Calculation Procedures for Installation of Suction Caissons

Transcription

1 Calculatn Prcedures fr Installatn f Suctn Cassns by G.T. Hulsby and B.W. Byrne Reprt N. OUEL 68/0 Unversty f Oxfrd Department f Engneerng Scence Parks Rad, Oxfrd, OX1 3PJ, U.K. Tel /83300 Fax Emal Cvl@eng.x.ac.uk ttp://www-cvl.eng.x.ac.uk/

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3 Desgn prcedures fr nstallatn f suctn cassns n clay and ter sls G.T. Hulsby 1 and B.W. Byrne 1 Keywrds: clay, fundatns, suctn cassns, nstallatn Abstract Suctn-nstalled skrted fundatns, ften referred t as suctn cassns, are beng ncreasngly used fr a varety f ffsre applcatns. In desgnng a cassn a getecncal engneer must cnsder te nstallatn prcess as well as te n-place perfrmance. Te purpse f ts paper s t present calculatn prcedures fr te nstallatn f a cassn n clay. Fr clay stes, te cassn wll ften be used as an ancr, wt te rat f te skrt lengt (L) t te dameter (D) as g as 5. Calculatn metds are presented fr determnng te resstance t penetratn f pen-ended cylndrcal cassn fundatns wt and wtut te applcatn f suctn nsde te cassn. Cmparsns f between predctns and case recrds are made. A cmpann paper (Hulsby and Byrne, 00) descrbes te calculatn prcedure fr nstallatn n sand sls. Fnally cmments are made ere abut nstallatn n s varety f sls ter tan mgeneus depsts f clay r sand. Intrductn A suctn cassn s a large cylndrcal structure, usually made f steel, pen at te base and clsed at te tp. It mgt be used eter as a sallw fundatn r as a srt stubby ple (ften called a suctn ancr). Te sallw fundatn ptn s mre cmmn at sandy sl stes (e.g. Bye et al., 1995; Hgervst 1980; Tjelta, 199; Tjelta, 1995; Tjelta et al., 1990) wlst te ancr/ple applcatn s cmmner n clay r layered sls (e.g. Cllat et al., 1996; Cllat et al., 1998; Erbrc and Hefer, 00; Lacasse, 1999; Sljell et al., 1998). Fgure 1 sws typcal dameter and skrt depts fr varus prjects reprted n te lterature (te fgure s taken frm Byrne (000) and wt furter data frm Tjelta (001)). Mre recently tere s an emergng applcatn f cassns as te fundatns fr ffsre wnd turbnes (Byrne et al., 00; Byrne and Hulsby, 003). Ts paper addresses nstallatn n clays and ter sls wlst a cmpann paper (Hulsby and Byrne, 00) cnsders nstallatn n sand. In te ancr applcatn te cassn wll be desgned s tat te skrt lengt (L) s muc greater tan te dameter (D) and te rat L/D mgt be as large as 5 (as swn n Fgure 1). As l and gas explratn eads furter ffsre and nt deeper water, t s lkely tat ancr applcatns wll becme mre cmmn. Tere are partcular advantages t usng te suctn cassn ver ter ancrng metds (e.g. drag ancrs), n tat te cassn can be accurately lcated, allwng cmplex mrng lne arrangements t be accmmdated. Te ablty t remve a cassn (by smply reversng te nstallatn prcedure) allws mrng lne arrangements t be altered ver te lfe f a prductn vessel; and remval at te end f te desgn lfe. After an ntal penetratn nt te seabed caused by self wegt, a suctn (relatve t seabed water pressure) s appled wtn te cassn, wc frces te remander f te cassn t embed tself, leavng te tp flus wt te seabed. Te purpse f ts paper s t present desgn calculatns fr te nstallatn f te cassn. Separate calculatns are f curse necessary t assess te capacty f te cassn nce nstalled eter as a sallw fundatn r as an ancr. Analyses are presented fr te magntude f te self-wegt penetratn, te relatnsp between suctn and furter 1 Department f Engneerng Scence, Parks Rad, Oxfrd OX1 3PJ 1

4 penetratn, and te lmts t penetratn tat can be aceved by suctn. Te analyses are classcal n te sense tat tey make smplfyng assumptns, brrwng tecnques frm bt ple desgn and bearng capacty tery. Mre rgrus analyses, usng fr nstance fnte element tecnques, culd be used fr partcular nstallatns. Te analyses presented ere suld, wever, prvde a reasnable apprxmatn fr desgn purpses. Smlar metds (altug dfferng n sme detals) t tse descrbed belw ave been publsed e.g. by Huse et al. (1999), but ur purpse ere s t draw tgeter a cmpreensve desgn metd and cmpare wt case recrds frm several surces. Installatn n Clay Fgure sws te key varables n te suctn cassn prblem, s far as te nstallatn s cncerned. Fr te purpses f te nstallatn calculatn te strengt f te clay s caractersed by an undraned strengt, wc s assumed t ncreases wt dept lnearly n te frm su = su + ρz. Te metds descrbed belw can readly be adapted t mre cmplex strengt varatns. Self-wegt penetratn Te resstance t penetratn s calculated as te sum f adesn n te utsde and nsde f te cassn, and te end bearng n te annular rm. Te adesn terms are calculated, fllwng usual practce n ple desgn, by applyng a factr α t te value f te undraned strengt. Te end bearng s calculated, agan fllwng standard bearng capacty analyses, as te sum f an N q and an N c term. Te result s: ( πd ) + α s ( πd ) + ( γ + s N )( πdt) V = αsu1 u1 u c (1) adesn n utsde adesn n nsde end bearng n annulus were su1 = su + ρ s te average undraned sear strengt between mudlne and dept, su = su + ρ s te undraned sear strengt at dept, α and α are adesn factrs n te utsde and nsde f te cassn (as used n undraned ple desgn) and N c s an apprprate bearng capacty factr fr a deep strp ftng n clay (typcally a value f abut 9 mgt be adpted). Fr undraned analyss N q = 1. Suctn-asssted penetratn Once te self-wegt penetratn pase as been cmpleted, s tat a seal s frmed arund te edge f te cassn, t wll be pssble t cmmence te suctn nstallatn pase. Te appled suctn n te cassn s s relatve t seabed water pressure,.e. te abslute pressure nsde te cassn s pa + γ ww s. Tere are a number f practcal lmts t te maxmum attanable value f s. Amngst tese are (a) te abslute pressure at wc te water cavtates (usually a small fractn f atmsperc pressure), (b) te mnmum abslute pressure tat can be aceved by te gven pump desgn, (c) te mnmum relatve pressure tat can be aceved by te pump. Te suctn causes a pressure dfferental acrss te tp plate f te cassn, wc results effectvely n an addtnal vertcal lad equal t te suctn tmes te plan area f te cassn. Te capacty s agan calculated as te sum f te external and nternal frctn, and end bearng term. Nte tat te verburden term s reduced n te end bearng calculatn by te suctn pressure, assumng tat te flw f sl under te rm ccurs entrely nwards. Te result s:

5 ( π D ) = α s ( πd ) + α s ( πd ) + ( γ s + s N )( πdt) V + s u1 u1 u c () wc s readly rearranged t: ( π D ) = α s ( πd ) + α s ( πd ) + ( γ + s N )( πdt) V + s u1 u1 u c (a) Nte tat f te varatn f sl strengt s nt smply lnear, all tat s necessary s t replace s u1 wt te average strengt frm mudlne t dept, and s u wt te strengt at dept. Equatn () gves a smple relatnsp between suctn and dept. Fr cnstant V and a lnear ncrease f strengt wt dept (s tat s u1 and s u are lnear functns f ), s s a quadratc functn f. Lmts t suctn asssted penetratn In addtn t te lmt mpsed by te maxmum avalable suctn, tere s a lmt t te dept f penetratn tat can be aceved by te actn f suctn. If te dfference between te vertcal stress nsde and utsde te cassn, at te level f te cassn tp, exceeds a certan amunt, ten lcal plastc falure may ccur, and furter penetratn may nt be pssble. Te mecansm may be tugt f as a reverse bearng capacty prblem, n wc te sl flws nt te cassn. Te average vertcal stress (relatve t lcal ydrstatc) nsde te cassn at tp level s relatvely πd αsu1 stragtfrward t estmate as s + γ +. Te trd term n ts expressn arses frm πd te dwnward frctn nsde te cassn, and ere t s assumed (fr smplcty) tat ts results n a unfrm ncrease f vertcal stress at all rad n te cassn. Nte tat te assumptn f a unfrm ncrease n vertcal stress wtn te cassn s clearly unreasnable at small values f D, but t wll be seen belw tat ts calculatn s nly needed at D values greater tan abut, fr wc te unfrm ncrease s a reasnable apprxmatn. Te relevant stress utsde te cassn s muc arder t estmate, snce te dwnward lad frm adesn n te utsde f te cassn wll enance te stress n te vcnty f te cassn, but ts enancement s dffcult t calculate. Hwever, makng te smplfyng assumptn tat te dwnward lad frm te adesn s carred by a cnstant stress ver an annulus wt nner and uter dameters D and D m, ts stress (agan relatve t lcal ydrstatc) may be calculated as πdα su1 γ +. Tus te reverse bearng capacty falure wuld ccur wen π( Dm D ) πd αsu1 πdαsu1 * s + γ + = γ + N c su, were N c πd π( Dm D ) * s a bearng capacty factr apprprate fr uplft f a bured crcular ftng. Substtutng te slutn fr s nt equatn () and smplfyng gves: D π D V * + N s s ( D ) c u = α u1 π 1+ + ( γ + su Nc )( πdt) ( Dm D ) (3) wc can be slved fr. Nte, wever, tat altug te abve equatn appears lnear n, n fact s u1 and s u are temselves lnear functns f, s tat te slutn agan nvlves slvng a quadratc. Furtermre t wuld be ratnal t assume tat D m ncreases wt penetratn, fr nstance n te frm Dm D = f, were f s a cnstant ladspread factr. A furter 3

6 develpment wuld be t allw te enancement f te stress t vary (say lnearly) frm zer at D t a maxmum at te cassn surface. m It s wrt, wever, cnsderng sme apprxmate slutns fr te maxmum penetratn. Fr many cases te fnal term (te end bearng) s small. We cnsder als te case were te appled lad V s small, and make te apprxmatn D D D. If we wrte D m = md, ten equatn (3) leads t te fllwng result fr ts smplfed case: * Nc su 1 1 () D α s u1 m * Te factr Nc α s lkely t be n te regn f abut 3, altug t culd vary cnsderably. Te factr su su1 wuld be 1.0 fr a mgeneus sl, and.0 fr te extreme f a sl wt a strengt ncreasng lnearly wt dept frm a value f zer at te surface. Te fnal factr vares frm 1.0 f m s assumed t be very large, t 0.75 f say m =. Te verall result s tat te calculated maxmum attanable value f D s lkely t be frm abut.5 fr stff clays (wt strengts apprxmately unfrm wt dept) t 5 fr sft nrmally cnsldated clays (wt strengts apprxmately prprtnal t dept). Te effect f accuntng fr te external lad V wuld be t ncrease tese values. Equatn (), wever, prvdes a useful estmate f te maxmum D rat f a suctn-nstalled cassn tat culd be relably nstalled n clay. If dfferent assumptns are made abut te way te external adesn lad enances te vertcal stress are made, te same brad cnclusns arse, altug te precse fgures wll vary. It suld be nted tat sme measured values f nstallatns ndcated tat ger D rats tan mpled by te abve calculatn may be acevable. Te abve may terefre be treated as a cnservatve calculatn. Nte als tat te end bearng calculatn n equatns (1) and () des nt take nt accunt any enancement f te stress level nsde r utsde te cassn due t te frctnal terms. Ts fllws cnventnal plng desgn calculatns, n wc n suc crrectn s usually ncluded. If ts effect was t be taken nt accunt, te factr γ n equatn (1) wuld be replaced by wcever πdα su1 πd αsu1 s te smaller f γ + r γ + (almst nvarably te frmer). Once π D D πd suctn s started, ( ) m γ s n equatn s replaced by te smaller f πd α s γ s + r π u1 ( D D ) πd αsu1 γ + (usually te latter except at very small suctn). In practce tese canges make πd very small dfferences t te calculatn. Te effect f nternal stffeners Mst suctn cassns nclude sme nternal structure, usually cnsstng f eter vertcal plates r annular plates, t prvde strengt and stffness t te cylndrcal sell, eter t suppress bucklng durng suctn-asssted penetratn, r (n te case f a cassn ancr) t renfrce te cassn at te pad-eye cnnectn. Te analyss fr te case f annular stffeners s nt cnsdered ere, but te use f vertcal stffeners results n nly a small cange n te calculatn. m

7 In prncple stffeners culd be lcated n te utsde f te cassn, but ts ptn des nt usually seem t be adpted. Te addtnal resstance ffered by te stffeners can be taken nt accunt by an adesn term f te frm α su1l, were l s te permeter lengt f te stffeners (usually apprxmately twce te plate lengt fr tn plate stffeners), and an end bearng term f te frm ( γ + sunc )A, were A s te end area f te stffeners. Te area n wc te suctn acts (n te left sde f Equatn ) suld als be reduced by A, altug ts crrectn wll usually be tny. Nte tat f te stffeners d nt extend te full dept f te cassn, apprprate crrectns are requred fr te value f used n te cntrbutn frm te stffeners, and n te apprprate s u1 and s u values. In te calculatn f te maxmum attanable dept usng suctn, nte tat te terms nvlvng adesn n te nsde f te cassn cancel, and ave n verall effect n te calculatn. Te same s true fr terms resultng frm te resstance frm nternal (but nt external) stffeners, s fr nternal stffeners nly Equatn () can stll be used. Example 1 Cnsder a suctn cassn f utsde dameter 1m, wall tckness 5mm and dept 5m. Suc a cassn mgt be cnsdered as a fundatn fr an ffsre structure. Te cassn s stffened by 30 plates 5mm tck and 00mm deep welded as radal fns n te nsde f te cassn, and extendng fr te tp m f te cassn nly. Te sl prfle s dealsed as a layer m tck f cnstant strengt 0kPa, wt belw tat a lnear ncrease f strengt frm 5kPa at m at a rate.5kpa/m. Te buyant unt wegt s taken as 6kN/m 3. Te end bearng factr N c s taken as 9, and te adesn factr α as 0.6 fr te utsde f te cassn and 0.5 fr nsde and fr te stffeners. Te maxmum appled vertcal lad (ncludng te wegt f te cassn and buyancy effects) s 1000kN and te water dept s 50m. Te calculatns descrbed abve ave been mplemented n a spreadseet-based prgram SCIP (Suctn Cassn Installatn Predctn). Fgure 3 sws te calculated lads requred t nstall te cassn n te absence f suctn. Fgure sws te predctns frm SCIP f te varatn f suctn wt dept requred fr nstallatn, and n ts case te maxmum suctn requred s 9kPa. Example : Predcted f nstallatn pressures cmpared t centrfuge tests Huse and Randlp (001) cnducted a seres f tests n te centrfuge at te Unversty f Western Australa, nvestgatng te nstallatn f suctn cassns n nrmally cnsldated clay. Te experments were carred ut at 10g. Te strengt prfle f te clay culd be dealsed as zer at te surface ncreasng wt dept at a gradent f 1kPa/m t a dept f 67mm ten at 0kPa/m (at prttype scale tese represent rates f ncrease f 1.kPa/m and 1.7kPa/m). Te effectve unt wegt f te sl (accuntng fr te 10g acceleratn) was determned t be 79kN/m 3. Te dmensns f te cassn were 30mm dameter, 0.5mm wall tckness and 10mm skrt lengt. (Equvalent prttype dmensns 3.6m dameter, 60mm wall tckness, 1.m skrt lengt). An effectve vertcal lad f 15.3N was appled t te cassn. Fgure 5 sws te penetratn resstance fr te cassn wtut usng suctn, swng tat mst f te resstance s n te skrt frctn. Fgure 6 sws an estmated suctn penetratn curve, wc sws gd agreement wt te expermental data reprted by Huse and Randlp (001). Te self-wegt penetratn amunts t 1mm and te maxmum suctn pressure requred s 13.9kPa. An adesn factr f 0.5 was used fr bt nternal and external walls. 5

8 Example 3: Predctn f plug falure A seres f tests were cnducted by Huse et al. (1999) n te labratry flr t nvestgate plug falure durng nstallatn f suctn cassns n nrmally cnsldated clay. Tey nvestgated tree cassns wt dameters 10.mm, 15.9mm and 37.mm. All cassns ad a wall tckness f 0. mm and an L/D rat f 8. In te fllwng a cmparsn s made fr te 15.9mm dameter cassn. Te sl strengt prfle was estmated by Huse et al. (1999) t be 75kPa/m and te effectve unt wegt t be 5.9kN/m 3. Te cassns were ntally pused nt te clay t a penetratn f apprxmately ne dameter befre te suctn was appled. Assumng a crcular end bearng capacty factr f 8.5 (Hulsby and Martn, 003), te maxmum calculated penetratn by SCIP tat s pssble befre a plug falure s expected s 83mm r an /D = 5.. Ts can be cmpared t te cnclusns drawn by Huse et al. (1999). Tey cmpare te vlume f water wtdrawn frm te cassn cavty durng nstallatn t te dsplaced vlume wtn te cassn (assumng eave as nt ccurred). Wen mre water s evacuated tan can be accunted fr by te nstalled prtn f te cassn, tey nfer tat plug eave as ccurred. Fgure 8 sws, fr tw nstallatns f te 15.9mm dameter cassn, te excess vlume f water remved, pltted aganst nrmalsed penetratn. Fr te cases swn, Huse et al. (1999) deduced tat plug falure ccurs at an L/D rat between and 5, wc agrees wt te predctn gven abve. Agan an adesn factr f 0.5 was used. Nte tat altug plug falure ccurred t was stll pssble t nstall te cassn furter. Installatn cntnues untl all water as been wtdrawn frm te nternal cavty. Te cnsequence f plug falure s tat te cassn cannt be nstalled t ts full desgn dept. Example : Nkssa Feld Installatn Ts calculatn nvlves sme mdfcatn t te basc prcedures descrbed abve t accunt fr te gemetry f te cassns used n te Nkssa feld ff te cast f West Afrca (Cllat et al., 1996; Cllat et al., 1998). Tw dfferent ancr szes were used dependng n te ladng cndtns. We wll nly cnsder te nstallatn f te smaller f te tw, defned by Cllat et al. (1998) as a Type I ancr. Te gemetry f te cassns s unusual, as tey ave a step cange n dameter part way dwn te cassn. Te bttm sectn s m n dameter and extends fr.8m wlst te tp sectn s.5m n dameter and s 7.5m lng. Te ancr can lug s lcated at te cange n cassn dameter. Te wall tckness fr te ppe sectns was 15mm and te desgn penetratn was 11.8m. Te larger tp sectn was t accmmdate any sl eave tat ccurred durng nstallatn. Internal stffenng plates are als beleved t ave been used. Hwever, tese are mtted n te calculatn ere, as tere s nsuffcent nfrmatn abut te detaled gemetry f te stffeners. Te wegt (n ar) f te cassn s gven as 1 tns wc cnverts t a submerged wegt f apprxmately 350kN. Cllat et al. (1998) gve a summary f te sl cndtns, wc ncludes average sear strengts as well as upper and lwer bund strengt envelpes. Fr te purpse f ts calculatn, te average strengt s taken, and s 5kPa at te surface ncreasng at 1.0kPa/m fr te frst 5m, belw wc te gradent canges t 1.67kPa/m. Te effectve unt wegt f te sl s taken as 6kN/m 3. Wlst Cllat et al. (1998) suggest an adesn factr f 0.3 based n mdel scale feld tests, but te calculatns ere sw an excellent agreement wt te measurements f an adesn factr f 0.5 (wc seems qute reasnable) s used. T accunt fr te effect f te ncrease n dameter f te tp sectn f te cassn, te nternal adesn factr was set t zer fr te tp sectn. End bearng s als taken nt accunt at te step between te tw dameters. Fgure 7 sws te suctn pressures requred cmpared t te average and range measured durng te feld nstallatn (n te bass f data presented by Cllat et al., 1998). Te slgt underestmatn f te requred suctn may be because te stffeners are nt taken nt accunt. 6

9 In te tree example calculatns were t s pssble t cmpare wt data, t s clear tat a gd relatn exsts between predcted and bserved beavur, usng reasnable estmates f sl parameters. Obvusly te key parameter tat s requred fr predctns f cassns n clay s te undraned strengt prfle, and an estmatn f te adesn factr α. Installatn n ter materals Layered materals Fgure 1 sws tat a number f nstallatns ave ccurred n layered materals. We descrbe brefly te ssues tat must be cnsdered durng te desgn fr tese stes. Sand ver Clay Te sequence f sand ver clay prbably wuld nt cause prblems fr nstallatn - typcally te nstallatn wuld prceed trug te sand (usng te calculatns gven by Hulsby and Byrne (00)), and nce nt te clay te resstance wuld n mst cases be lwer, and culd be calculated usng te same prncples as fr clay alne (altug wt a mdfcatn t te calculatn f te frctn). Clay ver Sand Clay ver sand s lkely t be mre prblematcal. Te cassn penetrates trug sand wen te appled suctn creates gradents n te sand wc degrades te tp resstance t almst zer. Te pressure dfferental als prvdes a net dwnward frce n te cassn, but ts cntrbutes less sgnfcantly t te nstallatn. Wtut te flw feld n te sl t mgt be mpssble t nstall te cassn, due t te g bearng resstance f te sand (especally f t s very dense). Durng nstallatn n clay t s te net dwnward frce caused by te pressure dfferental wc causes te cassn t be frced nt te sl. Wen te nstallatn ccurs n a layered sl tere are questns as t weter te cassn wll penetrate trug a sand layer after t as passed trug a clay layer, as t wll nt be pssble t develp te flw regme wc degrades te skrt tp resstance t near zer. Tere are several feld case studes wc prvde evdence tat nstallatn under tese cndtns may, wever, stll be pssble. Te mst ntable s te large scale deepwater penetratn test wc was cnducted durng te nvestgatns fr te Gullfaks C platfrm (Tjelta and Hermstad, 1986). Te sl prfle cnssts f a number f layers f medum t dense sand and clay. Te cne tp resstances reac 0-MPa n te denser sand layers, -10MPa n te medum sand layers and 1- MPa n te clay layers. Te fundatn cnssts f tw 6.5m dameter cylnders jned by a cncrete beam, te structure beng m n dept. A maxmum suctn f abut 80kPa (lnearly ncreasng wt dept) was requred t nstall te cassn t ts full dept. A water jettng system at te cassn tp was used durng te penetratn f te ntal sand layer, tus reducng te tp resstance. Remval was als pssble, requrng apprxmately 50kPa f verpressure (lnearly decreasng) at te maxmum dept. Furter references t suctn ancr nstallatn n layered materal can be fund n Senpere and Auvergne (198) and Tjelta (001). Te frmer descrbe te nstallatn n te Grm feld, were sl plug falure ccurred n all cassns. Te nstallatn was nneteless successful as a jettng prcedure was used t remve materal frm wtn te cassn. Tjelta (001) descrbes n ssues related t te Curlew, YME and Hardng felds but des nt gve specfc detals. Fnely nterbedded materals Tere s n partcular reasn t suppse tat fnely nterbedded materals wuld pse prblems, unless te cmpstn f te beds dffered n sme extreme way. Tere are, wever, n recrded cases n suc materals. 7

10 Stff (pssbly fssured) clay Tere s a cncern tat t mgt nt be pssble t nstall suctn cassns n stff clays. Te prncpal reasn s tat, gven tat suc materals are ften fssured, r are prne t fssurng, t may nt be pssble t frm te necessary seal arund te rm f te cassn fr penetratn t prceed. One pssblty s tat fracturng may ccur, wt water smply flwng trug te fssures. Ts prblem may be exacerbated by te fact tat te penetratn resstance n very stff clays wuld be g. Infrmatn fr ts case s relatvely scarce. In mst cases were stff clays ave been encuntered (.e. n te Vsund, Njrd and Aqula felds as dscussed by Sljell et al., 1998) te sl cndtns cnssted f a layer f sft clay verlyng muc stffer clay. In tese cases t appears tat te sft clay layer s deep enug s tat a seal culd be created. Wlst tere s n evdence t supprt weter r nt nstallatn n stff fssured clay s pssble r nt, t suld be nted tat te cndtn were a stff clay exsts at mudlne mgt be a rater scarce ccurrence. Carse materals Fr bvus reasns, extremely etergeneus materals wuld be lkely t cause prblems fr nstallatn f a suctn cassn. Materals wt a sgnfcant fractn f carse gravel r larger szes wuld almst certanly present an bstacle t nstallatn. Certan (but nt all) glacal tlls wuld terefre be prblematcal. Very pen gravels, even f nt partcularly carse, wuld present prblems n tat flws durng pumpng wuld be very g. Slts It s dffcult t d calculatns fr slts, because t s dffcult t determne weter draned and undraned beavur wuld be apprprate, and partally draned calculatns fr cassn penetratn ave nt been frmulated. Hwever, gven tat penetratn n clays and sands s relatvely stragtfrward, t wuld be expected tat reasnably mgeneus slts wuld nt pse dffcultes. Carbnate sls Erbrc and Hefer (00) present te case stry f te nstallatn f suctn ancrs at te Lamnara ste n te Tmr Sea. Wlst te nstallatn f te 9 ancrs was successful, te suctn pressures measured were sgnfcantly lwer tan tse predcted n te rgnal desgn calculatns. Erbrc and Hefer (00) reprt very lw values fr te adesn factr (f te rder f ) tat arse frm te back-analyss f te feld data. It s clear tat fr extremely fne-graned carbnate sls (as at te Lamnara case) te clay calculatn s apprprate, wle fr te carser materals te sand calculatn s apprprate. Because f te crusablty f carbnate materals, very lw values f K tan δ wuld prbably be apprprate n te frctn calculatn. Rcks It s unlkely tat suctn cassns culd be nstalled nt any but te very sftest f rcks. Specal cndtns Te nfluence f specal cndtns (e.g. sallw gas depsts wtn te dept f te cassn, rganc materal etc.) s almst unknwn and wuld ave t be dealt wt n an ad c bass. 8

11 Pumpng requrements Te flw capacty f pumps fr nstallatn n clay needs nly t be tat necessary (wt a sutable D margn) t remve te water frm te cassn as penetratn prceeds, tat s q = π v, were q s te requred flw rate and v s te vertcal penetratn velcty. In sands te capacty must als be suffcent t cpe wt te seepage beneat te fundatn. Ts can be assessed by cnventnal D skd seepage calculatns, gvng a ttal requred flw rate f q = π v + F, were F s a γ w dmensnless factr tat depends n D and k s te sand permeablty (Hulsby and Byrne, 00). Cnclusns In ts paper we present te calculatn prcedures tat are requred fr suctn cassn nstallatn n clay. Calculatns nclude tse fr self-wegt penetratn, penetratn under suctn and te lmts t te suctn asssted penetratn. Te calculatn prcedures are cmpared t case recrds, swng gd agreement wt te measured respnses. Te paper cncludes wt dscussn f ptental ssues wen nstallng suctn cassns n a varety f ter sls. Acknwledgements B.W.B. acknwledges generus supprt frm Magdalen Cllege, Oxfrd. Te autrs are grateful t Dr Andrew Huse fr prvsn f rgnal data fr use n examples and 3. Nmenclature D cassn dameter f lad spread factr fr vertcal stress enancement nstalled dept f cassn w egt f water abve mudlne K factr relatng vertcal stress t rzntal stress L cassn skrt dept l permeter lengt f stffeners wtn cassn m multple f te dameter tat te vertcal stress s enanced (.e. D m = md ) N q bearng capacty factr (verburden) N c bearng capacty factr (cesn) p a atmsperc pressure s suctn wtn te cassn wt respect t te ambent seabed water pressure s sear strengt at mudlne u0 s average sear strengt ver dept f skrt u1 s u sear strengt at cassn skrt tp t wall tckness V, V vertcal lad, effectve vertcal lad z vertcal crdnate belw te mudlne α adesn factr δ nterface frctn angle γ, γ unt wegt f sl, effectve unt wegt f sl γ w unt wegt f water ρ rate f cange f sear strengt wt dept 9

12 σ v, σ v subscrpts vertcal stress, effectve vertcal stress nsde cassn utsde cassn References Bye, A., Erbrc, C.T., Rgnlen, B. and Tjelta, T.I. (1995) Getecncal desgn f bucket fundatns Paper OTC 7793, Offsre Tecnlgy Cnference, Hustn, Texas Byrne, B.W. (000) Investgatn f suctn cassns n dense sand DPl Tess, Oxfrd Unversty Byrne, B.W. and Hulsby, G.T. (003) Fundatns fr ffsre wnd turbnes Pl. Trans. Ry. Sc. f Lndn, Seres A, 361, December, pp Byrne, B.W., Hulsby, G.T., Martn, C.M. and Fs, P. (00) Suctn cassn fundatns fr ffsre wnd turbnes Wnd Engneerng 6, N 3 Cllat, J-L., Bsard, P., Gramet, J-C. and Sparrevk, P. (1996) Desgn and nstallatn f suctn ancr ples at a sft clay ste n te Gulf f Gunea Paper OTC 8150, Offsre Tecnlgy Cnference, Hustn, Texas Cllat, J-L., Bsard, P., Sparrevk, P. and Gramet, J-C. (1998) Desgn and nstallatn f suctn ancr ples at a sft clay ste Prc ASCE Jur. f Waterway, Prt, Castal and Ocean Eng. 1, N, pp Erbrc, C.T. and Hefer, P.A. (00) Installatn f te Lamnara suctn ples a case stry Paper OTC 10, Offsre Tecnlgy Cnference, Hustn, Texas Hulsby, G.T. and Byrne, B.W. (00) Desgn prcedures fr nstallatn f suctn cassns n sand Submtted t Getecncal Engneerng Hulsby, G.T and Martn, C.M. (003) "Undraned Bearng Capacty Factrs fr Cncal Ftngs n Clay", Gétecnque, Vl. 53, N. 5, June, pp Huse, A.R., Randlp, M.F. and Brbas, M.E. (1999) Lmtng aspect rat fr suctn cassn nstallatn n clay Prc. 9 t Int. Symp. n Offsre and Plar Eng., Brest, France Huse, A.R. and Randlp, M.F. (001) Installatn and pull-ut capacty f stffened suctn cassns n cesve sedments Prc. 11 t Int. Symp. n Offsre and Plar Eng., Stavangar, Nrway Hgervst, J.R. (1980) Feld trals wt large dameter suctn ples Paper OTC 3817, Offsre Tecnlgy Cnference, Hustn, Texas Lacasse, S. (1999) Nnt OTRC Hnrs Lecture: Getecncal cntrbutns t ffsre develpment. Paper OTC 108, Offsre Tecnlgy Cnference, Hustn, Texas Senpere, D. and Auvergne, G.A. (198) Suctn ancr ples a prven alternatve t drvng r drllng Paper OTC 06, Offsre Tecnlgy Cnference, Hustn, Texas Sljell, E., Sparrevk, P., Haldrsen, K. and Karlsen, V. (1998) Cmparsn and back calculatn f penetratn resstance frm suctn ancr nstallatn n sft t stff clay at te Njrd and Vsund Felds n te Nrt Sea Prc SUT Cnf. n Offsre Ste Investgatn and Fundatn Beavur, Lndn, UK Tjelta, T.I. and Hermstad, J. (1986) Large-scale penetratn test at a deepwater ste Paper OTC 5103, Offsre Tecnlgy Cnference, Hustn, Texas Tjelta, T.I. (199) Getecncal aspects f bucket fundatns replacng ples fr te Eurppe 16/11-E Jacket Paper OTC 7379, Offsre Tecnlgy Cnference, Hustn, Texas Tjelta, T.I. (1995) Getecncal experence frm te nstallatn f te Eurppe Jacket wt bucket fundatns Paper OTC 7795, Offsre Tecnlgy Cnference, Hustn, Texas. Tjelta, T.I., Aas, P.M., Hermstad, J. and Andenaes, E. (1990) Te skrt pled Gullfaks C Platfrm nstallatn Paper OTC 673, Offsre Tecnlgy Cnference, Hustn, Texas 10

13 Tjelta, T.I. (001) Suctn ples: ter pstn and applcatn tday Prc. 11 t Int. Symp. n Offsre and Plar Eng., Stavangar, Nrway Fgures 0 Dameter (m) Draupner E Slepner T Sallw Fundatns YME Jack-up Dept (m) 15 0 Snrre TLP 5 Ancr Fundatns Gullfaks C Trals Lamnara Prject - Clay Prject - Layered 30 Prject - Sand L/D = 1 35 Fgure 1: summary f uses f cassn fundatns (frm Byrne (000) wt furter data frm Tjelta (001)) V' Mudlne z c t D D Fgure : utlne f suctn cassn 11

14 Lad wtut suctn (kn) Adesn End bearng Ttal 1.5 Dept z (m) Fgure 3: calculated lads n cassn fr Example 1 n te absence f suctn 0 Requred suctn s (kpa) Dept z (m) Fgure : calculated suctn fr Example 1 1

15 0 Lad wtut suctn (kn) Adesn End bearng Ttal 0.0 Dept z (m) Fgure 5: calculated lads fr Example n te absence f suctn 0 Requred suctn s (kpa) Calculated Experment 0.0 Dept z (m) Fgure 6: calculated suctn fr Example 13

16 Requred suctn s (kpa) Calculated Expermental 0.0 Dept z (m) Fgure 7: cmparsn f calculated and expermental suctn pressures fr Huse and Randlp (001) NC-IP experment, Example 3 Excess Vlume f Flud Remved (ml) Nrmalsed penetratn: / D Installatn Installatn Predcted level f plug falure 7 8 Fgure 8: varatn wt dept f excess vlume f water remved fr Example 3 1

17 Requred suctn s (kpa) Dept z (m) Fgure 9: Cmparsn between calculated and bserved suctn pressures at te Nkssa nstallatn, Example 15

18

19 Desgn prcedures fr nstallatn f suctn cassns n sand G.T. Hulsby 1 and B.W. Byrne 1 Keywrds: sand, fundatns, suctn cassns, nstallatn Abstract Suctn nstalled cassn fundatns are beng used r cnsdered fr a wde varety f ffsre applcatns rangng frm ancrs fr flatng facltes t sallw fundatns fr ffsre wnd turbnes. In te desgn f te cassns te nstallatn prcedure must be cnsdered as well as te n-place perfrmance. Te scpe f ts paper s t cnsder te calculatns apprprate fr te nstallatn f cassns n sands. Calculatn metds are presented fr determnng te resstance t penetratn f pen-ended cylndrcal cassn fundatns bt wt and wtut te applcatn f suctn nsde te cassn. Cmparsns are made wt case recrds. A cmpann paper (Hulsby and Byrne, 00) addresses te calculatn prcedure fr nstallatn n clays as well as ter sls. Intrductn Suctn cassns are large cylndrcal structures, usually made f steel, pen at te base and clsed at te tp. After an ntal penetratn nt te seabed caused by self wegt, a suctn (relatve t seabed water pressure) s appled wtn te cassn, wc frces te remander f te cassn t embed tself, leavng te tp flus wt te seabed. Te purpse f ts paper s t present desgn calculatns fr te nstallatn f cassns n sand. Wen te suctn s appled te pressure dfferental n te ld f te cassn effectvely ncreases te dwnward frce n te fundatn. Hwever, n sand te appled suctn als generates flw wtn te sl. Te pre pressure gradents are benefcal t te nstallatn prcess and must be accunted fr n te desgn calculatn. Separate calculatns are f curse necessary t assess te capacty f te cassn nce nstalled weter used as a sallw fundatn r ancr. Sme f te ssues tat need t be addressed fr te n-servce perfrmance f suctn cassns n sand are dscussed by Byrne and Hulsby (00, 003, 00). Te frst majr structure nstalled n dense sand usng suctn cassns was Statl s Draupner E rser platfrm (frmerly Eurppe 16/11 E) n te Nrt Sea. Ts was nstalled successfully durng 199 n 70 m water dept. Te cassn fundatns were 1m n dameter and te skrts were 6m lng, and desgned t be nstalled wt suctn. Te desgn fr te nstallatn was based n a cmbnatn f feld testng, labratry testng and fnte element mdellng (as descrbed by Tjelta, 199; Bye et al., 1995; Tjelta, 1995). Statl nstalled a secnd cassn funded structure n te Nrt Sea n 1996 (Slepner T). Durng te detaled desgn f ts structure Erbrc and Tjelta (1999) develped a desgn metdlgy usng desgn carts based n fnte element calculatns. Te analyses presented n ts paper dffer frm te fnte element apprac n tat tey are classcal n te sense tat tey emply smplfyng assumptns, brrwng tecnques frm bt ple desgn and bearng capacty tery. Mre rgrus analyses, usng fr nstance fnte element tecnques (as fr nstance utlned by Erbrc and Tjelta (1999)), culd be used fr partcular nstallatns. Te analyses presented ere suld, wever, prvde a reasnable apprxmatn fr desgn purpses. 1 Department f Engneerng Scence, Parks Rad, Oxfrd OX1 3PJ 1

20 Analyss We wll cnsder a crcular cassn f utsde dameter D and wall tckness t, s tat te nsde dameter s D = D t. It s useful als t defne te mean dameter D = ( D + D ). Fr mst cases t << D, s tat D D D. Te water dept s w, and te vertcal crdnate, measured as a dept belw mudlne, s z. Te current embedment f te cassn s and te egt f te cassn s c, see Fgure 1. Te unt wegt f water s γ w and f te sl s γ. Te buyant unt wegt f te sl s γ = γ γ w. Atmsperc pressure s p a. It s assumed tat te net dwnward vertcal lad n te cassn, wen t s submerged n water, s V. Ts s te wegt f te cassn, less any buyant effects and any part f te wegt supprted by craneage, plus any appled dwnward ladng e.g. frm te wegt f an attaced structure. Nte tat V wll vary wt te penetratn f te cassn n sme way tat s unrelated t te fllwng calculatns, as mre f te attaced structure becmes submerged, and as te lad taken by a crane s reduced. Te cassn s assumed t be a smple cylnder, altug n practce a number f cmplcatng features are ften emplyed suc as: (a) vertcal stffeners attaced t te nsde f te cassn, (b) annular stffeners attaced t te nsde f te cassn, (c) mre cmplex desgns suc as stepped cassns. Installatn Calculatns fr Sand Te nstallatn prcess can be brken nt tw cmpnents; (a) self-wegt penetratn and (b) suctn nstallatn. Te self-wegt penetratn n te absence f suctn s mprtant, as a seal s necessary at te edge f te fundatn n rder fr te suctn cmpnent t be perfrmed adequately. Te desgner wll need t understand te nteractn between te sl densty (and terefre peak frctn angle), te skrt wall tckness and te effectve vertcal lad (V ) actng n te fundatn s tat a suffcent penetratn nt te sand can be btaned. Once a seal can be assured te suctn pase can be cmpleted. Te desgner wll need t predct te requred suctn as a functn f dept f penetratn. Ts nfrmatn can be used t assess pump capacty, and te rate at wc suctn needs t be appled. Te nstallatn cntractr wll need t apprecate te mplcatns f varatns n appled suctn, s tat effectve cntrl f nstallatn s aceved. If te suctn s appled t quckly, ten lcalsed ppng may ccur. Ts culd prevent full nstallatn f te fundatn. Fnally te desgner needs t be aware f any lmtatns t te desgn, suc as te maxmum aspect rat tat can be nstalled wt suctn wlst avdng te pssblty f lquefactn f te nternal plug f sl. Fr te purpses calculatn an dealsed case f a fundatn n a mgeneus depst f sand (assumed draned) wll be cnsdered n ts paper. Self-wegt penetratn Te resstance n te cassn s calculated as te sum f frctn n utsde and nsde, and te end bearng n te annulus. Te frctnal terms are calculated n a smlar way as n ple desgn, by calculatng te vertcal effectve stress adjacent t te cassn, ten assumng tat rzntal effectve stress s a factr K tmes te vertcal effectve stress. Assumng tat te mblsed angle f frctn between te cassn wall and te sl s δ ten we btan te result tat te sear stress actng n te cassn s σ v K tan δ. Nte tat n te subsequent analyss te values f K and δ never appear separately, but nly n te cmbnatn K tan δ, s t s nt pssble t separate ut te effects f tese tw varables. Allwance s made, wever, fr te pssblty f dfferent values f

21 K tan δ actng n te utsde and nsde f te cassn. Te dfference n te fllwng analyss frm cnventnal ple desgn s tat te cntrbutn f frctn n enancng te vertcal stress furter dwn te cassn s taken nt accunt. Te end bearng s taken as te sum f N q and N γ terms n te cnventnal way, and t s assumed tat slutns fr a strp ftng f wdt t are apprprate fr te cassn rm. If (fllwng cnventnal ple desgn practce) n accunt s taken f te enancement f vertcal stress clse t te ple due t te frctnal frces furter up te cassn, ten te result fr te vertcal lad n te cassn fr penetratn t dept, n te absence f suctn, s gven by: γ γ t V = q γ frctn n utsde frctn n nsde end bearng n annulus ( K tan δ) ( πd ) + ( K tan δ) ( πd ) + γ N + γ N ( πdt) (1) Hwever, gnrng te enancement f te stress n ts case prves uncnservatve (.e. t wuld underestmate te frce and suctn requred fr full penetratn), s we develp ere a tery wc takes ts effect nt accunt. Cnsder frst te sl wtn te cassn. If we assume tat te vertcal effectve stress s cnstant acrss te sectn f te cassn, ten te vertcal equlbrum equatn fr a dsc f sl wtn te cassn (see Fgure ) leads t te equatn: ( K tan δ) ( πd ) σ ( K δ) d σ v σ v v = γ + = γ + tan dz πd D () dσ v σ v Wrtng D ( ( K tan δ) ) = Z ts equatn becmes = γ, wc as te slutn dz Z σ v = γ Z ( exp( z Z ) 1) fr σ v = 0 at z = 0. Te ttal frctnal terms n fact depend n te ntegral f te vertcal effectve stress wt dept, and we can als btan σ vdz = γ Z ( exp( Z ) 1 ( Z )). Fr small Z te ntegral smplfes t γ. 0 A smlar analyss fllws fr te stress n te utsde f te cassn. If we make te assumptn tat te enanced stress s cnstant between dameters D and D m = md, and furter assume tat tere s n sear stress n vertcal planes at dameter D, ten we btan te same results as fr nsde te cassn, but wt Z replaced by Z = D ( m 1) ( K tan δ) m ( ) If te mre realstc assumptn D = D + f z s made ten ( 1+ ( f z D )) 1) ( ( K δ) ) m Z = D tan, and an analytcal slutn t te equatn dσ v σ v = γ cannt be btaned (r at te very least s nt stragtfrward). Te equatn can, dz Z wever, readly be ntegrated numercally t gve te varatn f vertcal stress wt dept. If ts apprac s adpted ten t wuld be cnsstent t assume tat wtn te cassn at small z D te stress s nly enanced n an annulus between D n and D, were Dn = D f z. Ts leads t ( 1 ( 1 ( f z D )) ) ( ( K δ) ) Z = D tan, and te dfferental equatn fr te vertcal stress must. 3

22 agan be slved numercally. Te resultng slutn apples dwn t a value D n = 0. Belw ts te rgnal expressn fr Z s apprprate. z = D f, at wc In Equatn (1) te end bearng term accunts fr a trangular assumed stress dstrbutn acrss te tp f te cassn, see Fgure 3(a). Nw tat te stress nsde and utsde te cassn may be dfferent, te assumed stress dstrbutn acrss te tp f te cassn s as n Fgure 3(b). Te mean stress n te tp s calculated as fllws. Frst determne σ v and σ v. Fr all lkely cmbnatns f parameters σ < ; because tere s greater enancement f te stress wtn te cassn v σ v rater tan utsde. If σ v σ x σ end = σ v N q + γ t N t v γ < tn γ Nq were ten te stress dstrbutn s as swn n Fgure 3(b) and t x = + ( σ σ ) v γ N v Nq γ. If σ v σ v tn γ Nq ten all te flw ccurs utwards, x = 0 and σ = σ v N q + γ tnγ end. Accuntng fr tese effects f stress enancement, Equatn (1) becmes mdfed t: ( K tan δ) ( πd ) + σ dz ( K tan δ) ( πd ) + σ ( πdt) V = σ vdz 0 0 v end (3) In te specal case were m s taken as a cnstant and unfrm stress s assumed wtn te cassn ts can be expressed as: V = γ Z exp + γ Z exp Z Z 1 1 Z Z ( K tan δ) ( πd ) ( K tan δ) ( πd ) + σ ( πdt) end () Suctn-asssted penetratn If te pressure n te cassn s s wt respect t te ambent seabed water pressure,.e. te abslute pressure n te cassn s pa + γ ww s, ten t s assumed tat te excess pre pressure at te tp f te cassn s as,.e. te abslute pressure s pa + γ w( w + ) as. Tere s terefre an average dwnward ydraulc gradent f as γ n te utsde f te cassn and upward ydraulc gradent f ( a) s γ w 1 w n te nsde. Because te flw s mre restrcted nsde te cassn tan utsde, a s expected t be a factr smewat less tan 0.5. Calculatns fr a are presented later n ts paper. We assume tat te dstrbutn f pre pressure n te nsde and utsde f te cassn s lnear wt dept. Te slutns fr te vertcal stresses nsde and utsde te cassn are exactly as befre, except tat γ s replaced by γ + as utsde te cassn and by γ ( 1 a) s nsde te cassn. We furter assume tat te nternal vertcal effectve stress s reduced suffcently s tat te falure mecansm nvlves mvement f sl entrely nwards ( x = t n Fgure 3(b)). Te capacty, accuntng fr te pressure dfferental acrss te tp f te cassn, s agan calculated as te sum f te external and nternal frctnal terms, and te end bearng terms:

23 V + s ( πd ) = σ dz ( K tan δ) ( πd ) v 0 + σ vdz 0 ( K tan δ) ( πd ) + ( σ N + γ tn )( πdt) 5 v q γ (5) Were n general te external and nternal vertcal stresses are determned by numercal ntegratn usng te mdfed values f te effectve unt wegt n te utsde and nsde f te cassn. In te specal case were m s taken as a cnstant and unfrm stress s assumed wtn te cassn ts can be expressed as: V + s as ( πd ) = γ + Z exp 1 ( K tan δ) ( πd ) + γ + γ ( 1 a) ( 1 a) Z s Z exp s Z exp Z Z Z 1 Z Nq + γ tn 1 γ ( K tan δ) ( πd ) ( πdt) (6) Equatns (5) and (6) are eac lnear equatn n s, and can be used t slve fr te suctn requred t aceve a penetratn. Nte tat because f te assumptn f pure nward falure, Equatn (6) des nt reduce t exactly Equatn (3) n te absence f suctn. Te dfference, wc s very small, can be reslved as as fllws. Ntng tat ( 1 a) s σ v = γ + Z exp 1 and σ v = γ Z Z exp 1, Z tn γ tn γ fr σ v σ v ten x = t and Equatn (6) apples. Fr σ v σ v0 ten x = 0 and Nq Nq pure utward flw ccurs, and te fnal term n Equatn (6) suld be replaced by as Z Nq + γ tn ( πdt) γ + exp Z 1 γ. Fr ntermedate cases te last term s replaced by σ end ( πdt), were x t ( σ v σ v ) Nq σ end = σ v N q + γ t N γ and x = +. t γ Nγ It can be verfed tat tere are smt transtns between eac f tese cndtns. In eac case tere s an equatn tat can be slved fr s (fr te ntermedate case t s a quadratc, n te ter cases lnear). It can, wever, easly be verfed tat tat fr mst cases te utward flw and ntermedate slutns nly apply fr a very small range f penetratn at te begnnng f te suctn prcess, durng wc tere s a transtn n te flw drectn f te sand. Fr practcal purpses te transtn pase can be gnred. If te sand s nt mgeneus, but cnssts f a number f layers wt dfferent desgn values f γ, φ and K tan δ, ten te abve calculatn can be adapted n a reasnably stragtfrward way, altug te ntegrals fr te vertcal stress slutn becme even mre cumbersme. Of mre sgnfcance culd be canges f permeablty wt dept, snce ts mgt affect te pre pressure factr a. Cautn suld terefre be exercsed n ts case.

24 Lmts t suctn-asssted penetratn As te suctn s ncreased, te upward ydraulc gradent n te nsde f te cassn appraces te value at wc a ppng falure mgt be nduced. At ts stage te vertcal effectve stress nsde te cassn at te cassn tp (and n fact trugut te dept f te cassn) falls t zer. It s antcpated tat f attempts were made t ncrease te suctn furter, lcal ppng falures wuld be nduced, pssbly wt a majr nflw f water nt te cassn, but wtut sgnfcant furter penetratn. Ts cndtn wll ccur wen γ ( 1 a) s = 0,.e. s = γ ( 1 a). Substtutng ts nt te penetratn equatn (6) (fr te smplfed vertcal stress dstrbutn) and smplfyng we btan: γ πd γ V + = Z ( K δ) ( πd ) + ( γ tn )( πdt) ( a) ( a) exp Z 1 Z tan γ (7) 1 1 Slvng te abve equatn fr leads t te maxmum dept f penetratn tat can be aceved usng suctn. Nte because te equatn s transcendental n, and te factr a s a functn f D, te equatn needs t be slved teratvely. We can bserve, wever, tat te last term s typcally small. Fr small appled vertcal lads V, and takng D D D, te abve leads t te smple slutn ( K tan δ) = Z exp 1. If we gnre te effect f stress enancement,.e. fr D Z Z small Z, ten exp 1 D Z Z and we btan. Ts can be used Z ( K tan δ) t prvde an ntal estmate f te maxmum acevable penetratn wt suctn. Snce K tan δ s ften apprxmately 0.5, we cnclude tat n sand te lmt n suctn asssted penetratn s lkely t be f smlar magntude t te dameter. Nte tat ts lmt s muc smaller tan fr nstallatn n clays (Byrne and Hulsby, 00). In fact a slgtly mre strngent lmt n suctn-asssted penetratn can be establsed n te same bass as te reverse bearng capacty slutn used fr clays (Byrne and Hulsby, 00). Agan a plastc falure culd ccur wt flw f sl nt te cassn and wtut furter penetratn. Ts cndtn wll ccur wen σ v = Nqσ v. Tat s (fr te smplfed vertcal stress dstrbutn): ( 1 a) as s γ + Z = γ exp 1 Nq Z exp 1 (8) Z Z Altug Equatn (1) prvdes a mre cnservatve estmate f te lmt f suctn-asssted penetratn, snce N q s usually a large number (typcally mre tan 30), n fact t dffers very lttle frm te cndtn ( 1 ) = 0 Te effect f nternal stffeners γ a s dscussed abve. Te resstance f nternal axal stffenng plates can be taken nt accunt by addng resstance terms accuntng fr te frctn and te end bearng n eac plate. Fr te smplfed vertcal stress dstrbutn te frctnal terms wll be f te frm γ Z exp ( K δ) s l Z 1 Z tan, were l s te permeter lengt f te stffeners, and te end bearng terms wll be f te frm 6

25 ts Z Nq N A Z γ + γ exp 1 γ, were t s s te stffener tckness and A s te end area f te stffener. Once suctn s appled te frctn term s mdfed by replacng γ by ( 1 a) s γ, and te end bearng expressn becmes ( a) s ts Z Nq N A Z 1 + γ γ exp 1 γ. Nte te factr t s n ts expressn rater tan t fr te cassn wall: ts s because te sl flws t eter sde f te stffener. Furtermre te nfluence f te stffeners alters te expressn fr Z Z = ( πd ( K tan δ) + l( K tan δ) ) πd s. t If te stffeners d nt extend t te base f te cassn ten agan crrectns need t be made t te abve expressns t accunt fr ts. It suld be nted tug tat te calculatns fr te vertcal effectve stress at any level n te cassn ten may nvlve rater cumbersme ntegratns. External stffeners n sand wuld almst certanly cause prblems durng nstallatn, as ter tps wuld nt be n te regn were te effectve stress s reduced. As a result tey wuld attract a very large tp resstance. Annular stffeners, wc are ften used fr cassns n clay, wuld almst certanly prevent nstallatn n sand. Pressure factr a and flw calculatns Te factr a suld be 0.5 fr very sallw penetratn n a sl f unfrm permeablty, and wuld be a functn f D. As suctn s appled tere s te pssblty tat te sand wtn te cassn becmes lsened and tus exbts a ger permeablty. Fr smplcty ne can cnsder a permeablty k fr te sl utsde te cassn and k > k nsde te cassn. Te rat f k = k k wll affect te value f a. Fnte element analyses ave been used t calculate te value f a n a sl f unfrm permeablty fr a tn-walled cassn fr values f D up t 0.8 and fr values f k f f 1, and 5. Te results f tw separate studes (usng slgtly dfferent mes detals, Aldwnkle (199), Junadeen (00))) are swn n Fgure. An apprxmate ft fr k = 1 gven by: f a = a1 = c0 c1 1 exp (9) cd wt te values c 0 = 0. 5, c 1 = 0. 36, c = Ts equatn captures te trend f te calculatns reasnably well, altug fr D = 0 te value suld teretcally be 0.5 and fr very large D te factr wuld be expected t tend t zer. Te effects f dfferent k f values can be accunted fr by a smple calculatn n wc te ead lss wtn te cassn s reduced n nverse prprtn t te permeablty. Ts results n: 7

26 a = a k 1 ( 1 a1 ) + ak f f (10) were a 1 s te value frm Equatn 9. Fgure sws a cmparsn between calculated factrs usng Equatns 9 and 10 and numercally calculated factrs usng fnte element analyss. Te flw beneat te cassn due t te suctn can be determned usng Darcy s law as: kds q = F (11) γ w were F s a dmensnless factr tat depends n te rats D and k f. Calculated values f F usng fnte element analyss (Junadeen, 00) are presented n Fgure 5. If t s assumed tat te excess pressure acrss te base f te cassn s unfrm and f value s( 1 a), ten F can be estmated frm te expressn F = ( 1 a) πk f ( D). Te fant lnes n Fgure 5 sw te cmputed F values frm ts expressn wt a determned by equatns 9 and 10. It can be seen tat at large / D te results frm te fnte element analyss apprac ts value. Ts s because te assumptn f unfrm pressure acrss te base f te cassn s reasnable n ts case, wlst at sallw depts tere s a ger pressure twards te centre f te cassn, resultng n muc ger flws. As an example f te flw calculatn, fr a cassn f dameter 6m penetrated m nt a sl wt a unfrm permeablty f 10 m s, and wt an appled suctn f 58kPa te estmated flw wuld be 0.85 = m s. If te cassn was nstalled t ts dept n a perd 10 f urs, ten te pumpng rate smply t remve te water frm te cassn wuld be π 3 3 = m s. Suc a calculatn can be used t assess te relatve cntrbutns f te 3600 tw flw terms t te net requred pumpng capacty. Te calculatns descrbed n te precedng sectns ave been mplemented n a spreadseet-based prgram SCIP (Suctn Cassn Installatn Predctn). Ts s used fr te calculatns n te examples belw. In all tese examples te dameter ver wc te vertcal stress s enanced vares lnearly wt dept (.e. te ladspread factrs are f f = 1). = Example 1: tral nstallatns at Tenby and Sandy Haven Results are reprted ere f tw tral nstallatns f cassns made by Offsre Data Ltd at Tenby and Sandy Haven, n te sut cast f Wales. At Tenby (Example 1a) a m dameter, m g cassn was nstalled n dense sand. Fgure 6 sws a cmparsn between te calculated suctn and te measured data. Te data used fr te cmputatns n ts and subsequent examples are gven n Table 1. It can be seen tat te bserved suctn aganst penetratn respnse s ftted well, and tat te lmt t suctn-asssted penetratn f 1.m s als ftted: at ts dept n furter penetratn was bserved n spte f an ncrease n suctn. Te secnd case (Example 1b) s a m dameter cassn,.5m g and wt a wall tckness f 0mm, wc was nstalled at Sandy Haven. Fgure 7 presents te utput frm te SCIP prgram and cmpares t t te measured suctn aganst penetratn f te cassn. Te suctn ncreased apprxmately lnearly wt dept up t te full penetratn f.5m. 8

27 Te results frm te SCIP prgram ave been btaned by csng parameters t ft te data best. Te suctn aganst dept curve (wc s n fact almst a stragt lne) depends prncpally n te values f K tan δ and k f, and very lttle n ter quanttes. Clearly te abve fgures matc very clsely te bservatns at tese stes, and all te fgures n Table 1 are entrely plausble. Nte tat fr te purpses f te nstallatn a cnservatve calculatn (smewat unusually) wll requre ger estmates f te strengt parameters tan mgt be used fr a capacty calculatn. Example : Draupner E As descrbed n te ntrductn, ts structure was nstalled by Statl n 199 and was te frst jacket structure t be nstalled usng suctn cassns fr te fundatn. Te sl cndtns cnsst f a very dense sand, and a frctn angle f s estmated. As descrbed by Tjelta (199, 1995) te fundatns cnsst f 1m dameter cassns f skrt lengt 6m. Te wall tckness s taken t be 5mm. Tjelta (1995) descrbes te nstallatn prcedure and states tat te self wegt penetratn was aceved by fldng te jacket legs, tereby ncreasng te submerged wegt f te structure frm 1350t t 700t (.e. 66kN per fundatn). Internal stffeners ave been neglected as n nfrmatn s avalable abut te gemetry. Fgure 8 sws te predctns as gven by te spreadseet prgram SCIP cmpared t te range f feld measurements as btaned n ste fr te fur cassns and reprted by Tjelta (1995). Te permeablty factr was taken as 3.0 t prvde a gd crrelatn between te case recrd and te calculated suctn pressures. Example 3: Slepner T Te Slepner T structure was te secnd jacket t be nstalled by Statl n te Nrt Sea. Te fundatns are 15m n dameter and te skrt dept s 5m (Bye et al., 1995; Lacasse, 1999). Te wall tckness s taken t be 5mm and agan te nternal stffeners are neglected as tere s nsuffcent nfrmatn avalable n ts detal. Te sl cndtns cnsst f a very dense sand, and a frctn angle f 5 s used n te calculatns. Lacasse (1999) presents measured data frm te nstallatn, wc sw tat te self wegt penetratn s abut 1.95m. It s pssble t use ts nfrmatn t back-calculate te effectve vertcal lad appled t eac fundatn as ts s nt gven n te lterature. An effectve vertcal lad per fundatn f 1MN gves te apprprate selfwegt penetratn, and ts crrespnds t a wegt f te jacket f abut 8MN, wc s reasnable. Usng te parameter values n Table 1 prvdes a gd ft t te range f data n bserved suctn as reprted by Lacasse (1999), as swn n Fgure 9. Example : Labratry Tests Ts fnal example, swn n Fgure 10, reprts labratry scale tests by Sanam (003). Te cassn fundatn s 150mm n dameter wt a skrt lengt f 00mm (s tat, unlke te prevus cases, te L/D rat s greater tan 1). Te appled vertcal lad n tree tests reprted ere was 5N, 85N and 165N gvng a self-wegt penetratn f apprxmately 8mm, 9mm and 79mm. In ts partcular case, due t te cmbnatn f te dfferent varables, t s pssble fr te fundatn t be nstalled, even tug te L/D rat s greater tan 1.0. Fgure 10 sws te tree suctn aganst penetratn curves, cmpared t te teretcal calculatns. Te SCIP calculatn captures te trend f varatn between te curves as a functn f te appled lad. Te examples sw tat, wt plausble cce f nput parameters, te presented metd f analyss fts case recrds f nstallatn n sand well. It s apprecated tat tere are, f curse a number f parameters n wc te calculatn depends, s tat t a large extent ts matc can be 9