MECHANICAL MODELING OF CHEMO-MECHANICAL COUPLING BEHAVIOR OF LEACHED CONCRETE

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1 RILEM Inernaional Syoiu on Conree Moelling, 1-14 Oober 14, Beijing, China MECHANICAL MODELING OF CHEMO-MECHANICAL COUPLING BEHAVIOR OF LEACHED CONCRETE Bei Huang(1,3), Chunxiang Qian(), Shao Jianfu(3) (1) Shool of aerial Siene an Engineering, Nanjing Teh Univeriy,China () Shool of aerial Siene an Engineering, Souhea Univeriy,China (3) Laboraoire e Méanique e Lille, Polyeh-Lille, Frane Abra Bae on he analyi an exerienal reul obaine fro riaxial rain an re relaionhi of leahe onree, an elaolai oniuive oel oule wih leahing aage wa forulae. Two aage araeer an, whih refer o he ehanial an heial aage reeively, were rooe in hi aer. The lai ehani wa relae o eviaori hearing an he leahing aage wa ienifie a relaive variaion of oroiy. Boh elai an lai roerie were effe by leahing aage. Fro he iulaing reul, i eee ha he rooe oel wa able o eribe he ain feaure of ehanial behavior of eeniiou aerial in oun an egrae ae. 1. INTRODUCTION The leahing of aliu an be a aer of onern for he urabiliy of onree ruure. I inreae he oroiy [1-3] of he urfae layer, an erienally affe he reiane of he aerial o ehanial loa [4-7]. The leahing of aliu ay have a negaive influene on he long-er urabiliy of variou onree ruure. For inane, hi henoenon i riial in regar wih he urabiliy of nulear wae onainen for whih he require ervie life range fro a few hunre year o everal houan year. Conree i wiely ue in any engineering aliaion, whih are ofen uffere by he environenal aggreive oniion, uh a rain, flowing waer an ai flui. The long er loaing aaiy of hee ruure houl be an iue o be onerne. Many exerienal inveigaion an analyial an nuerial uie have been evoe o urabiliy analyi of een-bae aerial [9-13]. Conree i ooie aerial, onaining ifferen ale level of rou. So he aage an lai roerie of hi aerial i olex. In hi aer, an elaolai oniuive oel oule wih leahing aage i fore o eribe he ehanial roery of he leahe onree. 55

2 RILEM Inernaional Syoiu on Conree Moelling, 1-14 Oober 14, Beijing, China. OUTLINE OF THE GOVERNING EQUATION.1 Coniuive oel Bae on he exerienal inveigaion iue in referene [8], a new elaolai aage oel i rooe o ake ino aoun he ifferen ehani iue above. Two kin of aage houl be efine a follow: one i ehanial aage () ue o irorak in onree arix, anoher i leahing aage () ue o ioluion of aliu ion in onree arix leaing o inreae of he oroiy of aerial. Furherore, he ehai i u on he ifferen failure ehani in enile an oreive re ae. Wih auion of all rain, he oal rain enor i eooe he elai ar an lai ar: e (1) A enione above, we aue an ioroi behavior of een-bae aerial. The heroynai oenial an be exree a follow: e 1 (,,, ) = ( ) : C (, ):( ) (,, ) () = = = = = The fourh orer enor C (, ) i he elai iffne enor of aage aerial, he funion rereen he loke lai energy in lai harening of aage aerial, enoe he inernal variable of lai harening. The anar erivaion of he heroynai oenial yiel he ae equaion: = C(, ) : ( ) = e In he ae of ioroi aerial, following Hill noaion, he effeive elai iffne enor of aage aerial rereen in he general for: C(, ) (, ) K 3 k(, ) J (4) (, ) an k(, ) rereen he hear oulu an he bulk oulu of aage aerial reeively. The wo ioroi yeri forh orer enor K J 1 1 =, = -, 3 K I J I ijkl ik jl il jk I i he yeri fourh orer uni enor. enoe he eon orer uni enor. (3) an J are efine a: The inrini ehanial iiaion u verify he following funaenal inequaliy: : Y Finally, he rae for of he oniuive equaion i wrien a: (5) (6) 56

3 RILEM Inernaional Syoiu on Conree Moelling, 1-14 Oober 14, Beijing, China ' ' C(, ) : ( - ) C (, ) : ( - ) C (, ) : ( - ) C ' (, ) an ' C (, ) are he erivaion of he elai iffne enor wih ree o he ehanial aage an leahing aage reeively.. Daage oel..1 Mehanial aage The ehanial aage variable i aue o be ivie ino wo alar aage variable: one for enion an anoher for oreion : The weigh an are eerine a funion of he oal re enor : (7) (8) 1., (9) an rereen, reeively, he nor of alie re enor an oiive one of he alie re enor. Uner uniaixal oreive oniion, an 1.. On he oher han, in uniaxial enion e, 1. an. The oreive aage rierion i a funion of he generalize lai hear rain : 1 ex B Y Y, The enile aage rierion i a funion of he equivalen oiive ain ε eq : 1 ex B Y Y, The wo onan B an B onrol reeively he evoluion of enile an oreive ar of he aage. They an be eerine reeively uing an uniaxial oreion e an an uniaxial enile e. In orer o alulae he aage evoluion rae wih ree o he lai iorion an equivalen rain, a raial loaing i aue: Then, he rae for of general aage variable an be given: B B, ex[ ( - )] ex[ ( - )] (13) eq B eq Y, B Y, The rae fro of oniuive equaion beoe in he aben of laiiy evoluion: (1) (11) (1) 57

4 RILEM Inernaional Syoiu on Conree Moelling, 1-14 Oober 14, Beijing, China C e :, B ex[ B ( Y )] C e e eq, : 1 eq, C C.. Leahing aage A enione above, leahing inreae he oroiy of he onree arix. The leahing aage an be efine a follow: ( ) ( ) ( ) r (16) () an r are oroiy of leahe onree an oun onree reeively. Aoring o Gérar aliu a balane equaion [14], an be eribe a follow: M S Ca o oli where M an are he average olar a an eniy of aliu in he keleon. So enoe he oal aoun of aliu in oli keleon, Caoli i he aliu onenraion in oli keleon..3 Plai oel In orer o eribe ehanial behavior of onree in a large of ree, i i neeary o efine a nonlinear urve yiel urfae. The lai Mohr-Coulob or Druker-Prager ye rieria are no uiable. Bae on exerienal aa on yial onree [15], he quarai fro rooe by Pieruzzak i aae here o eribe he failure urfae of he onree. q q f 1-3 g f g f f (18) The araeer 1, an 3 are ue o eerine he be fi of failure urfae wih r 3 ree o exerienal aa. -, q 3J, g efine he eeneny 3 of he failure urfae on he Loe angle. For he ake of iliiy, we ake g =1. By aking a lai harening law, he yiel urfae an be eribe by he following funional fro: (14) (15) (17) ( 3 / f) f q - (,, ) g( ), (19) The alar value funion efine he lai harening law of aerial. Bae on he exerienal aa fro riaxial oreion e, he following relaion i eerine: (1 )[1. 1. ] b e () 58

5 RILEM Inernaional Syoiu on Conree Moelling, 1-14 Oober 14, Beijing, China The araeer b i onan an onrol lai harening rae, i he iniial yiel value of aerial. There i a raniion fro lai oreibiliy o ilaany. A nonaoiae lai flow rule i ue o eribe hi raniion. The lai oenial rooe by Pieruzzak fulfil uh a requireen an hen i aae here I Q q g I ln (1) I where I efine he inereion of he lai oenial urfae wih he I axi. The Q raniion fro oreibiliy o ilaany our a he oin =. I i aue ha he q raniion oin an be aroahe by a linear relaion. f- = q- g( ) I= () The araeer i he loe of he raniion line beween he oreibiliy an ilaany. Thi i one by alying he lai an aage onien oniion in a oule ye: f f f f By inrouing he oniuive equaion, lai harening law an aage rierion, one obain he ye o be olve o eerine he lai ulilier an inreen of aage: B Q B eq - ex( B ) ex( B eq ) f ' e f f ' e f - ( C (, ) : ) - ( C (, ) : ) f ' Q f Q f ' : C (, ) : - : C (, ) : 3. NUMERICAL SIMULATIONS The rooe elaolai oel aking ino aoun leahing egraaion i ileene ino he finie eleen oe THMPASA eveloe a LML. Thi oe ha been eveloe for nuerial oeling of oule hero-hyro-ehanial evoluion roble in orou eia. All araeer of rooe oel an be eerine by uing a erie of onvenional raixial oreion e erfore a ifferen onfining reure. A he beginning of he ieraion, he e of ae an inernal variable are known a n,,,,,. (3) (4) n n n n en n 59

6 RILEM Inernaional Syoiu on Conree Moelling, 1-14 Oober 14, Beijing, China Given inreen of oal rain an leahing aage o n1 n n1 n1 n n1 ha = +,.Uae he elai an lai roerie wih he urren value of leahing aage. Chek he yiel funion an aage funion, eq, n 1 n n ( n),,, f. If =, f, he elai reiion i aken a he reel oluion. Ele, alulae inreen of lai rain aoring o loaing ah uing Eq.(4). Uing he oniuive Eq.(7), he aiion inreen of re i oue; he urren value of re i hen uae. La exi an en bak he uae value o global ye. Figure 1 howe he oarion beween oel reiion an exerienal ae of onree wih ifferen leahing aage uner riaxial oreive rengh. In an overall way, here i a goo agreeen beween he iulaion an e ae. The rooe oel orrely rei he ain feaure of ehanial behavior of leahe onree. (MPa) D1 oun 5 4 oun alulae exerien D1 D 3 D D3 D3 1 P=3MPa 3 /(%) /(%) Figure 1 : Coaring he eing an alulaion reul of riaxial re-rain relaion of leahe onree 4. CONCLUSION In hi aer, he forulaion of an elaolai oel for leahe onree uner oreive-oinae ree i reene. Coare he ehanial reone of onree wih oun an egrae ale, he effe of leahing aage on ehanial behavior of onree have been aken ino aoun. Boh elai an lai roerie are affee by leahing aage. The rooe oel i alie o iulae yial laboraory e. I ee ha he rooe oel i able o eribe he ain feaure of ehanial behavior of onree in oun an leahing egrae ae. 51

7 RILEM Inernaional Syoiu on Conree Moelling, 1-14 Oober 14, Beijing, China REFERENCES [1] Kazuko, H. an Maahio, S., 'Change in ore ruure an ooiion of harene een ae uring he roe of ioluion ', Ce. Conr. Re, 35(5) [] Mainguy, M. an Ul F.J., 'Siilariy roerie of eineralizaion an egraaion of rak orou aerial ', In J Sol Sru. 38(1) [3] Jeffrey, J., Thoa, J., an Chen, J. 'Effe of ealifiaion on he iroruure an urfae area of een an rialiu iliae ae ', Ce. Conr. Re. 34(4): [4] Chriohe,C. an Raoul, F., 'Effe of he leahing of aliu hyroxie fro een ae on ehanial an hyial roerie ', Ce.Conr,Re. 7(3) (1997) [5] Chriohe,C. an Raoul, F.,'Leahing of boh aliu hyroxie an C-S-H fro een ae: oeling he ehanial behavior ', Ce.Conr.Re. 8(6) (1996) [6] Care, C. an Franoi, R., 'Effe on he leahing of aliu hyroxie fro een ae on ehanial roerie ', Ce.Conr.Re. 7(4) (1997) [7] Fauon, P. an LeBeo, P., 'Leahing of een: uy of he urfae layer ', Ce. Conr. Re, 6(11) (1996) [8] Huang, B. an Chunxiang, Q., 'Exerien uy of heo-ehanial ouling behavior of leahe onree ',Conr. Buil. Maer.5(11) [9] Heua, F. H. an Ul, F. J., 'Mehanial roerie of aliu leahe een ae: riaxial re ae an he influene of ore reure', Ce. Conr. Re. 13 (1) [1] Heua, F. H. an Ul, F. J., 'Porolai roerie of aliu-leahe een-bae aerial', Ce. Conr. Re. 8 (3) [11] Xie, S.Y., Shao, J.F. an Xu.,W. Y., 'Influene of heial egraaion on ehanial behavior of a lieone', In. J. Rok. Meh. Min. Si. 48 (11) [1] Yura, I., Xie, S.Y. an Burlion, N., 'Influene of heial egraaion on ehanial behavior of a eroleu een ae', Ce.Conr.Re. 41 (11) [13] Xie, S.Y., Shao, J.F. an Burlion, N., 'Exerienal uy of ehanial behavior of een ae uner oreive re an heial egraaion', Ce. Conr. Re. 38 (8) [14] Bellégo, C.L., Gérar, B. an Cabo,G.P., 'Coule ehanial an heial aage in aliu leahe eeniiou rurue', J. Eng. Meh. 19(3) (3) [15] Pieruzzak, S., Jiang, J. an Mirza, F. A., 'An elaolai oniuive oel for onree ', In. J.Sol. Sr. 4(7) (1988)