Experimental investigation of compressive concrete elements confined with shape memory Ni-Ti wires

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1 Fratur Mhani Conrt Conrt Strutur - Amnt, Durability, Monitoring Rtritting Conrt Strutur- B. H. Oh, t al. (d) 200 Kora Conrt Intitut, Soul, ISBN Exprimntal invtigation ompriv onrt lmnt onfind ith hap mmory Ni-Ti ir Z. Mirza M.S Studnt, Dpartmnt Civil Enginring, Univrity Thran, Iran M. Motavalli Pror, Had nginring trutur laboratory EMPA, Si M. Shkarhi Aoiat Pror, Thnial Faulty, Univrity Thran, Iran ABSTRACT: Strngning olumn i grat importan in rpair rtrit onrt trutur in failur a olumn ha riou onqun for trutural tability. Strngning onrt ylindr ith hap mmory alloy to improv ir dutility ompriv bhavior i narly a n ida. Aording to thi approah, upon xtrnal hating, a martnit-to-autnit pha tranformation tak pla matrial undrgo larg hrinkag train. Thi train nrgy an b ud to gnrat a ignifiant prtring for in onrt. In thi rarh axial loading tt r ondutd on RC onrt ylindr trngnd by prtring SMA ir, aftr tranforming from martnit to autnit pha by atuating m ignifiant rult r obtaind onrning tr-train urv, maximum tr, pak train initial young modulu (lati modulu). Th xprimntal rult tt data ould b an initial tp toard invtigation hap mmory ir for purpo ir appliation in trngning onrt olumn. INTRODOCTION Digning mor porful trutur trngning xiting building in diffrnt ondition, lad nginr to u flxibl, adaptabl our mart ytm. Shap mmory alloy (SMA) a a kind mart matrial, hav bn kn in rnt dad hav t bn ud muh in building indutry until rar rntly. Rarh on mart or intllignt matrial ytm ha bn going on for ovr a dad. But it ha bn mainly in fild mhani nginring or foud on pa trutur. Rntly tudy mart matrial to apply to ivil nginring ha bom a hot iu. To lit om tudi, halth monitoring mmbr, lf-rpairing, atuating trutural mmbr ar intrt. Th aim to mak trutur mor highly haratrizd by uing n thlogy to mak trutural prforman highr by uing mart matrial. W ar tudying poibility applying mart matrial to ivil trutur from vipoint trngning rgular ompriv mmbr in rinford onrt trutur by uing hap mmory ir a a kind mart matrial. It i ll kn that both trngth dutility onrt ompriv mmbr an b gratly improvd by onfinmnt uing om kind matrial. Th firt invtigation on ativ onfinmnt prforman r don by applying latral onfinmnt uing a ontant hydrauli prur a an ativ onfinmnt kpt ontant during loading hitory []. Ativ onfining onrt ylindr or rinford onrt olumn uing martniti, Ti-49.7Ni (at %), or autniti, Ti-50.3Ni (at %), hap-mmory-alloy ir i narly a n ida that hav bn propod ttd in thi rarh. Th rovry tr SMA i utilizd to apply prtring for in piral, hih, in turn appli larg ativ onfining prur on olumn, ida thi mthod ha bn propod in 2005 by Jank t all. [2] for firt tim. 2 THEORETICAL BACKGROUND Confinmnt an b atgorizd into to main typ ativ paiv onfinmnt. For onrt olumn ith tl rinformnt or xtrnal jakt, natur onfinmnt i paiv typ. In or ord, onfining prur i indud by tranvr dilation onrt or Poion fft. In om a paiv onfinmnt, an initial ativ onfining prur may

2 alo J D ( b h, prnt, T ) h for intan by injting an xpaniv grout btn a olumn an xtrnal () jakt. Th Hovr, proportionality indud fiint ativ D(h,T) prur i alld i mall moitur rlativ prmability to additional i paiv a nlinar onfinmnt funtion ngagd rlativ by humidity onrt h dilation tmpratur [3]. T (Bažant & Najjar Th hitory 972). Th onfinmnt moitur ma go balan bak rquir to a arly that a variation 903, a in A. tim Conidèr atr dribd ma pr onfinmnt volum fft onrt on (atr onrt ontnt olumn. ) b qual In to unit 960, divrgn Fr moitur Chinn [4], flux a J ll a Martin [5], xamind onrt ylindr hih r latrally prtrd in ir tudy y ud thin ontinuou ir. JThy hod that prtring ir (2) t dlayd dviation ylindr' axial loaddformation Th atr urv ontnt from an b lati xprd bhaviour a urv. um In or vaporabl ord, atr lati rang a xtndd. (apillary atr, atr Thy vapor, alo rportd adorbd that, atr) in ir xprimnt, n-vaporabl amount (hmially prtr bound) had atr only a light influn on n (Mill 966, axial Pantazopoulo apaity. & Th Mill ratio 995). initial It i onfining raonabl prur aud by prtr Ri to aum that vaporabl to atr unfind i a funtion onrt ompriv trngth f0 rlativ humidity, h, dgr a btn hydration, , In dgr ontrat, ilia xtniv fum ration, rarh Gardnr t al.[6], i.. (h,, ) hod ag-dpndnt that prtring orption/dorption ontinuou piral onfining iorm ir (Norling an Mjonll ignifiantly 997). inra Undr thi aumption load-baring apaity, by ubtituting vn for Equation olumn undr into Equation ntri 2 load. on Hr, ratio Ri obtain to f0 rangd from 0.2 to rar high valu Or tudi prtrd onfinmnt inlud uggtion for thnial implmntation. h Krtulovi_Opara Thidmann + ( D h) & + & + & n (3) [7] ud h t pot-tniond h hap-mmory alloy (SMA) ir in ordr to inra axial apaity rlativly mall ompat onrt ylindr. Thy hr /h i lop orption/dorption uggtd that latral prtr rdu mirorak formation, hih orrpondd ith prvi- iorm (alo alld moitur apaity). Th govrning quation (Equation 3) mut b ompltd ou by appropriat rult tri-axial boundary tting initial [8]. ondition. For Th rlation a btn ativ onfinmnt amount gnral vaporabl olution atr a ylindr rlativ humidity ubjtd i to alld a dtrminat adorption ytm iorm radial if prur maurd ith axial inraing har rlativity ovr urvd humidity urfa dorption a firt analyzd iorm by Filon in [9,0], oppoit In ordr a. Nglting to alulat ir onfining diffrn prur, (Xi t al. 994), tnil in trngth folloing, orption diffrnt iorm matrial ill ar b ndd. ud ith For rfrn ultimat to both trngth orption rapping dorption matrial, ondition. Th Equation By from ay, Xiao if t al. hytri [,2] i ud: moitur iorm ould b takn into aount, to diffrnt rlation, t vaporabl atr v rlativ humidity, mut () b u ud aording to ign variation () a rlativity humidity. Th hap orption u hr: iorm for i HPC onfinmnt i inflund trngth, by many paramtr, i ultimat trngth jakt, t i thikn pially tho that influn xtnt rat hmial ration, in turn, dtrmin por rapping matrial, a i radiu olumn. In ativ onfinmnt important variabl in ordr to trutur por iz ditribution (atr-to-mnt ratio, mnt hmial ompoition, SF ontnt, dtrmin uring tim bhavior mthod, tmpratur, a onfind mix onrt additiv, olumn t.). i In latral litratur onfining variou prur formulation du to an ation found to drib jakt. Th orption onfining iorm prur rmal i t b ontant onrt along (Xi t al. radial 994). Hovr, axial in ax prnt olumn papr mi-mpirial it i qualitativly xprion aumd propod to hav it by Norling Mjornll (997) i adoptd bau it lor xpliitly valu aount at mid-tion for volution btn hydration ti. Th initial ration onfining SF prur ontnt. on Thi onrt orption aud iorm by rad i prtr i alulatd uing Equation (2)[3]: T (2) i ( h,, ) G (, ) + S. a 0( g ) h (4) ith T bing man tnil for during pha tranformation SMA piral. 0( g Nominal ) ht i dird tnil for K (, S ) i pith piral onfinmnt a i ylindr radiu, S a ar mm 60 mm rptivly in thi rarh, Th ratio hr to fo for prtrd pimn in thi rarh phyially a btn bound (adorbd) atr ond i firt trm (gl iorm) rprnt trm (apillary iorm) rprnt apillary atr. Thi xprion i valid only for lo ontnt SF. Th fiint G rprnt amount atr pr unit volum hld in gl por at 00% rlativ humidity, it an b xprd (Norling Mjornll 997) a G (, ) k + k vg vg Figur.Cylindr loadd by axial prur onfind by ativ latral prur. hr k vg k vg ar matrial paramtr. From maximum amount atr pr unit volum that an fill all por (both apillary por gl por), on 3 an EXPERIMENTAL alulat K PROGRAM a on obtain 3. Matrial g 3.. Conrt 0.88 or G 0 Th matrial onumd in thi tudy for ating unfind (6) K (, ) onrt ylindr r typial kind g Portl mnt typ I-425, aggrgat ith maximum iz 2.5 mm mixtur proportion r onidrd Th matrial for rmal paramtr trngth. k Th mixtur proportion b alibratd xprimntal by fitting xprimntal pimn ar data prntd rlvant in to vg k vg g an Tabl fr (vaporabl) I. For obtaining atr rmal ontnt trngth in onrt, mnt variou ontnt ag (Di r Luzio 307kg/m & Cuati b). / ratio a 0.6 at rptivly. Th atr ontnt in mixtur r dignd a to rah a onitnt orkability a lump 2.2 Tmpratur btn 70 volution mm to 90 mm. Not Cylindr that, at ith arly 20 ag, mm in hight hmial 57.6 ration mm diamtr aoiatd r ith ud mnt to dtrmin hydration ompriv SF ration bhaviour ar xormi, unfind tmpratur onrt fild or i t uniform alo to provid for n-adiabati or ith ytm diffrnt vn trngth if nvironmntal ndd for jakting. tmpratur Th i mixing ontant. produr Hat ondution for onrt an or b a dribd folloing: onrt, mnt at lat for aggrgat tmpratur r t addd xding 00 C mixd, n (Bažant & onrt Kaplan mixtur 996), a by atd Fourir in la, mold. hih rad Spimn r n ovrd ith a t burlap loth, r lft in form for day. q Aftr λ T dmolding, all pimn r urd in (7) atr at room tmpratur for 28 day. Th pimn ndd for rapping r lft in laboratory hr q for i ar hat 7 day, flux, hil T i or pimn abolut r tmpratur, appd ttd λ i immdiatly. hat ondutivity; in thi (5) Proding FraMCoS-7, May 23-28, 200

3 Tabl. Formulation onrt mix ud for omprion tt. Grain iz Siz ditribution kg/m mm 50% mm 50% 940 Cmnt CEM I Watr Watr mnt ratio Apparnt dnity Ni-Ti ir Th SMA ir r upplid by Pha Tranformation Lab, Shool Mtallurgy Matrial Enginring, univrity Thran. Aording to upplir, hmial ompoition ir a 50.2% nikl 49.8 % titanium. Th ir tion a quar in iz mm mm. Th onvntional vauum ar-mlting thniqu ith tungtn ltrod on a atr-oold oppr ruibl a mployd to prpar alloy. Aftr vral rmlting for homognization, ingot a hot forgd n homognizd at 273 K for 2 hr. A rod mill a ud for hot rolling at 273 K from tion iz 0 mm 0 mm to mm mm through 24 pa. Th ir a old-rolld to obtain rdution prntag 20. For hap tting, ir a fatnd around ylindr ith 5.4 mm diamtr n annald at 773 K for 30 min. Tabl 2. Matrial proprti ud SMA-ir (NiTi ir, diamtr about mm) obtaind from tnil tt. Paramtr Valu Martnit pha T _25 _C ultimat trngth 800 MPa Elati modulu 25,000 MPa Strain at yild trngth % Autnit pha T _90 _C ultimat trngth 800 MPa Elati modulu 40,000 MPa Strain at yild trngth 2.5 % 3.2 Prparing ampl A SMA ir r tttd a a hap piral, r rappd around onrt or(fig. 2). In ordr to fix piral around or maintain ir tnion, tl anhoring lamp r mountd at to nd onrt ylindr Th lamp r 20 mm high 2 mm thik. 3.3 Exprimntal produr All pimn r ttd by MTS univral mahin a data aquiition ytm. Loading a applid motonially in a diplamnt ontrol mod ith a ontant rat 0.06 mm/, hih orrpond to a train rat pr min. Th load a applid to ntir ro tion, inluding onrt or SMA rapping. Tabl 3. Sampl pifiation. J ) D ( h, T h SMA Spimn Compriv Strngth (MPa) rappd Th proportionality fiint D(h,T) Z-A moitur 20 prmability it i a nlina Z-B rlativ humidity h tmpratur Z2-A & Najjar 20972). Th moitur ma balan Z2-B y that variation in tim atr ma Z3-A Z3-B volum 25 onrt (atr ontnt y ) b q Z5-A divrgn moitur flux J 25 Z5-B Y Z7-A 25 J Z7-B t Y Th ambld omputr data aquiition ytm a ud to rord Th data. atr Th ontnt aquird an data b xprd inludd applid axial load, vaporabl P atr axial dforma- (apillary a a tion onrt, Th vapor, valu adorbd diplamnt atr) btn n- loading plat (hmially r ud for bound) obtaining atr omplt n (Mil tr-train urv. Pantazopoulo Th pimn & Mill r 995). loadd It al-imot up to train aum at hih that all vaporabl pimn atr i a fu ra r tnd. Figur rlativ 3 ho humidity, tt h, t dgr up ith hydration a onrt ylindr undr dgr ompriv ilia fum loading. ration,, i.. ag-dpndnt orption/dorption (Norling Mjonll 997). Undr thi aum by ubtituting Equation into Equati obtain h + ( D h) h t h hr /h i lop orption/ iorm (alo alld moitur apa govrning quation (Equation 3) mut b by appropriat boundary initial onditi Th rlation btn amount atr rlativ humidity i alld iorm if maurd ith inraing humidity dorption iorm in th a. Nglting ir diffrn (Xi t al. folloing, orption iorm ill b rfrn to both orption dorption By ay, if hytri iorm ould b takn into aount, to Figur 2. SMA ir rlation, rappd vaporabl around onrt atr v or rlativ humi anhord ith tl lamp. b ud aording to ign varia rlativity humidity. Th hap iorm for HPC i inflund by many p 4 EXPERIMENTAL pially RESULTS tho AND that influn xtnt DISCUSSIONS hmial ration, in turn, dtrm trutur por iz ditribution (atrratio, axial mnt train hmial urvatur ompoition, on- SF Axial tr vru find onrt ar uring hon tim in Figur mthod, 5(a- ) tmpratur, for pimn ith to diffrnt t.). In unfind litratur onrt variou trngth. formulatio mix Th avrag axial found tr-train to drib rlationhip orption that obtaind for unfind onrt ylindr ar alo iorm hon onrt (Xi t al. 994). Hovr, in th papr mi-mpirial xprion pro Norling Mjornll (997) i adoptd b Proding FraMCoS-7, May 23-28, 200

4 J ) D ( h, T h () Th proportionality fiint D(h,T) i alld moitur prmability it i a nlinar funtion rlativ humidity h tmpratur T (Bažant & Najjar 972). Th moitur ma balan rquir that variation in tim atr ma pr unit volum onrt (atr ontnt ) b qual to divrgn moitur flux J t J (2) Th atr ontnt an b xprd a um vaporabl atr (apillary atr, atr vapor, adorbd atr) n-vaporabl (hmially bound) atr n (Mill 966, Pantazopoulo & Mill 995). It i raonabl to aum that vaporabl atr i a funtion rlativ Figur 3. humidity, (a) MTS univral h, dgr mahin, (b) hydration, Tt tup., dgr ilia fum ration,, i.. (h,, ) ag-dpndnt orption/dorption iorm (Norling Mjonll 997). Undr thi aumption by ubtituting Equation into Equation 2 on obtain h + h t ( D h) n (3) h hr /h i lop orption/dorption iorm (alo alld moitur apaity). Th govrning quation (Equation 3) mut b ompltd by appropriat boundary initial ondition. Th rlation btn amount vaporabl atr rlativ humidity i alld adorption Figur 4. Simplifid dformation martnit. iorm if maurd ith inraing rlativity humidity dorption iorm in oppoit in Figur 5. A hon in thi figur, mot intrting iu i big dformation SMA on- a. Nglting ir diffrn (Xi t al. 994), in folloing, orption iorm ill b ud ith find ylindr in omparion ith unfind rfrn to both orption dorption ondition. ampl, alo hon that initial portion By ay, if hytri moitur tr-train rpon onfind onrt i iorm ould b takn into aount, to diffrnt linar. Aftr ahiving unfind onrt rlation, vaporabl atr v rlativ humidity, mut trngth, axial tr axial train rlationhip b ud aording to ign variation mot pimn ho that tnd xhibitd rlativity humidity. Th hap orption an almot big linar dformtion ithout hang in iorm for HPC i inflund by many paramtr, tr, n a n inraing in tr a happnd pially tho that influn xtnt rat imilar to train linarly until firt ruptur in hmial ration, in turn, dtrmin por SMA piral. Suh bhavior onrt onfind in trutur por iz ditribution (atr-to-mnt uprlati matrial aftr xding unfind ratio, mnt hmial ompoition, SF ontnt, onrt trngth ha t bn rportd yt. Thi bhavior i almot imilar to tr-indud pha uring tim mthod, tmpratur, mix additiv, t.). In litratur variou formulation an b hang original Nitil hn loadd from a parnt martniti pha(fig. 4), on initial loading, found to drib orption iorm rmal onrt (Xi t al. 994). Hovr, in prnt matrial i fully autnit bhav in a linar papr mi-mpirial xprion propod by lati mannr. Hovr, at a train pr nt, Norling Mjornll (997) i adoptd bau it & xpliitly aount for volution hydration ration SF ontnt. Thi orption iorm rad ( h,, ) G (, ) + 0( g ) h 0( g ) h K (, ) (4) hr firt trm (gl iorm) rprnt phyially bound (adorbd) atr ond trm (apillary iorm) rprnt apillary atr. Thi xprion i valid only for lo ontnt SF. Th fiint G rprnt amount atr pr unit volum hld in gl por at 00% rlativ humidity, it an b xprd (Norling Mjornll 997) a r i a dpartur from linarity that mark initiation G (, ) martnit k + kformation. Th tranformation (5) vg vg pro i haratrizd by a platau rgion hr matrial ha a lo Young modulu xtnd, typially to a train 5 prnt, hr hr k vg k vg ar matrial paramtr. From maximum amount atr pr unit volum that an onfinmnt matrial i ompod fully dtinnd fill all por (both apillary por gl por), on martnit [4]. an alulat K By furr dformation a on obtain aftr firt ruptur in SMA piral, on about 6% axial train tr-train urvatur ho om drop 0 ri g ourrd, it G m that 0onfining prur a ontinud aftr drop inrad again aftr vry drop (6) K (, ) thi our vral 0tim, thi g mak om pot pak in urvatur. Rult hod that applying onfining prur uing Ni-Ti SMA ir Th improvd matrial paramtr ultimat ompriv k vg k vg trngth g an ultimat b alibratd train by fitting onrt xprimntal ylindr data rlvant at lat by to 200% fr (vaporabl) 500 %, rptivly. atr ontnt in onrt at variou ag (Di Luzio & Cuati 2009b) CONCLUSION Tmpratur volution Prtring Not that, at for arly in ag, in piral, did hmial t appli ration larg ativ aoiatd onfining ith prur mnt hydration olumn, SF bau ration ir ar xormi, a loally prtraind tmpratur fild did i t t apply uniform big ativ for n-adiabati onfinmnt ytm for, indd vn if Pot tnioning nvironmntal ha aud tmpratur paiv i ontant. onfinmnt Hat ondution furr nhanmnt dribd in axial in onrt, baring load, at lat thi for aud tmpratur inra t in an b tiffn, xding dutility 00 C (Bažant trngth & Kaplan ompriv 996), onrt Fourir or. la, Rult hih hod rad that applying onfin- by ing prur uing Ni-Ti SMA ir improvd ompriv q λ T trngth ultimat train onrt ylindr by 200% 500%, rptivly. (7) hr q i hat flux, T i abolut tmpratur, λ i hat ondutivity; in thi Proding FraMCoS-7, May 23-28, 200

5 J ) D ( h, T h Th proportionality fiint D(h,T) moitur prmability it i a nlina rlativ humidity h tmpratur & Najjar 972). Th moitur ma balan that variation in tim atr ma volum onrt (atr ontnt ) b q divrgn moitur flux J t J Th atr ontnt an b xprd a vaporabl atr (apillary a vapor, adorbd atr) n- (hmially bound) atr n (Mil Pantazopoulo & Mill 995). It i ra aum that vaporabl atr i a fu rlativ humidity, h, dgr hydration dgr ilia fum ration,, i.. ag-dpndnt orption/dorption (Norling Mjonll 997). Undr thi aum by ubtituting Equation into Equati obtain h h + ( D h) t h Th rult xprimntal ortial approah for axial tr-train onfinmnt prur an b ud in latral yli motoni bhaviour amnt olumn nrgy diipation, ridual tiffn olumn that i ativly onfind ith SMA piral ompar to unrtrittd or onfind olumn. hr /h i lop orption/ iorm (alo alld moitur apa govrning quation (Equation 3) mut b by appropriat boundary initial onditi Th rlation btn amount atr rlativ humidity i alld iorm if maurd ith inraing humidity dorption iorm in th a. Nglting ir diffrn (Xi t al. folloing, orption iorm ill b rfrn to both orption dorption By ay, if hytri iorm ould b takn into aount, to rlation, vaporabl (a) atr f 20 v Mpa rlativ humi b ud aording to ign varia rlativity humidity. Th hap iorm for HPC i inflund by many p ACKNOWLEDGEMENTS pially tho that influn xtnt hmial ration, in turn, dtrm Th author ould lik to thank Laboratory trutur por iz ditribution (atrratio, mnt hmial ompoition, SF Pha Tranformation at Shool Mtallurgy Matrial Enginring, univrity Thran, pially Dr M. Nili hi aitant Mr. H. Shahmir uring tim mthod, tmpratur, mix t.). In litratur variou formulatio for ir kind aitan. found to drib orption iorm onrt (Xi t al. 994). Hovr, in th papr mi-mpirial xprion pro Norling Mjornll (997) i adoptd b Figur 5. Axial tr-train urv unfind onfind ylindr for rfrn ylindr trngth (b,) f 25 Mpa. Proding FraMCoS-7, May 23-28, 200

6 REFERENCES J D ( h, T ) h () Eaton-Evan Th proportionality J, J M Duliu-Barton, fiint E G Littl, D(h,T) I i A Bron, alld Obrvation during mhanial tting Nitil, J. Mhanial prmability Enginring Sin, it Pro. i a IMhE nlinar Vol. funtion 222 Part moitur C rlativ humidity h tmpratur T (Bažant Fr & Najjar LJ, 972). Chinn Th J. Strngth moitur ma tiffn balan rquir pirally that prtrd variation onrt in ylindr. tim PCI J atr 962;7(3):55_62. ma pr unit Filon volum LNG. On onrt lati (atr quilibrium ontnt ) irular b qual ylindr to undr rtain pratial ytm load. Philoophial divrgn moitur flux J Tranation Royal Soity (London) Sri A 902;98:47. Gardnr NJ, God RM, Wong TF. Latrally prtrd J ntrially loadd lndr olumn. ACI Strut (2) t J 992;89(5):547_54. Harri, K. A.; Kharl, G., "Bhavior Modling Conrt Th atr Subjtd ontnt to Variabl an b Confining xprd Prur", a um ACI Matrial vaporabl Journal, atr V. 99, No. (apillary 2, Marh-April atr, 2002, atr pp. vapor, adorbd atr) n-vaporabl Harri, (hmially K. A.; bound) Kharl, G., atr "Exprimntal n (Mill Invtigation 966, Pantazopoulo Bhavior & Variably Mill Confind 995). Conrt", It i raonabl Cmnt to Conrt Rarh, Elvir Sin Ltd., 2003, pp aum that vaporabl atr i a funtion 880. Jank rlativ L, Chritoph humidity, Czadrki h, dgr a, Jürgn hydration, Ruthb, Maoud, Motavalli, Exprimnt ilia fum on ration, ridual load-baring, i.. apaity (h,, ) dgr prtrd ag-dpndnt onfind onrt orption/dorption olumn. Enginring iorm Strutur j.ngtrut Mjonll 997). Undr thi aumption (Norling Krtulovi-Opara N, Thidman PD. Ativ onfinmnt by ubtituting Equation into Equation 2 on onrt mmbr ith lf-tring ompoit. ACI obtain Matr J 2000;97(3):297_308. h + h t ( D h) n (3) h hr /h i lop orption/dorption iorm (alo alld moitur apaity). Th govrning quation (Equation 3) mut b ompltd by appropriat boundary initial ondition. Th rlation btn amount vaporabl atr rlativ humidity i alld adorption iorm if maurd ith inraing rlativity humidity dorption iorm in oppoit a. Nglting ir diffrn (Xi t al. 994), in folloing, orption iorm ill b ud ith rfrn to both orption dorption ondition. By ay, if hytri moitur iorm ould b takn into aount, to diffrnt rlation, vaporabl atr v rlativ humidity, mut b ud aording to ign variation rlativity humidity. Th hap orption iorm for HPC i inflund by many paramtr, pially tho that influn xtnt rat hmial ration, in turn, dtrmin por trutur por iz ditribution (atr-to-mnt ratio, mnt hmial ompoition, SF ontnt, uring tim mthod, tmpratur, mix additiv, t.). In litratur variou formulation an b found to drib orption iorm rmal onrt (Xi t al. 994). Hovr, in prnt papr mi-mpirial xprion propod by Norling Mjornll (997) i adoptd bau it & Li. xpliitly J, M.N.S. aount Hadi, Bhaviour for volution xtrnally onfind hydration hightrngth onrt SF olumn ontnt. undr Thi ntri orption loading, iorm Com- ration rad poit Strutur 62 (2003) Martin CW. Spirally prtrd onrt ylindr. ACI J 968;65(0):837_45. Mortazavi A, Pilakouta K, Son K. RC olumn trngning by latral prtnioning FRP. Contr Building, Matr ( h 2003;7(6_7):49_7.,, ) G (, ) + Pritly MJN, Sibl F. Dign 0imi ( g rtrit ) h maur for onrt maonry trutur. Contr Building Matr 995;9(6):365_77. (4) 0( g ) Shikh SA, Uzumri SM. h Analytial modl for onrt onfinmnt in tid olumn. Journal Strutural Enginring K (, ) ASCE 982;08(2): Xiao Y, Wu H. Compriv bhaviour onrt onfin by arbon fibr ompoit jakt. hr firt trm (gl iorm) J Matr rprnt Civil Eng 2000;2(2): phyially bound (adorbd) atr ond trm (apillary iorm) rprnt apillary atr. Thi xprion i valid only for lo ontnt SF. Th fiint G rprnt amount atr pr unit volum hld in gl por at 00% rlativ humidity, it an b xprd (Norling Mjornll 997) a G (, ) k + k vg vg (5) hr k vg k vg ar matrial paramtr. From maximum amount atr pr unit volum that an fill all por (both apillary por gl por), on an alulat K a on obtain K (, ) g G 0 g (6) Th matrial paramtr k vg k vg g an b alibratd by fitting xprimntal data rlvant to fr (vaporabl) atr ontnt in onrt at variou ag (Di Luzio & Cuati 2009b). 2.2 Tmpratur volution Not that, at arly ag, in hmial ration aoiatd ith mnt hydration SF ration ar xormi, tmpratur fild i t uniform for n-adiabati ytm vn if nvironmntal tmpratur i ontant. Hat ondution an b dribd in onrt, at lat for tmpratur t xding 00 C (Bažant & Kaplan 996), by Fourir la, hih rad q λ T (7) hr q i hat flux, T i abolut tmpratur, λ i hat ondutivity; in thi Proding FraMCoS-7, May 23-28, 200