Measuring crack width and spacing in reinforced concrete members

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1 Fratur Mhani Conrt and Conrt Strutur - Rnt Advan in Fratur Mhani Conrt - B. H. Oh, t al.(d) 200 Kora Conrt Intitut, Soul, ISBN Mauring rak idth and paing in rinford onrt mmbr S. Yair Alam, T. Lnormand, A. Loukili & J.P. Rgoin Eol Cntral d Nant, Fran ABSTRACT: Craking bhavior rinford onrt i uually undrtood by th raking a onrt prim rinford ith a ntral bar ubjtd to tnion. Bnding, hih i majority th ral a, i dalt in th Eurood by an mpirial adjutmnt th fiint. In thi papr an xprimntal program i dvid to tudy th trutural iz fft rinford onrt mmbr on rak idth and paing. Bnding tt ar prformd on thr diffrnt iz bam hih ar gomtrially imilar in to dimnion. Th main rinformnt ratio i ontant in all th bam kping th am numbr bar. Th ovr to th main rinformnt i alo ald ith th bam iz. Crak idth and rak paing ar maurd uing digital imag orrlation thniqu. Strain in th main rinformnt i maurd uing mbddd ltri train gaug. It i found that Eurood undrtimat th rak idth and rak paing. Maurd valu rak idth ho an important trutural iz fft, hih i not aountd by Eurood rak idth formula. INTRODUCTION Srviability limit tat (SLS) for rinford onrt (RC) trutur ar uually applid to nur thir funtionality and trutural intgrity undr rvi loading ondition. In urrnt dign od (EC2 EN 992), th rviability limit tat ar dfind by providing thr ontrol paramtr () Limitation tr in th matrial (2) Control rak idth and paing (3) Dfltion (hort trm and long trm) hk. Th maximum tr, dfltion and rak iz ar omputd from ritial ombination atual, applid load (alld rvi load), in onjuntion ith th trutur gomtry (typ and loation rinformnt) and boundary ondition. Hovr, it ill b n in thi papr that th rak iz alo dpnd on matrial ritan to rak groth, hih i not am a th matrial trngth and hih vari ith th iz th trutur. In thi papr an xprimntal tudy i prntd, in hih thr gomtrially izd bam r ttd in thr point bnding to obtain th xprimntal rak idth and rak paing, hn th trutur i ubjtd to rvi loading. 2 CRACK CONTROL IN RC STRUCTURES It i rognizd that raking in rinford onrt mmbr may b to form: () Craking du to rtraint providd by trutur to volum hang, and (2) raking du to applid load. In thi papr only th raking du to applid load i diud. Thr ar thr prinipal lmnt in th proviion rak ontrol (EC2 EN 992): () Th proviion minimum rinformnt ara (2) A mthod for alulating dign rak idth (3) Simplifid rul hih ill avoid th nity for xpliit alulation rak idth in mot normal ituation. 2. Dign Crak idth Th approah almot univrally ud to xplain th bai raking bhavior rinford onrt i to onidr th raking a onrt prim rinford ith a ntral bar hih i ubjtd to pur tnion. Bnding do influn th phnomna but thi i dalt ith in th Eurood by an mpirial adjutmnt th fiint. Aording to Eurood (EC2 EN 992), th dign rak idth an b dtrmind uing th folloing xprion = ( ε ε ) k r max m m, () hr, k = dign rak idth ; r,max = maximum rak paing ; ε m = man train in th rinformnt ; ε m = man train in onrt btn rak. In th xprion () ε m - ε m may b alulatd a: f t, ff σ k ( + ρ ) t p, ff ρ p, ff σ ε ε = 0. 6 m m E E (2)

2 hr J = D ( h, T ) h () σ = tr in th tnion rinformnt auming rakd Th proportionality tion ; ρ p,ff = Afiint /A,ff, hih D(h,T) i th i ratio alld ara moitur tnion prmability rinformnt and it i (A a nonlinar ) to th fftiv funtion tnion th rlativ ara humidity onrt h and around tmpratur th tl T (Bažant (A,ff ). Hovr, & Najjar 972). A,ff dpnd Th moitur impliitly ma upon balan th onrt rquir ovr that th providd variation on in th tim tnion th fa. atr S ma dtail pr unit in EC2 volum EN 992. onrt (atr ontnt ) b qual to th divrgn th moitur flux J 2.2 Maximum final rak paing Whn = rinformnt J i fixd at raonably lod (2) t paing (paing 5(+Φ/2)), aording to Eurood Th (EC2 atr EN ontnt 992) th an maximum b xprd final rak a th paing um th an vaporabl b alulatd atr a: (apillary atr, atr vapor, and adorbd atr) and th non-vaporabl (hmially φ r = bound) k k atr n (Mill 966, (3), max 2 Pantazopoulo & Mill 995). ρ p, ff It i raonabl to aum that th vaporabl atr i a funtion hr, rlativ humidity, h, dgr hydration,, and dgr Φ = bar ilia diamtr fum ; ration, = onrt, i.. ovr =; k(h,, k 2, ar ) fiint = ag-dpndnt dpnding orption/dorption upon tl-onrt iothrm bond proprti (Norling Mjonll and loading 997). typ Undr rptivly. thi aumption S EC2 and EN by 992 ubtituting for dtail. Equation into Equation 2 on obtain In quation (3) onrt ovr i xpliitly introdud into th xprion th rak idth a uggtd by A. Bby. H tudid th influn h = onrt ovr ovr th & tranfr + & lngth + & n (Bby (3) h t h 200). Th tranfr lngth inra monotonially ith th inra onrt ovr. Thi fft i introdud hr in /h th i alulation th lop th rak orption/dorption paing. Str in iothrm onrt (alo around alld th moitur rinformnt apaity). i dirtly Th dpndant govrning quation th tr (Equation tranfr 3) lngth mut btn ompltd onrt by appropriat and tl. boundary Sin raking and initial our ondition. in onrt at th Th point rlation hr btn tr xd th amount th tnil vaporabl ritan atr onrt, and rlativ thrfor, humidity rak paing i alld i a adorption funtion onrt iothrm ovr. if maurd In thi ith tudy, inraing onrt ovr rlativity to hight humidity th and bam dorption ratio i kpt iothrm ontant in th to tak oppoit into aount a. Nglting th fft thir diffrn ovrall trutur (Xi t al. iz 994), on th in rak th folloing, opning and orption rak paing. iothrm ill b ud ith rfrn to both orption and dorption ondition. By th ay, if th hytri th moitur 2.3 iothrm Analyi ould tt b takn data into aount, to diffrnt It rlation, ha bn vaporabl uggtd atr that v hn rlativ analyzing humidity, th mut tt data b ud rak aording idth to and th rak ign paing th variation in rinford th onrt rlativity tnil humidity. mmbr, Th folloing hap onidration th orption hould iothrm b for mad HPC (Commntary i inflund to by EN many 992): paramtr, pially - Th matrial tho that ud influn hould xtnt b imilar and to rat th matrial hmial u ration today in th and, building in turn, trutur. dtrmin Th por lo th bound trutur rbar, and por onrt iz qualiti ditribution l (atr-to-mnt than 20 N/mm 2 and ratio, tl mnt qualiti hmial l than ompoition, 400 N/mm 2 SF hould ontnt, not b uring ud. tim and mthod, tmpratur, mix additiv, t.). - Th In tr th litratur rang hould variou b formulation rviability an rang. b For found thi to purpo, drib rult th orption in th tr iothrm rang in normal tl from onrt 50 (Xi to 350 t al. N/mm 994). 2 hould Hovr, b onidrd in th prnt for tt papr involving th mi-mpirial dirt ation. xprion For indirt propod ation, by Norling Mjornll (997) i adoptd bau it tl xpliitly tr aount rang up for to th yilding volution tr hydration tl hould ration b and onidrd. SF ontnt. Thi orption iothrm rad - To dtrmin th rak paing th numbr rak prnt at th lat pha th tt i alay onidrd in it i th lot to th tabilizd raking, a givn by quation (3). ( h,, ) = G (, ) + In th litratur a vry ar data i found for th 0( g ) h dirt omparion btn th alulatd and (4) th xprimntal rak idth. 0( g ) h K (, ) 3 SIZE EFFECT IN CONCRETE Strutural hr th iz firt fft trm i (gl th iothrm) ntral problm rprnt in prdition phyially fratur. bound (adorbd) Fratur tt atr ar and normally th ond on- th dutd trm (apillary on rlativly iothrm) mall pimn rprnt and th thn apillary thi information atr. Thi i xprion xtrapolatd i valid to larg only trutur. for lo ontnt Th SF. Th qution fiint iz Gfft rprnt ha bom th amount a ruial onidration atr pr unit in volum th ffort hld to in dign th gl onrt por at trutur, rlativ for humidity, hih thr and invitably it an b xprd i a larg (Norling gap b- 00% tn Mjornll th 997) al a larg trutur (dam, rator ontainmnt, bridg) and laboratory tt. Th iz fft on trutural trngth i normally undrtood a th fft vg th vg haratriti trutur iz G (, ) = k + k (5) (dimnion) on th nominal trngth th trutur hn hr gomtrially k imilar trutur ar ompard vg and k vg ar matrial paramtr. From th (Bazant maximum 2002). amount atr pr unit volum that an fill In all all por quai-brittl (both apillary matrial por lik and onrt, gl por), fratur an alulat i prdd K a by on a gradual obtain diprd mirorak- on ing that our ithin a rlativly larg fratur pro zon ahad th rak tip a ontinuou 0 g rak. Whn a onrt trutur i loadd, th G train 0 nrgy produd by th applid load i onvrtd to (6) th K ( nrgy, ) = onumd to rat n fratur urfa and th nrgy aborbd 0 g in th fratur pro zon. For larg-iz trutur th lattr i ngligibl ompard to th formr, hra for a mall-iz Th matrial paramtr k vg and k vg and g an trutur th an b omparabl (Bazant 2002). b alibratd by fitting xprimntal data rlvant to Thrfor, th largr th trutur iz, th lor th fr (vaporabl) atr ontnt in onrt at nominal trngth. Hovr, th onrt trngth variou ag (Di Luzio & Cuati 2009b). approah a ontant hn th iz th onrt trutur bom vry larg. 2.2 Tmpratur volution 3. Not Siz that, fft at arly on rak ag, in idth th hmial ration aoiatd ith mnt hydration and SF ration It i obviou that th raking bhavior i alo inflund by trutural iz. A rnt tudy ha hon ar xothrmi, th tmpratur fild i not uniform for non-adiabati ytm vn if th nvironmntal that th raking in plain onrt i iz dpndant tmpratur i ontant. Hat ondution an b mhanim (Alam & Loukili 2009). It a obrvd dribd in onrt, at lat for tmpratur not that hn gomtrially imilar pimn ar ttd xding 00 C (Bažant & Kaplan 996), by undr am loading and boundary ondition, th Fourir la, hih rad propagation rak i not th am in larg bam a it i in mall bam. A numrial tudy (Ouyang q = λ T & Shah 994) rinford onrt bad on fratur mhani rul ha alo hon th raking (7) bhavior hr q to i b iz th dpndant. hat flux, Thy T i alulatd th abolut rak idth tmpratur, in tnil and mmbr λ i th ith hat ontant ondutivity; ntral in rinformnt and mmbr lngth but varying ro thi - Proding FraMCoS-7, May 23-28, 200

3 tional ara. Thy found that rak idth dra a th idth th mmbr inra. Rult r not ompard ith xprimntal data. Thy found that prviouly obtaind xprimntal data i vry attrd bau rak idth dpnd, not only on th gomtry and loading ondition th trutur, but alo on th iz th trutur. In th urrnt dign approah (Equation () & (2)), rak idth i valuatd primarily uing mpirial mthod that rquir om mpirial ontant. Th iz fft on th rak idth annot b aountd for by th onvntional analyi unl additional mpirial ontant ar ud (Shah t al. 995). A limitd amount xprimntal data i availabl in th litratur onrning th tudy iz fft on th rak idth and rak paing. Mot th rult dal ith th rinford onrt mmbr ubjtd to tnion or having mall dimnion(commntary to EN 992). In thi papr an xprimntal program i dvid to tudy th fft trutural iz on th rak idth and rak paing. Thr iz bam ith gomtrially imilar lngth and hight, but ith ontant thikn ar ttd in thr-point bnding. Th tnil rinformnt ratio i kpt ontant; hovr, th onrt ovr to th rinformnt a ald aording to th ovrall iz th bam. Th aim thi tudy i to valuat th onrt rak idth and rak paing xprion prnt in th Eurood (quation -3) ith th xprimntally maurd rak idth and paing. 4 EXPERIMENTAL PROGRAM 4. Matrial Th onrt ud to prpar th bam i mad from Portland mnt typ 52.5, and, aggrgat & atr uing th mix proportion in Tabl (). Tabl. Conrt mix dign dtail. Cmnt (Portland 52.5) 32 kg/m 3 Sand 88 kg/m 3 Coar aggrgat (5-2.5 mm) 936 kg/m 3 Watr 29 kg/m 3 Th ompriv trngth onrt i ttd at 28 day uing ylindrial pimn ith diamtr 0m and hight 20m and i found to b 40 N/mm 2. Sin th bam ar rinford ith rbar, a upr platiizr ith a doag 0.25% by ight mnt i addd to inra th orkability frh onrt. Th longitudinal rinformnt bam i ontitutd dformd bar ith 0, 4 & 20 mm in diamtr, hil, th tranvr rinformnt i pro- Th proportionality fiint D(h,T) Pantazopoulo & Mill 995). It i ra vidd by dformd J = bar D ( h, ith T ) 6mm h in diamtr. Th tl bar in both a ar typ f yk 500 MPa. 4.2 Bam moitur prmability and it i a nonlina th rlativ humidity h and tmpratur Thr iz bam & Najjar ar ttd. 972). Th dimnion moitur ma balan th bam ar givn that in th Tabl variation 2. Th in tim bam hav th atr a ma ontant idth (b volum = 00 mm), onrt hovr, (atr th ontnt lngth ) b q and hight ar ald. divrgn Conrt th ovr moitur at th flux tnion J fa th bam i alo ald ith am proportion btn diffrnt iz bam. Th bam ar rinford ith a ontant = rinformnt J ratio by vary- t ing th diamtr th bar; hovr, th numbr bar i kpt ontant. Th Stl atr tirrup ontnt ar ud an b in xprd th a ara high har. To th vaporabl hangr bar atr 6mm diamtr ar ud to upport (apillary a vapor, tl and adorbd tirrup. Th atr) bar and ar th non- ut hr th tirrup (hmially ar not providd bound) (Fig. atr ). n (Mil Tabl 2. Spimn gomtry. aum that th vaporabl atr i a fu rlativ humidity, h, dgr hydration Bam b h L l ρ dgr ilia fum ration, ovr, i.. = = ag-dpndnt orption/dorption mm mm mm mm % mm (Norling Mjonll 997). Undr thi aum Small D 00 by 00 ubtituting Equation.99 0 into Equati obtain Mdium D Larg D h = & + & + h t h D hr /h i th lop A th orption/ iothrm (alo alld moitur apa govrning quation (Equation 3) mut b by appropriat boundary and initial onditi Th rlation btn th amount A Stion A-A atr and rlativ humidity i alld iothrm if maurd ith inraing D2 humidity and dorption iothrm in th a. Nglting thir diffrn A (Xi t al. th folloing, orption iothrm ill b rfrn to both orption and dorption By th ay, if th hytri th iothrm ould b takn into aount, to rlation, vaporabl atr A v rlativ humi Stion A-A b ud aording to th ign th varia rlativity humidity. Th hap th D3 iothrm for HPC i inflund by many p A pially tho that influn xtnt and hmial ration and, in turn, dtrm trutur and por iz ditribution (atrratio, mnt hmial ompoition, SF uring tim and mthod, tmpratur, mix t.). In th litratur variou A formulatio Stion A-A found to drib th orption iothrm Figur *. Gomtry onrt and rinformnt (Xi t dtail. al. 994). Hovr, in th *Th figur i not ald. papr th mi-mpirial xprion pro Norling Mjornll (997) i adoptd b Proding FraMCoS-7, May 23-28, 200

4 4.3 J = D ( Tt h, produr T ) h () All th xprimnt ar prformd uing th am tting Th mahin proportionality ith ontrolld fiint diplamnt. D(h,T) alld Th tt moitur tup prmability i hon in Figur and it i 2. a Th nonlinar load i funtion applid at th mid rlativ pan humidity ith a ylindrial h and tmpratur jak, nuring T (Bažant th point & Najjar load. 972). Th load Th i moitur tranfrrd ma to balan th bam rquir uing a that rubbr th variation pad, to avoid in tim th onrt th atr damag ma pr at unit th load volum point. onrt Th tt (atr i arrid ontnt out ) uing b qual a ontant to th vrtial divrgn diplamnt th moitur rat 0.5 flux J mm/min. Th diplamnt i maurd uing a lar nor, hih maur th diplamnt at th mid tion th = J (2) bam t undr th load. Th nor i attahd to a tl hangr, hih i upportd at th upport to tak Th into atr aount ontnt th ttlmnt an b xprd bam at a th upport. th vaporabl atr (apillary atr, atr um vapor, and adorbd atr) and th non-vaporabl (hmially bound) atr n (Mill 966, Sytm Pantazopoulo & Mill 995). It i raonabl to aquiition aum that th vaporabl atr i a funtion rlativ humidity, h, dgr hydration,, and tl d- dgr ilia fum ration,, i.. = (h,, ) forma- = ag-dpndnt orption/dorption iothrm (Norling Mjonll 997). Undr thi aumption and by ubtituting Equation into Equation 2 on obtain Light projtor h + h t ( D h) = n (3) h & + & + hr /h i th lop th orption/dorption Figur iothrm 2. Tt (alo tup. alld moitur apaity). Th govrning quation (Equation 3) mut b ompltd by For appropriat ah bam, boundary to ltri and initial train ondition. gaug ar attahd Th to rlation th lor btn fa th tnion amount tl at vaporabl mid pan to atr maur and th rlativ longitudinal humidity train i alld in tl adorption during th tt iothrm (Fig. 3). if maurd ith inraing rlativity humidity Rult and ar dorption diud hr iothrm for thr in point th oppoit bnding tt a. on Nglting thr iz thir diffrn bam. Aftr (Xi th t al. fabriation, 994), in th folloing, bam r orption tord at iothrm 20 C and ill rlativ b ud humidity rfrn 50% to for both 24 orption hour. Aftr and th dorption rmoval ondition. mold, ith th By th bam ay, r if tord th hytri in 00% rlativ th humidity moitur for iothrm 28 day ould b takn into aount, to diffrnt rlation, vaporabl atr v rlativ humidity, mut b ud aording to th ign th variation th rlativity humidity. Th hap th orption iothrm for HPC i inflund by many paramtr, pially tho that influn xtnt and rat th hmial ration and, in turn, dtrmin por trutur and por iz ditribution (atr-to-mnt ratio, mnt hmial ompoition, SF ontnt, uring tim and mthod, tmpratur, mix additiv, t.). In th litratur variou formulation an b found to drib th orption iothrm normal Figur 3*. Strain gaug attahd to th tl bar at mid pan. *vi onrt bfor (Xi th t pouring al. 994). onrt. Hovr, in th prnt papr th mi-mpirial xprion propod by Norling Mjornll (997) i adoptd bau it & 4.4 xpliitly Digital aount imag orrlation for th volution hydration ration and SF ontnt. Thi orption iothrm Th maurmnt rak idth and rak paing rad i arrid out uing a digital imag orrlation ytm. Th digital imag orrlation i an optial mthod to maur th urfa diplamnt fild btn ( h,, to ) = tim G ( intant., ) Thi thniqu ha + alrady bn applid on onrt 0( g (Alam )& h Loukili 2009, Choi & Shah 997, Lalr t al. 200, Corr (4) t al. 2007). It i bad on th omparion to imag bad on Kgrayal (, ) rordd bfor 0( g ) h and aftr dformation. Th firt imag i alld th rfrn and th ond i th dformd imag. Th diplamnt fild i thn dtrmind through th hr th firt trm (gl iothrm) rprnt th movmnt th ubimag in an ara dfind a th phyially bound (adorbd) atr and th ond orrlation zon. Th orrlation onit onidring a gmnt (ubimag) in th rfrn imag trm (apillary iothrm) rprnt th apillary atr. Thi xprion i valid only for lo ontnt and loating that gmnt (ubimag) in th dformd imag, hr th maximum liklihood i SF. Th fiint G rprnt th amount atr pr unit volum hld in th gl por at 00% ahivd. In thi tudy, a ommrial tar rlativ humidity, and it an b xprd (Norling Vi2D i ud to prform th imag orrlation. Th Mjornll 997) a iz ubimag i takn a 29x29 pixl, hih i rgularly pad in th rfrn imag ( iz 392x040 G (, ) = pixl) k + in kth form a grid. Eah ubimag in th rfrn imag i orrlatd to th on (5) vg vg in dformd imag by alulating a orrlation fiint hr k vg in th and orrlation k vg ar matrial ara around paramtr. th ubimag. From th Th maximum rolution amount th ytm atr pr dpnd unit volum dirtly that on an th ditribution fill all por (both gray apillary lvl hih por dpnd and gl por), on th txtur on an alulat th matrial. K a on To obtain obtain a random pattrn, a pkl pattrn blak and hit paint i prayd onto th urfa th pimn. 0 Th g imag on a ingl fa 0.88 th + pimn 0.22 G ar apturd uing 0 to digital amra, hih giv 256 lvl gray intnity. Camra ar plad (6) K (, ) = 0 in uh a ay to film an g ara 5x0 m by ah amra at ithr id th mid pan. Th mid pan portion i filmd by both amra. Th matrial Th mid paramtr pan tion k vg i and takn k vg a and th grfr- n b alibratd to rlat by th fitting maurmnt xprimntal valu data rlvant th to to an amra fr (vaporabl) a hon in atr Figur ontnt 4. in onrt at variou ag (Di Luzio & Cuati 2009b). 50 mm 2.2 Tmpratur volution 00 mm Mid pan, rfrn lin for to amra Not that, at arly ag, in th hmial ration aoiatd ith mnt hydration and 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 00 C (Bažant & Kaplan 996), by Fourir la, CAM hih rad CAM 2 5 mm Figur q = λ4. T Camra zon for digital imag orrlation. (7) hr q i th hat flux, T i th abolut tmpratur, and λ i th 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 and it i a nonlina th rlativ humidity h and tmpratur & Najjar 972). Th moitur ma balan that th variation in tim th atr ma volum onrt (atr ontnt ) b q divrgn th moitur flux J t = J Th atr ontnt an b xprd a th vaporabl atr (apillary a vapor, and adorbd atr) and th non- (hmially bound) atr n (Mil Pantazopoulo & Mill 995). It i ra aum that th 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 Figur 5. Maurmnt rak opning diplamnt (COD) and rak paing in mall (D) bam. h = h t h & + & + 5 RESULTS AND DISCUSSION Th maurmnt rak opning diplamnt (COD) and rak paing by digital imag orrlation i prntd in Figur 5. COD i maurd a diplamnt jump on th urfa th bam. Multipl rak ar found, but only th maximum COD i onidrd in th furthr analyi Th rak idth maurd uing digital imag orrlation thniqu i plottd againt th rak idth obtaind uing urood rak idth formula (q. ) a a funtion tl train ε m. Th rak idth i maurd at th mouth th rak i.. at th lot fibr th bam, hr th rak idth i maximum. Th rult ar hon in Figur 6 for omparion. It an b n that urood formula undrtimat th rak idth for all th thr iz. Th diffrn btn maurd and alulatd valu xd hn th train i highr. Figur 4 ho th omparion for a tr rang undr yild limit tl. 0,5 0,4 ) 0,3 m (m x a W k,m 0,2 hr /h i th lop th orption/ iothrm (alo alld moitur apa govrning quation (Equation 3) mut b by appropriat boundary and initial onditi Th rlation btn th amount D3 atr and rlativ humidity i alld D2 iothrm if maurd D ith inraing Cal~tt humidity and dorption iothrm in th a. Nglting thir diffrn (Xi t al. 0, th folloing, orption iothrm ill b rfrn to both orption and dorption 0 By th ay, if th hytri th 0 0, 0,2 0,3 0,4 0,5 W k,xp (mm) iothrm ould b takn into aount, to rlation, vaporabl atr v rlativ humi Figur 6. Comparion xprimntal rak idth (W k,xp ) and alulatd maximum b rak ud idth aording (W k,max ) during to th rak ign formation tag (ε m < yild rlativity limit). humidity. Th hap th th varia iothrm for HPC i inflund by many p A mor dtail pially obrvation tho th that fft influn iz xtnt on and th urood alulatd hmial rak ration opning and, i mad in in turn, th dtrm Figur 7. It i lar trutur that th and alulatd por iz rak ditribution idth (atrratio, mnt for mall hmial iz bam ompoition, but th SF mor or l omparabl rror xd ith uring iz inra. tim and mthod, tmpratur, mix t.). In th litratur variou formulatio found to drib th orption iothrm onrt (Xi t al. 994). Hovr, in th papr th mi-mpirial xprion pro Norling Mjornll (997) i adoptd b Proding FraMCoS-7, May 23-28, 200

6 J = ) 0,6 moitur 0,2 prmability and it i a nonlinar ε = 0,4 x funtion 0-3 ) & mnajjar 972). Th moitur ma balan ε = 0,6 x 0 rquir -3 (m 0,08 that W th variation in tim th atr ma pr unit k volum onrt (atr ontnt ) b ε qual = 0,9 x 0 to th -3 0,04 divrgn th moitur flux J 0,00 D ( h, T h Spimn iz (mm) () Eurood 2 EN 992 Exprimnt Th proportionality fiint D(h,T) i alld th rlativ humidity h and tmpratur T (Bažant t = J (2) Figur Th 7. atr Siz fft ontnt xprimntal an b and xprd alulatd a maximum th um rak idth. th vaporabl atr (apillary atr, atr vapor, and adorbd atr) and th non-vaporabl Th rak idth obtaind from Eurood formula (hmially bound) atr n (Mill 966, do not tak into aount iz fft. Hovr, th Pantazopoulo & Mill 995). It i raonabl to valu obtaind ar diffrnt for thr iz aum that th vaporabl atr i a funtion bam. But, thi hould not b onidrd a iz fft a th Eurood formula dpnd only on th rlativ humidity, h, dgr hydration,, and dgr ilia fum ration,, i.. = (h,, ) onrt ovr and diamtr th bar, hovr, = ag-dpndnt orption/dorption iothrm th tru iz fft i th fft th dimnion (Norling Mjonll 997). Undr thi aumption and th trutur on th ovrall fratur mhanim. A by ubtituting Equation into Equation 2 on th trutur bom uffiintly larg th iz obtain th htrognity bom ngligibl ompard to th iz th trutur and matrial follo a brittl failur. hhovr, hn th iz th trutur bom h uffiintly t h mall th iz htrognity = & + & + & n (3) bom omparabl to th iz th trutur and th matrial and th matrial follo a dutil failur. hr /h i th lop th orption/dorption iothrm (alo alld moitur apaity). Th govrning quation (Equation 3) mut b ompltd 200 by appropriat boundary and initial ondition. Th rlation btn th amount vaporabl atr and rlativ humidity i alld adorption 50 iothrm if maurd ith inraing rlativity ) humidity m and dorption iothrm in th oppoit a. ( m x 00Nglting thir diffrn (Xi t al. 994), in a th folloing, orption iothrm ill b ud ith r,m rfrn to both orption and dorption ondition. Eurood 2 EN 992 By 50 th ay, if th hytri th moitur iothrm ould b takn into aount, Exprimnt to diffrnt rlation, vaporabl atr v rlativ humidity, mut b ud 0 aording to th ign th variation th rlativity humidity. Th hap th orption Spimn iz (mm) iothrm for HPC i inflund by many paramtr, Figur pially 8. Maximum tho that paing influn rak, xtnt omparion and rat maurd hmial valu ith ration th alulatd and, valu. in turn, dtrmin por th trutur and por iz ditribution (atr-to-mnt ratio, Th mnt maximum hmial paing ompoition, btn rak SF ontnt, i alo maurd uring tim hn and tl mthod, tr tmpratur, a qual to mix 300 additiv, N/mm 2. Thi t.). paing In th litratur i ompard variou (Fig. formulation 8) ith th paing an b obtaind found to from drib th th Eurood orption formula iothrm (q. 3). normal It i n onrt that i (Xi undrtimatd t al. 994). for Hovr, th mdium in th (D2) prnt and larg papr (D3) th izd mi-mpirial bam. Th xprion raon may propod b that th by onrt Norling bom Mjornll mor (997) brittl i hn adoptd th bau iz th it bam inra. Thu th rak propagation i muh fatr xpliitly (Alam aount & Loukili for th 2009) volution and nrgy hydration rla rat ration i highr and SF in ontnt. larg trutur Thi orption (Kaplan iothrm 96). Hovr rad for mall trutur, rak propagation i muh lor and train nrgy i mainly rlad du to miroraking in th fratur pro zon. Sin th prn rinformnt hindr th dvlopmnt fratur pro zon, mor rak ar ( h,, ) = G (, ) + 0( g ) h bing formd to rla th train nrgy tord (4) in th matrial. 0( g ) h K (, ) 6 CONCLUSION An hr xprimntal th firt trm invtigation (gl iothrm) prformd rprnt to tudy th th phyially fft bound trutural (adorbd) iz on atr rak idth and th and ond rak paing trm (apillary in rinford iothrm) onrt rprnt trutur th undr apillary rvi atr. loading. Thi xprion Th rult i valid ho only that for th lo maurd ontnt valu SF. mor Th fiint or l agr G ith rprnt th alulatd th amount valu atr lo pr train unit volum and mall hld bam in th iz. gl But por thr at 00% i a ignifiant rlativ humidity, iz fft and it on an th b xprimntal xprd (Norling rak idth Mjornll and 997) rak a paing, hih i not inorporatd in th urrnt Eurood dign formula. G (, ) = k + k vg vg (5) REFERNCES hr k vg and k vg ar matrial paramtr. From th Alam, maximum S.Y. & amount Loukili, A. atr Etud pr unit d fft volum d éhll that an ur la propagation d fiur dan l béton par la thniqu d fill all por (both apillary por and gl por), on orrélation d imag, Rnontr AUGC. Saint-Malo. an Fran. alulat K a on obtain Bazant, Z.P Saling trutural trngth. London: Hrm Pnton. 0 g Bby A.W Calulation Crak Width, PrEN G (Final draft). 0 Chaptr Bby A.W Crak ontrol proviion in th n urood for th dign onrt trutur. (6) K (, ) = 0 ACI Spial publiation 204: g Corr, D.; Aardi, M., Grahan-Brady, L. & Shah, S.P Gigital imag orrlation analyi intrfaial dbonding Th matrial paramtr k vg and k vg and g proprti and fratur bhaviour in onrt. Enginring an b Fratur alibratd Mhani by fitting 74: xprimntal data rlvant to Choi, fr S. (vaporabl) & Shah, S.P atr Maurmnt ontnt in dformation onrt on at variou onrt ag ubjtd (Di Luzio to omprion & Cuati uing 2009b). imag orrlation. Exprimntal Mhani 37(3): EN 992--, Dmbr Eurood 2: Dign onrt 2.2 trutur Tmpratur Part -: volution Gnral rul and rul for building. Brul. Europan Committ for Standardization (CEN). Jaob, Not that, J-P. Jun at arly ag, Commntary in th Eurood hmial 2. Brul, ration Europan Conrt ith Platform mnt ASBL. hydration and SF ration aoiatd Kaplan, ar xothrmi, M. F. 96. th Crak tmpratur Propagation fild and i th not Fratur uniform for Conrt. non-adiabati ACI Journal ytm proding vn if 58(): th nvironmntal Lalr, J.S.; Kan, D.T. & Shah, S.P Mauring thr tmpratur i ontant. Hat ondution an b dimnional damag in onrt undr omprion. ACI dribd Matrial in journal onrt, 98(6): at lat for tmpratur not Ouyang, xding C. & 00 C Shah, S.P. (Bažant 994. Fratur & Kaplan nrgy approah 996), for by Fourir prditing la, raking hih rad rinford onrt tnil mmbr. ACI Strutural Journal 9(): Shah, S.P.; Sartz, S.E. & Ouyang, C Fratur Mhani onrt: Appliation fratur mhani (7) to q = λ T onrt, rok and othr quai-brittl matrial. Nyork: hr John Wily q i & on. th hat flux, T i th abolut tmpratur, and λ i th hat ondutivity; in thi Proding FraMCoS-7, May 23-28, 200