in F igure 9 and correspond ing foo tno te regard ing the es t ima t ion o f fa i lure

probab i l i ty) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

F igure 11 2-D I l lus tra t ion of con tac t face be tween sh ip’s hu l l accord ing to R iska (1987) . . . 18

F igure 12 Iceberg s truc ture in terac t ion i l lus tra t ing reg ions of spa l ls (Jordaan , 1996) . . . . . . . . . . 18

F igure 13 I l lus tra t ion of nom ina l con tac t area (Jordaan e t a l ., 2005b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

F igure 14 I l lus tra t ion of loca l pressure des ign area (Jordaan e t a l ., 2005b) . . . . . . . . . . . . . . . . . . . . . . . . . . 21

F igure 15 Concep t i l lus tra t ion for Pond In le t and Hobson’s Cho ice med ium sca le inden ta t ion tes ts (Da ley , 1994) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 F igure 16 Prepared faces for the 1990 Hobson’s Cho ice f la t inden tor faces (Da ley , 1994) . 24 F igure 17 MY ice crush ing aga ins t the Mo l ikpaq . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 F igure 18 D is tr ibu t ion of pressures for a MY ice impac t on the Po lar Sea 1982 . . . . . . . . . . . . . . . . . 25 F igure 19 Measured nom ina l pressure area re la t ionsh ip from ice is land inden tor tes ts (Mas terson e t a l ., 1992) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 F igure 20 Comp i la t ion of pressure area da ta inc lud ing examp le des ign curves (No te tha t p lo t inc ludes loca l and g loba l pressures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 F igure 21 I l lus tra t ion of loca l pressure da ta inc lud ing CSA /API des ign curve ( i .e . 8 .5A

) , ISO des ign curve as we l l as compar ison w i th an exposure based loca l pressure curve and 25 impac ts per year as descr ibed in Sec t ion 2 .3 .3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 F igure 22 Nom ina l area for sh ip pene tra t ion in to an ice f loe used to de term ine average or nom ina l ice pressure (R iska , 1987) - area ex ten t is bas ica l ly the impr in t of bow in to ice . (No te tha t areas o f spa l l ing near the edge o f the f loe are inc luded in the nom ina l area.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 F igure 23 Average pressure-area da ta and leas t squares reg ress ion (R iska , 1987) . . . . . . . . . . . . . . . 29 F igure 24 Measured ice fa i lure pressure versus con tac t area for a w ide range of in terac t ion

and load ing s i tua t ions for var ious ice types , tempera tures and s tra in ra tes (B lanche t , 1990 af ter Sanderson , 1988) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 F igure 25 Nom ina l pressure area re la t ionsh ip from f ie ld da ta (Jordaan e t a l . 2005b) . . . . . . . . . . 31 F igure 26 I l lus tra t ion of the sens i t iv i ty of Nom ina l Pressure to a) Cp and b) Dp . . . . . . . . . . . . . . . . . 32 F igure 27 H is tog ram and exceedence probab i l i t ies of s imu la ted and observed ind iv idua l

(paren t) rams for MV Arc t ic 1984 , for P = 3 .0 A

, s

= 1 .5MPa ; s

= 0 .2 (Car ter e t a l ., 1996) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 F igure 28 MV Arc t ic measuremen ts , peak of ten even ts (Frederk ing , 1998 , Jordaan e t a l .,

2005b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

F igure 29 Average peak pressure vs . impac t speed for Po lar Sea tr ia ls (S t . John , 1984) . . . . . 36

F igure 30 Average pressure on a 0 .33 m

subpane l area as a func t ion of ve loc i ty and bergy

b i t mass from bergy b i t impac t tr ia ls (R i tch e t a l ., 2008) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

F igure 31 Examp le of loca l pressure measuremen ts on a s ing le pane l for a Po lar Sea 1983 in terac t ion even t – 1 subpane l area = 0 .1516m

(Jordaan e t a l. , 2007 and Tay lor e t a l ., 2009) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 F igure 32 I l lus tra t ion of a ramm ing even t las t ing a few seconds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 F igure 33 Loca l pressure parame ter α vs . loca l con tac t area (Jordaan e t a l. , 1993) . . . . . . . . . . . . . 38 F igure 34 D is tr ibu t ions of loca l pressures for d ifferen t pane l areas , loca l pressure parame ter

α the exponen t ia l f i t to the d is tr ibu t ion ta i l for the Bergy B i t impac t tr ia ls (R i tch e t a l ., 2008) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 F igure 35 Loca l pressure parame ter α vs loca l con tac t area for Oden, Terry Fox and Po lar

Sea sh ip ram tr ia ls (Jordaan e t a l. , 2007 and Tay lor e t a l ., 2009) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 F igure 36 P lo t of x

vs . area for sh ip ram and bergy b i t impac t da ta inc lud ing exposure

effec ts (Jordaan e t a l. , 2007 and Tay lor e t a l ., 2009) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 F igure 37 I l lus tra t ion of inf luence of exposure ( i .e . number of annua l even ts) in de term in ing

des ign d is tr ibu t ions for annua l max imum pressures for des ign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 F igure 38 Loca l pressure curves for 10

and 10

annua l exceedence probab i l i t ies for 1000 , 5 second rams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 F igure 39 I l lus tra t ion of spa t ia l pressure-area re la t ion (Da ley , 2004) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 F igure 40 Typ ica l spa t ia l pressure-area re la t ionsh ip from Po lar Sea 1982 even t (Frederk ing 1999) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 F igure 41 Process pressure-area for 5 .4m /s g lanc ing co l l is ion w i th 4-5m th ick ice on Lou is

S . S t-Lauren t (Frederk ing , 1998) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 F igure 42 Process PA for Lou is S . S t-Lauren t – 4m /s aga ins t 1-2 m th ick f loe (Frederk ing , 1999) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 F igure 43 Upper-bound process pressure-area curve f i t to bergy b i t impac t E23_B17_162

(Frederk ing and R i tch , 2009) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 F igure 44 Process pressure-area curve for Grapp l ing Is land grow ler tes ts (IMP 27) . . . . . . . . . . . . 50 F igure 45 Hobson’s cho ice da ta show ing d iscre te fa i lures (Da ley e t a l ., 1998) – No te tha t

reference to 12 MN sys tem capac i ty is incorrec t . Sys tem capac i ty was 13 .5 MN , and

d isp lacemen t con tro l led and se t to s top a t less than 150mm (Mas terson and Frederk ing ,

2010) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

F igure 46 Prog ress ion of spa t ia l pressure-area curves from Po lar Sea 1983 even t #410 (Da ley , 2004) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 F igure 47 Schema t ic of g loba l frac ture event dur ing med ium sca le Hobson’s Cho ice ice

inden ta t ion tes t NRC 01 a s low load ing tes t (Frederk ing e t a l . 1990) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 F igure 48 Med ium sca le ins i tu tes t ing (Mas terson e t a l ., 1999) w i th in terac t ion area of 1 .0 m2 : (a) 0 .3 mm s─1 , duc t i le fa i lure ; (b) 10 mm s─1 , br i t t le fa i lure . Cour tesy Dan Mas terson . Damaged ice a t lower ra tes is ev idenced by the permanen t depress ion w ithou t spa l ls ( lef t) . Damaged ice a t fas ter ra tes show frac ture around the h igh -pressure reg ion (r igh t) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 F igure 49 I l lus tra t ion of s tra in deve lopmen t w i th t ime for an app l ied s tress as a func t ion of t ime inc lud ing Burgers mode l approx ima t ion in (a) (Sanderson , 1988) . . . . . . . . . . . . . . . . . . . . . . . . 56 F igure 50 Un iax ia l load ing of pure po lycrys ta l l ine ice and inf luence of s tra in ra te and

tempera ture (Sanderson 1988 af ter Ha l lam , 1986) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 F igure 51 Inf luence of conf in ing pressure on max imum s tress d ifference (dev ia tor ic s tress)

for mu l t ip le s tra in ra tes (f igure from Sanderson 1988) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 F igure 52 I l lus tra t ion of ice fa i lure process inc lud ing loca l ized con tac t near the cen ter of the

ice shee t as a resu l t of non -s imu l taneous fa i lure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 F igure 53 I l lus tra t ion of compress ive ice fa i lure assoc ia ted w i th HPZs and the correspond ing f luc tua t ions in forces (Jordaan , 2001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 F igure 54 Processes tha t charac ter ize ice fa i lure a t h igh load ing ra tes inc lud ing (b) f ina l s ta te of v iscous f low ( i .e . Burgers mode l in F igure 49 reduced to s ing le dashpo t) once damage has occurred across the fu l l layer and even before crushed ma ter ia l is ex truded . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 F igure 55 Inf luence of conf in ing pressure on damage ra te and resu l tan t fa i lure pressure

(Meg l is e t a l ., 1999 , Jordaan , 2001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

F igure 56 Comp i la t ion of pressure-area da ta i l lus tra t ing sca le effec t (Sanderson , 1988) . . . . . 61

F igure 57 I l lus tra t ion of non-s imu l taneous fa i lure us ing br i t t le wax inden ta t ion tes ts (Ashby

e t a l ., 1986) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

F igure 58 Geome tr ic non-s imu l taneous fa i lure mode l and assump t ions (Sanderson , 1988

af ter Ashby e t a l ., 1986) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

F igure 59 Theore t ica l curve of Ashby e t a l ., 1986 w i th L i =1 , P

= 15MN and ∆L = 0 .02 m bounded by exper imen ta l da ta (Sanderson , 1988) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 F igure 60 a) Exper imen ta l tes t se tup by Tuhkur i (1995) w i th ice b lock be ing pushed ou t of a conf inemen t box ; b) l ine-l ike surface prof i le fo l low ing tes t w i th 40mm gap . . . . . . . . . . . . . . . . 65 F igure 61 Concep tua l d is tr ibu t ion of HPZs for d ifferen t in terac t ion geome tr ies : HPZs tend to be concen tra ted a long or in the case of (3) w i th in the do t ted l ines (Jordaan and X iao , 1999) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 F igure 62 I l lus tra t ion of pressure averag ing across a s truc ture face hav ing nons imu l taneous

fa i lure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 F igure 63 Compar ison of pressure averag ing mode l resu l ts w i th ISO pred ic t ions for arc t ic cond i t ions (Spencer and Morr ison , 2012) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 F igure 64 I l lus tra t ion of sca le effec t in ma ter ia ls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 F igure 65 Sca le effec ts from labora tory and f ie ld inden tor tes ts for d ifferen t s izes and

inden ta t ion ra tes (af ter L i e t a l ., 2005) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 F igure 66 Loca t ion of cracks for inves t iga t ion of propaga t ion and forma t ion of cracks

i l lus tra t ing tens i le and shear s tress zones (Zou , 1996) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 F igure 67 Spa l l ing frac ture idea l iza t ion , show ing : (a) shear crack spa l l ing mechan ism ( ; (b)

w ing crack e lemen ta l s tress ana lys is and grow th mode l used to es t ima te probab i l i ty of spa l l ing (X iao , 1997 and Tay lor , 2010) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 F igure 68 Con tac t be tween ver t ica l s ided s truc ture and broad ice shee t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 F igure 69 Square b lock of e las t ic br i t t le ma ter ia l w i th one HPZ (Pa lmer e t a l ., 2009) . . . . . . . . 79 F igure 70 Es t ima ted pressure-area re la t ionsh ip from s imp le ho t spo t mode l (Pa lmer e t a l ., 2009) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 F igure 71 I l lus tra t ion of frac ta l crush ing of a br i t t le so l id hav ing an order r =4 and where

each cub ic e lemen t fragmen t has a probab i l i ty p of be ing crushed in to n sub e lemen ts (here p = 0 .75 and n = 8) . To ta l force F

is carr ied by a frac ta l h ierarchy of e lemen ts of d imens ion d

or less (Pa lmer and Sanderson , 1991 af ter Turco t te , 1986)) . . . . . . . . . . . . . . . . . . . . . 81 F igure 72 Compar ison of ice s treng th da ta (Sanderson , 1988) w i th frac ta l mode ls by Pa lmer

and Sanderson , 1991 (β = 0 .25) , Parsons , 1991 (β = 0 .8) and We iss , 2001 (β = 0 .6) –

f igure from We iss (2001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

F igure 73 I l lus tra t ion of g loba l in terac t ion force , F

dur ing a ram even t and response of vesse l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 F igure 74 I l lus tra t ion of d ifferen t in terac t ion s tages as a sh ip rams prog resses (Jordaan e t a l .,

2007) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 F igure 75 Sca t ter p lo ts vs . sor ted and ranked force da ta for Oden and Po lar Sea tr ia ls

(Fug lem e t a l . 1999) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 F igure 76 Examp le t ime trace for ver t ica l bow force from K igor iak , Oc tober 1981 tr ia ls (Car ter e t a l ., 1996) – no te force is in MN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 F igure 77 Examp le t ime trace for ver t ica l bow force from MV Arc t ic 1984 tr ia ls (Car ter e t a l . , 1996) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 F igure 78 S imu la t ion of t ime dependen t force from K igor iak ram w i th 10m th ick MY ice

hav ing pressure-area re la t ionsh ip P = 3 .0 A

(Car ter e t a l ., 1996) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 F igure 79 S imu la t ion of t ime dependen t force from MV Arc t ic ram w i th 10m th ick mu l t iyear ice hav ing pressure area re la t ionsh i p P = 3 .0 A

(Car ter e t a l . , 1996) . . . . . . . . . . . . . . . . . . . . . . . . . 95 F igure 80 H is tog ram and exceedence probab i l i t ies of s imu la ted and observed ind iv idua l

(paren t) rams for K igor iak , Oc tober 1983 for P = 3 .0 A

, s

= 1 .5MPa ; s

= 0 .2 (Car ter e t a l . , 1996) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 F igure 81 H is tog ram and exceedence probab i l i t ies of s imu la ted and observed ind iv idua l (paren t) rams for MV Arc t ic 1984 , for P = 3 .0 A

, s

= 1 .5MPa ; s

= 0 .2 (Car ter e t a l . , 1996) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 F igure 82 Compar ison be tween observed and s imu la ted peak forces for ice in terac t ion even ts w i th the icebreaker Oden, 1991 . Resu l ts inc lude f lexura l fa i lure (Car ter e t a l . , 1996) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 F igure 83 MV Arc t ic CAC4 sh ip ram s imu la t ion inc lud ing ver t ica l bow force , ver t ica l bow d isp lacemen t ( ice th ickness 19 .9m , sh ip speed 7 .24 kno ts , Cp = 3 .7 MPa , Dp = -0 .19) . No te tha t impac t phase c lear ly def ined . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 F igure 84 MV Arc t ic CAC4 sh ip ram s imu la t ion inc lud ing ver t ica l bow force , ver t ica l bow d isp lacemen t ( ice th ickness 23 .4 m , sh ip speed 1 .58 kno ts , Cp = 3 .13 MPa , Dp = -0 .2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 F igure 85 MV Arc t ic CAC4 sh ip ram s imu la t ion inc lud ing ver t ica l bow force , ver t ica l bow

d isp lacemen t and pene tra t ion ( ice th ickness 16 .6 m , sh ip speed 3 .9 kno ts , Cp = 3 .63

MPa , Dp = -0 .46) . Impac t phase end iden t if ied as po in t where ver t ica l acce lera t ion is zero ( i .e . second der iva t ive of sh ip .y = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 F igure 86 Paren t d is tr ibu t ion for max imum ver t ica l bow force correspond ing to in i t ia l impac t phas e for MV Arc t ic CAC4 type vesse l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 F igure 87 Con tac t area for in i t ia l impac t phase for MV Arc t ic CAC4 type vesse l . . . . . . . . . . . . . . 102 F igure 88 Max imum t ime correspond ing to in i t ia l impac t phase for MV Arc t ic CAC 4 type

vesse l . Mode 1 corresponds to the ma jor i ty of s imula ted impac ts w i th in i t ia l impac t crush ing phase w i th dura t ion less than 4 seconds fo l lowed by beach ing phase . Mode 2 re la tes to impac t scenar ios (excep t for severa l ex tremes) w i th sof ter ice such tha t crush ing occurs through fu l l dura t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 F igure 89 H is togram and exceedence probab i l i t ies of s imu la ted ind iv idua l ‘paren t’ rams for K igor iak s ize vesse l us ing P = 3 .0 A

, s

= 1 .5MPa , s

= 0 .2 and i l lus tra ted exponen t ia l f i t to the ta i l of the ‘paren t’ d is tr ibu t ion (Car ter e t a l ., 1996) . . . . . . . . . . . . . . . . . . . 109 F igure 90 I l lus tra t ion of ex trema l F

d is tr ibu t ion based on the number of impac ts us ing

the exponen t ia l d is tr ibu t ion as a bes t f i t to the ta i l of the ‘paren t’ d is tr ibu t ion (af ter Car ter e t a l ., 1996) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 F igure 91 Probab i l is t ic des ign loads based on Cp = 3 ±1 .5 and Dp = -0 .4 ±0 .2 for des ign s tra tegy correspond ing to 1% probab i l i ty of exceedence as we l l as the o ld and bes t f i t F

des ign curve (af ter Car ter e t a l ., 1996) . See Eq ( 19 ) for d iscuss ion on a

, b

, a

, b

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 F igure 92 MV Arc t ic measured vs . s imu la ted pressure-area da ta where Cp is mode led as

lognorma l d is tr ibu t ion and Dp a norma l d is tr ibu t ion (af ter Frederk ing 1998) . . . . . . . . . . . . . 113 F igure 93 Inf luence of d is tr ibu t ion type , lognorma l or We ibu l l on samp l ing of g loba l

pressure parame ter Cp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 F igure 94 C lasses of ex treme d is tr ibu t ions (Jordaan , 2005a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 F igure 95 Ex trema l ana lys is exerc is ing Fmax sof tware for MV Arc t ic CAC1 type vesse l

mode l ing pressure area parame ter Cp as lognorma l d is tr ibu t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

F igure 96 Con tr ibu t ing Cp and Dp for des ign cond i t ion based on the max imum of 100 rams

per year and a 10

annua l exceedence cr i ter ia ( i .e . 10

exceedence probab i l i ty ) for MV

Arc t ic CAC1 s imu la t ion mode l ing Cp as lognorma l d is tr ibu t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117