Engineered cementitious composites with low volume of cementitious materials

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1 Fratur Mhani Conrt Conrt Strutur - High Prforman, Fibr Rinford Conrt, Spial Loading Strutural Appliation- B. H. Oh, t al. (d) 2 Kora Conrt Intitut, ISBN Enginrd mntitiou ompoit ith lo volum mntitiou matrial J. Zhou, S. Quian & K. van Brugl Dlft Univrity Thnology, Dlft, th Nthrl G. Y Ghnt Univrity, Gnt, Blgium ABSTRACT: Enginrd mntitiou ompoit (ECC) i an ultra dutil mnt-bad matrial rinford ith fibr. It i haratrizd by high tnil dutility tight rak idth ontrol. Thank th xllnt prforman, ECC i mrging in broad appliation nhan th loading apaity th durability trutur. Hovr, ECC alo fa a limitation on dimnional tability on onomial utainabl iu. In gnral, a larg amount mntitiou matrial, tn mor than 7% by ight, i ud in ECC no oar aggrgat i allod b addd. Th high volum mntitiou matrial in ECC rult in a larg drying hrinkag ngativ fft on matrial ot matrial grnn. In thi papr, a n vrion ECC i dignd ith lo volum mntitiou matrial about 25% by ight, inluding Portl mnt, blat furna lag ilia fum, a larg amount fillr aggrgat, inluding limn podr rivr. In thi mix, only.2% fibr by volum i mixd, hih i 6% doag tard ECC. Exprimntal tudy rval that th nly dvlopd ECC ho tnil dutility 2% rlativly lo hrinkag. Conidring th lo mntitiou matrial fibr ontnt, th nly dvlopd ECC might hav a rdud ot inrad matrial grnn. INSTRUCTION ECC, hort for Enginrd Cmntitiou Compoit, i a la ultra dutil fibr rinford mntitiou ompoit originally invntd at th Univrity Mihigan in th arly 99 (Li 993). Thi group matrial i haratrizd by high dutility in th rang 3-7% tight rak idth around 6 µm. Figur ho a typial tnil tr-train urv ECC it tight rak idth ontrol (Wimann & Li 23). Unlik plain onrt normal fibr rinford onrt, ECC ho a mtal-lik proprty aftr firt raking. Th uniqu tnil train-hardning bhavior high dutility rult from an laborat dign uing a miromhani modl taking in aount th intration among fibr, matrix fibr-matrix intrfa (Li & Lung 992). Th rak idth ECC i lfontrolld around 6 µm ithout th prn tl rinformnt, muh mallr than th typial rak idth obrvd in th tl rinford onrt. ECC thu ho lor atr prmability (Lph & Li 25) bttr durability (Li 27, Sahmaran t al. 28, Sahmaran & Li 28) ompard ith tard onrt. Thrfor, th u ECC an prolong th rvi lif trutur rdu th maintnan rpair ot. Noaday ECC i mrging in broad appliation, uh a ECC link lab on bridg dk (Mihigan DOT 25), ECC oupling bam in high-ri building nhan thir imi ritan, ompoit ECC/tl bridg dk om onrt rpair appliation (Kunida & Rokugo 26). Figur. Tnil tr-train urv tight rak idth ontrol ECC (Wimann & Li 23). In normal onrt, aggrgat oupy a ignifiant volum thu play an important rol in th mhanial proprti th dimnional tability onrt (Nvill 995). Hovr, ith th prn fibr, th addition aggrgat may au ball-

2 ing J = at D ( mixing h, T ) h poor fibr diprion (D Kokr () & van Zijl 24). Th fft bom mor pronound hn Th th proportionality maximum partil fiint iz inra. D(h,T) Fibr i alld diprion moitur i prmability on th ruial it i far a nonlinar affting funtion th uniqu th rlativ train-hardning humidity proprti h tmpratur ECC. T Poor (Bažant fibr & Najjar diprion 972). lad Th moitur a dra ma balan in dutility rquir vn that th abn variation in th tim train-hardning th atr ma bhavior pr unit (Torigo volum t onrt al. 23). (atr Thrfor, ontnt th ) iz b qual amount th divrgn aggrgat th ar moitur limitd in flux ECC. J Fin ilia ith a maximum grain iz 25 µm a man iz µm i typially ud a fin aggrgat in ECC. = Th J ontnt i uually l than 3% (2) by t th ight olid matrial. Th lo volum Th atr th high ontnt volum an b mntitiou xprd a matrial th um rult th in vaporabl larg drying atr hrinkag ngativ fft (apillary atr, atr on matrial ot matrial grnn (Yang t al. vapor, adorbd atr) th non-vaporabl 27). (hmially bound) atr n (Mill 966, Zhou t al. (29a) hav dvlopd a omplmntary approah improv th fibr diprion in ECC Pantazopoulo & Mill 995). It i raonabl aum that th vaporabl atr i a funtion by proprly adjuting matrial mixing qun. Thi rlativ humidity, h, dgr hydration, approah advan th dvlopmnt ECC, ith dgr ilia fum ration, high volum. With thi onpt,, i.. = a (h, n, vrion ECC i dignd ith lo volum mnti- ) = ag-dpndnt orption/dorption iothrm (Norling Mjonll 997). Undr thi aumption tiou matrial 25% by ight high volum by ubtituting Equation in Equation 2 on fillr aggrgat. In thi mix, only.2% fibr obtain by volum i mixd, hih i 6% doag tard ECC. Exprimntal tudy rval that th nly dvlopd ECC ho h tnil dutility 2% = & + & + & n (3) rlativly h t lo hrinkag. h hr 2 IMPROVED /h i th lop th orption/dorption FIBER DISPERSION BY iothrm (alo alld moitur apaity). Th ADJUSTING THE MIXING SEQUENCE govrning quation (Equation 3) mut b ompltd by appropriat boundary initial ondition. Figur 2 illutrat th tard ECC mixing qun (Zhou t al. 29a). Th tard mixing Th rlation btn th amount vaporabl atr rlativ humidity i alld adorption qun i arrid out a follo: all podr iothrm if maurd ith inraing rlativity liquid matrial ar firt mixd for vral minut humidity dorption iothrm in th oppoit fibr ar thn addd. Th rhologial proprti a. Nglting thir diffrn (Xi t al. 994), in ECC mortar (ithout fibr) dtrmin fibr ditribution in matrix. Conquntly, if th frh propr- th folloing, orption iothrm ill b ud ith rfrn both orption dorption ondition. ti do not rah th ondition for good fibr ditribution, although th mix dign i appropriat, ECC By th ay, if th hytri th moitur iothrm ould b takn in aount, to diffrnt rlation, vaporabl atr v rlativ humidity, mut b ud aording th ign th variation th rlativity humidity. Th hap th orption iothrm for HPC i inflund by many paramtr, pially tho that influn xtnt rat th hmial ration, in turn, dtrmin por trutur por iz ditribution (atr--mnt ratio, mnt hmial ompoition, SF ontnt, uring tim mthod, tmpratur, mix additiv, t.). In th litratur variou formulation an b found drib th orption ) Mix all iothrm normal podr matrial onrt (Xi t al. 994). Hovr, in th prnt Figur 2. Stard mixing qun. papr th mi-mpirial xprion propod by Norling Mjornll (997) i adoptd bau it q 2) Mix all liquid matrial ill xpliitly not ho aount good for tnil th proprti volution (Yang hydration t al. 29). ration SF ontnt. Thi orption iothrm rad Figur 3 illutrat th n ECC mixing qun (Zhou t al. 29a). Propr amount podr liquid matrial ar firt mixd, aiming at th propr rhologial proprti for a good fibr ditribution. Thn, fibr ar addd. Aftr fibr ar ( h,, ) = G (, ) + ( g ) h mixd homognouly, th rt podr /or liquid (4) matrial ar addd tailor th orkability th mhanial proprti ECC. ( g A a rult, ) h by adjuting th proing qun, ECC an ho mor K (, ) robut frh hardnd proprti. In thir tudy, Zhou t al. (29a) ok th atr mixing hr qun th firt trm a an (gl xampl iothrm) invtigatd rprnt th influn phyially bound diffrnt (adorbd) mixing qun atr by th omparing ond th trm rult (apillary th iothrm) uniaxial tnil rprnt tt th fibr apillary ditribution atr. analyi. Thi xprion Th n i mixing valid only qun for lo ith ontnt to atr SF. addition Th fiint tp rultd G rprnt in mor th than amount 5 tim inra atr pr unit th volum tnil train hld in apaity th gl por 5-4% at % inra rlativ humidity, th ultimat tnil it an trngth. b xprd Th inrad (Norling tnil Mjornll train 997) apaity a ultimat tnil trngth r attributd th improvd fibr diprion upportd by th trong orrlation btn th tnil G (, ) = k + k (5) train apaity vg th vg fibr ditribution fiint. hr k vg k vg ar matrial paramtr. From th 3 maximum EXPERIMENTS amount atr pr unit volum that an fill all por (both apillary por gl por), on 3. an alulat Matrial K a on obtain Thr far r invtigatd in th xprimntal program a givn in Tabl : ) addition ilia g fum, 2) addition G3) diffrnt mixing qun. Rivr ith th iz ranging from.25 (6) K (, ) =.5 mm a mixd in ECC. Th addition g might au poor partil paking on th urfa fibr thu a poor fibr-matrix intrfa. Silia fum Th a matrial thrfor paramtr addd in kordr improv th fibr-matrix alibratd intrfa. by fitting Tabl xprimntal 2 giv th data mix rlvant propor- vg k vg g an tion fr (vaporabl) ECC. Th nly atr dvlopd ontnt in ECC onrt ith Portl variou mnt, ag limn (Di Luzio podr & Cuati 29b). blat furna lag at (BFS) (Zhou t al. 29b) a ud a a rfrn (Mixtur S) in thi tudy. 2.2 Tmpratur volution Not that, at arly ag, in th hmial ration aoiatd ith mnt hydration SF ration ar xothrmi, th tmpratur fild i not uniform for non-adiabati ytm vn if th nvironmntal tmpratur i ontant. Hat ondution an b dribd in onrt, at lat for tmpratur not xding C (Bažant & Kaplan 996), by Fourir la, hih rad = λ T 3) Mix th fibr (7) hr q i th hat flux, T i th abolut tmpratur, λ i th hat ondutivity; in thi Proding FraMCoS-7, May 23-28, 2

3 ) Mix propr amount podr matrial 4) Mix th rt podr /or liquid matrial tailor th frh hardnd proprti 2) Mix propr amount podr liquid matrial 3) Mix th fibr homognouly 3.2 Mixing Juring = D ( h, T ) h Mixtur S-3 r mixd folloing th tard mixing qun, hil Th proportionality mixtur S4 fiint S5 r D(h,T) mixd folloing moitur th n prmability mixing qun. it Folloing th tard mixing th rlativ qun, humidity all olid h matrial tmpratur i a nonlina r firt mixd & ith Najjar atr 972). Th uprplatiizr moitur ma at balan lo pd for that minut th variation thn at in high tim pd th for atr 2 ma minut. Aftr fibr volum r onrt addd, th (atr ampl ontnt a ) b q mixd at high pd divrgn for anothr th 4 moitur minut. flux Folloing th n mixing qun, all olid matrial x- J pt r firt mixd ith atr uprplatiizr at lo pd t for minut at high = J pd for 2 minut. Thn fibr r addd mixd at high pd Th for atr anothr ontnt 2 minut. an Aftr b xprd fibr r mixd homognouly, th vaporabl atr a mixd (apillary at a a high pd for 2 vapor, mor minut. adorbd In ordr atr) liminat th fft (hmially mixing tim, bound) to atr mixing - n (Mil th non- qun r ondutd Pantazopoulo in th & am Mill tal 995). mixing It i ra tim 7 minut. aum that th vaporabl atr i a fu Th frh ECC rlativ a at humidity, in oupon h, dgr pimn hydration ith th dimnion dgr 24 ilia 6 fum mm3 ration, ov- rd ith plati = ht. ag-dpndnt Aftr 24 hour orption/dorption uring, th, i.. = pimn r (Norling dmouldd Mjonll 997). urd Undr at room thi aum tmpratur by 2 C ubtituting RH Equation 5% for anothr in Equati 27 day. obtain rlation, vaporabl atr v rlativ humi found drib th orption iothrm onrt (Xi t al. 994). Hovr, in th papr th mi-mpirial xprion pro Norling Mjornll (997) i adoptd b 3.3 Uniaxial tnil tt h = & + & + h t h Th oupon pimn at th ag 28 day r Figur 3. N mixing qun. ud in th uniaxial tnil tt. Four maurmnt r arrid out hr for ah mixtur. /h i th lop th orption/ Tabl. Far invtigatd in th xprimntal program. Figur 4 ho iothrm tt (alo t-up. alld Bfor moitur tting, apa Mixtur Silia fum S Mixing qun oupon pimn govrning r d quation for (Equation a flat urfa 3) mut b four aluminum plat r glud on to nd S Non Non Stard by appropriat boundary initial onditi ah pimn. Th rlation pimn btn a fixd th on amount th S2 Y Non Stard tt t-up by lamping atr th rlativ aluminum humidity plat-glud i alld S3 Y Y Stard nd ith to iothrm pair tl if maurd plat, hih ith r inraing S4 Non Y N onntd th humidity loading dvi. dorption Thn, to iothrm LVDT in th S5 Y Y N r attahd a. on both Nglting id thir diffrn pimn (Xi t al. maur th pimn th folloing, dformation. orption Th iothrm tt r ill b ondutd undr rfrn diplamnt both ontrol orption ith a loading rat.5 By mm/. th ay, Th tting if th gaug hytri lngth th dorption a 7 mm. iothrm ould b takn in aount, to Tabl 2. Mix proportion (ight %). b ud aording th ign th varia rlativity humidity. Th hap th Mixtur CEM I 42.5 N BFS Limn podr Silia fum S iothrm PVA fibr for HPC Watr i inflund SP by many p S.3.7. pially tho that influn xtnt.2 (vol.%.5.5 hmial ration, in turn, dtrm S trutur.2 (vol.%) por.525 iz ditribution.2 (atrratio,.2 mnt (vol. %) hmial.525 ompoition,. SF S3& uring tim mthod, tmpratur, mix S (vol.%).5.8 t.). In th litratur variou formulatio Proding FraMCoS-7, May 23-28, 2

4 J = ) D ( h, T h Th proportionality fiint D(h,T) i alld moitur prmability it i a nonlinar funtion th rlativ humidity h tmpratur T (Bažant & Najjar 972). Spimn Th moitur ma balan rquir that th variation in tim th atr ma pr unit LVDT volum onrt (atr ontnt ) b qual th divrgn th moitur flux J Stl plat = J (2) t Th atr ontnt an b xprd a th um th vaporabl atr (a) (apillary atr, atr vapor, adorbd atr) T th non-vaporabl (hmially bound) atr n (Mill 966, Pantazopoulo & Mill 995). It i raonabl 3 mm aum that th vaporabl atr i a funtion rlativ humidity, h, dgr Stl hydration, bar, dgr ilia Stl fum ration,, i.. = (h,, ) 4 mm = ag-dpndnt plat orption/dorption iothrm (Norling Mjonll 997). Undr thi aumption by ubtituting Equation in Equation 2 on Bolt obtain hr /h i th lop T th orption/dorption iothrm (alo alld (b) moitur apaity). Th Figur govrning 4. Uniaxial quation tnil (Equation tt t-up. 3) mut b ompltd by appropriat boundary initial ondition. 3.4 Th Drying rlation hrinkag btn maurmnt th amount vaporabl atr rlativ humidity i alld adorption Drying iothrm hrinkag if maurd maurmnt ith inraing r ondutd rlativity for mixtur humidity S2 dorption S5. Th frh iothrm ECC in a th at oppoit in thr a. prim Nglting pimn ith th dimnion mm 3 thir diffrn (Xi t al. 994), in th folloing,. Aftr orption 24 hour iothrm ald ill uring b ud at room ith tmpratur rfrn both 2 C, orption th pimn dorption r dmouldd ondition. By th initial ay, lngth if th hytri th prim pimn th moitur a maurd. iothrm ould Thn, b th takn pimn in aount, r to xpod diffrnt room rlation, tmpratur vaporabl atr 2 C v rlativ RH humidity, 5%. Th mut drying b ud hrinkag aording maurmnt th ign bgan th variation latd for th around rlativity humidity. day. Th lngth Th hap hang th th pimn orption a iothrm maurd for HPC ith i a inflund lngth gaug. by many paramtr, pially tho that influn xtnt rat th hmial ration, in turn, dtrmin por 4 trutur RESULTS por AND iz DISCUSSION ditribution (atr--mnt ratio, mnt hmial ompoition, SF ontnt, 4. uring Uniaxial tim tnil mthod, tt tmpratur, mix additiv, Th t.). typial In th uniaxial litratur tnil variou tr-train formulation urv an S- b 5 found at th ag drib 28 day th ar orption plottd iothrm in normal Figur onrt 5. (Xi Th t tnil al. 994). train apaity Hovr, in th ultimat prnt tnil papr trngth th mi-mpirial alulatd by xprion avraging th propod rult by Norling Mjornll (997) i adoptd bau it th four maurmnt for ah mixtur ar givn in () Aluminum plat h = glud & + on th & + & n (3) h t h Spimn pimn Figur xpliitly 6 aount Figur 7, for rptivly. th volution Undr th hydration uniaxial ration tnil loading, SF ontnt. all mixtur Thi S-5 orption ho multiplraking rad bhavior. Th mixtur S-5 at 28 day x- iothrm hibit th tnil train apaity ranging.5-3.7% th ultimat tnil trngth ranging MPa. Th fft ilia fum i invtigatd by omparing th rult S ith S2 S4 ith S5. Th ( h,, ) = G (, ) + ( g ) h addition ilia fum rult in 22-5% inra (4) tnil train apaity 8-3% inra ultimat tnil trngth. Th inra ( g an b ) attributd h K (, ) th improvd fibr-matrix intrfa, hih ha bn obrvd in an xprimntal tudy (Yan t al. 999). Th mixtur S2 S3 r both mixd folloing hr th th tard firt mixing trm (gl qun. iothrm) Bid rprnt th matrial phyially ud in bound S2, (adorbd) a alo atr addd in S3 th ond th th amount trm (apillary a iothrm) am rprnt a th tal th amount apillary th atr. othr Thi olid xprion matrial. i Th valid fibr only ontnt for lo a ontnt thrfor SF. drad Th fiint from 2% G.2% rprnt by volum. th amount A illutratd atr in pr Figur unit volum 6 hld 7, hn in th ECC gl por ar mixd at % fol- loing rlativ th humidity, tard mixing it an qun, b xprd th addition (Norling Mjornll rult 997) in a bad tnil proprti ECC. Th tnil train apaity i drad by 85%, th ultimat tnil trngth i drad by 26%. G (, ) = k + k (5) Th n mixing vg qun vg a adoptd for mixtur S5 rovr th good tnil proprti. Comparing hr kth tnil train apaity ultimat tnil vg k vg ar matrial paramtr. From th trngth maximum amount S3 S5, atr hih pr hav unit th volum am mix that proportion, fill all por th adjutd (both apillary mixing por qun gl improv por), on th an mhanial an alulat proprti K a on obtain ECC. S5 xhibit 4. tim tnil train apaity.2 tim ultimat tnil trngth S3. Th bttr tnil prforman might b bau th improvd fibr g ditribution by adjuting th mixing G qun. In mixtur S5, th (6) ontnt K (, ) i = up 5% by ight th fibr ontnt i a lo a.2% by volum, g hih i only 6% th fibr ontnt in S2. Hovr, S5 ho a omparabl tnil train apaity 2.2 % ultimat tnil Th trngth matrial paramtr 3.5 MPa. k vg Th lor k vg doag g an mntitiou b alibratd matrial by fitting xprimntal fibr rdu data th rlvant ot improv fr (vaporabl) th grnn atr ECC. ontnt in onrt at variou ag (Di Luzio & Cuati 29b) Tmpratur volution S2 Not 4that, at arly ag, in th hmial ration Tnil tr (MPa) aoiatd ith mnt hydration SF ration S ar xothrmi, 3 th tmpratur fild i not uniform S5 for non-adiabati ytm vn if th nvironmntal 2 S4 tmpratur i ontant. Hat ondution an b dribd in onrt, at lat for tmpratur not S3 xding C (Bažant & Kaplan 996), by Fourir la, hih rad q = λ T Strain (%) (7) Figur hr 5. q Typial i th uniaxial hat tnil flux, tr-train T i th urv abolut S-5 at tmpratur, th ag 28 day. λ i th hat ondutivity; in thi Proding FraMCoS-7, May 23-28, 2

5 Tnil train apaity (%) S S2 S3 S4 S5 Figur 6. Tnil train apaity S-5 at th ag 28 day. Ultimat tnil trngth (MPa) S S2 S3 S4 S5 Figur 7. Ultimat tnil trngth S-5 at th ag 28 day. 4.2 Drying hrinkag maurmnt Th mixtur S5 alo ho advantag on th dimnional tability. Figur 8 ho th drying hrinkag S2 S5 maurd for 9 day. Eah valu rprnt th avrag drying hrinkag thr maurmnt. Du th abn oar aggrgat, th drying hrinkag ECC i highr than normal onrt. At th ag day, S2 ho a drying hrinkag 273 µtrain, hil S5 ho a drying hrinkag 48 µtrain. Th addition rult in around 45% dra in th drying hrinkag. Shrinkag ( ^-6) Ag (day) Figur 8. Drying hrinkag S2 S5 at room tmpratur 2 C RH 5%. S2 S5 5 CONCLUSIONS J = ) D ( h, T h Proprly adjuting Th ECC proportionality proing qun fiint improv th fibr moitur ditribution prmability thu th it tnil i a nonlina D(h,T) proprti ECC. Folloing th rlativ thi humidity onpt, h a vrion tmpratur ECC ith lo & volum Najjar 972). mntitiou Th moitur matrial ma balan a dvlopd. Bid, that th ilia variation fum in a tim alo th addd atr ma in ECC in ordr volum improv onrt th fibr-matrix (atr ontnt intr-fa proprti divrgn th tnil th proprti moitur flux ECC. J b q Bad on th xprimntal rult th abov diuion, th folloing onluion an b dran: - Th addition ilia = fum J rult in th inra t tnil train apaity ultimat tnil trngth. Th inra an b Th attributd atr ontnt th improvd an b fibrmatrix intrfa. xprd a th vaporabl atr (apillary a - Proprly adjuting mixing qun improv th vapor, adorbd atr) th non- tnil proprti ECC ith high volum. (hmially bound) atr n (Mil Th ECC mixtur ith 5% (by ight) Pantazopoulo & Mill 995). It i ra.2% (by volum) fibr ho a omparabl tnil aum that th vaporabl atr i a fu train apaity 2.2 % ultimat tnil trngth rlativ humidity, h, dgr hydration 3.5 MPa. dgr ilia fum ration, - Th addition rult in a grat amount, i.. = = ag-dpndnt orption/dorption dra in th drying hrinkag. (Norling Mjonll 997). Undr thi aum - Conidring th lo mntitiou matrial by ubtituting Equation in Equati fibr ontnt, th nly dvlopd ECC i xptd obtain hav a rdud ot inrad matrial grnn. h = & + & + h t h REFERENCES D Kokr, D. & van hr Zijl, G. 24. /h i Extruion th lop nginrd th orption/ mnt-bad ompoit iothrm matrial. (alo In alld M. di Prio moitur t al. apa (d.), Fibr-Rinford govrning Conrt; quation Pro. (Equation 6th RILEM 3) Sympoium on FRC by (BEFIB appropriat 24), Varnna, boundary Italy, pp. initial 3-onditi 3. Th rlation btn th amount mut b Kunida, M. & Rokugo, K. 26. Rnt progr on atr rlativ humidity i alld HPFRCC in Japan. J. Adv. Conr. Th. 4(): 9-33 Lph, M.D. & Li, iothrm V.C. 25. Watr if maurd prmability ith rakd inraing mntitiou ompoit. humidity In Pro. dorption th Int. Conf. iothrm on Fratur, papr a. Nglting thir diffrn (Xi t al. in th Li, V.C. & Lung, C.K.Y. th folloing, 992. Thory orption tady iothrm tat ill b multipl raking rfrn rom diontinuou both orption fibr rinford dorption brittl matrix ompoit. ASCE J. Eng. Mh. 8(): By th ay, if th hytri th Li, V.C From iothrm miromhani ould b trutural takn nginring in aount, to th dign mntitiou rlation, vaporabl ompoit for atr ivil v nginring appliation. b JSCE ud J. aording Strut. Mh. Earthquak th ign Eng. th varia rlativ humi (2): rlativity humidity. Th hap th Li, V.C. 27. Enginrd iothrm mntitiou for HPC ompoit i inflund (ECC) by many p matrial, trutural durability prforman. In E. Nay (d.), Conrt pially Contrution tho that Enginring influn Hbook, Chaptr 24. hmial Boa Ran: ration CRC Pr., in turn, dtrm xtnt Mihigan DOT 25. trutur Bridg dk por going iz jointl: ditribution mnti-(atrtiou ompoit ratio, improv mnt durability hmial link lab. ompoition, Con- SF trution Thnology uring tim Rarh Rord mthod, : tmpratur, -4. mix Nvill, A.M. 995, Proprti Conrt, 4th dition. t.). In th litratur variou formulatio Longman Sintifi & Thnial Ltd. Sahmaran, M., Li, V.C. found & Andrad, drib C. 28. th Corroion orption ritan prforman onrt tl-rinford (Xi t al. nginrd 994). Hovr, mnti- in th iothrm tiou ompoit bam. papr ACI th Matrial mi-mpirial J. 5(3): xprion pro Norling Mjornll (997) i adoptd b Proding FraMCoS-7, May 23-28, 2

6 Sahmaran, J = D ( h, TM. ) h& Li, V.C. 28. Durability mhanially () loadd nginrd mntitiou ompoit undr highly alkalin nvironmnt. Cm. Conr. Comp. 3(2): Torigo, Th S., proportionality Horikohi, T., Ogaa, fiint A., Sai, D(h,T) T. & Hamada, i alld T. moitur 23. Study prmability on valuation mthod it i a for nonlinar PVA fibr funtion ditribution th rlativ in nginrd humidity mntitiou h ompoit. tmpratur J. Adv. T (Bažant Conr. & Najjar Th. (3): 972) Th moitur ma balan rquir Wimann, M.B. & Li, V.C. 23. Hygral bhavior nginrd mntitiou ompoit (ECC). Int. J. for Rra- that th variation in tim th atr ma pr unit volum tion Building onrt (atr Monumnt ontnt 9(5): ) b qual th Yan, divrgn H., Sun W. th & Chn, moitur H flux Efft J ilia fum tl fibr on th dynami mhanial prforman high-trngth onrt. Cm. Conr. R. 29(3): Yang, = E. Yang, J Y. & Li, V.C. 27. U high volum (2) fly ah t improv ECC mhanial proprti matrial grnn. ACI Matrial J. 4(6): Yang, Th E. atr Sahmaran, ontnt M. Yang, an Y. b & Li, xprd V.C. 29. a Rhologial th ontrol vaporabl in prodution atr nginrd (apillary mntitiou atr, atr om- th um vapor, poit, ACI adorbd Matrial atr) J. 6(4): th non-vaporabl Zhou, (hmially J., Qian, S., bound) Copuroglu, atr O., Y, G., van Brugl, K. & Li, V.C. 29a. Improvd fibr ditribution n (Mill 966, mhanial proprti Pantazopoulo & Mill nginrd 995). mntitiou It i raonabl ompoit by aum adjuting that proing th vaporabl qun. In atr draft. i a funtion Zhou, rlativ J., Qian, humidity, S., Sirra h, Bltran, dgr M.G., hydration, Y, G., van Brugl,, dgr K. & Li, ilia V.C. 29b. fum Dvlopmnt ration,, i.. nginrd = (h, mntitiou ag-dpndnt ompoit ith orption/dorption limn podr blat iothrm furna, ) = lag. Aptd by Matrial Strutur. (Norling Mjonll 997). Undr thi aumption by ubtituting Equation in Equation 2 on obtain h + h t ( D h) = n (3) h & + & + hr /h i th lop th orption/dorption iothrm (alo alld moitur apaity). Th govrning quation (Equation 3) mut b ompltd by appropriat boundary initial ondition. Th rlation btn th amount vaporabl atr rlativ humidity i alld adorption iothrm if maurd ith inraing rlativity humidity dorption iothrm in th oppoit a. Nglting thir diffrn (Xi t al. 994), in th folloing, orption iothrm ill b ud ith rfrn both orption dorption ondition. By th ay, if th hytri th moitur iothrm ould b takn in aount, to diffrnt rlation, vaporabl atr v rlativ humidity, mut b ud aording th ign th variation th rlativity humidity. Th hap th orption iothrm for HPC i inflund by many paramtr, pially tho that influn xtnt rat th hmial ration, in turn, dtrmin por trutur por iz ditribution (atr--mnt ratio, mnt hmial ompoition, SF ontnt, uring tim mthod, tmpratur, mix additiv, t.). In th litratur variou formulation an b found drib th orption iothrm normal onrt (Xi t al. 994). Hovr, in th prnt papr th mi-mpirial xprion propod by Norling Mjornll (997) i adoptd bau it & xpliitly aount for th volution hydration ration SF ontnt. Thi orption iothrm rad ( h,, ) = G (, ) + ( g ) h ( g ) h K (, ) (4) hr th firt trm (gl iothrm) rprnt th phyially bound (adorbd) atr th ond trm (apillary iothrm) rprnt th apillary atr. Thi xprion i valid only for lo ontnt SF. Th fiint G rprnt th amount atr pr unit volum hld in th gl por at % 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 th 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 g (6) Th matrial paramtr k vg k vg g an b alibratd by fitting xprimntal data rlvant fr (vaporabl) atr ontnt in onrt at variou ag (Di Luzio & Cuati 29b). 2.2 Tmpratur volution Not that, at arly ag, in th hmial ration aoiatd ith mnt hydration SF ration ar xothrmi, th tmpratur fild i not uniform for non-adiabati ytm vn if th nvironmntal tmpratur i ontant. Hat ondution an b dribd in onrt, at lat for tmpratur not xding C (Bažant & Kaplan 996), by Fourir la, hih rad q = λ T (7) hr q i th hat flux, T i th abolut tmpratur, λ i th hat ondutivity; in thi Proding FraMCoS-7, May 23-28, 2