A local bond stress-slip model for reinforcing bars in self-compacting concrete

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1 Fratur Mhani of Conrt Conrt Strutur - Amnt, Durability, Monitoring Rtrofitting of Conrt Strutur- B. H. Oh, t al. (d) 200 Kora Conrt Intitut, Soul, ISBN A loal bond tr-lip modl for rinforing bar in lf-ompating onrt P. Dnrk, G. D Shuttr & L. Tar Ghnt Univrity, Ghnt, Blgium ABSTRACT: Th for tranfr in rinford onrt i providd by th onrt-to-tl bond. Thi phnomnon ha idly bn tudid for onvntional vibratd onrt (CVC). For lf-ompating onrt (SCC) hovr l tt rult ar availabl. To fill in thi lak to dvlop adaptd tard for prditing th bond of rinformnt in SCC, an xprimntal program ha bn t up. Th bond trngth of rinformnt bar ith diffrnt diamtr ha bn ttd by man of bam-tt pimn. During tting th bond tr-lip rpon a rordd. From th tt rult it an b n that th maximum bond trngth of SCC i lightly highr than for CVC hn mall bar diamtr ar tudid. For largr bar diamtr th diffrn bom mallr. Comparion of th tt data ith bond modl indiatd that th bond lau undrtimatd th bond trngth for SCC a ll a for CVC. Thrfor an adjutmnt of th bond modl ha bn mad. INTRODUCTION Rinford onrt i far from homognou. It i built up of tl onrt th onrt itlf i not homognou nithr. Rinford onrt lmnt ar baially dignd o that th onrt an arry th ompriv tr th tl an rit th tnil tr. Thrfor a good for tranfr btn th to matrial i nary hih an only b ahivd by an intration btn both matrial, hih i providd by bond btn th rinformnt bar th onrt. Th bond ha an important influn on th bhaviour of rinford lmnt in th rakd tag. Crak idth dfltion ar inflund by th ditribution of bond tr along th rinformnt bar by th lip btn th bar th urrounding onrt. Du to th importan of th intration btn tl onrt a lot of rarh ha bn don in th pat. In all th projt th main fou a on th rinformnt bar, it gomtrial haratriti ho th haratriti influn th bond trngth. With th apparan of n onrt typ, uh a tl-fibr rinford onrt high trngth onrt, qution aro about th bond trngth ahivd ith th onrt typ, th main fou of th rarh on bond hiftd to th onrt it ompoition (Martin 2002). Th am qution an b formulatd for lfompating onrt. A onrt typ hih, in frh tat, ha th ability to flo undr it on ight, fill th rquird pa or formork ompltly produ a dn adquatly homognou matrial ithout a nd for ompation (D Shuttr t al. 2007). Th advantag ar lar: no nd for vibration of th onrt, a highr quality of th finihd lmnt, rdud ontrution tim,. Th lf-ompatability i ahivd by adding a uprplatiizr to th mixtur by rduing th amount of oar aggrgat. Although lfompating onrt (SCC) i a rlativly n matrial, alrady a lot of rarh ha bn don on th durability th orkability of th onrt typ (D Shuttr t al. 2008). L tudi hav bn fouing on th mhanial proprti mor in partiular th bond apt. Som program hav bn arrid out to dtrmin th for tranfr btn onrt rinformnt in lf-ompating onrt. Th tudi ho that th bond trngth of tl in SCC i not lor than for onvntional vibratd onrt (CVC), may b vn highr in om a (Almida t al. 2008, Chan t al. 2003, Zhu t al. 2004, Dhn t al. 2004). Nvrthl thr i a grat attr in th rult. To gt a bttr inight in th diffrn in bond trngth btn onvntional vibratd onrt lf-ompating onrt to dvlop modifid modl dribing th bond tr-lip bhaviour, thi rarh program ha bn t up.

2 2 J EXPERIMENTAL D ( h, T ) h PROGRAM () Th Th ommon proportionality ay to tt offiint th bond trngth D(h,T) of i rbar alld in moitur onrt prmability i by man of it i pull-out a nonlinar tt (RILEM funtion 973). of th rlativ Th bhaviour humidity of h th tmpratur typ of pimn T (Bažant i quit & Najjar diffrnt 972). from Th that moitur in rinford ma balan lmnt rquir ubjtd that th to variation bnding. in tim of th atr ma pr unit volum Th bam of onrt tt pimn (atr ontnt uggtd ) b by qual RILEM to th rommndation divrgn of th RC6 moitur part flux (RILEM J 973) i mor uitabl to valuat th bond trngth of rinford lmnt ubjtd to bnding. Th pimn, oniting of 2 J half-bam, i loadd on top introduing (2) t bnding momnt in th bam. In thi ay a mor raliti Th atr tr ontnt ditribution an inid b xprd around a th th um bar i of ratd. th vaporabl atr (apillary atr, atr vapor, adorbd atr) th non-vaporabl 2. (hmially Matrial bound) atr n (Mill 966, Pantazopoulo & Mill 995). It i raonabl to Thr aum typ that of th onrt vaporabl hav atr bn ud: i a funtion 2 podrtyp of rlativ lf-ompating humidity, h, onrt dgr of hydration, on onvntional, vibratd dgr of onrt. ilia fum Mor ration, dtail about th mixing, i.. (h,, ) produr ag-dpndnt th ud orption/dorption matrial an b found iothrm in (Dnrk (Norling Mjonll 2008). Th 997). mix Undr proportion thi aumption onrt trngth by ubtituting ar ummarizd Equation in Tabl into. Equation 2 on obtain Tabl. Mix dign for SCC CVC mix. Matrial (kg/m³) SCC SCC2 CVC CEM I 52,5 N S 0/4 mm 853 & & + & n 640 (3) h Gravl 2/8 mm Gravl 8/6 mm Limton fillr hr Watr / i th lop of th orption/dorption iothrm Suprplatiizr (alo alld moitur apaity). - Th govrning f ub (N/mm²) quation (Equation 7.73) mut 62. b ompltd 58.4 by f (N/mm²) appropriat boundary 63.7 initial ondition f t,fl Th (N/mm²) rlation btn th 7.2 amount 6.8 of vaporabl 6.2 atr f t,p (N/mm²) rlativ humidity 5.0 i alld 4.4 adorption 4. iothrm if maurd ith inraing rlativity humidity Th lf-ompating dorption onrt iothrm SCC2 in ha th a oppoit omparabl a. Nglting ompriv thir diffrn tnil trngth (Xi t al. a 994), th onvntional th folloing, vibratd orption onrt iothrm CVC, ill a a b ud intndd. ith in Th rfrn firt lf-ompating to both orption onrt dorption SCC, ondition. ith th am By th W/C ay, ratio, if ha th a ignifiantly hytri highr of th trngth. moitur iothrm Bid ould th onrt b takn typ, into th aount, tl to bar diamtr diffrnt ha rlation, bn vaporabl varid. In thi atr rarh v rlativ program, humidity, 5 diffrnt mut nominal b ud aording diamtr to of th th ign mbddd of th variation rinformnt of th bar rlativity r hon: humidity. 2, 20, Th 25, hap 32 of 40 th mm. orption iothrm for HPC i inflund by many paramtr, 2.2 pially Spimn tho dtail that influn xtnt rat of th hmial ration, in turn, dtrmin por To trutur tt th bond por trngth iz ditribution of rinforing (atr-to-mnt bar in th diffrnt ratio, mnt onrt hmial typ, ompoition, th tard SF bam-tt ontnt, gomtry, uring tim a dribd mthod, in tmpratur, th RILEM mix rommndation, t.). i In ud. th litratur Th pimn variou dimnion formulation dpnd an on b additiv, th found bar to iz. drib Thr th typ orption of pimn iothrm of ar normal ud dpning onrt (Xi on th t al. bar 994). diamtr. Hovr, A typ in I pimn th prnt i ud papr for th ttd mi-mpirial rinforing xprion bar ith propod a diamtr by mallr Norling than Mjornll 6 mm. (997) A typ i II adoptd i ud for bau bar btn 6 mm n 32 mm, a third typ i ud it for bar xpliitly qual aount to or largr for than th 32 volution mm. An of xampl hydration i givn ration for a typ SF I pimn ontnt. (Fig. Thi ). orption iothrm rad Th prribd bond lngth i 0 tim th bar diamtr φ. Hovr thi lad to yilding, in om a vn ruptur, of th rinformnt bar bfor rahing th ultimat bond trngth. Thrfor mot of th pimn ar at ith a bond ( h,, ) G (, ) + 0( g ) h lngth of 5 tim φ. (4) phyially bound (adorbd) 650 atr th ond atr. Thi xprion 2φ8 2φ6 i valid only for lo 0 ontnt ( g ) h 50 K (, ) plati tub 2 φ hr th firt trm (gl iothrm) rprnt th trm (apillary iothrm) rprnt th apillary of SF. Th offiint G rprnt th amount of atr pr unit volum hld in th gl por at 00% φ6 rlativ humidity, it an b xprd (Norling Mjornll 997) a 6 x Figur. Siz rinformnt of bam tt pimn typ I G (, ) k + k (dimnion in mm). vg vg 2.3 hr Tting k vg produr k vg ar matrial paramtr. From th maximum amount of atr pr unit volum that an During fill all por th tt, (both apillary th pimn por r gl loadd por), at on a ontant an alulat rat Korrponding a on obtain to an inra in tl tr of 30 N/mm² pr minut. K (, ) Spradr tl profil Stl ollar ith LVDT' Bam Tt Spimn Not that, at arly ag, in th hmial ration Support 80 Hydrauli jak Load ll g G Fram anhord on tt floor 0 g Figur 2. Tt t-up for bam tt pimn. hr q i th hat flux, T i th abolut tmpratur, For all pimn λ i typ, th hat th ondutivity; atuator a in poitiond in th ntr of th pimn th thi total (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 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 00 C (Bažant & Kaplan 996), by Fourir la, hih rad q λ T (7) Proding of FraMCoS-7, May 23-28, 200

3 load P a tranfrrd by man of a pradr tl profil to ah half-bam (Fig. 2). A load ll maurd th load applid to th pimn during th tt. Th lip of th bar, at it fr nd, a rordd uing 3 linar variabl diffrntial trur (LVDT) on both id of th pimn. Loading ontinud until th lip at on nd of th pimn rahd 3 mm. For th half-bam ith 3 mm lip th bar a fixd in a lamping dvi o that th tt ould b ontinud ithout furthr lip at thi id of th pimn. Loading ontinud until th lip at th ond half of th pimn xdd 3 mm a ll. 2.4 Tt rult From th obtaind tt rult, valu of th bond tr along th urfa of th bondd rinforing bar an b drivd. Th formula to alulat th total for ating in th rinforing bar dpnd on th gomtry of th pimn ud. Th man bond tr an b alulatd by auming th for F in th rinforing bar to b tranfrrd to th onrt in th ylindrial zon of th mbdmnt lngth l d : τ F σ d l. π. φ 4. k d () by riting l d a k.φ σ th tnil tr in th rinforing bar. Thi tr i, a mntiond arlir, a funtion of th applid total load P th gomtry of th pimn. σ β. P A (2) Th fator β an b dtrmind from th pimn dimnion ha a valu of.25 for pimn typ I (diamtr 2 mm),.50 for pimn typ II (diamtr mm).75 for pimn typ III (diamtr mm). To valu ar of major intrt: th ultimat bond trngth τ R th o-alld haratriti bond trngth τ M. Th ultimat bond trngth i dfind a th bond tr orrponding to th ultimat load rordd during tting. Th haratriti bond trngth i alulatd a th man valu of th bond tr orrponding to a lip of 0.0 mm, 0.0 mm.00 mm. Both valu diffr for th to halv of th pimn Influn of th onrt typ Th main goal of th tudy i to ompar bond trngth for lf-ompating onrt ith tho for onvntional vibratd onrt. In figur 3 on of th rordd bond J tr D ( h, T ) lip h urv (man of 4 maurmnt) i plottd for bar diamtr 20 mm diffrnt onrt Th ompoition. proportionality In offiint tabl 2 th D(h,T) valu of th haratriti moitur prmability bond trngth it th i a ultimat bond trngth of th ar rlativ givn for humidity all pimn h typ tmpratur nonlina a ll a th tard & Najjar dviation 972). (DEV). Th moitur ma balan that th variation in tim of th atr ma Tabl 2. Tt rult volum for bam tt of onrt ith bond (atr lngth of ontnt 5φ. ) b q τ M divrgn DEV of th τ R moitur DEV flux J [N/mm²] [N/mm²] [N/mm²] [N/mm²] SCC SCC J SCC t SCC SCC Th 0.55 atr ontnt 9.86 an 0.93 b xprd a SCC of th vaporabl atr SCC (apillary a SCC vapor, 0.29 adorbd 8.60 atr) 2.03 th non- SCC (hmially 0.28 bound) 9.77 atr 0.85 n (Mil SCC Pantazopoulo 0.29 & 7.48 Mill 995) It i ra CVC aum 0.73 that th 9.88 vaporabl 0.75 atr i a fu CVC rlativ 0.53 humidity, 9.46 h, dgr 0.82 of hydration CVC CVC dgr 0.28 of ilia fum 8.0 ration,.00, i.. CVC ag-dpndnt orption/dorption 2.09 (Norling Mjonll 997). Undr thi aum 32.0 by ubtituting Equation into Equati obtain Diam. 20 mm Bond Strngth [N/mm²] h & + & + hr / i th lop of th orption/ 6.0 iothrm (alo alld moitur apa govrning quation (Equation 3) mut b 2.0 by appropriat boundary initial onditi Th rlation btn th amount of 8.0 atr rlativ humidity i alld SCC iothrm if maurd SCC2 ith inraing 4.0 CVC humidity dorption iothrm in th a. Nglting thir diffrn (Xi t al th folloing, orption iothrm ill b Slip [mm] rfrn to both orption dorption Figur 3. Bond tr lip diagram for bar diamtr 20 mm. By th ay, if th hytri of th iothrm ould b takn into aount, to Comparing th diffrnt typ of onrt for th rlation, vaporabl atr v rlativ humi am bar diamtr, CVC SCC2 (hih hav b ud aording to th ign of th varia almot th am ompriv trngth) hav omparabl valu for th haratriti bond tr τ M, x- rlativity humidity. Th hap of th iothrm for HPC i inflund by many p pt for bar diamtr 2 mm for hih a ignifiant pially tho that influn xtnt diffrn btn th 2 onrt i notid. Th hmial ration, in turn, dtrm diffrn for th ultimat bond tr τ R i omhat largr. For all tt on SCC2, τ R i abov th trutur por iz ditribution (atrratio, mnt hmial ompoition, SF ultimat bond tr of CVC. uring tim mthod, tmpratur, mix Whn th bond tr-lip rlation of th diffrnt onrt typ ar plottd for tt on pimn t.). In th litratur variou formulatio found to drib th orption iothrm ith a rinforing bar of th am diamtr, it an b onrt (Xi t al. 994). Hovr, in th n that th bond trngth of SCC i largr than papr th mi-mpirial xprion pro tho of SCC2 CVC (a a xptd du to Norling Mjornll (997) i adoptd b th highr ompriv trngth) at all tr lvl, Proding of FraMCoS-7, May 23-28, 200

4 rulting J D ( h, T ) in a h tpr urv. For bar diamtr () of 40 mm th urv for SCC2 CVC ar almot idntial Th proportionality for mall lip valu, offiint hil D(h,T) th bond i alld tr lvl moitur for SCC prmability for th am it i lip a nonlinar i highr. funtion For all othr of th diamtr, rlativ humidity th bond h tr tmpratur for th T (Bažant SCC2 pimn & Najjar 972). ar highr Th moitur for th am ma lip balan a rordd rquir for that th th CVC variation pimn. in tim of In th om atr a ma th pr tr unit vn volum approah of onrt th valu (atr for ontnt SCC. ) b qual to th divrgn of th moitur flux J Influn of th bar diamtr Whn th rult of all tt ar ompard, it an b n that an J inra in th bar diamtr rult in (2) a t dra of τ M τ R. A th onrt trngth influn Th atr th ontnt bond proprti an b xprd of th onrt, a th um th bond of th tr vaporabl i normalid atr by th root of th ompriv (apillary atr, atr vapor, trngth: adorbd atr) th non-vaporabl (hmially bound) atr n (Mill 966, Pantazopoulo τ R τ R, n & Mill 995). It i raonabl to aum that f th vaporabl atr i a funtion of rlativ humidity, h, dgr of hydration, (3), dgr of ilia fum ration,, i.. (h,, ) In ag-dpndnt Figur 4, τ R,n i orption/dorption plottd for all onrt iothrm mix (Norling ttd Mjonll bar diamtr. 997). Undr thi aumption by Th ubtituting diffrn Equation in th normalizd into Equation ultimat 2 bond on trngth obtain for th onvntional vibratd onrt th lf-ompating onrt i largt for bar diamtr of 2 mm. Th diffrn bom mallr for highr bar diamtr, but th rult for lfompating onrt h ar highr in all a. Thr & + & + & n (3) ar no ignifiant diffrn btn th normalizd ultimat bond trngth of SCC SCC2, xpt in a hr / i th lop of th orption/dorption of a 40 mm rinformnt bar. iothrm (alo alld moitur apaity). Th By inraing th bar diamtr, th lip at ultimat bond tr u i inraing in all a. No ig- govrning quation (Equation 3) mut b ompltd by appropriat boundary initial ondition. nifiant diffrn an b notid btn th rult for lf-ompating onrt th rult for Th rlation btn th amount of vaporabl atr rlativ humidity i alld adorption onvntional vibratd onrt. 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 to both orption dorption ondition. By th ay, if th hytri of th moitur iothrm ould b takn into aount, to diffrnt rlation, vaporabl atr v rlativ humidity, mut b ud aording to th ign of th variation of th rlativity humidity. Th hap of th orption iothrm for HPC i inflund by many paramtr, pially tho that influn xtnt rat of th 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 th litratur variou formulation an b Figur found 4. to Normalizd drib ultimat th orption bond trngth iothrm for diffrnt of normal diamtr onrt (Xi onrt al. ompoition. 994). Hovr, in th prnt papr th mi-mpirial xprion propod by Norling Mjornll (997) i adoptd bau it xpliitly Crak aount pattrn for th volution of hydration Aftr ration tting th SF rak ontnt. pattrn Thi apparing orption on iothrm urfa rad of th pimn a rordd. No big diffrn btn th rak pattrn for CVC th lf-ompating onrt SCC SCC2 r notid. In almot all a th rak pattrn a limitd to th zon in hih atual bond btn th r- ( h,, ) G (, ) + 0( g ) h inforing bar th onrt a poibl, o along (4) th bonding lngth. An xampl of on of 0 th ( g rak pattrn ) h of th K (, ) pimn i givn in Figur 5. 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 of SF. Th offiint G rprnt th amount of atr pr unit volum hld in th gl por at 00% rlativ humidity, it an b xprd (Norling Mjornll 997) a Figur 5. Crak pattrn for on of th pimn of CVC ith bar G ( 2, mm ) diamtr. k + k vg vg 3 hr PREDICTION k vg k vg MODELS ar matrial paramtr. From th maximum amount of atr pr unit volum that an In fill litratur all por (both a lot of apillary modl por to prdit gl th por), ultimat on bond an alulat trngth, K orrponding a on obtain lip quation to drib th bond tr-lip bhaviour an b found. In th modl vral paramtr uh a bar diamtr, onrt 0 g 0.88 ovr, onrt G ompriv trngth, 0 ar inorporatd. (6) K (, ) All quation hav bn tablihd by linar or 0 g non-linar rgrion on tt rult ith varying paramtr, but motly for onvntional vibratd onrt Th ith matrial ompriv paramtr trngth k vg in k vg th rang g an btn b alibratd 20 by 50 fitting MPa. F xprimntal tt hav data bn rlvant don on to high fr trngth (vaporabl) onrt atr ith ontnt ompriv in onrt trngth at abov variou 60 ag MPa. (Di Luzio Th ompriv & Cuati 2009b). trngth of th onrt ud in thi rarh projt ar all around 60 MPa or highr for th SCC mixtur. 2.2 Tmpratur volution Not that, at arly ag, in th hmial ration 3. Bond tr lip rlation aoiatd ith mnt hydration SF ration A ar modl xothrmi, for th th bond tmpratur tr- lip fild bhaviour i not uniform i rquird for non-adiabati to b abl ytm to mak vn alulation if th nvironmntal of th rak pattrn, tmpratur rak i idth, ontant.. Hat Thrfor ondution a rlationhip an b ha dribd bn propod in onrt, in th at Cb-Fib lat for Modl tmpratur Cod 990 not (Fig. xding 6). It onit 00 C (Bažant of an inraing & Kaplan firt 996), branh up by to Fourir th ultimat la, hih bond rad tr. Thi branh i follod by a platau during hih lip i inraing for ontant q bond λ T tr, aftr hih bond tr tart (7) to dra for inraing lip valu. Finally a ontant ridual bond trngth i rahd hih i du hr q i th hat flux, T i th abolut to pur frition btn th rinforing bar ith th tmpratur, λ i th hat ondutivity; in thi rakd onrt lug th urrounding onrt: Proding of FraMCoS-7, May 23-28, 200

5 Figur 6. Prdition modl for th bond tr lip rlationhip aording to MC90 Huang t al. τ τ. for 0 (4) τ τ < 2 τ τ. τ τ 3 ( ) 2 τ τ < 2 3 < (6) 3 (7) Th paramtr in thi modl hav bn prribd in th od for onfind unonfind normal trngth onrt ith good or othr bond ondition. Huang t al. (993) propod valu for th paramtr for normal high trngth onrt undr good bond ondition (Tabl 3 4). Tabl 3. Valu for th prdition quation aording to Cb-Fip MC90 (999) for good bond ondition. Confind onrt Unonfind onrt.0 mm 0.6 mm mm 0.6 mm 3 ditan bt. rib.0 mm τ τ f 0.4 τ 0.5 τ Tabl 4. Valu for th prdition quation aording to Huang t al. (996) for good bond ondition. High trngth onrt Normal trngth onrt 0.5 mm 0.6 mm 2.5 mm 0.6 mm 3 ditan bt. rib.0 mm τ 0.4. f m 0.4. f m τ τ 0.4 τ Both modl (CEB-Fip onfind onrt Huang high trngth onrt) ar ompard ith th maurd bond tr-lip bhaviour of th pimn (Fig. 7 to 9). It an b n that th prditd valu alulatd ith th Huang-modl for high trngth onrt ovrtimat th bond trngth in all a. For th MC90-modl, th valu ar undrtimatd for mall diamtr in th rang of th maurd J D ( h, T ) valu h for largr bar diamtr. Th bar diamtr Th ha alo proportionality an influn offiint on th lip D(h,T) orrponding ith moitur th ultimat prmability bond trngth it a i an a nonlina b n on th graph. of th rlativ Both modl humidity hovr h tmpratur hav fixd valu of thi & Najjar lip valu 972). rgardl Th moitur th bar ma diamtr. that th variation in tim of th atr ma balan volum of onrt (atr ontnt ) b q 32.0 divrgn of th moitur flux J Bond Strngth [N/mm²] SCC 6.0 Th atr ontnt an b xprd a of th vaporabl atr (apillary a 2.0 vapor, adorbd atr) th non- Cb-Fip MC90 Huang 8.0 (hmially bound) atr 2 mm n (Mil 20 mm Pantazopoulo & Mill 995). It i ra 25 mm 32 mm mm aum that th vaporabl atr i a fu rlativ humidity, h, dgr of hydration dgr of Slip ilia [mm] fum ration,, i.. Figur 7. Comparion of maurd ag-dpndnt bond tr orption/dorption lip bhaviour for SCC ith prdition (Norling modl. Mjonll 997). Undr thi aum by ubtituting Equation into Equati obtain Bond Strngth [N/mm²] Bond Strngth [N/mm²] t J h SCC2 & + & + rfrn to both orption dorption Norling Mjornll (997) i adoptd b 6.0 hr / i th lop of th orption/ 2.0 iothrm (alo alld moitur apa Cb-Fip MC90 govrning quation (Equation Huang 3) mut b mm by appropriat boundary initial onditi 20 mm mm 32 mm Th rlation btn th amount of 40 mm atr rlativ humidity i alld iothrm if maurd ith inraing Slip [mm] humidity dorption iothrm in th Figur 8. Comparion a. of maurd Nglting bond tr thir lip diffrn bhaviour (Xi t al. for SCC2 ith prdition modl. th folloing, orption iothrm ill b 32.0 By th ay, if th hytri CVC of th 28.0 iothrm ould b takn into aount, to 24.0 rlation, vaporabl atr v rlativ humi b ud aording to th ign of th varia 20.0 rlativity humidity. Th hap of th 6.0 iothrm for HPC i inflund by many p pially tho that influn xtnt 2.0 hmial ration, in turn, dtrm Cb-Fip MC90 Huang 8.0 trutur por iz ditribution 2 mm (atrratio, 4.0 mnt hmial 20 mm 25ompoition, mm SF 32 mm 40 mm uring tim mthod, tmpratur, mix t.). 0.75In th.00 litratur variou formulatio found to Slip drib [mm] th orption iothrm Figur 9. Comparion onrt of maurd (Xi bond t al. tr 994). lip bhaviour Hovr, in th for CVC ith prdition papr modl. th mi-mpirial xprion pro Proding of FraMCoS-7, May 23-28, 200

6 J Out D ( of h, T ) thi h it an b onludd that th modl () hould b modifid to tak in to aount th fft of th Th bar diamtr. proportionality offiint D(h,T) i alld moitur prmability it i a nonlinar funtion 3.2 of th Maximum rlativ humidity bond trngth h tmpratur T (Bažant & Najjar 972). Th moitur ma balan rquir To that gt th variation a bttr in prdition tim of th of atr th ultimat ma pr bond unit trngth volum of mor onrt ophitiatd (atr ontnt modl ) ar b qual nary. to th Som divrgn of th of modl th moitur to prdit flux J th ultimat bond trngth ar ho in tabl 5 ith th ud unit ytm. Ky paramtr in th quation ar th ratio of th onrt J ovr to th bar diamtr φ, th (2) ratio of th bar diamtr to th bond lngth l d th t root Th of th atr ompriv ontnt trngth an b xprd f. a th um of th vaporabl atr (apillary atr, atr vapor, adorbd atr) th non-vaporabl Tabl 5. Prdition modl for bond trngth. (hmially bound) atr n (Mill 966, Author Equation Unit Pantazopoulo & Mill 995). It i raonabl to Elighaun τ R φ. f SI aum Efahani* that th τ R vaporabl 4.73.[ ( φ ) +0.5]/[ atr ( φi ) +5.5]. a funtion f SI of rlativ Harajli humidity, τ R [.2+3. h, dgr ( φ ) +50. of hydration, ( φ l d )]. f, Pi dgr Huang** of ilia τ R fum 0.45.f ration, m, i.. (h,, SI ) Orangun τ R [ ( φ ) +53. ( φ l d )]. f ag-dpndnt orption/dorption iothrm Pi MC 90 τ R 2.5. f k (Norling Mjonll 997). Undr thi aumption SI * Equation i valid for f > 50 MPa by ** Equation ubtituting i valid Equation for f btn 60 into 20 Equation MPa 2 on obtain In figur 0 to 2 a omparion i mad btn th obtaind valu th prditd on for th diffrnt onrt mix in & + a bond tr & + & n vru bar (3) h diamtr diagram. It ho an undrtimation of th ultimat bond trngth in all a, xpt for th hr Huang / modl i th (996) lop of hih th orption/dorption i dvlopd for high iothrm trngth (alo onrt. alld moitur Th prditd apaity). valu Th i omtim govrning quation only 40% (Equation of th 3) rordd mut b on. ompltd Som modl by appropriat giv bond boundary trngth initial indpndntly ondition. from th Th bar diamtr, rlation btn othr m th amount to prdit of vaporabl th trnd quit atr good rlativ but giv humidity valu that i alld ar too adorption lo,.g. iothrm modl if by maurd (Orangun t ith al. 977; inraing Harajli rlativity 994). Thrfor humidity th dorption offiint iothrm out of in th th Orangunmodl a. Nglting hav bn thir r-dtrmind diffrn (Xi by t linar al. 994), rgr- in oppoit ion th folloing, bad on th orption obtaind iothrm rult. ill b ud ith rfrn to both orption dorption ondition. By th ay, if th hytri of th moitur iothrm ould b takn into aount, to diffrnt 30,0 rlation, vaporabl atr v rlativ humidity, SCCmut b ud 25,0 aording to th ign of th variation Elighaun of th Efahani rlativity humidity. Th hap of th orption 20,0 Harajli iothrm for HPC i inflund by many paramtr, Huang pially 5,0 tho that influn xtnt rat Orangun of th hmial MC90 0,0 ration, in turn, dtrmin por trutur por iz ditribution (atr-to-mnt 5,0 ratio, mnt hmial ompoition, SF ontnt, uring 0,0tim mthod, tmpratur, mix additiv, t.). In 5th litratur 5 25variou 35 formulation 45 an b found to drib th φ [mm] orption iothrm of normal Figur onrt 0. Bond (Xi t trngth al. 994). vru bar Hovr, diamtr in omparion th prnt of modl papr th tt mi-mpirial rult for SCC. xprion propod by Norling Mjornll (997) i adoptd bau it τr [N/mm²] xpliitly aount for th volution of hydration 30,0 ration SF ontnt. Thi orption iothrm SCC2 25,0 Elighaun rad Efahani 20,0 Harajli τr [N/mm²] Huang 5,0 Orangun ( h,, ) G (, ) MC90 + 0,0 0( g ) h 5,0 0,0 0( g ) h K ( ) 5 5, φ [mm] Figur. Bond trngth vru bar diamtr omparion of modl tt rult for SCC2. hr th firt trm (gl iothrm) rprnt th phyially bound (adorbd) atr th ond 30,0 trm (apillary iothrm) rprnt th apillary CVC atr. 25,0Thi xprion i valid only for lo Elighaun ontnt of SF. Th offiint G Efahani rprnt th amount of 20,0 Harajli atr pr unit volum hld in th gl por at 00% Huang rlativ 5,0 humidity, it an b xprd (Norling Orangun Mjornll 997) a MC90 τr [N/mm²] 0,0 5,0 G (, ) k + k 0,0 vg vg φ [mm] hr k vg k vg ar matrial paramtr. From th Figur maximum 2. Bond amount trngth of vru atr bar pr diamtr unit volum omparion that an of modl tt rult for CVC. fill all por (both apillary por gl por), on an alulat K Du to th fat a on obtain that th bond lngth ha bn kpt ontant in th tt, th trm ith l d bom ontant. Th dtrmind offiint 0 gfor both lfompating 0onrt r almot idntial, but th G offiint for th onvntional vibratd onrt (6) K (, ) diffrd. Th n quation 0 g ar givn in Tabl 6. Th good orrlation btn th prditd th maurd bond trngth an b notid in Figur 3 (for Th SCC matrial mixtur). paramtr k vg k vg g an b alibratd by fitting xprimntal data rlvant to Tabl fr 6. (vaporabl) Modifid prdition atr modl ontnt for bond in trngth. onrt at Conrt variou typ ag (Di Equation Luzio & Cuati 2009b). Unit SCC τ R [ ( φ )]. f m SI CVC 2.2 Tmpratur τ R volution [ ( φ )]. f m SI 30,0 aoiatd ith mnt hydration SF SCC ration τr,ma [N/mm²] 20,0 5,0 5,0 20,0 25,0 30,0 τ R,prd [N/mm²] (4) Not that, at arly ag, in th hmial ration ar xothrmi, th tmpratur fild i not SCC2 uniform for non-adiabati ytm vn if th nvironmntal 25,0 tmpratur i ontant. Hat ondution an b dribd in onrt, at lat for tmpratur not xding 00 C (Bažant & Kaplan 996), by Fourir la, hih rad q λ T (7) hr q i th hat flux, T i th abolut Figur 3. Corrlation btn maurd valu prditd valu tmpratur, for SCC ith th λ modifid i th hat quation. ondutivity; in thi Proding of FraMCoS-7, May 23-28, 200

7 3.3 Slip orrponding to maximum bond trngth A an b n in Figur 7, th lip orrponding to th momnt of maximum bond trngth i inflund by th rinforing bar diamtr. For mallr diamtr th maximum bond trngth i largr but th lip i mallr. In th bond modl out of MC90, no influn of th bar diamtr on th valu of i notid, although it i larly prnt in th xprimntal rult. Mot author uggt a fixd valu for, hil othr uggt valu that dpnd on th lar rib paing 0. Som of th valu for onfind rinforing bar ar ummarizd in Tabl 7. Tabl 7. Prdition modl for bond trngth. Author Equation Unit Harajli SI Huang.0 mm (normal trngth onrt) SI 0.6 mm (high trngth onrt) SI MC 90.0 mm SI Oh.04 mm SI A omparion btn th prditd valu for th xprimntal dtrmind valu i givn in Figur 3. Non of th modl giv a good prdition of th lip orrponding ith th maximum bond trngth. Th lar rib paing, hih i inraing for inraing bar diamtr, i influning th lip valu. No big diffrn ar notid btn lfompating onvntional onrt (xpt for bar diamtr 40 mm), a ll a no ignifiant diffrn an b n btn th valu for SCC ompard to th valu of SCC2 CVC. So it an b onludd that th onrt typ (SCC or CVC) th ompriv trngth of th onrt do not hav an influn on. [mm] 3,0 2,5 2,0,5,0 0,5 0,0 5,000 0,000 5,000 20,000 25,000 0 [mm] SCC SCC2 CVC Harajli Huang (HSC) Oh MC90 Figur 3. Clar rib paing vru lip omparion of modl tt rult. A rgrion analyi ha bn prformd to dtrmin a good rlationhip btn th lar rib paing 0 of th ttd rinforing bar th obrvd lip orrponding to th maximum bond trngth: 0.( J0.006) Th n propod Th quation proportionality i plottd offiint in Figur 4 togthr ith moitur th obtaind prmability tt rult. it i a nonlina D(h,T) of th rlativ humidity h tmpratur & Najjar 972). Th moitur ma balan 3,0 that th variation in tim of SCC th atr ma 2,5 volum of onrt (atr ontnt SCC2 ) b q CVC divrgn of th moitur flux J [mm] 2,0,5,0 0,5 ) D ( h, T h t J (8) Prop. modl Th atr ontnt an b xprd a 0,0 of th vaporabl atr (apillary a 5,000 0,000vapor, 5,000 20,000 adorbd 25,000atr) th non- 0 [mm] (hmially bound) atr n (Mil Figur 4. Clar rib paing vru lip Comparion of tt Pantazopoulo & Mill 995). It i ra rult ith n propod modl. aum that th vaporabl atr i a fu Th quation rlativ of Tabl humidity, 6 th quation h, dgr (8) of an hydration no b ud in th dgr MC90 of ilia modl fum (quation ration, 4 till, 7) i.. to rpla th xprion ag-dpndnt for τ. orption/dorption (Norling Mjonll 997). Undr thi aum by ubtituting Equation into Equati 4 CONCLUSIONS obtain Bad on th obtaind rult, th folloing onluion an b mad: & + & + h a. Th bond trngth of lf-ompating onrt i a high a th bond trngth for onvntional vibratd onrt hn hr larg / bar i diamtr th lop ar of th tudid. For mallr bar iothrm diamtr, (alo th alld bond trngth moitur of apa orption/ SCC i lightly highr, govrning ith quation th largt (Equation diffrn 3) mut b ouring for th mallt by appropriat bar diamtr. boundary initial onditi b. For qual atr Th to rlation mnt btn ratio th th ompriv trngth of atr th podr-typ rlativ lf-ompating humidity i alld amount of onrt i highr iothrm (du to th if limton maurd fillr ith ontnt), o ar humidity th maximum dorption haratriti iothrm in th inraing bond trngth. a. Nglting thir diffrn (Xi t al.. Th lip orrponding th folloing, to orption th maximum iothrm bond ill b trngth i inraing rfrn for inraing to both orption bar diamtr. dorption By th ay, if th hytri of th Conidring th iothrm bond modl, ould b th takn folloing into aount, an to b onludd: rlation, vaporabl atr v rlativ humi a. Th bond tr-lip b ud aording modl out to of th MC90 ign of do th varia not implmnt th rlativity influn humidity. of th bar Th diamtr, hap r-oulting in a modl iothrm that undrtimat for HPC i inflund th ultimat by many p th bond trngth for pially mall tho bar diamtr that influn xtnt approah th valu hmial for τ R for ration larg bar, diamtr. in turn, dtrm b. Th bond tr trutur lip modl por do iz not ditribution tak into (atrratio, of mnt th bar hmial diamtr on ompoition, th lip SF aount th influn orrponding ith uring th ultimat tim bond mthod, trngth. tmpratur, mix. Almot all t.). xiting In modl th litratur for prditing variou formulatio th ultimat bond trngth found to undrtimat drib th orption th atual iothrm valu for SCC a onrt ll a for (Xi CVC t al. 994). Hovr, in th papr th mi-mpirial xprion pro Norling Mjornll (997) i adoptd b Proding of FraMCoS-7, May 23-28, 200

8 J d. D ( Almot h, T ) hall modl nglt th influn of () th lar rib paing on th lip orrponding ith th ultimat Th proportionality bond trngth. offiint D(h,T) i alld moitur. A modifiation prmability an b it mad i a nonlinar to th modl funtion to gt of th a bttr rlativ prdition humidity of h th ultimat tmpratur bond T trngth, (Bažant a & diud. Najjar 972). Th moitur ma balan rquir that th variation in tim of th atr ma pr unit volum of onrt (atr ontnt ) b qual to th REFERENCES divrgn of th moitur flux J CEB-FIP Modl Cod 990. Comité Euro-Intrnational du Béton, JLauan, Fran (2) Chan, t Y. & Chn Y. & Liu Y Dvlopmnt of bond trngth of rinformnt tl in lf-onolidating onrt, Th atr ACI Strutural ontnt Journal, an 00 b xprd (4) a th um D of Shuttr, th vaporabl G. Bol, atr V. (d) 2007, Proding of th (apillary atr, atr 5th Intrnational RILEM Sympoium on Slf-Compating vapor, adorbd atr) th non-vaporabl Conrt, RILEM Proding PRO54, RILEM Publiation bound) atr n (Mill 966, (hmially D Pantazopoulo Shuttr, G. && Barto, Mill P. & 995). Donom It P. i & raonabl Gibb, J to aum Slf-Compating that th Conrt, vaporabl Caithn, atr Whittl i a funtion Publihing of Dhn, rlativ F. humidity, & Holhmahr, h, dgr K. & of Wiβ hydration, D , Slf- dgr Compating of ilia Conrt fum (SCC) ration, Tim Dvlopmnt of th Matrial Proprti th Bond Bhaviour,, i.. LACER, (h, 5, ) Dnrk, ag-dpndnt P. & D Shuttr, orption/dorption G. & Tar, L iothrm Bond (Norling Strngth Mjonll of Rinforing 997). Bar Undr in Slf-Compating thi aumption Conrt: by Exprimntal ubtituting Dtrmination, Equation 3rd into North Equation Amrian Confrn on th Dign U of Slf-Conolidating Conrt 2 on obtain (SCC2008), Chiago, USA Harajli, MH Dvlopmnt/pli trngth of rinforing bar mbddd h in plain fibr rinford onrt, ACI Strutural Journal, 9, & + & + & n (3) h hr / i th lop of 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 of 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 to both orption dorption ondition. By th ay, if th hytri of th moitur iothrm ould b takn into aount, to diffrnt rlation, vaporabl atr v rlativ humidity, mut b ud aording to th ign of th variation of th rlativity humidity. Th hap of th orption iothrm for HPC i inflund by many paramtr, pially tho that influn xtnt rat of th 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 th litratur variou formulation an b found to drib th orption iothrm of normal onrt (Xi t al. 994). Hovr, in th prnt papr th mi-mpirial xprion propod by Norling Mjornll (997) i adoptd bau it Harajli, xpliitly MH. aount Numrial for th bond volution analyi uing of xprimntally drivd SF loal ontnt. bond la: Thi A porful orption mthod iothrm for hydration ration rad valuating th bond trngth of tl bar. Journal of Strutural Enginring Huang, Z. & Engtröm, B. & Magnuon, J Exprimntal invtigation of th bond anhorag bhaviour of dformd bar in high trngth onrt. Rport 94:4, ( h Chalmr,, ) G ( Univrity, of ) Thnology, + Chalmr Martin, H Bond Prforman 0of ( gribbd Bar ) h (Pull-Out- Tt) Influn of Conrt Compoition Conitny, Proding of th 3rd Intrnational Sympoium: (4) 0( g Bond in Conrt from Rarh to Stard, ) h , K (, ) Budapt Mnz d Almida Filho, F., t al Bond-lip Bhavior of Slf-Compating Conrt Vibratd Conrt uing hr Pull-out th firt Bam trm Tt, (gl Matrial iothrm) rprnt Strutur, 4,. th Orangun, phyially CO. bound & Jira, (adorbd) JO & Brn, atr JE A th rvaluation ond trm of tt (apillary data on dvlopmnt iothrm) lngth rprnt pli. th ACI apillary Journal. 74(3), Thi xprion i valid only for lo ontnt atr. Oh, of SF. B.H. Th & Kim, offiint S.H GRaliti rprnt Modl th for amount Loal Bond of atr Str-lip pr unit of volum Rinford hld Conrt in th undr gl por Rpatd 00% Loading. Journal of Strutural Enginring. 33(2), rlativ humidity, it an b xprd (Norling RILEM Thnial rommndation for th Tting Mjornll U of Contrution 997) a Matrial: RC6, Bond Tt for Rinforing Stl: 2. Pull-out Tt, Matrial Strutur. RILEM Thnial rommndation for th Tting G ( U, ) of Contrution k + k Matrial: RC6, Bond Tt for Rinforing Stl:. Bam Tt, Matrial Strutur, vg vg Zhu, hr W. k& vg Sonbi, k M. vg ar & Barto, matrial P.J.M. paramtr Bond From intrfaial proprti amount of of rinformnt atr pr unit in lf-ompating volum that on- an th maximum fill rt, all por Matrial (both apillary trutur, por 37, gl por), on an alulat K a on obtain K (, ) 0 g G 0 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 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 00 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 of FraMCoS-7, May 23-28, 200