A constitutive model for unsaturated cemented soils under cyclic loading

Transcription

1 A contitutiv modl for unaturatd cmntd oil undr cyclic loading C. Yang 1, Y.J. Cui 2,3, J.M. Prira 2,3, M.S. Huang 1 1. Dartmnt of Gotchnical Enginring, Tongji Univrity, Shanghai, China 2. Ecol National d Pont t Chaué (ENPC) Navir-CERMES, 6-8 Avnu Blai Pacal, Cité Dcart, Cham-ur-Marn, F Marn-la-Vallé Cdx 2, Franc 3. Univrité Pari-Et, UR Navir, Marn-la-Vallé, Franc Corronding author Prof. Yu-Jun CUI Ecol National d Pont t Chaué, CERMES 6-8 Avnu Blai Pacal, Cité Dcart, Cham-ur-Marn F MARNE-LA-VALLEE CEDEX 2 Franc cui@crm.nc.fr Phon: Fax: Pla cit thi articl a: Yang t al., A contitutiv modl for unaturatd cmntd oil undr cyclic loading, Comutr and Gotchnic, 35 (28),

2 Abtract: On th bai of latic bounding urfac modl, th damag thory for tructurd oil and unaturatd oil mchanic, an latolatic modl for unaturatd loic oil undr cyclic loading ha bn laboratd. Firtly, th dcrition of bond dgradation in a damag framwork i givn, linking th damag of oil tructur to th accumulatd train. Th Barclona Baic Modl (BBM) wa conidrd for th uction ffct. Th latolatic modl i thn intgratd into a bounding urfac laticity framwork in ordr to modl train accumulation along cyclic loading, vn undr mall tr lvl. Th validation of th rood modl i conductd by comaring it rdiction with th xrimntal rult from multi-lvl cyclic triaxial tt rformd on a natural lo amld bid th Northrn Frnch railway for high d train and about 14 km far from Pari. Th comarion how th caabiliti of th modl to dcrib th bhaviour of unaturatd cmntd oil undr cyclic loading. Ky word: lo; contitutiv modl; uction; bounding urfac laticity; damag; cyclic loading. 1 Introduction Th Frnch high-d railway lin btwn Pari and Lill (TGV Nord) cro a widrad rang of lo doit. During th vry rainy aon btwn Wintr 21 and Sring 22, intability roblm caud by th formation of inkhol wr obrvd nar th railway foundation, with dth u to 7m. Firt laboratory cyclic tt hav howd that thi intability would rlat to th cyclic bhaviour of th involvd loic oil, an aolian doitd dimnt. A thi loic oil contain a ignificant fraction of carbonat (16%), cial attntion hould b aid to th ffct of cmntation in th analyi of tt rult a wll a in contitutiv modlling. Not that in unaturatd tat, th clay fraction containd in th oil (about 16%) can alo lay a cmntation rol, vn though it cmntation lvl i variabl, a a function of th dgr of aturation of th oil. Thi i a articular oint of unaturatd fingraind oil whn conidring th cmntation ffct. Natural cmntd oil ar oftn namd tructurd oil bcau thy how a tructural trngth, i.. additional trngth inducd by th cific arrangmnt of olid grain and th cmntation btwn th olid articl. Howvr, th bond may rnt a fragil bhaviour and b damagd undr mchanical loading, articularly undr cyclic loading. Rarch on contitutiv modl and damag thory for tructurd oil ha bn on of th imortant toic in th fild of oil mchanic in rcnt yar. Svral author hav tudid th ffct of bond damag of tructurd oil from a thortical oint of viw. Among othr, th work of Burghignoli t al. (1998), Sharma & Fahy (23a, b) conidr, in trm of conqunc of damag, th oibility of chang in th iz and ha of th latic domain (yild urfac), and at th am tim, th oibility of dcra in th ovrall oil tiffn. Aftr th comlt damag of bond, it i gnrally acctd that initially tructurd oil will tnd to th am critical tat a th quivalnt untructurd oil do ( Gn & Nova, 1993; Chai t al., 25 for intanc). In ordr to quantify th bond damag roc, Baudt & Stallbra (24) dfind a nitivity cofficint to rrnt tructur and it dgradation for all ty of loading. Vaunat & Gn (23) rood a could formulation btwn th latic train of bond and th total latic train of oil and incororatd it into th modifid Cam-Clay Modl. On th bai of latolaticity, Carol t al. (21) tablihd a t of damag thory to dlv into th 2

3 damag volution of both iotroic and aniotroic matrial ytmatically. A on fficint tool to imulat th mchanical bhaviour of oil undr cyclic loading, th bounding urfac thory ha bn xtnivly alid to variou ty of oil, cially to clay and and (Dafalia & Hrrmann (1982), Zinkiwicz t al. (1985), Pator t al. (1985), Khalili t al. (24)). Chai t al. (25) mloyd th bounding urfac thory to dcrib th mchanical bhaviour of aturatd lo undr cyclic loading. Howvr, to th author knowldg, thr ha bn no ublication about th contitutiv modl of unaturatd tructurd lo undr cyclic loading. A far a th unaturatd act ar concrnd, intniv rarch ha bn mad ovr rcnt yar. Imortant contribution in th fild of contitutiv modlling of artially aturatd oil hav hown that an aroriat framwork nd th u of two indndnt tat variabl. Nt tr and matric uction ar oftn ud (, among othr, Alono t al., 199; Whlr & Sivakumar, 1995). Not that othr choic ar oibl ( for intanc Prira t al. (25)). In trm of cmntation ffct, Lrouil & Barboa (2) rortd that uction incra lad to highr trngth and tiffn of both oil matrix and bond. Garitt t al. (26) xtndd th Barclona Baic Modl (BBM, Alono t al., 199) tarting from th contribution of Vaunat & Gn (23), thu lading to a modl for tructurd oil taking into account unaturatd tat. An nrgy thrhold from which bond damag ffctivly occur ha bn introducd in thi xtnion of BBM. It corrond to th amount of latic nrgy that th bond matrial i abl to tor without damag. Thi ar aim at dvloing an latolatic modl with damag for unaturatd tructurd oil undr cyclic loading within th framwork of bounding urfac thory. Laboratory xrimnt ar imulatd in ordr to validat th rood modl. 2 Gotchnical rorti of th tudid lo Th oil tudid i takn from Northrn Franc, 14 km from Pari along TGV lin, at a ditanc of 25 m from th railway and a dth of 2.2 m. Intact bloc hav bn amld. Laboratory idntification howd that thi lo i a tyical homognou yllowih-gry, orou calcarou lo (calcium carbonat, CaCO 3, u to 16%). It ha a low laticity indx 3 (PI = 6), low dry dnity ( ρ d = 1.39Mg/m ), low dgr of aturation (Sr = 53%), low clay fraction (% < 2µm = 16). Th grain iz ditribution curv i dictd in Figur 1. X-ray diffractomtry how that th aml i mainly comod of quartz. Analyi on th clay fraction (<2 µm) indicat that it involv kaolinit, illit and intrtratifid illit-mctit. Th microtructur of th oil wa obrvd at Scanning Elctron Microco (SEM) and i hown in Figur 2. In Figur 2-a, a larg aggrgat of about 2 µm in diamtr i obrvd togthr with larg intr-aggrgat or (u to 3 µm in diamtr). Aggrgat ar mad u of ilt grain with diamtr btwn 15 and 3 µm cmntd togthr by clay latlt or calcium carbonat, in accordanc with th grain iz ditribution. Th ubangular ha of th grain and thir act ar tyical of lo (Bardn t al.,1973; Grabowka-Olzwka, 1975; Oiov & Sokolov, 1995). Figur 2-b rnt SEM obrvation of a damagd aml aftr on-million-cycl loading in an odomtr cll. Obviouly, th original oil tructur i dtroyd, larg intr-aggrgat or diaar, and oil articl ar rditributd, lading to a mor comact microtructur. Th oil watr rtntion curv wa dtrmind uing omotic tchniqu for uction control (Cui & Dlag 1996, Dlag t al. 1998), and it i hown in Figur 3. It aar that th air 3

4 ntry valu i at a uction valu clo to zro, robably du to th high oroity of th lo tudid. 3 A contitutiv modl for unaturatd tructurd oil undr cyclic loading It i aumd in thi tudy that th oil invtigatd do not rnt any rat dndnt bhaviour. Cyclic loading ar thu dalt with a a uccion of quai-tatic tat. Obviouly, thi aumtion cannot b valid if th loading frquncy i imortant. 3.1 Elatic contitutiv rlationhi bad on th damag thory of bond Th cmntd oil i conidrd a a mixtur comod of th olid matrix and th bond (Figur 4), ach on bing aociatd to it own tr and train tat. Total volum V t of cmntd oil i dfind a V t = V m + V v + V b (1) whr th ubcrit m, v, and b rfr to th olid matrix, void and bond rctivly. A artition of th total tr btwn matrix and bond contribution i aumd a follow = m + b, m q= q + q b (2) whr and q ar rctivly th nt iotroic and dviatoric tr in th triaxial tr ac. Th bond i rgardd a a brittl matrial. It i thu aumd that th bonding matrial can undrgo only rvribl latic train. Bond dgradation may occur according to accumulatd train. With th dfinition of bond concntration β = Vb / Vt, th total latic volumtric train incrmnt dε can thn b drivd a whr ε m, ε b dε = (1 β) dε + βdε (3) m b ar aarnt latic volumtric train of matrix and bond, dfind ovr olid matrix ha (volum V m + V v ) and bond ha (volum V b ) rctivly. Similarly, th total latic dviatoric train can b givn a dε = ( 1 β ) dε + βdε (4) q qm qb In ordr to quantify th bond dgradation and it ffct on th ovrall bhaviour, following th rooal of Vaunat & Gn (23) and Carol t al. (21), th following rlation ar aumd dε / dε = χ ; dε / dε = χ (5) L L L L b qb q 1 whr χ and χ 1 ar oitiv calar mallr than 1, L i a calar accounting for th nrgy thrhold of damag occurrnc, and L i th damag volution variabl, which i a function of th accumulatd total train: 4

5 L ε = k ξ + k ξ, ξ dε () α β q =, q ξ (6) = dε q whr k α, k β ar matrial contant to b dtrmind. From abov quation (3), (4), (5) and (6), th total latic train incrmnt inducd by th total tr can b xrd a d K b dε = (1 β) 1 βχ + (1 β) χ Km Km, dq G b dεq = (1 β) 1 βχ1+ (1 β) χ1 3Gm Gm dε = ( CB1 A1C11) ( AB1 B A1), dεq = ( C Adε ) A1 L L L> L (7) and, K b L L A = β (1 β) χ ( 1 gn( dε ) ε k α ) 1 Km K b L L A1 = β (1 β) χ gn( dεq) ε k β Km G b L L B = β (1 β) χ1 gn( dε ) εqk α Gm G b L L B1 = β (1 β) χ1 ( 1 gn( dεq) εqk β ) 1 Gm d K b L L C = ( β 1) + β (1 β) χ ε ( gn( dεv) kαdε + gn( dεq) kβdεq ) Km Km dq G b L L C11 = ( β 1) + β (1 β) χ1 εq ( gn( dεv) kαdε + gn( dεq) kβdεq ) 3Gm Gm whr, G, K, G ar th bulk and har moduli of bond and olid matrix rctivly. Kb b m m Morovr, a for aturatd cmntd oil, th dformation du to uction i aumd to b ditributd btwn th olid matrix and bond according to th ratio of bond concntration β. Accordingly, th latic train incrmnt inducd by uction i drivd a dε 1 β β = + d Km Kb (8) whr K m i th bulk modulu of olid matrix undr uction. It hould b notd that th bulk modulu with rct to uction of th bonding matrial i aumd to b qual to that rlatd to man rur. A hyical intrrtation of thi aumtion li in th fact that th matrial contituting th cmnt i charactrid by a oroity conidrably finr than th macrooroity of th lo. From thi oint of viw, it i xctd that th cmnt will rmain fully aturatd undr uual uction to which th tudid lo i ubmittd in itu. A a conqunc, bcau of th validity of Trzaghi ffctiv tr in th domain of oitiv uction but aturatd oil, bulk moduli with rct to man rur and uction ar th am. 5

6 Finally, with Equation (7) and (8), th total latic train incrmnt of unaturatd cmntd oil can b obtaind a dε = dε + dε + dε dε dε dε m b q = qm + qb (9) Thu th train incrmnt in bond ar obtaind uing Equation (4) and (5) and th tr incrmnt in bond can b drivd a d = K dε dq b b b b = 3Gb dε qb (1) Furthrmor, th corronding tr incrmnt in olid matrix can b givn by Equation (2). 3.2 Unaturatd mchanical bhaviour of tudid oil In ordr to invtigat th mchanical bhaviour of lo in unaturatd tat, th loadingcolla (LC) yild curv rood by Alono t al. (199), and th watr rtntion curv (WRC) rood by van Gnuchtn (198) ar ud in thi tudy. LC yild urfac i givn in (, ) lan a * = c c ( ) λ () κ m λ ( ) κ m (11) * whr, ar rconolidation tr for a givn uction and for aturatd condition c rctivl y, and i a rfrnc nt man tr. Th oil comrion cofficint in unaturatd tat i givn a [ ] λ() = λ()(1 r )x( β ) + r (12) whr λ () i th oil comrion cofficint in aturatd tat, r i a contant rlatd to th maximum tiffn of th oil, and β i a aramtr which control th rat of incra of oil tiffn with uction. Th yild urfac in triaxial tr ac (, q, ) can b tablihd, a dictd in Figur 5 whr i a variabl introducd in th BBM modl to dcrib th oil cohion chang du to uction chang. i givn a = k (13) Not that both bc and contribut to th aarnt cohion incra. Following th dgradation of bond, bc dcra gradually and th tnil tr of th oil aroach finally. Th watr rtntion curv (WRC) i writtn a 6

7 1 Sr () = 1 + Sr n ( β ) m (14) β Sr, n and m ar oil aramtr and can b obtaind by fitting th xrimntal curv ( Figur 3). Th articular ca of contant watr contnt ituation i of intrt. Undr thi aumtion, th cific watr volum vw i alo a contant. According to th dfinition of vw (Whlr, 1996): v = 1+ = 1+ S (15) w w r whn dv w =, th rlationhi btwn th incrmnt of void ratio and dgr of aturation can b dducd a follow ds S r r = d (16) Combind with th watr rtntion curv (Equation 14), th couling rlation btwn oil dformation and uction variation i dducd in th ca of contant watr contnt tt. 3.3 Platic contitutiv rlationhi bad on bounding urfac thory Th modl undr dvlomnt i aimd at imulating th cyclic bhaviour of unaturatd loic oil. A a conqunc, it aar imortant to includ in th modlling framwork om fatur that nabl th occurrnc of irrvribl train along th cyclic loading tag vn if th load cycl rmain in th domain of mall dformation. Th choic of th bounding urfac thory ha bn mad in thi ar. It i combind with th rviouly dcribd framwork for damag and unaturatd oil dcrition. A comlt t of quation of an latolatic modl for unaturatd tructurd oil undr cyclic loading i now formulatd. Choic of tr variabl To account for th ffct of bond damag on th latic dformation of oil, a air of tr variabl σ = ( q, ) T in th triaxial ac i dtrmind a blow: L L = + x( ) bc ; x( Simultanouly, th hardning aramtr i givn a q = q+ L L q (17) ) bc = (1 + χ), χ = χx( L L) (18) Yild urfac quation Hr th formulation rood by Pator t al. (1985) i ud. According to th fitting of xrimntal curv of th dilatancy cofficint and th tr ratio, th latic otntial 7

8 urfac quation i dvid a followd: * + α g G( σ,, L, ) = q Mg( + )(1+ 1/ αg)[1 ( ) ] + (19) Furthrmor, th corronding yild urfac can b givn a * + α f F( σ,, L, ) = q M f( + )(1+ 1/ α f)[1 ( ) ] + (2) whr M g i th lo of th critical tat lin, and α g i a contant rlatd with th dilatancy cofficint. M f, α f ar contant without dfinit hyical maning, but with M f M g aociatd with th rlativ dnity of oil. A in Dafalia & Hrrmann (1982), th bounding urfac i aumd to coincid with th yild urfac. Non-aociatd flow rul Th non-aociatd flow rul i aumd, and givn by T T nf dσ dε = ( dε, dεq ) = ngl/ U H LU / (21) with n gl/ U and n f, normal vctor to rctivly th latic otntial urfac during loading, th latic modulu during loading or or unloading and bounding urfac, and H L / U unloading. Hardning law A for th hardning law, with rct to on cifid valu of uction, th hardning aramtr i dndnt on th volumtric train a wll a th dviatoric train imultanouly ε q d = d m + d q qm εm εm ε (22) and th hardning law mloyd can b xrd a 1+ m = ε m λm km ξ ξ ε ξ ε ε ε qm qm = = ββ 1x( βξqm) qm qm qm qm m (23) whr β, β1ar th hardning cofficint, and ξ i th abolut accumulation of latic dviatoric train, a ξ qm qm qm = dε (24) Combind with th LC yild curv (Equation 11), th volution of hardning aramtr aturatd tat i drivd * in 8

9 d * * 1+ ξ m qm = dε m + ββ 1x( βξqm ) dε qm λ() κm εqm (25) * According to th conitncy condition, df( σ,, L, ) =, and with th non-aociatd flow rul and hardning law abov, th latic modulu on th bounding urfac H BS L can b obtaind. Maing rul during loading According to bounding urfac thory, th latic modulu, H L / U, at th currnt tr oint P BS i a function of th latic modulu, H L / U, at th corronding imag tr oint P I on th bounding urfac. Thi allow for latic train gnration within th domain dlimitd by th bounding urfac, during both loading and unloading tag. Hr a radial maing rul btwn th currnt tr oint and imag tr oint on th bounding urfac i mloyd, that i, amount of latic modulu of currnt tr oint i a function of th ditanc btwn th currnt oint and it imag. With th conidration of th bond damag and unaturatd oil mchanic, th maing rul i dfind in th nwly tranlatd coordinat ytm (, q ). A n in Figur 6, th maing origin during loading P OL i dfind a th lft intrction oint of bounding urfac with th abcia axi, and th imag oint i dtrmind by th intrction btwn th bounding urfac and th lin conncting th maing origin to th currnt tr oint. Th cific dfinition of th radial maing rul on th latic modulu at th currnt tr oint during loading i writtn in th following way: H r L BS δ L = HL δ (26) with L [ 1 x( )] r = r + L L (27) whr r i th maing xonnt of th quivalnt untructurd oil during loading, and δ and δ ar th ditanc btwn th maing origin and rctivly, th imag oint P (, q ), and th currnt oint P ( q, ) in th ( O,, q) tr ac ( Figur 6). I I I Platic modulu during unloading During unloading, th latic modulu of currnt tr oint i aumd to b corrlatd with th tr ratio, ηu of th tart oint during unloading, and i dcribd a: H U r U η U ηu HU, < 1 M g Mg = ηu HU, 1 M g (28) 9

10 whr H, r ar th initial latic modulu and xonntial during unloading. U U Thrfor, th latic modulu abov (Equation 26 or 28) combind with th flow rul (Equation 21), giv th latic train incrmnt vctor dε during loading and unloading. Loading critria According to th laticity thory, th loading critria hould b givn a follow: T nf dσ >, H L T nf dσ =, H L T nf dσ <, HU Loading Nutral loading Unloading (29) 3.4 Dtrmination of modl aramtr Mot of th aramtr of th rood modl can b obtaind dirctly from laboratory xrimnt, or indirctly by fitting analyi of corrlativ tt rult. For intanc, tt that involv iotroic draind comrion ( loading and unloading ) at diffrnt contant uction * valu rovid data to find c,, λ, κm, r, β, tt that involv a drying-wtting cycl at a givn nt man tr rovid data to find κ, draind har tt at diffrnt uction valu rovid data to find M, k, and tt of oil articl analyi may rovid data to dtrmin g χ, χ1, β. A a firt timat, it i aumd that β i clo to χ and that χ 1 = χ. Th aramtr rlatd to th bounding urfac lik α f, αg, β, β 1 can b obtaind by trial, a uggtd by Zinkiwicz t al. (1985) and Pator t al. (1985). 4 Modl validation To invtigat th caability of thi latolatic modl to dcrib th bhaviour of tructurd unaturatd oil undr cyclic loading, cyclic triaxial tt ar imulatd and th numrical rult comard to xrimntal rult obtaind in th laboratory. Sinc th natural watr contnt in th lo rofil i xctd to chang du to aonal ffct, th ffct of initial watr contnt on lo bhaviour i invtigatd on th 2.2 m aml. Thr diffrnt watr contnt ar invtigatd mor rcily: 18% (natural watr contnt), 23% and 29%. Th initial watr contnt wr obtaind in th laboratory by adding watr uing a wt filtr ar. All aml wr firt conolidatd with a confining tr of 25 kpa. Thn th ingl or multi-lvl cyclic loading with a frquncy of.5 Hz wr alid uing a cyclic triaxial cll dcribd by Cui t al. (27). Thr aml with th abov watr contnt (aumd to b contant during th whol tt) ar firt cyclically hard to a dviator valu of 15 kpa. Subquntly, vral cycl of loading and unloading at diffrnt lvl of dviator tr ar rformd. At ach lvl, th ak dviatoric tr incra by 15 kpa and ach lvl of loading run 1 cycl until th aml rach failur. Th comarion of rult btwn xrimnt and modl rdiction i dictd in Figur 7 in trm of axial tr v. numbr of cycl. Th modl aramtr ud ar litd in Tabl 1. Figur 7 alo rnt th ffct of th account for bonding and it damag in th imulation. A xctd, th modl i abl to rroduc volumtric train 1

11 accumulation with th load cycl. Furthrmor, th conidration of bond damag in th modl giv much bttr imulation rult, cially for ca (a) (w = 18%) and ca (b) (w = 23%). 5 Concluion In thi ar, a modl for dcribing th mchanical and hydraulic bhaviour of cmntd unaturatd lo i rntd. Thi oil i a tyical homognou yllowih-gry, orou calcarou lo, mainly comod of quartz and fldar with om clay. SEM obrvation how th rnc of larg aggrgat with aociatd intr-aggrgat or. Th rnc of clay latlt and calcium carbonat may act a bond to cmnt th olid grain. Thi oil i charactrizd by low laticity, low natural dgr of aturation, low clay fraction, and rlativly high calcium carbonat contnt. On th bai of th bounding urfac modl, damag thory and unaturatd oil mchanic, an latolatic modl which includ tructur damag for unaturatd lo undr cyclic loading ha bn laboratd. Th chon law for bond dgradation link tructur damag to th accumulation of train. Th BBM modl wa conidrd for th uction ffct. Multi-lvl cyclic triaxial tt wr imulatd to vrify th rdiction of th modl. Diffrnt watr contnt wr conidrd. Th outcom i ncouraging a th modl m to b abl to rdict th bhaviour of unaturatd cmntd oil undr cyclic loading. Th currnt contitutiv modl for unaturatd cmntd oil i till comlicatd, with many aramtr ndd to b dtrmind by variou xrimnt. In th futur, focu hould b ut on th imlification of th cmnt damag art of thi modl. Furthrmor, th bounding urfac thory hould b modifid to rflct th hytrtic bhaviour of oil undr cyclic loading. 11

12 Rfrnc Alono E.E., Gn A. & Joa A. A contitutiv modl for artially aturatd oil. Géotchniqu 199; 4(3): Bardn L., Mc Gown A. & Collin K. Th colla mchanim in artly aturatd oil. Eng. Gol. 173; 7:49-6. Baudt B. & Stallbra S.A contitutiv modl for tructurd clay. Géotchniqu 24; 54(4): Burghignoli A., Miliziano S., & Soccodato F.M. Th ffct of bond dgradation in cmntd clayy oil. Proc. Sym. on Gotchnical Enginring of Hard Soil - Soft Rock, Balkma; Carol I., Rizzi E. & Willam K. On th formulation of aniotroic latic dgradation. I. Thory bad on a udo-logarithmic damag tnor rat. Intrnational Journal of Solid and Structur 21; 38(4): Chai H.Y., Cui Y.J. & Lu Y.F. Simulation of lo bhavior undr cyclic loading. Chin Journal of Rock Mchanic and Enginring 25; 24(23): Cui Y.J. & Dlag P. Yilding and latic bhaviour of an unaturatd comactd ilt. Géotchniqu 1996; 46(2): Cui YJ, Tang AM, Marcial D, Trrau J-M, Marchadir G, Boulay X. U of a diffrntial rur tranducr for th monitoring of oil volum chang in cyclic triaxial tt on unaturatd oil. Journal of Gotchnical Tting 27;3(3): Dafalia Y.F. & Hrrmann L.R. Bounding urfac formulation of oil laticity. In: Soil Mchanic-Tranint and Cyclic Load, Pand, G.N. and Zinkiwicz, O.C., d. Wily; 1982; Dlag P., Howat M., Cui Y.J., Th rlationhi btwn uction and wlling rorti in a havily comactd unaturatd clay. Enginring Gology 1998, 5(1-2): Garitt B., Vaunat J. & Gn A. A contitutiv modl that incororat th ffct of uction in th cmntd gological matrial. Unaturatd Soil 26 - Proc. of th Fourth Intrnational Confrnc on Unaturatd Soil, ASCE; 26; Gn A. & Nova N. Conctual ba for a contitutiv modl for bondd oil and wak rock. Proc. Sym. on Gotchnical Enginring of Hard Soil - Soft Rock, Balkma; Grabowka-Olzwka B. SEM analyi of microtructur of lo doit. Bull. Int. A. Eng. Gol. 1975; 11: Khalili N., Habt M.A. & Valliaan S. A bounding urfac modl for granular oil ubjct to cyclic loading. In: Comutational Mchanic, WCCM VI in Conjunction with APCOM 4; 24. Lrouil S. & Barboa A. Combind ffct of fabric, bonding and artial aturation on yilding of oil. Proc. Aian Conf. On Unaturatd Soil 2; Oiov V. I. & Sokolov V.N. Factor and mchanim of lo collaibility. In: Gni and Prorti of Collaibl Soil; E. Drbyhir t al. d; Kluwr Acadmic Publihr; 1995; Pator M., Zinkiwicz O.C. & Lung K.H. Siml modl for tranint oil loading in arthquak analyi (II):non-aociativ modl for and. Intrnational Journal for Numrical and Analytical Mthod in Gomchanic 1985; 9: Prira JM, Wong H, Dubujt P, Dangla P. Adatation of xiting bhaviour modl to unaturatd tat: Adatation to CJS modl. Intrnational Journal For Numrical and Analytical Mthod In Gomchanic 25; 29(11): Sharma S.S. & Fahy M. Cyclic dformation charactritic of cmntd calcarou oil. Dformation charactritic of Gomatrial, ISLyon-3. Lyon, Franc: Balkma; 23; 12

13 Sharma S.S. & Fahy M. Dgradation of Stiffn of Cmntd Calcarou Soil in Cyclic Triaxial Tt. Journal of Gotchnical and Gonvironmntal Enginring 23; 129(7): van Gnuchtn M.Th. A clod-form quation for rdicting th hydraulic conductivity of unaturatd oil. Soil Sci. Soc. Am. J. 198; (44): Vaunat J. & Gn A. Bond dgradation and irrvribl train in oft argillacou rock. Proc. of th 12th Panamrican Confrnc on Soil Mchanic and Gotchnical Enginring; 23. Whlr S.J. & Sivakumar V. An lato-latic critical tat framwork for unaturatd oil. Géotchniqu 1995; 45(1): Whlr S.J. Incluion of cific watr volum within an lato-latic modl for unaturatd oil. Canadian Gotchnical Journal 1996; 33(1): Zinkiwicz O.C.,Lung K.H. & Pator M. Siml modl for tranint oil loading in arthquak analyi (I): baic modl and it alication. Intrnational Journal for Numrical and Analytical Mthod in Gomchanic 1985; 9:

14 Lit of Tabl Tabl 1. Paramtr ud in imulation of th cyclic triaxial har tt Lit of Figur Figur 1. Grain iz ditribution curv of th tudid lo. Figur 2. SEM obrvation of aml from a dth of 2.2m; a) Intact aml; b) Damagd aml. Figur 3. Watr rtntion curv of th tudid lo. Figur 4. Schmatic arrangmnt of oil tructur (aftr Garitt t al., 26) Figur 5. Thr-dimnional viw of yild urfac in (,q,) tr ac Figur 6. Maing rul in bounding urfac modl Figur 7. Multi-lvl cyclic triaxial tt for aml with 3 diffrnt watr contnt: a) w=23%; b) w=18%; c) w=29% 14

15 Prcnt finr by ma, % Equivalnt diamtr, µm Figur 1. Grain iz ditribution curv of th tudid lo. a) b) Figur 2. SEM obrvation of aml from a dth of 2.2m; a) Intact aml; b) Damagd aml. 15

16 1 Suction (MPa) Watr contnt (%) Figur 3. Watr rtntion curv of th tudid lo: xrimntal curv (ymbol) and curv fittd uing van Gnuchtn modl (continuou lin). V t =V m +V v +V b Matrix, V Bond, V b Void, V v Figur 4. Schmatic arrangmnt of oil tructur (aftr Garitt t al., 26) 16

17 q LC bc o * Figur 5. Thr-dimnional viw of yild urfac in (,q,) tr ac q q P OL ( ) o P(, q ) δ δ 1 η n (, ) P q I I I ( ) Figur 6. Maing rul in bounding urfac modl 17

18 Axial train, % Thi modl, with bond Thi modl, without bond Exrimnt Modl without bond w=18% Modl with bond Cycl numbr Exrimntal data a) 4 3 Thi modl, with bond Thi modl, without Modl bond without bond Exrimnt Modl with bond w=23% Axial train, % 2 1 Exrimntal data Cycl numbr b) 18

19 Thi modl, with bond Thi modl, without bond Modl without bond Exrimnt 2.5 w=29% Modl with bond Axial train, % Exrimntal data Cycl numbr c) Figur 7. Multi-lvl cyclic triaxial tt for aml with 3 diffrnt watr contnt: a) w=23%; b) w=18%; c) w=29% 19

20 Tabl 1. Paramtr ud in imulation of th cyclic triaxial har tt λ κ m u m M g M f α g α f β β r L r U χ =χ 1 β k α =k β u b r β k κ K b bc q bc c * H U (kpa) (kpa) (kpa) (kpa) (kpa) (kpa) (MPa) n m β Sr