Crack width control of reinforced concrete one-way slabs utilizing expansive strain-hardening cement-based composites (SHCCs)

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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 Crak width ontrol rinford onrt on-way lab utilizing xpaniv train-hardning mnt-bad ompoit (SHCC) H.D. Yun, S.W. Kim & Y.O. L Dpartmnt Arhittural Enginring, Chungnam National Univrity, Dajon, South Kora T. Izuka, Y. Sakaguhi & K. Rokugo Dpartmnt Civil Enginring, Gifu, Japan S.C. Lim Dro-Japan Co., Ltd, Kanazawa, Japan ABSTRACT: In thi papr, th mthod to rpla part th onrt at th tnil bottom on-way lab with xpaniv SHCC ha bn ud to improv raking bhavior durability RC mmbr. Thi papr xplor th trutural appliation an xpaniv SHCC th rult tt on fiv imply upportd lab ar dribd. Th fft xpaniv admixtur thikn SHCC layr (2 4mm) on th ultimat flxural load, firt rak load, rak width paing, th load-dfltion rlationhip on-way lab wa invtigatd. Th rult indiat that th u SHCC ovr at th bottom lab ha ignifiantly inrad th initial rak load, yild load, ultimat load, whil th u xpaniv admixtur in SHCC matrial had littl fft on tho on-way lab with a SHCC layr. Conidrabl rdution in rak width paing wa obrvd for lab with a SHCC layr thi tndny i rmarkabl for lab with an xpaniv SHCC layr thikr SHCC layr. INTRODUCTION. Bakground Plain onrt i wak in tnion but an fftiv trong matrial in omprion. Rinformnt i an ntial lmnt in rinford onrt (RC) trutur ovroming th low tnil trngth onrt by arrying th tnil tr. Nvrthl, rak in RC trutur our during onrt hardning or du to nvironmntal fft aftr onrt olidifying. Craking on th xtrm RC mmbr i on th main fator influning th durability RC mmbr bau urfa rak an prmit hmial ration to gnrat th oxidation rinformnt urfa. Thrfor, rak ontrol i ntial to ontrol th orroion rinformnt bar. Strain-hardning mnt-bad ompoit (SHCC) i a nw la fibr-rinford mnt ompoit (FRCC) ompoit matrial oniting mnt pat, ilia, fly ah, hort rom fibr. Th SHCC xhibit a pudo trainhardning bhavior aompanid by multipl raking in uniaxial tnion. Th multipl raking haratriti SHCC nhan th imprmability durability thi nw matrial. Howvr, uh rih mix matrial ha alrady bn known to hrink ignifiantly at arly ag, whih i likly to b aud mainly by autognou hrinkag. At th tag SHCC hardning, autognou hrinkag lad to rak whih dtriorat th durability raking bhavior SHCC matrial..2 Objtiv Thi papr xplor th trutural appliation an xpaniv SHCC to improv th rak-damag bhavior RC flxural mmbr. Th rult tt on tn imply upportd lab ar dribd. Th fft th typ SHCC (PE.5 PVA.8) thikn SHCC layr (2 4mm) on th ultimat flxural load, firt rak load, rak width paing, th load-dfltion rlationhip on-way lab wa invtigatd. 2 EXPERIMENTAL PROGRAM 2. Spimn manufatur Thi xprimntal program two paramtr ar: th typ SHCC (with or without xpaniv admixtur) th layr thikn (2 4mm) th

2 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). Th moitur ma balan rquir that th variation in tim th watr ma pr unit volum onrt (watr ontnt w) b qual to th divrgn th moitur flux J t w = J (2) Th watr ontnt w an b xprd a th um th vaporabl watr w (apillary watr, watr vapor, adorbd watr) th non-vaporabl (hmially bound) watr w n (Mill 966, Pantazopoulo & Mill 995). It i raonabl to aum that th vaporabl watr i a funtion rlativ humidity, h, dgr hydration,, dgr ilia fum ration,, i.. w =w (h,, ) = Figur ag-dpndnt. Stion rinformnt orption/dorption dtail lab. iothrm (Norling Mjonll 997). Undr thi aumption by ubtituting Equation into Equation 2 on obtain SHCC. Th main part th xprimntal program u ight RC lab: a Control RC lab, four RC lab with diffrnt layr thikn for two normal SHCC, h thr RC lab with + diffrnt layr ( D h) = & + & + w& n (3) thikn h for h an xpaniv SHCC. Eah lab had an ovrall dpth 8 mm, width 4 mm, lngth,8 mm. Th lab wr ompod whr RC ubtrat / h i th lop th orption/dorption SHCC layr, xpt for th Control lab. iothrm (alo alld moitur apaity). Th govrning Cro-tional quation dimnion (Equation 3) mut th b rinformnt ompltd by arrangmnt appropriat boundary th lab ar initial givn ondition. in Figur, an Th ovrviw rlation btwn th xprimntal th amount pimn vaporabl i givn watr in Tabl. rlativ humidity i alld adorption iothrm Th Control if maurd RC lab, with i.. inraing RC-S, wa rlativity dignd humidity with 3 MPa dorption ompriv iothrm trngth onrt in th oppoit 4 a. MPa Nglting yild trngth thir diffrn tl. Th (Xi longitudinal t al. 994), rin- th formnt following, orption both tnion iothrm omprion will b ud onitd with rfrn thr to dformd both orption bar 6 mm dorption in diamtr, ondition. orrponding th way, to a if rinformnt th hytri ratio th., moitur rp- By iothrm tivly. Shar would rinformnt b takn into wa aount, arrangd two to diffrnt inur rlation, th flxural vaporabl failur watr th v RC rlativ lab. humidity, Th tranvr mut b rinformnt ud aording onitd to th ign dformd th variation bar mm th in rlativity diamtr humidity. at 25 mm ntr. Th hap th orption iothrm For th for HPC two RC i inflund lab (NS-2 by many NS-4), paramtr, layr high trngth SHCC with PE fibr, 2 mm pially tho that influn xtnt rat th 4 mm thik, rptivly, wr ubtitutd for th hmial ration, in turn, dtrmin por onrt urrounding th main flxural rinformnt, a hown in Figur. Th pifid ompr- trutur por iz ditribution (watr-to-mnt ratio, iv mnt trngth hmial SHCC ompoition, pimn wr SF 6 ontnt, MPa. uring Th dimnion tim mthod, rinformnt tmpratur, onfiguration mix additiv, t.). th SHCC-layrd In th litratur lab variou ar th formulation am a tho an th b found Control to drib lab, RC-S. th orption iothrm normal onrt It i (Xi gnrally t al. 994). known Howvr, that rih mixtur in th prnt hrink papr ignifiantly th mi-mpirial in th arly xprion tag du to propod autognou by Norling Mjornll (997) i adoptd bau it xpliitly aount for th volution hydration ration SF ontnt. Thi orption iothrm rad w ( h,, ) = G (, ) + ( g ) h ( g ) h K (, ) (4) whr th firt trm (gl iothrm) rprnt th phyially bound (adorbd) watr th ond trm (apillary iothrm) rprnt th apillary watr. Thi xprion i valid only for low ontnt SF. Th fiint G rprnt th amount watr 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) hrinkag. Thi autognou hrinkag lad to rak that whr may k vg xarbat k vg ar th matrial raking paramtr. bhavior From d-thra maximum th trutural amount prforman watr unit th volum SHCC mat- that an rial. fill all In th por prnt (both invtigation, apillary por an xpaniv gl por), SHCC on ha an bn alulat dvlopd K a on to rdu obtain hrinkag rak in high trngth SHCC uing a high volum mnt. For th two lab pimn (ES-2 ES-4), a layr xpaniv SHCC wa plad g on th bottom w G ah lab to invtigat th fft xpaniv SHCC on th initial rak trngth rak damag mitigation SHCC-layrd g lab. Eah pi- (6) K (, ) = mn had a diffrnt SHCC layr thikn (2 4 mm). Th matrial paramtr k vg k vg g an b alibratd by fitting xprimntal data rlvant to 2.2 Matrial fr (vaporabl) watr ontnt in onrt at All variou th mix ag proportion (Di Luzio u & Cuati th dry 29b). wight th ingrdint. Th plain onrt mixtur inlud 5 mm maximum-iz oar aggrgat fin aggrgat, 2.2 Tmpratur ordinary volution Portl mnt, two kind high Not rang that, at watr-rduing arly ag, in admixtur, th hmial ration watr. Th aoiatd ommon with matrial mnt ud hydration in th SHCC SF mixtur ration ar ar ordinary xothrmi, Portl th tmpratur mnt, ilia fild i with not uniform maximum for non-adiabati grain iz 2 m pifi gravity 2.6 g/m 2 ytm vn if th nvironmntal, watr, a high rang watr-rduing admixtur, a dry vioity agnt that nhan th tmpratur i ontant. Hat ondution an b dribd in onrt, at lat for tmpratur not workability th mixd matrial, avoid matrial grgation, xding C improv (Bažant th fibr & Kaplan ditribution 996), during Fourir mixing. law, In whih addition, rad high-dnity polythyln by (PE) fibr an xpaniv additiv, whih i ttringit q = λ T alium hydrat ombind formation (7) typ, a pifi gravity 3.5 g/m 3, wr ud for whr th xpaniv q i th SHCC. hat High flux, trngth T i SHCC th pimn tmpratur, wr rinford λ i with th PE hat fibr. ondutivity; in abolut thi Proding FraMCoS-7, May 23-28, 2

3 PE fibr, with a diamtr 2 lngth 2 mm, wr manufaturd with a tnil trngth 2,6 MPa an lati modulu 88 GPa. Th SHCC mixtur wr prpard in an Omni mortar mixr bau th rlativly high mixing ffort impartd by thi typ mixr failitat th diprion mall diamtr PE ynthti fibr. Th dry ingrdint, i.., th mnt, ilia, dry vioity agnt, ynthti fibr, wr mixd firt until a homognou mixtur wa rahd (bad on olor viual apparan). Thi tp wa followd by th addition watr th high rang watrrduing admixtur, with a mixing tim thr minut. Thr dumbbll-hapd pimn wr prpard from ah mixtur, a hown in Figur 2. Th ttd tion lngth wa mm th ro-tion wa 3 x 3 mm. All tnil pimn wr d moldd 24 hour aftr ating. Aftr dmolding, thy wr air-urd at 74ºF at 65% rlativ humidity for four wk. Jak Load ll Diplamnt trur Spimn Figur 2. St-up pimn for th dirt tnion tt. Spimn Figur 3. St-up for th four-point bnding tt RC on-way lab. Ball J D ( h, T h 2.3 Tting mthod Th proportionality fiint D(h,T) To valuat th tnil moitur prforman prmability ah SHCC it i a nonlina pimn, dirt tnion tt wr ondutd aording to Japan Soity Enginr rommnda- th rlativ humidity h tmpratur & Najjar 972). Th moitur ma balan tion (f. hunking mhanim uing lamp jig) (Japan Soity Civil Enginr 28). Th dirt that th variation in tim th watr ma tnil loading apparatu volum i hown onrt in Figur (watr 2. ontnt Two w) b q idntial loading divrgn fixtur wr th ud: moitur on hingd flux J huk wa onntd to th loading bar from a hrankd loading jak plad on th tl fram; on = J fixd huk wa mountd t on th bottom ba th tl fram. Th uppr fixtur wa pulld by th load along th two guid Th pin. watr Tnil ontnt load w wr an introdud to th tnil pimn th vaporabl along th watr ntral w b xprd a axi (apillary wa via th pulling ation vapor, th uppr adorbd fixtur. watr) Th applid tnil load (hmially wa maurd bound) uing a load watr ll w n (Mil th non- with a apaity Pantazopoulo kn intalld & in Mill th uppr 995). part It i ra th loading dvi. aum Two that linar th variabl vaporabl diffrntial trur (LVDT) watr i a fu rlativ wr humidity, mountd h, on dgr th two hydration id th pimn for dformation maurmnt dgr ilia fum ration, a wll a tt ontrol. Th diplamnt th ntral mm rgion th dumbbll-hapd pi-, i.. w =w = ag-dpndnt orption/dorption (Norling Mjonll 997). Undr thi aum mn wa maurd by man two LVDT, th tnil train wa by alulatd ubtituting by dividing Equation thi maurd diplamnt obtain by th rfrn lngth into Equati mm. LVDT holdr wr pially dignd to allow ay adjutmnt ntring ftting for th h LVDT trur. Th diplamnt + ( D hrat ) = wa &.25 + & + w h h mm/minut. All lab wr ttd a imply upportd lab undr four-point loading whr with / h a i nt th pan lop,7 th orption/ mm har pan iothrm 75 mm. (alo Bnding alld tt moitur wr apa diplamnt-ontrolld govrning by quation impoing (Equation an avrag 3) mut b diplamnt undr by th appropriat two loading boundary point, a hown initial onditi in Figur 3. Th ontrolld Th rlation diplamnt btwn rat th wa amount.4 mm/minut. Slab watr wr ttd rlativ in a tting humidity ytm i alld that u a 5 kn iothrm apaity loading if maurd fram. with During inraing flxural tting, th humidity dformation dorption undr th iothrm two in th loading point rotation at both nd th lab a. Nglting thir diffrn (Xi t al. wr maurd uing two LVDT. Crak formation th following, orption iothrm will b wr viually obrvd, at pifid yild rfrn to both orption dorption By th way, if th hytri th iothrm would b takn into aount, two rlation, vaporabl watr v rlativ humi b ud aording to th ign th varia Hydrauli jak rlativity humidity. Th hap th iothrm for HPC i inflund by many p pially tho that influn xtnt Rollr hmial ration, in turn, dtrm trutur por iz ditribution (watrratio, mnt hmial ompoition, SF Diplamnt trur uring tim mthod, tmpratur, mix t.). In th litratur variou formulatio found to drib th orption iothrm onrt (Xi t al. 994). Howvr, in th papr th mi-mpirial xprion pro Norling Mjornll (997) i adoptd b Proding FraMCoS-7, May 23-28, 2

4 D h T h (, () load, th rak numbr width wr miroopially Th maurd proportionality ovr a fiint 4 mm ntral D(h,T) zon i alld th moitur lab tnil prmability fa. Dfltion it i a undr nonlinar th point funtion load th rlativ th rotation humidity at both h nd tmpratur lab wr T rordd (Bažant & during Najjar tting. 972). Th moitur ma balan rquir that th variation in tim th watr ma pr unit volum onrt (watr ontnt w) b qual to th divrgn 3 EXPERIMENTAL th moitur RESULTS flux J 3. Mhanial proprti SHCC = J (2) Figur t 4 provid th uniaxial tnion tt rult from fiv dumbbll-hapd SHCC pimn. Mot Th th watr tnil ontnt pimn w an how b a xprd imilar trnd a th to ah um othr. vaporabl An lati rpon watr w i (apillary obrvd up watr, to th watr firt vapor, rak load adorbd th SHCC. watr) Aftr th th non-vaporabl firt rak, th (hmially tnil tr bound) inra with watr an inra w n (Mill in th train; 966, Pantazopoulo & Mill 995). It i raonabl to aum that th vaporabl watr i a funtion rlativ humidity, h, dgr hydration,, 8 dgr ilia fum ration,, i.. w =w (h,, ) = ag-dpndnt 6 orption/dorption iothrm Avrag (Norling Mjonll 997). Undr thi aumption 4 by ubtituting Equation into Equation 2 on obtain Tnil train (MPa 2 h + D h) = & + & + w& Tnil train ( n h h (a) SHCC-PE Figur 4. Dirt tnil bhavior SHCC matrial. whr / h i th lop th orption/dorption iothrm (alo 8 alld moitur apaity). Th govrning quation (Equation 3) mut b ompltd by appropriat 6 boundary initial ondition. Th rlation btwn th amount vaporabl Avrag watr rlativ 4 humidity i alld adorption iothrm if maurd with inraing rlativity humidity 2 dorption iothrm in th oppoit a. Nglting thir diffrn (Xi t al. 994), in th following, orption iothrm will b ud with rfrn to both orption dorption ondition. By th way, if th hytri th moitur Compriv train (µ) iothrm would b takn into aount, two diffrnt (a) SHCC-PE rlation, Figur vaporabl 5. Compriv watr rpon v rlativ SHCC humidity, matrial. mut b ud aording to th ign th variation th rlativity humidity. 2 Th hap th orption iothrm for HPC i inflund by many paramtr, 6 pially tho that influn xtnt rat th hmial ration 2, in turn, dtrmin por trutur por iz ditribution (watr-to-mnt Avrag 8 ratio, mnt hmial ompoition, SF ontnt, uring tim 4 mthod, tmpratur, mix additiv, t.). In th litratur variou formulation an b found to drib th orption iothrm normal onrt (Xi t al. 994). Howvr, Dfltion (mm) in th prnt papr th mi-mpirial (a) xprion SHCC-PE propod by Norling Figur Mjornll 6. Flxural (997) bhavior i adoptd SHCC matrial. bau it Compriv tr (MPa) Bnding tr (MPa) ( (3) xpliitly aount for th volution hydration ration SF ontnt. Thi orption iothrm thu, multipl rak dvlop up to th pak tr. rad A major rak i gnrally obrvd whn th tnil tr rah th pak tr. Byond th pak tr, th tnil tr drop gradually du to om th fibr pulling out from th matrix or braking w ( h,, ) = G (, ) + nar th major rak. Th high trngth SHCC ( g ) h (SHCC-PE) with.5% PE fibr how avrag (4) firt-rak tnil trngth MPa, rptivly. Th avrag ( g train ) apaity h i K (, ).43%. Figur 4b how th tnil rpon th xpaniv SHCC (Ex-SHCC-PE), whih ha an xpaniv additiv rplamnt 8% in trm th volum whr th firt mnt. trm Thi (gl Ex-SHCC-PE iothrm) rprnt matrial th how phyially highr bound firt-rak (adorbd) trngth watr l train th ond apaity trm (apillary than th SHCC-PE iothrm) without rprnt th xpaniv th apillary admixtur watr. Thi rplamnt. xprion Th i xpaniv valid only admixtur for low with- ontnt SF. Th fiint G rprnt th amount watr pr unit volum hld in th gl por at % rlativ humidity, it an b xprd (Norling Mjornll 8 997) a Tnil train (MPa 6 G (, ) = k + kavrag 4 vg vg 2 maximum amount watr pr unit volum that an fill all por (both apillary por gl por), on Tnil train ( an alulat K a on obtain (b) Ex-SHCC-PE Compriv tr (MPa) 8 K ( ) 6, = 4 b alibratd 2 by fitting xprimntal data rlvant to variou ag (Di Luzio & Cuati 29b). Compriv train (µ) 2.2 Tmpratur volution (b) Ex-SHCC-PE Not that, at arly ag, in th hmial ration aoiatd with mnt hydration SF ration ar xothrmi, 2 th tmpratur fild i not uniform for non-adiabati ytm vn if th nvironmntal 6 tmpratur i ontant. Hat ondution an b Avrag dribd 2 in onrt, at lat for tmpratur not xding C (Bažant & Kaplan 996), by 8 Fourir law, whih rad Bnding tr (MPa) 4 = λ T Dfltion (mm) (5) whr k vg k vg ar matrial paramtr. From th g w G g Avrag Th matrial paramtr k vg k vg (6) g an fr (vaporabl) watr ontnt in onrt at q (7) whr q i th hat flux, T i th abolut tmpratur, (b) λ Ex-SHCC-PE i th hat ondutivity; in thi Proding FraMCoS-7, May 23-28, 2

5 D ( h, T h rlativity humidity. Th hap th Norling Mjornll (997) i adoptd b in 8% appar to hav had littl fft on th raking pattrn th high trngth SHCC. Th om- hown in Figur 7a Th b. proportionality For omparion, fiint th load D(h,T) RC ubtrat SHCC layr ompoit lab ar priv tr vru train rpon th high vru dfltion moitur urv a prmability onvntional RC it onway i a nonlina trngth SHCC pimn ar hown in Figur 5. Th pak trngth orrponding train in th SHCC pimn ar larly gratr than tho in th onrt pimn. Th xpaniv admixtur lab i givn in th rlativ two figur. humidity Bad h on th tmpratur bnding tt rult, & Tabl Najjar 972). how Th a omparion moitur ma balan th flxural prforman that th variation th on-way in tim lab. From th watr ma a omparion with volum a omparabl onrt onvntional (watr ontnt RC w) b q addition rult in an inra in ompriv train lab, th addition divrgn th SHCC layr th at moitur th bottom flux J at pak trngth, a hown in Figur 5. th RC lab inra both th initial rak load Th tati modulu latiity th SHCC pimn inra with an inra in ompriv in Figur 8. = J th flxural tiffn aftr th rak load, a hown t trngth, lik th onvntional mnt-bad ompoit. Invtigating th omplt flxural load vru dfltion urv th lab pimn, ignifiant Th watr ontnt w an b xprd a Figur 6 prnt th flxural tr vru midpan dfltion urv SHCC prim. For onvn- SHCC-layrd lab diffrn btwn onvntional RC lab an th b vaporabl notd. It i watr lar that w (apillary th wa tional onrt, an abrupt drop our oon aftr th initial rak load inra vapor, ignifiantly adorbd watr) by layring th non- firt rak load. Th maximum load flxural th SHCC matrial (hmially at th bottom bound) on-way watr lab. w n (Mil trngth ar at th firt rak. Howvr, SHCC matrial how a dutil pot-raking bhavior aftr th lab with a mallr aum layr that thikn. th vaporabl No ignifiant watr i a fu Thi phnomnon Pantazopoulo i notd alo & for Mill SHCC-layrd 995). It i ra firt rak load. Th typial bnding rpon th diffrn i vidnt rlativ among humidity, th dformation h, dgr apaiti, dfind a th dgr mid-pan ilia dfltion fum ration, at th pak, i.. w =w hydration SHCC pimn ar imilar to thir tnil rpon. An lati rpon i obrvd up to th firt rak load. Thn th bnding tr inra with an inra in th mid-pan dfltion; thu load th lab = pimn, ag-dpndnt all th orption/dorption pimn. Thi finding i in ontrat (Norling to Mjonll prviou 997). tt rult Undr for thi aum th plain onrt by prim ubtituting (Zhang t al. Equation 26, Lung into t Equati multipl rak dvlop at th bottom urfa th al. 27, Shin t al. obtain 27, Yun & Rokugo, 28) prim up to th modulu ruptur, whr a major onitnt with th rult for th ECC-layrd RC rak i obrvd. Th ultimat flxural tr inra about tim in omparion with that prntd in Tabl h indiat that SHCC-layrd bam obrvd by Maalj & Li (995). Th rult + ( D h) = & + & + w th onvntional onrt. Th flxural trngth lab xhibit a mall inra h in th hultimat load a th Ex-SHCC-PE matrial i.8 tim largr ompard to onvntional RC lab. than that th SHCC-PE matrial. Bad on th rult, it may b onludd that whr th addition a SHCC layr / h i th lop th orption/ an improv th initial raking flxural iothrm trngth (alo a RC alld on-way moitur lab. apa 3.2 Flxural bhavior RC on-way lab Spifially, th addition govrning quation an xpaniv (Equation SHCC 3) mut b Th load vru mid-pan dfltion urv for th layr an rult in by a ignifiant appropriat improvmnt boundary for initial th onditi Th rlation btwn th amount Tabl. Comparion on th flxural prforman RC on-way lab pimn. watr rlativ humidity i alld Spimn Initial rak Yilding Ultimat iothrm if Inra maurd prntag with * inraing Load Dfltion Load Dfltion Load Dfltion humidity dorption iothrm in th kn mm kn mm kn mm a. Nglting % thir diffrn (Xi t al. RC-S th following, orption iothrm will b NS rfrn to both orption dorption ES NS By th way, 47 if th hytri th ES iothrm would 8 b takn into aount, two rlation, vaporabl watr v rlativ humi * Th prntag initial raking trngth inra ompard to onvntional RC lab. b ud aording to th ign th varia Tabl 2. Craking bhavior RC on-way lab pimn. iothrm for HPC i inflund by many p Spimn Load tag pially tho that influn xtnt 25kN 5kN 75kN hmial Yilding ration, in turn, dtrm No. Avrag No. Avrag No. Avrag No. Avrag Maximum rak rak width rak rak width rak rak widthtrutur rak rak por width iz rak ditribution width (watrratio, a mnt mm hmial mm ompoition, SF a mm a mm a mm uring tim mthod, tmpratur, mix RC-S NS t.). 49 In th.28 litratur.33 variou formulatio ES found 54 to drib.22 th.6 orption iothrm NS onrt 35 (Xi.28 t al. 994)..2 Howvr, in th ES papr 5 th mi-mpirial.28.8 xprion pro J Proding FraMCoS-7, May 23-28, 2

6 D h T h (, () apaity a pavmnt to rit initial raking. Th proportionality fiint D(h,T) i alld moitur prmability it i a nonlinar funtion 3.3 th rlativ Craking humidity bhavior h RC tmpratur on-way lab T (Bažant & A Najjar photo 972). miroop Th moitur quippd ma with balan a 5x ln rquir a that monitor/omputr th variation in wr tim ud th to watr monitor ma th pr dvlopmnt onrt width (watr variation ontnt rak w) b that qual dvlopd to th unit volum divrgn ovr a 4 mm th ntr moitur lngth flux at J th tnil fa th t w = 2 J (Norling Mjonll 997). Undr Dfltion thi (mm) aumption by ubtituting (a) RC Equation lab layrd with into SHCC-PE Equation matrial 2 on obtain Figur 7. Rpon RC on-way lab pimn. RC-S D h) = h NS-2 ES-2 (2) Th watr ontnt w an b xprd a th um 8 th vaporabl watr w (apillary watr, watr vapor, 6 adorbd watr) th non-vaporabl (hmially bound) watr w n (Mill 966, 4 Pantazopoulo & Mill 995). It i raonabl RC-S to aum that 2 th vaporabl watr i a NS-2 funtion rlativ humidity, h, dgr hydration, NS-4, dgr ilia fum ration,, i.. w =w (h,, ) = ag-dpndnt orption/dorption iothrm h + h 8 & + & + ( n (3) w & xpliitly aount for th volution hydration ration SF ontnt. Thi orption iothrm bottom lab during loading. rad Tabl 2 ontain information on th raking bhavior onvntional SHCC-layrd on-way lab, giv data on th numbr rak avrag width rak at prdfind loading tag, w ( h,, ) = G (, ) + i.. 25, 5, 75 kn, th yilding ( load. Th g ) h fft a layr SHCC on rak mitigation i lar from (4) Tabl 2. Th SHCC-layrd lab how uprior ( g ) h K (, ) 2 4 watr pr unit volum hld in th gl RC-S por at % rlativ 2 humidity, it an b xprd ES-2 (Norling ES-4 Mjornll 997) a ( ) Dfltion G, = k + k (mm) vg vg (b) RC lab layrd with Ex-SHCC-PE matrial 8 RC-S NS-4 ES-4 whr th firt trm (gl iothrm) rprnt th phyially 8 bound (adorbd) watr th ond trm (apillary iothrm) rprnt th apillary 6 watr. Thi xprion i valid only for low ontnt SF. Th fiint G rprnt th amount (5) whr k vg k vg ar matrial paramtr. From th maximum amount watr pr unit volum that an fill all por (both apillary por gl por), on an alulat K a on obtain 6 whr / h i th lop th orption/dorption g iothrm 4 (alo alld moitur apaity). Th w G 4 govrning quation (Equation 3) mut b ompltd (6) K (, ) = by appropriat 2 boundary initial ondition. 2 g Th rlation btwn th amount vaporabl watr rlativ humidity i alld adorption iothrm if maurd with inraing rlativity Th matrial paramtr k Dfltion (mm) Dfltion (mm) vg k vg g an humidity dorption iothrm in th oppoit b alibratd by fitting xprimntal data rlvant to (a) RC lab layrd with layr thikn 2mm (b) RC lab layrd with layr thikn 4mm a. Nglting thir diffrn (Xi t al. 994), in fr (vaporabl) watr ontnt in onrt at th Figur following, 8. Initial orption bhavior iothrm RC on-way will lab pimn. b ud with variou ag (Di Luzio & Cuati 29b). rfrn to both orption dorption ondition. By th way,.2 if th hytri th moitur 6 RC-S 2.2 Tmpratur RC-S volution iothrm would b NS-2 takn into aount, two diffrnt NS rlation, vaporabl ES-2 watr v rlativ humidity, mut Not that, at ES-2 arly ag, in th hmial ration NS-4 NS-4 b ud aording to th ign th variation th aoiatd 4 with mnt hydration SF ration.2 ES-4 ES-4 rlativity humidity. Th hap th orption ar xothrmi, th tmpratur fild i not uniform 3 iothrm for HPC i inflund by many paramtr, for non-adiabati ytm vn if th nvironmntal.8 pially tho that influn xtnt rat th tmpratur 2 i ontant. Hat ondution an b hmial ration, in turn, dtrmin por.4 dribd in onrt, at lat for tmpratur not trutur por iz ditribution (watr-to-mnt xding C (Bažant & Kaplan 996), by ratio, mnt. hmial ompoition, SF ontnt, Fourir law, whih rad uring tim mthod, tmpratur, mix additiv, t.). In th litratur (a) Th variou avrag rak formulation width an b q = λ T (b) Th rak numbr (7) found to drib th orption iothrm normal onrt (Xi t al. 994). Howvr, in th prnt Figur 9. Variation avrag rak width lab pimn a funtion whr load. q i th hat flux, T i th abolut papr th mi-mpirial xprion propod by tmpratur, λ i th hat ondutivity; in thi Norling Mjornll (997) i adoptd bau it Avrag rak width (mm) Numbr rak 6 Proding FraMCoS-7, May 23-28, 2

7 D ( h, T h raking ritan, with finr a highr numbr rak than th onvntional RC lab. Tabl 2 rptivly provid information rgarding th maximum width rak at th yild load th avrag width numbr rak for th ES ri lab at prdtrmind loading tag. Th RC lab with a layr xpaniv SHCC how finr rak than th NS ri lab. In partiular, thi phnomnon i notworthy for th initial loading tag th RC lab with a thin SHCC layr, a hown in Figur 9a b. Figur how thr ri pitur illutrating th rak width inra a a funtion loading for th Control RC lab, NS- 4 ES-4 pimn. Th ht al in th uppr part Figur i a rfrn for hking Th th proportionality poition th fiint rak. D(h,T) Th ri pitur moitur indiat prmability a ignifiant diffrn in th raking bhavior th rlativ th humidity thr pimn. h tmpratur it i a nonlina From Figur, it & an Najjar b onludd 972). Th that moitur th rak ma balan width in th SHCC that layr th maintain variation a in low tim valu th b-watau th apparan volum multipl onrt fin (watr rak ontnt in w) b q ma th SHCC matrial. divrgn Th multipl th moitur rak aommodat furthr impod dformation a oon a thy flux J form. An xpaniv admixtur rdu th autognou hrinkag rtraining = J tr in th high t trngth SHCC. From th rult, it i hown that xpaniv SHCC i fftiv for rduing th initial Th watr ontnt w an b xprd a rak tndny, rduing th rtraind tnil th vaporabl watr w (apillary wa vapor, adorbd watr) th non- (hmially bound) watr w n (Mil Pantazopoulo & Mill 995). It i ra aum that th vaporabl watr i a fu rlativ humidity, h, dgr hydration dgr ilia fum ration,, i.. w =w = ag-dpndnt orption/dorption (Norling Mjonll 997). Undr thi aum by ubtituting Equation into Equati obtain + ( D 25kN 5kN 5kN Figur. Variation rak width RC SHCC-layrd lab a funtion load. h h h) = h & + & + whr / h i th lop th orption/ govrning quation (Equation 3) mut b by appropriat boundary initial onditi Th rlation btwn th amount watr rlativ humidity i alld iothrm if maurd with inraing humidity dorption iothrm in th a. Nglting thir diffrn (Xi t al. th following, orption iothrm will b iothrm (alo alld moitur apa 75kN 75kN rfrn to both 75kN orption dorption By th way, if th hytri th iothrm would b takn into aount, two rlation, vaporabl watr v rlativ humi b ud aording to th ign th varia rlativity humidity. Th hap th iothrm for HPC i inflund by many p pially tho that influn xtnt hmial ration, in turn, dtrm trutur por iz ditribution (watrratio, mnt hmial ompoition, SF uring tim mthod, tmpratur, mix 8kN 5kN t.). In th litratur variou formulatio found to drib 2kN th orption iothrm RC-S pimn NS-S-4 pimn onrt ES-S-4 (Xi t pimn al. 994). Howvr, in th papr th mi-mpirial xprion pro Norling Mjornll (997) i adoptd b w Proding FraMCoS-7, May 23-28, 2

8 D h T h (, () tr, inraing th initial rak trngth. Th proportionality fiint D(h,T) i alld moitur prmability it i a nonlinar funtion 4th CONCLUSION rlativ humidity h tmpratur T (Bažant & Najjar 972). Th moitur ma balan rquir that Thi th tudy variation invtigat tim th flxural th watr prforman ma unit volum raking onrt bhavior (watr RC on-way ontnt w) lab b layrd qual to with th divrgn diffrnt typ th moitur thikn flux J SHCC. For thi purpo, ight on-way SHCC-layrd RC lab, inluding a Control RC lab, wr dignd ttd. To = xamin J th fft a layr SHCC on (2) th t tnil fa th flxural raking bhavior on-way RC lab, diffrnt typ layr Th watr ontnt w an b xprd a th um thikn SHCC wr applid to th tnil rgion th vaporabl RC lab. watr w (apillary watr, watr vapor, Th rplamnt adorbd watr) 8% xpaniv th non-vaporabl admixtur in (hmially volum mnt bound) inra watr th w n firt (Mill tnil 966, rak Pantazopoulo th ompriv & Mill 995). flxural It i trngth raonabl high to aum trngth that SHCC th vaporabl matrial ompard watr to i a high funtion trngth rlativ SHCC humidity, matrial without h, dgr an xpaniv hydration, admixtur,, dgr whra ilia th tnil fum ration, trngth, i.. train w =w apaity (h,, dra. ag-dpndnt Th addition orption/dorption an xpaniv admixtur iothrm ap- ) = (Norling par to Mjonll hav littl 997). fft Undr on th thi raking aumption pattrn by high ubtituting trngth SHCC Equation undr dirt into tnil Equation flxural 2 on obtain loading. From th bnding tt SHCC-layrd RC lab, it i found that th appliation a layr SHCC h at th bottom on-way RC + lab inra ( D h) = & + & + w& n (3) flxural h trngth h iffn. Th improvmnt th flxural prforman inra aording to th layr thikn tnil prforman th SHCC whr applid. / h i th lop th orption/dorption Spifially, RC lab with a layr xpaniv SHCC iothrm (alo how alld highr moitur initial rak apaity). trngth Th govrning flxural tiffn quation aftr (Equation initial 3) raking mut b ompard ompltd to by th appropriat Control high boundary trngth SHCC-layrd initial ondition. lab. Th high Th rlation dutility btwn multipl th amount raking apaity vaporabl watr SHCC ar rlativ rponibl humidity for uh i alld a prforman adorption improvmnt. if But maurd th flxural with prforman inraing rlativity improv- iothrm humidity mnt SHCC-layrd dorption RC iothrm mmbr in i l th dramati oppoit a. than Nglting th trngthning thir diffrn fft (Xi SHCC t al. applid 994), to in th plain following, onrt orption mmbr, iothrm a rportd will by b prviou ud with rarhr. to both orption dorption ondition. rfrn By th way, if th hytri th moitur iothrm would b takn into aount, two diffrnt rlation, REFERENCE vaporabl watr v rlativ humidity, mut b ud aording to th ign th variation th Japan Soity Civil Enginr. 28. Rommndation for rlativity humidity. Th hap th orption dign ontrution high prforman fibr rinford for mnt HPC ompoit i inflund with multipl by many fin paramtr, rak. Con- iothrm pially rt Enginring tho that Sri influn 82, Japan. xtnt rat th hmial Lung, C.K.Y., ration Chung,, Y.N. in & Zhang, turn, J. dtrmin 27. Fatigu por nhanmnt onrt bam with ECC layr. Cmnt trutur por iz ditribution (watr-to-mnt Conrt Rarh 37(5): ratio, Maalj, mnt M. & Li, hmial V.C ompoition, Introdution train-hardning SF ontnt, uring nginrd tim mntitiou mthod, ompoit tmpratur, in dign mix additiv, rinford t.). onrt In th flxural litratur mmbr variou for improving formulation durability. an ACI b Strutural Journal 92(2): found to drib th orption iothrm normal Shin, S.K., Kim, J.H. & Lim, Y.M. 27. Invtigation th onrt trngthning (Xi t al. fft 994). DFRCC Howvr, applid in to plain th prnt onrt papr bam. th Cmnt mi-mpirial Conrt xprion Compoit 29(6): propod by Norling Mjornll (997) i adoptd bau it xpliitly aount for th volution hydration ration SF ontnt. Thi orption iothrm Yun, H.D. & Rokugo, K. 28. Craking mitigation flxural bhavior onrt bam layrd with train- rad hardning mnt ompoit (SHCC). 8th Intrnational Sympoium on Utilization High-Strngth High- Prforman Conrt; Pro. intrn. ymp., Tokyo, w Otobr ( h,, 28. ) = G (, ) + Zhang, J., Lung, C.K.Y. & Chung, Y.N. 26. Flxural prforman layrd ECC-onrt ompoit bam. ( g ) h Compoit Sin Thnology 66(-2): (4) ( g ) h K (, ) whr th firt trm (gl iothrm) rprnt th phyially bound (adorbd) watr th ond trm (apillary iothrm) rprnt th apillary watr. Thi xprion i valid only for low ontnt SF. Th fiint G rprnt th amount watr 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) whr k vg k vg ar matrial paramtr. From th maximum amount watr pr unit volum that an fill all por (both apillary por gl por), on an alulat K a on obtain K (, ) = g w G g (6) Th matrial paramtr k vg k vg g an b alibratd by fitting xprimntal data rlvant to fr (vaporabl) watr ontnt in onrt at variou ag (Di Luzio & Cuati 29b). 2.2 Tmpratur volution Not that, at arly ag, in th hmial ration aoiatd with 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 law, whih rad q = λ T (7) whr q i th hat flux, T i th abolut tmpratur, λ i th hat ondutivity; in thi Proding FraMCoS-7, May 23-28, 2