Nonlinear Behavior of Pile-Soil Subjected to Torsion due to Environmental Loads on Jacket Type Platforms

Transcription

1 WSEAS ANSACIONS on FLUID MECHANICS Nonlnar Bhavor of Pl-Sol Sbjctd to orson d to Envronmntal Loads on Jackt yp Platforms M.. EMAMI AZADI, Assstant Profssor, Dpartmnt of Cvl Eng., Azarbajan.M. Unvrsty, abrz IAN dr.mam@azarnv.d and S. NODAL, Profssor, Dpartmnt of Gotchncal Eng., Unv. of Scnc & chnology, NOWAY s.nordal@hotmal.com and M.SADEIN, M.Sc. Stdnt Dpartmnt of Cvl Eng., Unv. of abrz, abrz, IAN msadn@yahoo.com Abstract: - In th prsnt stdy, th torq-twst bhavor of non-lnar pl-sol systm rlatd to th wavcrrnt loadng on Jackt typ offshor platform s nvstgatd. h non-lnarts of pl-sol wth rspct to both dpth and th twst angl of pl ar consdrd. h basc dffrntal qlbrm qatons of th plsol systm ar drvd basd on hypr- lastcty thory of sol. A nmrcal cntral fnt dffrnc mthod s appld basd on smplfcaton of strss fld arond th pl lmnts whch taks nto accont changs n th sco ndary shar strss componnts and also non-lnarts d to non-homognos sol condton. hs mthod ss a on-dmnsonal msh along pl-sol ntrfac. It also taks nto accont th changs n G of sol wth rspct to th twst angl of pl. In a sparat work, th smlatd torq-twst bhavor of pl-sol systm basd on ths analyss approach s compard wth th rslts of mor rfnd fnt lmnt analyss by sng contnm mchancs thory and also fll scal pl-sol tst rslts (Emam,2002). h torq-twst rslts by sng th proposd approach hav bn sd to stdy th bhavor of two jackt-pl-sol systms ndr sa nvronmntal and accdntal loadng. Ky-Words: - Pl-Sol ntracton, Jackt-Pl-Sol systm, Pl-Sol Non-lnarts, Dsk Modl of Sol, orq- wst (t-t) transfr crvs 1 Introdcton In th rcnt yars, th ntgratd analyss of Jackt-pl-sol systms has bn on of th man concrns of th offshor ndstry. In ths rgard, modlng of pl-sol ntracton has bcom an mportant ss. hrfor, most fforts n th past thr dcads hav bn pt nto modlng th pl-sol ntracton ndr axal and latral loadng. In th xstng API cod for offshor pl dsgn, th so-calld t-z, q-z and p-y crvs ar appld to smlat th non-lnar pl-sol ntracton bhavor ndr axal and latral loadng, rspctvly. Howvr, th rcnt stds show that th torq-twst ntracton of pl-sol systm n som cass can not b nglctd. Hnc, thr s a nd for sch ffct whch cold b consdrd wth a torq-twst (t-t) typ crv smlar to t-z, q-z and p-y crvs as dscrbd n API P2A. h topc of torsonal pl-sol ntracton has bn focs of only fw stds n th rcnt dcads. Howvr, th lastc pl-sol ntracton bhavor has bn ntally stdd by wll-known athors sch as Polos(1975) and andolph(1982) and Stoll(1976).andolph(1982) nvstgatd th torq-twst bhavor of rgd pls as wll as lastc flxbl pls. Polos(1975) mad a lnar lastc pl-sol assmpton basd on contnm mchancs approach and appld bondary ntgral qaton tchnq to obtan charts for pl's torsonal flxblty as a fncton of pl's gomtry and rlatv stffnss.whl andolph n hs ponrng ISSN: Iss 4, Volm 3, Octobr 2008

2 WSEAS ANSACIONS on FLUID MECHANICS work, appld thory of lastcty to obtan th dffrntal qaton for th torsonal pl-sol ntracton. H sd a rathr smpl strss fld assmpton arond sngl pl and obtand closd forms for hs analytcal soltons. Stoll (1976) n hs sm- analytcal mthod sd th pl-sol torq-twst data to back-fgr th shar modls of sol (G). hn h showd that t mght b mor conomc and also rathr accrat to s twst data from pl tsts to prdct th axal bhavor of pl-sol systm nstad of prformng mor costly axal larg damtr pl tsts. In th most rcnt work, Manl and Gladys(2002) has proposd a qt smpl strngth of matral basd mthod to smlat th bhavor of pl fondaton ndr torson. H dd not laborat frthr and nor mntond th rslts of applcaton of sch mthod. Hs proposton was basd on th assmpton of vrtal fxty of pl fondaton at a crtan dpth. In th prsnt stdy, a st of torq-twst (t-t) ntracton crvs smlar to th pl-sol axal and latral ntracton crvs (t-z), (q-z) and (p-y) ar dvlopd basd on dsk sol dscrt lmnt approach (s Emam, 1998). 2 hortcal Backgronds h da of fnt dsk or strp dalzaton of sol mdm arond th pl has bn ntrodcd n th rcnt yars by svral athors sch as Grand and Nordal(1979), Nogam and Konaga(1989), Wolf and Mk(1992) and Svano t al.(1993). h concpt s basd on dalzaton of pl-sol ntracton as fnt ncopld crclar dsks as llstratd n Fg.1. Varos forms of sol dsks hav bn sd so far sch as rgd, lastc dformabl and lasto-plastc dsks. In ths work a nw (t-t) modl s ntrodcd whch s dvlopd basd on th dalzaton of th pl-sol systm by a st of ncopld magnary fnt dsks. Each dsk as shown n Fg.1 rprsnts th torsonal ntracton btwn th pl and ts srrondng sol. hs nw modl s an xtnson of (t-z) typ dsk modl by Grand and Nordal (1979) and Nordal t al. (1985) for torq-twst problm. Also n ths nw modl, a tangnt stffnss formlaton s sd nstad of scant stffnss as appld n th prvos modl. h maxmm moblzd shar strss ndcd d to appld torq at th pl-sol ntrfac s dtrmnd basd on Mohr-Colomb thory. hs approach s rathr smpl bt dffrnt from th prvos modl. h appld torq n th pl d to nvronmntal or vn accdntal loadng on th jackt platform s carrd and dstrbtd throgh ths magnary dsks to th grond. h ndcd shar strsss may b assmd to vary xponntally towards zro at th dgs of th ach dsk. Plan stran condtons ar assmd ovr ach pl-sol dsk (.. stran componnts assmd to b constant throgh th dsk thcknss). h sol condton s assmd to b n-drand (clay) ndr short trm loadng hnc ts volm cold b consdrd as constant aftr ndrgong shar dformatons. h rads of ach fnt dsk (rd) s assmd to b (η) tms th rads of th pl (r). Hr (η) may b chosn to b n th rang of to b sffcnt for approxmaton of shar stran dstrbton n th sol. From smpl contnm mchancs, th shar stran of th plsol (γ) may b calclatd as follows: (1) whr (τ rθ ) s th shar strss ndcd by torq arond th pl and (G ) s th tangnt shar modls of th sol whch may b calclatd from th followng mprcal rlatonshp obtand by Lango(1991) throgh srs of traxal tsts on clay: (2) Whr (G) s th ntal shar modls of th sol, (α) and (β) ar th matral paramtrs fond by Svano t al. (1993) for varos sol typs. h practcal rang of (β) s btwn 1 and 4. Eqvalnt vals of β can b fond for sand typ sols (s Emam, 1998). In Eq.2 (τ rθ )ps dnots th pl-sol ntrfac shar strss at falr. If w tak an xponntal form dstrbton for τ ovr th magnary dsk rads as: (3) Combnng, th Esq. (1) to (3) and ntgratng Eq. (1) abov may lad to: (4) ISSN: Iss 4, Volm 3, Octobr 2008

3 WSEAS ANSACIONS on FLUID MECHANICS h angl of twst (ϕ) may thn b comptd as follows: (5) Sbsqntly from smpl contnm mchancs thory, w can compt th corrspondng torq () as follows: Fg.1 Dsk Idalzaton of Pl-Sol Systm (6) From Eq. (6) by assmng dffrnt vals for (τ rθ ), for th gvn sgmnt of pl may b obtand. Whl th corrspondng angl of twst (ϕ) at th pl-sol ntrfac can also b fond. A st of t-ϕ vals can thn b comptd whch wll charactrz th socalld (t-t) pl-sol ntracton crvs. A vrfcaton stdy of (t-t) modl prsntd hr whch nclds comparson wth othr mthods and also xprmntal rslts, s prformd and gvn n a sparat rport by Emam(2002). h (t-t) crvs ar thn sd for ntgratd jackt-pl-sol analyss (s Moan t al.1997 and Emam, 1998). 2.2 Elasto-Plastc Modlng of Pl-Sol Sprngs A gnral lasto-plastcty modl for a on nod sprng has bn mplmntd nto sfos program (s.g. Emam, 1998). hs modl s sd hr wth th loadtransfr dsplacmnt charactrstc crvs sch as (tz), (p-y), (q-z) and (t-t) as dscrbd n th prvos sbscton. h man fatrs of th modl may b otlnd as:. Plastcty modl nclds an sotropc typ hardnng/softnng whch mpls that th xtnson or contracton of th yld srfac s allowd.. Hardnng or softnng may b assocatd wth th prsntd dsk for axal and latral loadng of pl-sol systm.. h modl acconts for th chang n th loadng drcton n th XY plan by mans of an ntracton srfac.. No scalng of load stp d to plastfcaton of th pl-sol ntracton lmnt s prformd.. No coplng s allowd btwn th varos load transfr-dsplacmnt crvs rlatd to th pl-sol dsk Pl-Sol Elmnt Formlaton On nod fnt lmnt qvalnt to th pl-sol ntracton dsk s consdrd wth 6DOFs as follows (s.g. Emam, 1998): U=[w Φ] (7) Whr, w and Φ rprsnt th sb-vctors of th translatonal and rotatonal dgrs of frdom. Oftn th rotatonal dgrs of frdom ar st to zro and hnc k rdcs to 3x3 bt n ths work w hav also consdrd th pl-sol torsonal stffnss trm n th lastc stffnss matrx of pl-sol dsk lmnt. o compt th plastc stffnss matrx, w consdrd gnralzd strans/dsplacmnts as follows: = φ q (8) hn, w hav: S = φ Q (9) Dcomposng th ncrmntal dsplacmnt nto lastc and plastc parts, w can wrt: d = d + d p (10) h corrspondng lastc forc-dsplacmnt rlatonshp can b xprssd as follows: ds = k d (11) h corrspondng plastc stran rat rlatonshp can thn b wrttn accordng to th normalty rl as: F d p = dλ. (12) S ISSN: Iss 4, Volm 3, Octobr 2008

4 WSEAS ANSACIONS on FLUID MECHANICS h sotropc hardnng rl can thn b appld as follows: d = H. dλ (13) h yld condton can thn xprssd as follows: Γ = S X ( ) = 0 (14) p h gradnt to th yld srfac can thn comptd as follows: F g = (15) S And also: g F = (16) h lasto-plastc stffnss of th pl-sol dsk lmnt can thn stablshd applyng th consstncy condton as follows: Jackt-Pl-Sol Systm Stffnss Formlaton h comptd strctral and pl-sol dsk lmnt stffnss matrcs ar transformd from local to a global coordnat systm as follows: K p, gl = ψ K pψ (22) Whr ψ ndcat th vctor of cosn drctons for ach lmnt () n th abov qaton (s for.g. Przmnck,1968 and Znkwch,1989). h transformd lmnt stffnss matrcs thn ar assmbld n a global stffnss matrx as: r n K = A. K. A (23) = 1 p, gl In whch A s a systm stffnss transformaton matrx, rlatng th lmnt Dofs nto global coordnat systm (s for.g. Przmnck, 1968 and ddy, 1989). Altrnatvly, a sprposton approach may b adoptd to transform th lmnt stffnss matrcs nto th systm stffnss matrx K r. K can thn b pdatd aftr ach ncrmntal stp. r F F F =. ds +. d (17) S Combnng th abov qatons, w gt th followng matrx rlatonshp: g. K ( d gdλ) + g. H. dλ = 0 (18) Hnc, w can obtan th ncrmnt of scalng factor as: 1 dλ = ( g. K. g g. H ). g. K. d (19) Usng th abov Eqatons, w mght obtan th followng lasto-plastc stffnss rlatonshp for th pl-sol ntracton dsk: ds = K. d = K ( d d g. dλ ) (20) p p = Whr sbstttng n Eq.20 for d λ from Eq.19 abov, w shall obtan: 1 ds = [ K K. g( g. K. g g. H ). g. K ]. d (21) Eq.21 shows that th lasto-plastc stffnss of th plsol ntracton dsk n ths cas s a fncton of nonlnar lastc (hypr-lastc= K ) stffnss, gradnt ( g ) and sotropc typ plastc hardnng fncton of th pl-sol dsk ( H ). Fg.2 Dobl Bondng yld srfac concpt Plastcty Formlaton for Strctral Mmbrs h normalty rl on strctral lmnt can b xprssd as follows (s Sord t al,(1986)) : δv = G. λ = [ g ]. λ (24) p In whch, δv p rprsnts th ncrmntal plastc dsplacmnt vctor at strctral lmnt lvl. h [g ] dnots th gradnt matrx on th rght-hand-sd of Eq.24 whch s also mltpld by scalng ncrmnt. h g lmnts rprsnt th Grn fncton of strctral bam mmbr sd to modl th Jackt and Pls whch can b comptd as: Γ g = (25) S ISSN: Iss 4, Volm 3, Octobr 2008

5 WSEAS ANSACIONS on FLUID MECHANICS Whr, Γ dnots th plastc ntracton fncton for th strctral bam lmnt as shown n Fg.2 blow. S rfrs to th gnral forc vctor at th nod () of bam lmnt. For th tblar jackt stl mmbrs th followng plastc ntracton formla was gvn by Sord t al, (1986): N Γ = Cos π. 2 N 2 M y + ( ) 2 p M p M 2 z = 0 (26) In whch N, N P,M y, M z and M p dnot th axal forc, plastc axal forc, th bndng momnts abot z and y axs and th plastc momnt of th bam lmnt, rspctvly. A knmatc hardnng rl s appld at lmnt plastcty lvl n accordanc wth a two layr bondng srfac systm. Hnc, th transton from th ntal yld srfac to th fll yld stat can b achvd by translaton of th nnr yld srfac towards th otr srfac n a ndrctonal mannr. h stffnss matrx for th strctral mmbr may b wrttn as follows: S = K. v (27) Whr K and v dnot th tangnt stffnss and th lastc dsplacmnt ncrmnt, rspctvly. h lattr can b wrttn n th followng mannr: v = v (28) v p Combnng Eqs.27 and 28 abov mght yld th followng ncrmntal forc-dsplacmnt rlatonshp: S = K.( v G. λ ) (29) h consstncy rl rqrs that th forc vctor drng th yld has to rman on th yld srfac, that s to say: Γ Γ =. S = G. S = 0 (30) S Sbstttng for S n Eq.30 from -H-S of Eq.29, w can obtan th followng rlatonshp: Γ = G. S = G K.( v G. λ) (31) hn λ can b comptd from Eq.31 as follows: 1 λ = ( G. K. G ).( G. K. v) (32) placng for λ now n Eq.29, wll yld th followng lasto-plastc stffnss rlatonshp: S = [ K = K p. v G ( G K G ) 1 G K ] v (33) Solton Procdr h solton procdr can b adoptd to solv th problm s an tratv-ncrmntal on. h nonlnar dynamc qaton of moton of th vssl mpact on th jackt platform s ntgratd n th tm doman by mans of HH-α algorthms (Hlbr t al, 1976). hs algorthm s actally basd on th Nwmark s-β famly of schms, howvr, t ntrodcs som nmrcal dampng by mans of tm avragng. h dynamc ncrmntal qlbrm qaton thn rads: ( M + M a ) (1 + α ) K( r r (1 + α ) C( r) C r n r α ( ) n r n ) rn+ 1 αk( r) rn = (1 + α ) F, n+ 1 αf, n (34) Whr, n and n+1 dnot two consctv tm stats. h ffct of α paramtr s to damp ot hghr ordr frqncy contrbtons nto th global platform rspons. M, M a, C(r) and K(r) rprsnt th strctral mass matrx, th hydrodynamc addd mass matrx, th dampng matrx and th rstorng forc matrx, rspctvly. h nmrcal ntgraton of Eq.5 can b prformd by mans of a convntonal prdctorcorrctor schm. hs mthod allows for tm-stp scalng n th prdctor phas n ordr to brng th forc stats back to th yld srfac. 3 Cas Stds h prsntd modl abov s appld for ntgratd statc and dynamc analyss of two Jackt platforms, a 4-lg Malaysan Jackt and an 8-lg North-sa Jackt, rspctvly. h dscrpton of strctral and f ondaton systm of ths two platforms ar g vn n mor dtal by Emam (1998). 3.1 Cas 1: A 4-lg Malaysan Jackt Strctral Systm h strctr s a lght 4-lg Jackt nstalld n shallow watrs offshor Malaysa. h fnt lmnt modl of th Jackt and ts 4 sngl pl fondaton s shown n Fg.3. h bracng systm of th jackt comprss only cross X-typ bracng. h dck spportng modl has bn modld by an addtonal lght fram at th top of th jackt wth a hght of abot 7.5m abov man watr lvl. h Jackt-pl connctons hav not bn modld. ISSN: Iss 4, Volm 3, Octobr 2008

6 WSEAS ANSACIONS on FLUID MECHANICS Fg.4 Statc spons of 4-Lg Jackt Platform Fg.3 FE Modl of 4-Lg Jackt-Pl-Sol systm Fondaton Systm h fondaton of th Jackt as dscrbd abov conssts of 4 sngl vrtcal pls drvn throgh th sol layrs as shown n Fg.3. h pls ar mad of stl tblar sctons wth a yld strngth of 470MPa whch ar drvn nto a dpth of abot 45m. h sol condton hr s vrtally vard n ordr to prform a snstvty stdy on th nflnc of (p-y) crvs as wll as (t-t) crvs stffnss and capacts. h pls hr ar spposd to b nplggd ntally. Howvr, drng th paramtrc stds th pls n som cass ar spposd to b spportd on thr tps. h dtal dscrpton of sol layrs s gvn n Emam (1998) Load Dscrpton h load vctor conssts of gravty, wav and crrnt ndcd componnts. Howvr, to nvstgat th nflnc of th torq (torson momnt) on abl.1 Load Data for 4-Lg Jackt Platform Fg.5 Dformd Modl of 4-Lg Jackt-Pl-Sol systm ndr Shp Impact at md-nod of El.340 th bhavor of pls and th whol platform, t s assmd that a larg part of strctr s shldd and thrfor d to that a larg torson momnt s ndcd on th strctr. h gravty load on th strctr s comptd as th sm of th Jackt slfwght, th wght of top faclts and that of pls. h slf-wgh of Jackt s dstrbtd ovr th jonts of strctr proportonally. h wght of topsd dck s dstrbtd at for cornr nods of dck qally (s abl.1). h hydrodynamc forcs consst of wav and crrnt ndcd forcs whch ar comptd accordng to a modfd form of Morson's qaton (s for.g. Chakrabart, 1987, Emam t al, 2002) sng a Stok's 5 th ordr wav thory and a Whlr strtchng of crrnt profl to th sa srfac. ISSN: Iss 4, Volm 3, Octobr 2008

7 WSEAS ANSACIONS on FLUID MECHANICS Fg.6 Dformd Modl of 4-Lg Jackt-Pl-Sol systm ndr Shp Impact at nod.1 of El.335 Fg.9 Zoomd Vw of Shp Impact at Md-nod of El.335 of 4-Lg Jackt-Pl-Sol Systm Fg.7 Dformd Modl of 4-Lg Jackt-Pl-Sol systm ndr Shp Impact at Md-nod of El.335 Fg.8 Dformd Modl of 4-Lg Jackt-Pl-Sol systm ndr Shp Impact at Nod.2 of El.335 Fg.10 Zoomd Vw of Shp Impact at Nod 2 of El.335 of 4-Lg Jackt-Pl-Sol Systm ISSN: Iss 4, Volm 3, Octobr 2008

8 WSEAS ANSACIONS on FLUID MECHANICS Smmary of slts It s sn n Fg.4 that for lowr vals of latral sol rsstanc (p4-y) th global load factor for th stdd 4-lg jackt s mor snstv for th choc of torsonal rsstanc of th pl-sol systm. As sn, for th cas of (p4-y) for whch th latral rsstanc of sol has bn factord by 0.1 consdrng th corrspondng torq-twst rsstanc (t4-t) has rsltd n a qt sgnfcant ncras of th ovrall systm rsstanc and ts stffnss. hs synthtc crvs mght b th cas whn th pl s spportd on a vry loos satratd sol wth vry lttl latral rsstanc and/or th cas that th pl s nd-barng wth short lngth whl takng most ts rsstanc from ts tp rsstanc. Whl ncras of latral sol rsstanc by a factor of 10.0 (p2-y) has rsltd n a mch stffr global rspons bt ncldng (t2-t) for th sam plsol systm had no consdrabl chang on th global jackt-pl-sol systm rspons.h lattr shows th coplng ffcts of (p-y) and (t-t) for th pls spportd on rlatvly stff sols aganst latral movmnts. For th cas of sol wth ncrasng G wth dpth (p1-y), th global systm rspons bcoms stffr than th thr prvos ons (p2-y), (p3-y) and (p4-y). It may b notd that only for th sak of ths paramtrc stdy th (t-z) s not vard. Fg.5 shows th dformd modl and plastc ntracton vals of th 4-lg Malaysan Jackt-Pl- Sol systm ndr a spply vssl mpact at md-nod ts man lg lmnt no.340. Fgs.6 to 8, show th dformd modls for ths jackt platform ndr spply shp collsons at nods 1, 2 and md-nod of ts bracng lmnt 335, rspctvly. It can b sn that th ht man lg mmbr has bn damagd at ts mdnod and compltly dntd n a scal 1:1 dformd modl. Howvr, th ovrall jackt-pl-sol systm has bn affctd vry sgnfcantly by ths typ mpact. It s obvos that th ovrall dformaton mod of jackt-pl-sol systm s twst (torson mod). A closr xamnaton of th nodal dsplacmnts at nods.110 and 120 at pl hads on th rght hand sd of th jackt platform ndcatd abot 1.108m of dffrnc n movmnt n global X- drcton d to ths knd of mpact. hs vrfd that ndr ths typ spply vssl mpact, th spportng pls wll sstan a sgnfcant latral dsplacmnt. Howvr, on th ht lg tslf a rathr consdrabl twst has also bn obsrvd drng shp mpact. h pl-sol torq-twst (t-t) moblzaton crvs n ths cas hav also spportd th prsntd or man da Fg.11 FE Modl of 8-Lg Jackt-Pl-Sol Systm n ths artcl that th torq-twst pl-sol ntracton bhavor can not b nglctd n all cass. As sn, th mpact at th md-span of th bracng lmnt 335 has rsltd n a plastc hng formaton at ths mmbr at th ht pont. Howvr, th mpact at th nod 1 and n partclar at 2 of ths lmnt has rsltd n a sgnfcant ovrall dformaton of th platform. On th othr hand, th shp mpact at th md-nod of th bracng lmnt 335 has casd a sgnfcant twst n th man lg clos to t. Fgs.9 and 10 show th zoomd vws of th dformd modls of th jackt platform ndr th bracng mpact mods. h sprng lmnts at th mpact pont can b sn whch modl th shp-strctr mpact typ whch can b takn as lastc or n-lastc. 3.2 Cas-2: An 8-lg North-Sa Jackt Strctral Systm h fnt lmnt modl of th 8-Lg Jackt strctr sd n ths cas stdy s shown n Fg.11. h strctr conssts of two longtdnal and for transvrs frams. Longtdnal frams bracng systm comprs manly sngl dagonal bracs and only X-bracs at th frst and th ffth story. ISSN: Iss 4, Volm 3, Octobr 2008

9 WSEAS ANSACIONS on FLUID MECHANICS abl.2 Wav Load Data for 8-Lg Jackt Platform Smmary of slts It can b sn n Fg.12 that th dsplacmnt rspons at nod 101 n y-drcton drng th ntal phas (.. abot mpact draton) s almost th sam for th Jackt platform wth and wthot consdrng th torsonal stffnss of th pl-sol systm. Whl, th rspons crvs of th two systms aftr ths phas partclarly aftr t=1.5sc show a tangbl dffrnc. h maxmm dsplacmnt of nod 101 n y-drcton at tm t=1.5sc for th Jackt-pl-sol systm wthot consdrng (t-t) stffnss s abot 0.022m whl for th sam systm wth havng (t-t) ffct s lss than 0.012m. h transvrs frams hav only K-bracs. h spportng dck has bn modld as a trss and th topsd faclts by a pyramd fram. h dscrptons of strctral and non-strctral lmnts n dtal ar gvn n Emam (1998) Fondaton Systm h fondaton of th Jackt n ths stdy s modld as qvalnt sngl pls pntratng nto a dpth of 28m blow md-ln. D to th rlatvly short lngth of th dsgnd skrt pls n ths cas, thy hav bn grotd at th bottom whr th pls hav pntratd nto a sand layr. Hnc, th pl-tp s consdrd to b plggd to nsr th nd-barng rsstanc. Snc th latral rsstanc may b moblzd at th ppr part of th sol, th dsgnd pl condton s not modfd and wll b sd n th frst part of ths stdy. h plssol ntracton s modld as non-lnar dsks as dscrbd abov. h dtal dscrpton of pl-sol s gvn n Emam (1998) Load Dscrpton h gravty, nvronmntal and accdntal loadng ar appld on th Jackt platform. h gravty load conssts of slf-wght of jackt, topsd dcks, pls and pl gds. h slf-wght of jackt s appld on ach lmnt as dstrbtd load and also th othr parts ar consdrd as qvalnt nodal loads. An accdntal load s consdrd as th shp mpact ndcd forc on th horzontal bracng (lmnt: 305) of th jackt platform as shown n Fg.11. h shp s consdrd to hav a mass of 5000tons and a maxmm spd of 2.0m/sc. h mpact pont on th horzontal bracng s takn to b th md-span. hn n addton of latral forc a torsonal momnt s appld on th man lg lmnt from smpl strctral mchancs thory. Fg.12 Dynamc spons of 8-Lg Jackt Platform at Nod 101 n Global Y-Drcton hs shows that consdrng (t-t) rsstanc has rsltd n a mch stffr rspons (abot 45% dffrnc). At tm aftr t=15sc th rspons crvs of th platform wth and wthot (t-t) ffct bcom almost constant wth magntds of abot 0.028m and 0.022m (ab.21.4% dffrnc). It s obsrvd n Fg.13 that th rspons at nod 101 n global x-drcton s almost th sam for th jackt-pl-sol systm wth and wthot (t-t) ffct ntl t=1.0sc bt at tm t=1.5sc a rathr small dffrnc abot 0.001m s obsrvd. hn at t=4sc th dsplacmnt rspons for systm wth torson stffnss s abot stffr than th systm wth no sch stffnss. Aftr tm t=15sc th rspons crvs ar almost constant wth ltmat dsplacmnts of abot m and m, rspctvly. Smlar trnds ar obsrvd for th rsponss at nod 301 n x and y-drctons. ISSN: Iss 4, Volm 3, Octobr 2008

10 WSEAS ANSACIONS on FLUID MECHANICS (t-t) for th stdd cas. hs stdy showd that th ffct of torsonal bhavor of pl-sol systm cold not b always nglctd as oftn s assmd n th offshor ndstry. Fg.13 Dynamc spons of 8-Lg Jackt Platform at Nod 101 n Global X-Drcton Howvr, th maxmm dsplacmnts at nod 301 n global y-drcton wr abot 0.07m (.. 33%) largr than th pak dsplacmnt at nod 101. h pak dsplacmnt at nod 301 n global x-drcton was abot m at tm t=1.5sc compard to a pak val of m at nod 101. Aftr ths pont slght dffrnc s obsrvd. h ltmat dsplacmnt s abot m compard to th val m (max. dffrnc abot 0.001m). 4 Conclsons A rathr smpl torq-twst (t-t) modl basd on dsk dalzaton of pl-sol ntracton and smpl contnm mchancs thory s dvlopd smlar to API's (t-z), (p-y) and (q-z) modl. It s obsrvd that for th cas of 4-lg offshor Jackt platform th nflnc of sol torsonal stffnss on th global systm bhavor s gratly dpndnt on th latral pl-sol rsstanc. hs mans that thr s a strong coplng btwn (p-y) and (t-t) s obsrvd for th cass stdd. It s also concldd that th pl-sol systm rspons and ts ovrall falr mod manly dpnds on th typ of shp mpact on th strctral mmbrs of th jackt platform. It s sn that soft mpact mod on bracng mmbrs n most cass localzs th damag by formaton of plastc hngs at th mpact ara and whl th hard mpact on th man lg mmbr may ndc an ovrall falr mod of jackt-pl-sol systm. Moblzaton of Pl-Sol and ts falr mod hnc cold b affctd by th typ of dynamc mpact or hydrodynamc loadng on th jackt sprstrctr tslf. It s also shown that for th cas of 8-Lg Jackt platform th global dynamc rspons of th systm ndr shp mpact on a horzontal bracng s sgnfcantly nflncd aftr ntal phas (mpact draton) by th choc of frncs: [1] API P2A- LFD (1993): Plannng, Dsgn and Constrcton of Fxd Offshor Platforms, Amrcan Ptrolm Insttt, USA. [2] Chakrabart S.K. (1987):"Hydrodynamcs of Offshor Strctrs, WI. Prss, UK. [3] Emam Azad, M.. (1998): Analyss of Statc and Dynamc Pl-Sol-Jackt Bhavor, Dr.ng. hss, NNU, Norway. [4] Emam Azad, M.. (2002): Vrfcaton of Dsk Pl-Sol Modl, port PSPF H, Intrnal port for Marn sarch Inst., Norway. [5] Emam Azad, M.. and Moan. (2002):" Inflnc of Wav-In-Dck Forcs on th lablty of Jackt-Pl-Sol Systm", Proc. of ICOPMAS 2002, amsar, Iran. [6] Emam Azad M.., Holmaas. (2005):"A nw tst vrson of sfos comptr program", Norway. [7] Grand, L. and Nordal, S. (1979): Crrnt rnds n th Safty of Offshor Strctrs, Proc. of th 17th Int. OC, USA. [8] Lango, H.V.(1991): Cyclc Shar Modls of ntact Clays, Dr.ng hss, NH, Norway. [9] Manl, A. N. and Gladys, C. D. (2002): Eqvalnt or Vrtal Fxty Dpth of Latral and Axally Loadd Pls, On-Ln Prsntaton, J. of Gotc.Eng, ASCE, USA. [10] Moan., Hllan, O. and Emam Azad, M.. (1997): Non-lnar Dynamc vs. Statc Analyss of Jackt Systms for Ultmat Lmt Stat Chck, Proc. of Marn chnology Confrnc, Ednbrogh, UK. [11] Nogam,. and Konaga, K. (1989), m Doman spons of Dynamcally Loadd Sngl Pls, J. of Mch. Eng., ASCE, Vol.112, USA. [12] Nordal, S., Grand, L. and Janb, N.(1985), Prdcton of Pl Bhavor, Dv. of Gotchncal Eng., Bl.15, NH, Norway. [13] Polos, H.G. (1975): orsonal spons of Pls, J. of Gotchncal Eng., ASCE, Vol.101, USA. [14] Przmnck. (1968):"h Matrx Strctral Analyss", Prntc-Hall Nw, York, USA. [15] andolph, M.F. (1982): Pls Sbjctd to orson, J. of Gotchncal Eng., ASCE, Vol.107, USA. ISSN: Iss 4, Volm 3, Octobr 2008

11 WSEAS ANSACIONS on FLUID MECHANICS [16] ddy J.N. (1985), :"An Introdcton to th Fnt Elmnt Mthod", Mc-Graw Hll Company, Nw York, USA. [17] Sord. and Amdahl J. (1986):"Usfos Comptr Program for Ultmat Strngth Analyss of Framd Offshor Strctrs", hory Manal, Sntf, Norway. [18] Stoll, U.W. (1976): orsonal spons of Pls, J. of Gotchncal Eng., ASCE, Vol.102, USA. [19] Svano, G., Madshs, C. and Lango, H. (1993): On th Valdty of Non-lnar Sprng Idalzaton for Sol-Pl Intracton, Proc. of Erodyn '93, rondhm, Norway. [20] Wolf, J.P. and Mk, J.W. (1992): Dynamc spons of Sngl Pls, J. of Gotchncal Eng., Vol.120, USA [21] Znkwcz, O.C. and aylor.l. (1989): "h Fnt Elmnt Mthod", Vol.1, Basc Formlaton, Mc-Graw Hll Company, Nw York, USA. ISSN: Iss 4, Volm 3, Octobr 2008