Numerical Assessment of Cargo Liquefaction Potential

Transcription

1 Numrical Assssmnt of Cargo Liqufaction Potntial Li Ju, Dracos Vassalos, Evanglos Boulougouris Ship Stability Rsarch Cntr, Dpartmnt of Naval Architctur, Ocan & Marin Enginring, Univrsity of Strathclyd, 100 Montros Strt, Glasgow G4 0LZ, Scotland, U Abstract Liqufaction of fin particl cargos, rsulting in cargo shift and loss of stability of ships, has causd th loss of many livs in marin casualtis ovr th rcnt past yars. Sinc th dangrs of cargo liqufaction hav long bn known to th shipping industry, th qustion of why th phnomnon is rsurfacing now would b a lgitimat on. With this in mind, an UBC3D-PLM modl basd on FEM thory in th commrcial softwar PLAXIS is prsntd in this papr as a mans to considr soil DSS (Dirct Simpl Shar) tst to vrify th modl and a mthod is prsntd to assss cargo liqufaction potntial. Shaking tabl tsts with diffrnt amplitud, frquncy and initial dgr of saturation of cargos ar studid to prdict tim-domain charactristics. Th proposd mthod could b usd as a rfrnc in support of a suitabl rgulatory framwork to addrss liqufaction and its ffct on ship stability. Highlights A numrical mthod is prsntd to assss th onst of cargo liqufaction. Th mthod usd could prdict tim-domain charactristics. Shaking tabl tsts with diffrnt amplitud, frquncy and initial dgr of saturation of cargos ar analysd. Th mthod could b usd to support th dvlopmnt of a suitabl rgulatory framwork to addrss cargo liqufaction. ywords Cargo Liqufaction; UBC3D-PLM Modlling; Ship Stability 1. Introduction Liqufaction of minral ors, such as or fins from India and nickl or from Indonsia, th Philippins and Nw Caldonia, rsulting in cargo shift and loss of ship stability, has bn a major caus of marin casualtis ovr th past fw yars. Such a transition during ocan carriag can caus a suddn loss of stability of th carrying vssl. Whil cargos ar loadd on board a vssl, th matrial is xposd to mchanical agitation and nrgy input in th form of ngin vibrations, vssl motions and wav impact, rsulting in a gradual sttling and compaction of th cargo. Th gaps btwn th particls bcom smallr in th procss with th corrsponding por prssur progrssivly incrasing. As a rsult, th watr holding ability or matric suction of particls dcrass and th watr in th intrstllar spacs coms togthr to form a liquid layr that allows th cargo abov to mov rlativ to

2 th cargo blow as if th two layrs wr part of a liquid, hnc th trn liqufaction. Altrnativ outcoms includ th formation of a wt bas that may lad to shift of th whol cargo abov and th potntial loss of th vssl or th formation of fr surfac comprising havy slurry that could lad to structural damag of th outr shll or intrnal bulkhads and/or loss of stability again. Th UBC3D-PLM modl is a powrful constitutiv modl, which is a 3-D xtnsion of th UBCSAND modl introducd by Baty & Byrn (1998). Th Mohr-Coulomb yild condition in a 3-D principal strss spac is usd. Th bulk modulus of watr is dpndd upon th dgr of saturation, which is spcifid via PLAXIS input, nabling th prdiction of th por prssur volution in unsaturatd particls. 2. y Faturs of UBC3D-PLM 2.1. Yild surfac Mohr-Coulomb yild function gnralizd in 3-D principal strss spac is usd in UBC3D- PLM modl (Alxandros & Vahid, 2013) as prsntd in Figur 1. Fig. 1. Mohr-Coulomb yild surfac in principal strss spac. Th critical yild surfac could b dfind as givn by Equation (1): f m max 2 min ( max 2 min c cot ) sin p mob (1) Whr, σ max and σ min ar th maximum and minimum principal strsss rspctivly, c is th cohsion of th soil, φ p is th pak friction angl of th soil and φ mob is th mobilisd friction angl during hardning.

3 2.2. Elasto-plastic bhaviour Th lastic bhaviour, which occurs within th yild surfac is controlld by two paramtrs xprssd in trms of th lastic bulk modulus B and th lastic shar modulus G as shown blow: B k B p PA P A m (2) G k G p PA P A n (3) Whr, p is th man ffctiv strss, P A is th rfrnc strss (usually qual to 100kPa), k B and k G ar th bulk and shar modulus numbrs rspctivly and, m and n ar th lastic xponnts which dfin th rat dpndncy of stiffnss. Th hardning rul as rformulatd by Tsgay (2011) in UBC3D-PLM modl is givn as: d sin mob p 1.5G p P A np P A sin 1 P m sin mob pak 2 R f d (4) Whr, dλ is th plastic strain incrmnt multiplir, np is th plastic shar modulus xponnt, φ mob is th mobilisd friction angl, which is dfind by th strss ratio, φ pak is th pak friction angl and R F is th failur ratio n f /n ult, ranging from 0.5 to Cyclic mobility This bhaviour is prsntd in Figur 2 picturing th procss of cyclic mobility of dns sand. Th stiffnss dgradation is computd as follows: p G, p G primary E dil (5) E dil min( 110* dil, fac post ) (6) Whr ε dil is accumulation of th plastic dviatoric strain, which is gnratd during dilation of th soil lmnt and th input paramtr fac post is th valu of th xponntial multiplir trm.

4 Fig. 2. Undraind cyclic shar strss path rproducd with UBC3D-PLM for dns sand. Cyclic mobility, stiffnss dgradation and soil dnsification ar rfrncd on th graph Undraind Bhaviour Th incrmnt of th por watr prssur is computd by th following quation: dp w n w d v (7) Whr, w is th bulk modulus of th watr, n is th soil porosity and dε v is th volumtric strain of th fluid. Th bulk modulus of watr is dpndnt upon th dgr of saturation of th soil. Th bulk modulus of th unsaturatd watr is dfind as follows: unsat w S air sat w air sat 1 S w (8) Whr w sat is th bulk modulus of th saturatd watr and air is th bulk modulus of air, which quals 1kPa in this implmntation having th minimum valu that allows avoiding th gnration of por prssurs during modlling dry sand S is th dgr of saturation. 3. Validation of th UBC3D-PLM in Elmnt Tst 3.1. Validation of th UBC3D-PLM in Monotonic Loading Th validation of th UBC3D-PLM in monotonic loading is prsntd in this sction. Th input paramtrs for modlling th tri-axial comprssion tst (TxC) and th dirct simpl shar tst (DSS) on loos Syncrud sand ar givn in Tabl 1. Th rsults of th UBC3D- PLM ar in a good agrmnt with th xprimntal data (Publa & Byrn & Philips, 1997) as shown in Figur 3.

5 Fig. 3. Monotonic Loading. (Lft: undraind tri-axial comprssion, right: undraind simpl sharing). Tabl 1. UBC3D input paramtrs for all th validation tsts. Paramtr Syncrud S.(TxC, DSS) Frasr S. (Cyclic DSS) p Cargo(FEM) cv k B k G (TxC) p G (DSS) p G m n np R f N1(60) fac hard fac post 3.2. Validation of th UBC3D-PLM in Cyclic Loading Th bhaviour of loos Frasr sand undr cyclic dirct simpl shar is modlld and th numrical rsults ar compard with xprimntal data as publishd by Sriskandakumar (2004). Th rlativ dnsity (RD) of th tstd sand is 40%. In Figurs 4, th volution of

6 strss-strain is prsntd. Th applid CSR quals Th vrtical applid strss is 100 kpa. Th 0 factor is assumd to b 1 for simplification. (a) Vrtical ffctiv strss-shar strss curv (b) Simulation rsults and xprimnt data Fig. 4. Cyclic DSS strss controlld (RD=0.4 CSR=0.08 v =100kpa). 4. Cargo Liqufaction in a Finit Elmnt Schm 4.1. Evaluating Cargo Liqufaction Th soil-watr charactristic curv is th basis for stimating th dynamic analysis of particls. Unsaturatd particls ar composd of thr phass; including particl sklton (solid), por watr (liquid) and por air (gas). Th air-watr intrfac is subjctd to surfac tnsion. In th unsaturatd particls, th por air prssur and por watr prssur ar unqual with th lattr gratr than th first. Th intrfac is subjctd partly to por air prssur and partly to largr por watr prssur. Th prssur diffrnc (i.., por air prssur minus por watr prssur) across th intrfac of air and watr is calld th matric suction. Matric suction is gnrally th ky paramtr dscribing th mchanical proprty of unsaturatd particls.

7 In th capillary tub, th surfac btwn por air and por watr displays a curvd intrfac. Th fluid prssur of th intrfac with th tub sid walls is discontinuous. If th upsid of th intrfac is connctd with th atmosphr, th upsid prssur intrfac is largr than th watr prssur. Th prssur diffrnc is calld matric suction. S dpnds on th curvatur of th intrfac and surfac tnsion. S u a u w (9) Th soil-watr charactristic curv (SWCCs) rlats th watr contnt or dgr of saturation to matrix suction of a particl. A rprsntativ SWCCs is shown in Fig 5. It can b sn that diffrnt iron or has diffrnt watr holding ability. With th cargo compaction, th volum dcrass rsulting in incrasing por watr prssur and dcrasing matric suction of cargos. Cargos cannot hold any watr in th cas whn suction quals zro. Watr is progrssivly displacd in th hold bas, which may rsult in som portions or all of th cargo dvloping a flow stat. For arthquak liqufaction, th acclration is larg and soil could b rgardd as undraind soil, whr acclration for cargo liqufaction is small and th watr could drain from cargos. Whn th dgr of saturation is 100% and watr coms out from th cargos, th cargos may display movmnt bhaviour that charactriss liquids. Thrfor, suction=0 is takn as th onst of cargo liqufaction. Fig. 5. Soil-watr charactristic curvs. Fig. 6. Cntrifug tst modl Cntrifug Tst Th influnc of th dgr of saturation on th fr fild rspons is invstigatd. Th gomtry of layr is shown in Figur 6. Locations L, N, O ar monitord through th tst. Th initial dgr of saturation is supposd to b uniform. Th dgr of saturation involvs: S=99.0%, 97.0% and 94.0%. Th initial strss may hav a grat influnc on th rsults and th initial strss usd is du to th gravity action during all th tsts. Th boundary conditions ar dfind as: at th bas of layr, th vrtical displacmnt is blockd, and th input nrgy is sinusoidal horizontal acclration with 2 amplitud 0.02m/ s and frquncy 2HZ. At th latral boundaris, th horizontal displacmnt is blockd. Th modl paramtrs ar listd in Tabl 1.

8 (a) Dgr of saturation=94%

9 (b) Dgr of saturation=97.0%

10 (c) Dgr of saturation =99.0% Fig. 7. Evolution of suction, ffctiv strss and por watr prssur of th column during cntrifug tst.

11 From Figur 7, it can b sn that variation of th dgr of saturation has a significant influnc on matric suction, ffctiv strss and por watr prssur gnration. Whn th matric suction dcrass to 0, th dgr of saturation turns 100%. From th figur, aftr full dgr of saturation, th por watr prssur incrass rapidly and th ffctiv strss dcrass to zro with liqufaction occurring immdiatly. Whn th dgr of saturation is lss than 94%, th onst of liqufaction at point L could b dlayd to 23s. With th incras in th initial dgr of saturation, th onst of liqufaction bcoms asir Shaking Tabl Tst Shaking tabl tsts considring sway motion of a ship with diffrnt amplitud, frquncy and initial dgr of saturation of cargos ar invstigatd to prdict tim-domain charactristics during liqufaction basd on UBC3D-PLM Modl in commrcial softwar PLAXIS. Th gomtry of layr is shown in Figur 8. Locations M, L,, P, O and N ar monitord through th tst. Th initial dgr of saturation is supposd uniform and varis as 99%, 95.16% and 92.38%. Th frquncy varis as 0.25HZ, 0.35HZ and 0.5HZ. Th amplitud varis as 0.02m, 0.04m and 0.06m. Th boundary conditions ar dfind as: rigid box is usd in th shaking tabl tst; at th bas of layr, th vrtical displacmnt is blockd, and th input nrgy is sinusoidal horizontal displacmnt condition. At th latral boundaris, th horizontal displacmnt is fr and has th sam motion as th bas of th box. Th initial strss du to gravity is shown in Figur 8. Fig. 8. Shaking tabl tst modl. (Lft: monitor points, right: th ffctiv strss contour aftr gravity action). From Figur 9 in th calculation of amplitud 0.04m, frquncy 0.25HZ and dgr of saturation 95.16%, it can b sn that th soil nar locations L, O and is at th limit of liqufaction du to svr contraction. Locations M and P show dilation and N has a high ffctiv strss, hnc difficult to liqufy. Emphasis could b put on th middl column of location O. From Figur 9, it can b sn that th highr dgr of saturation, frquncy and amplitud, th asir th onst of liqufaction. Du to th intraction btwn soil and rigid box, liqufaction of th soil displays mor complicatd bhaviour from th curvs of ffctiv strss. From (a) to (c), variation of th amplitud and frquncy hav small impact on liqufaction, whilst dgr of saturation has just th opposit ffct.

12 a) Evolution of suction during shaking tabl tst b) Variation with amplitud c) Variation with frquncy d) Variation with dgr of saturation Fig. 9. Evolution of suction at th middl of th column during shaking tabl tst. 5. CONCLUSIONS Tsts for monotonic loading and cyclic loading agr wll with xprimntal data. Th Finit Elmnt Mthod combind with th UBC3D-PLM modl could b usd to valuat th potntial for cargo liqufaction. Accurat dscription of cargo proprtis is th ky factor to prdict cargo liqufaction. With th highr dgr of saturation, frquncy and amplitud, cargo is lss rsistant to liqufaction. Among ths thr factors, th only on that can b controlld is th dgr of saturation. Rducing th dgr of saturation of cargos will normously rduc th nsuing problms of cargo ships during transportation of granular cargos. This mthod in th papr could b potntially usd as a rfrnc and possibly support th dvlopmnt of cargo liqufaction assssmnt basd on tim domain analysis.

13 Rfrncs Baty, M. and Byrn, P., 1998 An Effctiv Strss Modl for Prdicting Liqufaction Bhaviour of Sand ASCE Gotchnical Earthquak Enginring and Soil Dynamics (gotchnical spcial publication III), Vol. 75(1), pp Ptalas, Alxandros. and Galavi, Vahid., 2013 Plaxis Liqufaction Modl UBC3D-PLM PLAXIS Rport. Publa, H., Byrn, M., and P.Philips, P., 1997 Analysis of canlx liqufaction mbankmnts prototyp and cntrifug modls Canadian Gotchnical Journal, Vol. 34, pp Sriskandakumar, S., 2004 Cyclic loading rspons of frasr sand for validation of numrical modls simulating cntrifug tsts Mastrs Thsis, Univrsity of British Columbia, Dpartmnt of Civil Enginring. Tsgay, A., 2011 Plaxis Liqufaction Modl PLAXIS Rport. G.R. Martin, W.D.L. Finn, and H.B. Sd., 1975 Fundamntals of liqufaction undr cyclic loading Journal of th Gotchnical Enginring Division, ASCE, 101.