Fratur Mhani of Conrt and Conrt Strutur - High Prforman, Fibr Rinford Conrt, Spial Loading and Strutural Appliation- B. H. Oh, t al. (d) 2 Kora Conrt Intitut, ISBN 978-89-78-82-2 Fibr rinford onrt haratrization through round panl tt - part I: xprimntal tudy F. Minlli & G.A. Plizzari Univrity of Bria, Italy ABSTRACT: Standard tt mthod for dtrmining th mhanial proprti of Fibr Rinford Conrt (FRC) ar proprly dfind if thy rprodu th atual trutural bhavior. Among many propoal, th round panl tt m to hav all potntial to bom an ay-to-u tool and, at th am tim, a rliabl produr for th haratrization of FRC, in trm of toughn and pot-raking ontitutiv ohiv la. A omparion btn diffrnt tt typologi for haratrizing FRC i rportd and diud in th prnt papr, hit pial mphai on th diffrnt attr that ah tt produ. Tt ar prformd on bam a ll a on panl. All pimn hrin ompard hav th am onrt mhanial proprti and fibr ontnt. Aim of th xprimntal invtigation i to ritially diu advantag and diadvantag of ah tting produr, fouing on th appliability of th mthod and on th rliability of rult toard a onitnt haratrization of th trutural bhavior. A n gomtry for th panl tt i hrin propod and diud in ordr to mak th panl air to pla, handl and tt, thrfor avoiding on of th major drabak hih limit an xtniv utilization of th panl tt. Suitabl orrlation among th diffrnt fratur and nrgy paramtr dfind in th aumd tandard ar finally rportd, rulting vry uful for a harmonization of th availabl tandard. INTRODUCTION Fibr Rinford Conrt (FRC) i gaining an inraing intrt among th onrt ommunity for th rdud ontrution tim and labor ot. For thi raon, many trutural lmnt ar no rinford ith tl fibr a partial or total ubtitution of onvntional rinformnt (rbar or ldd mh; di Prio t al.24b). Bid ot iu, quality mattr ar of paramount importan for a ontrution and FRC alo fulfill th rquirmnt in fibr allo for mor ditributd rak ith a mallr opning that nhan durability (Shumahr, 26). Contrution matrial rquir Standard for mauring thir mhanial proprti and for quality ontrol. At th am tim n matrial rquir n rul in building od and pial guidlin for trutural dign (Vandall, 24; CEN, 23). A far a FRC i onrnd, dign guidlin ar alrady availabl in om Countri (Rilm, 23; di Prio t al.24; CNR, 26) and ork i in progr for inluding thm in th oming n fib Modl Cod (2). In th guidlin, trutural dign i uually bad on dign valu of th matrial paramtr that ar normally dtrmind by dividing th haratriti valu by a partial afty fator (γ M ). Mhanial proprti of FRC ar traditionally dtrmind from bam tt that ar uually bad on a thr (CEN, 23) or four point bnding hm (UNI, 23). Early xprin ith th lo volum fration of fibr that ar noaday motly ud in prati (V f <.8-.%), vidn that th haratriti valu dtrmind from bam tt (CEN, 23; UNI, 23) ar quit lo bau of th high attr in bam tt rult. It hould b obrvd that thi attr i not rlatd to th matrial itlf by i mainly du to th mall fratur ara (ranging from 6 to 8 m 2 ). Suh a attr bom partiularly high hn lo ontnt (2- kg/m 3 ) of maro tl fibr (lngth ranging btn 3 and 6 mm) ar ud (Sorlli t al.2). It i ommonly aptd that FRC ith a lo volum fration of fibr ar partiularly uitabl for trutur ith a high dgr of rdundany hr tr rditribution may our. Bau of thi rditribution, larg fratur ara ar involvd (ith a high numbr of fibr roing thm) and, thrfor, trutural bhavior i mainly govrnd by th man valu of th matrial proprti. Furthrmor, bau of th larg fratur ara, th attr of xprimntal rult from trutural tt i rmarkably lor than that obtaind from bam tt. A typial xampl i hon in Figur, hih xhibit a t of urv obtaind from a tandard (bnding) tt on nothd pimn (Fig. a) and from trutural tt on full al lab on grad mad of th am mat-
rial J = (Fig. D ( h, T ) b); h th diffrnt attr btn matrial () and trutural tt i larly vidnt, a a onfirmation Th of th proportionality abov prntd offiint diuion. D(h,T) i alld moitur In ordr prmability to obtain a and mor it i raliti a nonlinar valu funtion of th attr of th rlativ of FRC humidity matrial h tt, and tmpratur pimn ith T (Bažant largr fratur & Najjar ara 972). ar Th ndd; moitur thi ma uggt balan th rquir u of largr that th bam variation or diffrnt in tim pimn of th atr lik ma lab, pr hr unit tr volum rditribution of onrt may (atr alo ontnt our. ) b qual to th divrgn A quar of panl th moitur a propod flux J to imulat a portion of prayd onrt in tunnl lining appliation (EN 488-, 24). Hovr, in it i imply upportd = along J th hol bordr, any gomtrial (2) ir- t rgularity involv that th ral upport may vary in diffrnt Th atr pimn; ontnt in fat, an although b xprd th upport a th um an li of in th a vaporabl prft (and atr ontrolld) plan, pimn ar (apillary atr, atr normally dformd bau of hrinkag fft. Th vapor, and adorbd atr) and th non-vaporabl rak pattrn i thrfor hardly prditabl (th atual thr point on hih any rigid body tak up- (hmially bound) atr n (Mill 966, Pantazopoulo & Mill 99). It i raonabl to port ar gnrally randomly loatd along th four aum that th vaporabl atr i a funtion of dg) and th dtrmination of th ontitutiv la rlativ humidity, h, dgr of hydration, for rakd onrt bom vry diffiult., and dgr of ilia fum ration, A Round Dtrminat Panl (RDP), i.. tt = (h, a propod by ASTM (24); it i a tatially dtrminat, ) = ag-dpndnt orption/dorption iothrm (Norling Mjonll 997). Undr thi aumption and tt (a round lab having a diamtr φ=8 mm and a by ubtituting Equation into Equation 2 on thikn of 7 mm, ith thr upport at 2 dgr) hr th rak pattrn i prditabl and th obtain pot-raking matrial proprti an b adquatly dtrmind. Hovr, handling h and plaing uh a + ( D h) = & + & + & n (3) pimn h t i quit h ompliatd du to th larg iz and, onquntly, high ight (9 kg). In addition, tandard rvo-ontrolld loading mahin may not hr fit ith th /h i th lop of th orption/dorption gomtry of th panl, hih i too big iothrm (alo alld moitur apaity). Th for many of thm. Th nd of having a pimn govrning quation (Equation 3) mut b ompltd air to handl brought th Author to om up by appropriat boundary and initial ondition. ith a propoal of a mallr round panl having a diamtr of 6 mm and a dpth of 6 mm, ith a Th rlation btn th amount of vaporabl atr and rlativ humidity i alld adorption ight of only 4 kg. iothrm if maurd ith inraing rlativity humidity and dorption iothrm in th oppoit a. Nglting thir diffrn (Xi t al. 994), in th 4folloing, orption iothrm ill b ud ith rfrn to both orption and dorption ondition. By 3 th ay, if th hytri of th moitur iothrm ould b takn into aount, to diffrnt rlation, 2 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 and rat of th.... 2. 2. 3. 3. hmial ration and, CTODin m [mm] turn, dtrmin por Figur trutur. Exprimntal and por iz rult ditribution from bnding (atr-to-mnt tt on nothd bam ratio, (di mnt Prio t hmial al. (), 24). ompoition, SF ontnt, uring tim and mthod, tmpratur, mix additiv, t.). Th In prnt th litratur papr fou variou on formulation th omparion an b of diffrnt found to tt drib for FRC th orption matrial iothrm ttd during of normal th lat onrt f yar (Xi t at al. th 994). Univrity Hovr, of Bria. in th A prnt omparion papr th btn mi-mpirial bam and xprion panl tt, propod a diuion by on Norling th mallr Mjornll round (997) panl hrin i adoptd propod bau a ll a it Nominal Str N [MPa] th xpliitly orrlation aount btn for th vral volution fratur of proprti hydration obtaind ration from and diffrnt SF ontnt. Standard Thi ar orption alo prntd. iothrm rad Load [kn] Load v. Cntral dfltion 3 ( 3 h,, ) = G (, ) + ( ) 2 g h 2 ( g Slab P22 /,7 ) h Vf=,38 % K (, ) Slab P2 /,7 Vf=,38 % Slab P2 /,7 Vf=,38 % 2 3 4 6 Cntral dfltion [mm] (4) hr th firt trm (gl iothrm) rprnt th phyially bound (adorbd) atr and th ond trm (apillary iothrm) rprnt th apillary Figur atr. 2. Thi Exprimntal xprion rult i valid from full-al only for lab lo on ontnt grad mad of th am FRC a for Figur (di Prio t al. 24). of SF. Th offiint G rprnt th amount of atr pr unit volum hld in th gl por at % rlativ humidity, and it an b xprd (Norling 2 MATERIALS, SET UP, EXPERIMENTAL Mjornll 997) a RESULTS AND DISCUSSION Among G (, mor ) = k than + k omparativ xprimnt arrid out on bam and panl (6 tt on mall () vg vg round panl and 2 on larg round panl), th folloing hr kdiuion vg and k vg ill ar matrial dal ith paramtr. a numbr From of tt th prformd maximum amount on mmbr of atr ontaining pr unit ithr volum 2 that or an 3 kg/m fill all 3 of por hookd-nd (both apillary tl fibr por and having gl a por), lngth on of an mm alulat and a diamtr K a on of obtain mm (th apt ratio L/φ i ). Fibr hav a irular ro tion and a tnil trngth of MPa. Bid th FRC pimn, plain onrt.88 +.22 bam Gand panl r alo g mad. (6) K (, ) = Tabl rport th main gomtrial haratriti of th fiv tting typologi g tudid hrin; th ight of ah pimn, auming a dnity of 24 kn/m Th matrial 3, i alo paramtr outlind. k vg and k vg and g an b In alibratd ordr to by tudy fitting th xprimntal bhavior of all data pimn rlvant up to to fr failur, (vaporabl) inluding atr any poibl ontnt untabl in onrt branh aftr variou raking, ag (Di a diplamnt Luzio & Cuati ontrolld 29b). tting m- at thod a adoptd. Th quipmnt hon in Figur 3 a utilizd for all bam tt, hra th dimnion 2.2 Tmpratur of th round volution panl pimn, aording to ASTM, Not that, a alrady at arly mntiond, ag, in rquird th hmial utilizing ration a diffrnt aoiatd quipmnt, ith mnt xhibitd hydration in Figur and 4. SF In th ration firt a, ar xothrmi, an INSTRON th 274 tmpratur mahin fild a i ud not uniform (having a for lod non-adiabati loop and a ytm maximum vn load if of th 3 nvironmntal kn). In th ond tmpratur a, i th ontant. diplamnt Hat ondution a impod an by b adopting dribd an in ltro-mhanial onrt, at lat r for tmpratur jak (having not a maximum xding load C of (Bažant kn and & a Kaplan trok of 996), 3 mm) by plad Fourir into la, a tl hih fram rad (Fig. 4); no lod loop a providd in thi a. Mor rntly, a tl upporting q = and λ T loading ytm a dignd for prforming (7) tt on mall round panl uing th INSTRON mahin. Figur and Figur 6 ho a mall round panl hr rady q i to tt th and hat th flux, tl upporting T i th ytm abolut to b tmpratur, ud in th and rvo-ontrolld λ i th hat mahin. ondutivity; in thi Proding of FraMCoS-7, May 23-28, 2
A CMOD (Crak Mouth Opning Diplamnt)- ontrolld produr a adoptd for th nothd bam (UNI and CEN prrib a noth ith a diffrnt dpth) hra a diplamnt-ontrolld tt (r ontrol of th ltro-mhanial jak) a prformd ith th big round panl tt, rulting in an intability of th rpon immdiatly aftr th pak of th onrt matrix. For mor dtail onrning th gomtry, tt t-up and intrumntation, on an rfr to Marinoni t al. (27). Tabl. Main gomtri haratriti of pimn. *Larg Round Panl rfr to th tandard tt of ASTM (24). Spimn Lngth [mm] Hight [mm] Noth [mm] Wight [kg] Loading Shm Bam UNI 6 2 32.4 3 point Bam CEN 4 29.7 4 point Dimnion Thikn Wight Loading [mm] [mm] [kg] Shm Larg Round Panl* (RPL) 8 (radiu) 7 9. Cntral point load Small Round Cntral Panl 6 (radiu) 6 4.7 point load (RPS) Squar Panl (SP) 6 (id) 86.4 Cntral point load In th latt mall round panl, ttd ith th rvo-ontrolld mahin availabl in th laboratory, a fititiou CMOD a t in a rgion lo to th midpoint in th bottom panl urfa. By impoing a vry mall opning of thi point, a muh mor rfind and tabl ontrol of th tt a poibl, ithout th uddn load drop xprind in all prviou panl (both larg and mall) ttd ith a impl r jak. Thi rnt improvmnt in th tt t-up guarantd a hlpful rfinmnt of th tt, pially onrning th rak monitoring and it u for matrial haratrization, a hon J = D ( in th h, T ) ond h part of thi rarh rport. Aftr th pak load, Th on proportionality th load path offiint a tabilizd, th tt a moitur ondutd prmability undr a trok-ontrol and it i a nonlina D(h,T) produr, a for of bam th tt. rlativ humidity h and tmpratur & Najjar 972). Th moitur ma balan that th variation in tim of th atr ma volum of onrt (atr ontnt ) b q divrgn of th moitur flux J t = J Th atr ontnt an b xprd a of th vaporabl atr (apillary a vapor, and adorbd atr) and th non- (hmially bound) atr n (Mil Pantazopoulo & Mill 99). It i ra aum that th vaporabl atr i a fu rlativ humidity, h, dgr of hydration dgr of ilia fum ration,, i.. = = ag-dpndnt orption/dorption (Norling Mjonll 997). Undr thi aum by ubtituting Equation into Equati Figur 4. St up for prforming obtain Larg Panl tt. h h + ( D h) = t h & + & + Figur 3. St up for prforming bam tt. hr /h i th lop of th orption/ iothrm (alo alld moitur apa govrning quation (Equation 3) mut b by appropriat boundary and initial onditi Th rlation btn th amount of atr and rlativ humidity i alld iothrm if maurd ith inraing humidity and dorption iothrm in th a. Nglting thir diffrn (Xi t al. th folloing, orption iothrm ill b rfrn to both orption and dorption By th ay, if th hytri of th iothrm ould b takn into aount, to rlation, vaporabl atr v rlativ humi Figur. St up for prforming b ud aording Larg Panl to tt. th ign of th varia rlativity humidity. Th hap of th Svral LVDT iothrm (Linar for Variabl HPC i inflund Diplamnt by many p Trandur) r pially ud in ah tho tt that to influn maur xtnt th and vrtial diplamnt hmial (undr ration th load and, point and turn, in dtrm othr loation) trutur and th rak and por opning iz ditribution (inluding (atrratio, Diplamnt hmial in ompoition, nothd SF th Crak Tip Opning bam). In th bam uring tt, tim intrumnt and mthod, r tmpratur, plad mix for mauring th t.). point In load th litratur diplamnt/ variou in formulatio th front and rar fa, found th rak to drib idth (CTOD) th orption both iothrm in th front and bak onrt fa, and (Xi th t CMOD al. 994). gaug. Hovr, in th Conrning th papr round th panl, mi-mpirial bid th xprion ntral pro Norling Mjornll (997) i adoptd b Proding of FraMCoS-7, May 23-28, 2
J = ) D ( h, T h () Th proportionality offiint D(h,T) i alld moitur prmability and it i a nonlinar funtion of th rlativ humidity h and tmpratur T (Bažant & 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 divrgn of th moitur flux J t = J (2) Th atr ontnt an b xprd a th um of th vaporabl atr Figur 6. Stl upporting fram (apillary atr, atr for prforming Small Panl tt. vapor, and adorbd atr) and th non-vaporabl (hmially bound) atr n (Mill 966, diplamnt Pantazopoulo of & th Mill bottom 99). id It and i th raonabl CMOD, a to alrady aum rportd, that th vaporabl 3 LVDT r atr alo i a dipod funtion for of th rlativ maurmnt humidity, of h, th dgr thr of rak. hydration, Th thr, and intrumnt dgr of ilia r plad fum ration, at a ditan, i.. of 2 =mm (h,from ) th = midpoint, ag-dpndnt to mak orption/dorption thir plamnt ay. iothrm Th maurmnt (Norling Mjonll lngth 997). a Undr mm, thi hih aumption gnrally and allod by ubtituting intrpting Equation th rak. Figur into Equation 7 ho 2 a pitur obtain ith th intrumntation on a round panl mall on prior tting. h + h t ( D h) = n (3) h & + & + hr /h i th lop of th orption/dorption iothrm (alo alld moitur apaity). Th govrning quation (Equation 3) mut b ompltd by appropriat boundary and initial ondition. Th rlation btn th amount of vaporabl atr and rlativ humidity i alld adorption iothrm if maurd ith inraing rlativity humidity and 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 and dorption ondition. Figur By th 7. Intrumntation, ay, if th bottom hytri id of a of mall th round moitur panl. iothrm ould b takn into aount, to diffrnt rlation, Figur vaporabl 8-Figur atr ho v th rlativ xprimntal humidity, urv mut of b a ud ri aording of xprimnt to th ign mad of th of variation diffrnt pimn rlativity from humidity. th am onrt Th hap bath. of Figur th orption 8 and of th Figur iothrm 9 rport for HPC th i Nominal inflund Str by many (aording paramtr, to a linar pially tr tho ditribution that influn th rakd xtnt and tion) rat of vru hmial th CTOD ration for both and, CEN in turn, and UNI dtrmin bam tt por th hra trutur Figur and por and iz Figur ditribution xhibit (atr-to-mnt th load v. th ratio, ntral mnt vrtial hmial diplamnt ompoition, of both SF larg ontnt, and mall uring round tim panl and mthod, mad of tmpratur, th idntial mix matrial. additiv, A xptd, t.). In th litratur pot-pak variou bhavior formulation i imilar for an th b to found typ to drib of bam tt, th orption hih ar iothrm haratrizd of normal by a rathr onrt larg (Xi attr. t al. A 994). mallr Hovr, diprion in an th b prnt n in papr th th panl mi-mpirial plot: thi i xprion furthr onfirmd propod from by Figur Norling 2, Mjornll hih ho (997) th load-diplamnt adoptd bau urv it & of xpliitly mall round aount panl for at th ith volution High Strngth of hydration Conrt ration and ith and to SF fibr ontnt. ontnt: Thi 3 orption and 6 kg/m iothrm 3. rad Figur 4 and Figur xhibit th offiint of variation from th diprion of prviou figur, it rult that th offiint i dfinitly muh mallr in panl than in th orrponding bam tt, both ( h,, ) = G (, ) + for larg and mall round panl. ( g ) h (4) Nominal Str N [MPa] 7 6 Comparion UNI Bam Stl fibr ( g FF ) (, ) h 2 kg/m³ 3 kg/m³ rlativ humidity, and it an b xprd (Norling.. 2 2. 3 3. 4 4. G (, ) = k + k CTODm [mm] vg vg () Figur 8. Nominal tr-ctod of Bam tt aording to UNI, for FRC ith 2 and 3 kg/m 3. hr k vg and k vg ar matrial paramtr. From th maximum 7 amount Comparion of atr pr CEN unit Bam volum that an fill all por (both apillary Stl fibr por FF and gl por), on an 6alulat K a on obtain Nominal Str N [MPa] 4 K (, ) = 3 2 K hr th firt trm (gl iothrm) rprnt th 4 phyially bound (adorbd) atr and th ond trm (apillary iothrm) rprnt th apillary 3 atr. Thi xprion i valid only for lo ontnt of SF. 2 Th offiint G rprnt th amount of atr pr unit volum hld in th gl por at % Mjornll 997) a g 2 kg/m³ 3 kg/m³ g.88 +.22 G Th matrial paramtr k vg and k vg and b alibratd by fitting xprimntal data rlvant to.. 2 2. 3 3. 4 4. CTODm [mm] (6) g an fr (vaporabl) atr ontnt in onrt at variou ag (Di Luzio & Cuati 29b). Figur 9. Nominal tr-ctod of Bam tt aording to 2.2 Tmpratur volution CEN, for FRC ith 2 and 3 kg/m 3. Not that, at arly ag, in th hmial ration aoiatd With th ith aformntiond mnt hydration thr and LVDT, SF ration rak idth ar xothrmi, gratr than th tmpratur 2 mm r fild maurd i not uniform ith a pot-raking for non-adiabati load ytm highr than vn on if th third nvironmntal of th pak load. tmpratur Suh an i intrumntation ontant. Hat i ondution not rquird an by th b ASTM dribd Standard, in onrt, hih at tat lat that for on tmpratur hould only not alulat xding th C nrgy (Bažant aborption & that Kaplan i dfind 996), by th by vrtial Fourir load la, and hih th vrtial rad diplamnt. By monitoring th rak idth, ho loation i prditabl bau q = λ Tof th tatially dtrminat upport ytm, (7) it a alo poibl to om up ith nominal tr (from lati analyi) v. rak idth plot, a a hr q i th hat flux, T i th abolut uitabl tool for th mhanial haratrization of tmpratur, and λ i th hat ondutivity; in thi Proding of FraMCoS-7, May 23-28, 2
FRC matrial and for th dfinition of implifid tr-rak idth ohiv ontitutiv la. Figur 3 rport a typial xprimntal urv of th rak idth v. load. Th thr rak loation ar in mot of a in good agrmnt ith th xptation (2 ) and thir valu ar rathr imilar on to ah othr. 3 Comparion LARGE ROUND PANEL Stl fibr FF 3 2 Load [KN] 2 kg/m³ 2 3 kg/m³ J = (i.. D (hfinding, T ) h tandard bam tt ridual tr or pot-raking trngth a tatd by bam tandard but uing round panl tt). To thi aim, offiint th follo- D(h,T) Th proportionality ing produr amoitur undrtakn: prmability and it i a nonlina. Find orrlation thhumidity diffrnt hparamtr of btn th rlativ and tmpratur rquird by diffrnt tandard uing xprimntal r- balan & Najjar 972). Th moitur ma ult; that th variation in tim of th atr ma 2. Givn th orrlation, valu of) b q volum ofalulat onrtavrag (atr ontnt th quivalnt (UNI) or loal (CEN) pot-raking divrgn of th moitur flux J trngth (bam tt) from th xprimntal valu of nrgy aborption from = panl; J valu of th pot3. Calulat th haratriti t raking trngth from panl aounting for a lor xprimntal attr;th atr ontnt an b xprd a 4. Compar th of valu of quivalnt pot-raking th vaporabl atr (apillary a trngth dtrmind from bam tt (dirt vapor, and adorbd atr)mthod) and th non- ith tho from larg and mall panl tt. (hmially bound) atr (Mil n Pantazopoulo & Mill 99). It i ra aum that th vaporabl atr i a fu rlativ humidity, h, dgr of hydration dgr of ilia fum ration,, i.. = = ag-dpndnt orption/dorption (Norling Mjonll 997). Undr thi aum by ubtituting Equation into Equati obtain 2 3 4 Diplamnt [mm] Figur. Load-Diplamnt urv of Larg Round Panl Tt aording to ASTM, for FRC ith 2 and 3 kg/m3. 2 Comparion SMALL ROUND PANEL Stl fibr 2 kg/m³ 3 kg/m³ 2 3 4 Diplamnt [mm] Figur. Load-Diplamnt urv of Small Round Panl Tt, for FRC ith 2 and 3 kg/m3. Th offiint of variation, a an indiator of th tt-rult attr, a alulatd for all proprti and indx dfind in th diffrnt tandard, both for quantiti hih rfr to th rviability limit tat (SLS, Fig. 4) and ultimat limit tat (ULS, Fig. ). On again, a ignifiant lor offiint of variation an b outlind for panl tt in omparion ith bam tt. It m orth uing th lo attr of panl tt for th dtrmination of mor uitabl fratur proprti onitnt ith th on dtrmind from th & + & + hr /h i th lop of th orption/ iothrm (alo alld moitur apa govrning quation (Equation 3) mut b Figur 2. Load-Diplamnt urv of Small Round Panl by appropriat boundary and initial onditi Tt, HSC panl, FRC ith 3 and 6 kg/m3. Th rlation btn th amount of atr and rlativ humidity i alld Comparion SMALL ROUND PANEL iothrm if maurd ith inraing Stl fibr FF humidity and dorption iothrm in th a. Nglting thir diffrn (Xi t al. th folloing, orption iothrm ill b rfrn to both orption and dorption By th ay, if th hytri of th iothrm ould b takn into aount, to rlation, vaporabl atr v rlativ humi b ud aording to th ign of th varia 2 kg/m³ rlativity humidity. Th hap of th 3 kg/m³ iothrm for HPC i inflund by many p pially tho that influn xtnt and hmial ration and, in turn, dtrm trutur and por iz 2ditribution (atr 2 [KN] hmial ompoition, SF ratio, Load mnt Figur 3. Crak idth-load Small Round Panl mix uring timurv andofmthod, tmpratur, Tt, HSC panl, FRC andlitratur 6 kg/m3. variou formulatio t.).ithin3th found to drib th orption iothrm Figur 6, a an xampl, th orrlation onrt (Xidrib t al. 994). Hovr, in th btn th quivalnt pot-raking trngth of th papr th mi-mpirial xprion pro UNI tandard and th nrgy aborption of th Norling Mjornll (997) i adoptd b Avrag Crak Width [mm] Load [KN] 2 h + ( D h) = h h t Proding of FraMCoS-7, May 23-28, 2
ASTM J = D ( panl h, T ) h at SLS. On hould not that th () nrgy aborption rlvant for th SLS a onvntionally Th dfind proportionality by th author offiint a th D(h,T) nrgy i maurd moitur at prmability mm diplamnt and it for i a th nonlinar laial funtion round alld panl, of th rlativ hra humidity at 3.7 h mm and (jut tmpratur by aling T (Bažant th dimnion) & Najjar 972). for th Th mall moitur panl. ma Th balan to valu rquir rfr that to th rak variation tag in hih tim of ar th ignifiant atr ma for pr gnral unit ituation volum of rlatd onrt to (atr rviability ontnt limit ) b tat qual (ompar, divrgn a an xampl, of th moitur Fig. flux and J Fig. to th 3).. t Comparion offiint of variation Stl Fibr Proprti dtrmind at SLS = J (2) Th atr ontnt an b xprd a th um.4 2 kg/m³ of.4th vaporabl atr (apillary atr, 3 kg/m³ atr vapor, and adorbd atr) and th non-vaporabl (hmially.3 bound) atr n (Mill 966, Pantazopoulo.24 & Mill 99). It i raonabl to.23 aum that th vaporabl atr i a funtion of.2 rlativ humidity, h, dgr of hydration,.6, and.4 dgr of ilia fum ration,, i.. = (h,, ).9. = ag-dpndnt orption/dorption iothrm.8. (Norling Mjonll 997). Undr thi aumption and by. ubtituting Equation into Equation 2 on UNI CEN RPL RPS obtain Figur 4. Coffiint of variation alulatd for all paramtr rquird by th tandard onidrd in th prnt xprimntal h ampaign. + ( D h) = & + & + & n (3) h t h Comparion offiint of variation hr /h i th Stl lop Fibr of th FF orption/dorption Proprti dtrmind at ULS iothrm (alo alld moitur apaity). Th govrning. quation (Equation.46 3) mut b ompltd 2 kg/m³ by appropriat boundary and initial ondition. 3 kg/m³.4th rlation btn th.37 amount of vaporabl atr and rlativ humidity i alld adorption.32 iothrm.3 if maurd ith inraing rlativity humidity and dorption iothrm in th oppoit.23.23 a..9.2 Nglting thir diffrn (Xi t al. 994), in. th folloing, orption iothrm ill b ud ith rfrn. to both orption and dorption ondition..8 By th ay, if th hytri of th moitur iothrm ould b takn into aount, to diffrnt. rlation, UNI vaporabl atr CEN v rlativ RPL humidity, RPS mut Figur b ud. aording Coffiint to of th variation ign alulatd of th variation for all paramtr rlativity rquird humidity. by th tandard Th onidrd hap of in th prnt orption x- of th primntal iothrm ampaign. for HPC i inflund by many paramtr, pially tho that influn xtnt and rat of th hmial Thirtn ration omparativ and, tudi in turn, ar dtrmin rportd ith por diffrnt trutur point and por in th iz plot, ditribution ah on (atr-to-mnt rfrring to th avrag ratio, mnt of at lat hmial thr round ompoition, panl pr SF ri. ontnt, Diffrnt uring fibr tim and ontnt, mthod, fibr tmpratur, matrial, mix fibr additiv, oktail, t.). In fibr th gomtry litratur and variou onrt formulation la ar an onidrd found to in drib th plot. th Figur orption 7 iothrm ho th of idntial normal b orrlation onrt (Xi alulatd t al. 994). ith Hovr, th paramtr in th at prnt ULS. From papr th mi-mpirial to plot, on an xprion noti that propod a linar rgrion Norling btn Mjornll th (997) to quantiti i adoptd rprnt bau ll by it th xpliitly trnd and aount that th for offiint th volution of variation of hydration R 2 i quit ration mall. and SF ontnt. Thi orption iothrm rad 8 ( h,, ) = G (, ) + ( g ) h E L, RPL [J] 6 4 Rlation Larg Round Panl - UNI Bam ; SLS of SF. Th offiint G rprnt th amount of atr.pr unit. volum. hld. in 2. th gl 2.por 3.at % 3. f q (-,6) UNI Bam [MPa] rlativ humidity, and it an b xprd (Norling Figur Mjornll 6. Corrlation 997) a btn nrgy aborption and quivalnt pot raking trngth: Claial Larg Round Panl tt ASTM v. Bam Tt UNI, rviability limit tat. G (, ) = k + k () 6 vg vg Rlation Larg Round Panl - UNI Bam ; ULS hr k vg and k vg ar matrial paramtr. From th maximum amount of atr pr unit volum that an fill all por (both apillary por and gl por), on 4 an alulat K a on obtain E L,4 RPL [J] ( g ) h K (, ) 3 g.88 +.22 G 2 K (, ) = E L,4 RPL = 27.23 f q (.6-3) UNI g R 2 =.86 (4) hr th firt trm (gl iothrm) rprnt th phyially E L, RPL = 26.84 f q (-,6) UNI 2 bound (adorbd) atr and th ond R 2 =.8 trm (apillary iothrm) rprnt th apillary atr. Thi xprion i valid only for lo ontnt (6) Th matrial paramtr k vg and k vg and g an b alibratd by fitting xprimntal data rlvant to.. 2. 3. 4. fr (vaporabl) atr f q (.6-3) UNI ontnt Bam [MPa] in onrt at Figur variou 7. ag Corrlation (Di Luzio btn & Cuati nrgy aborption 29b). and quivalnt pot raking trngth: Claial Larg Round Panl tt ASTM v. Bam Tt UNI, ultimat limit tat. 2.2 Tmpratur volution Not Th that, to at rlationhip arly ag, in found th ar hmial a follo: ration aoiatd ith mnt hydration and SF ration ar EL, xothrmi, = 26.84 fq(th.6) tmpratur fild i not uniform for () E non-adiabati L,4 = 27.23 f ytm vn if th nvironmntal q(.63) tmpratur i ontant. Hat ondution an b dribd in onrt, at lat for tmpratur not hr: xding C (Bažant & Kaplan 996), by Fourir E L, i la, th nrgy hih rad aborption for th larg round panl up to a vrtial diplamnt of mm (t by th q author); = λ T E L,4 i th nrgy aborption for th larg round (7) panl up to a vrtial diplamnt of 4 mm (dfind hr in th q i ASTM th Standard); hat flux, T i th abolut tmpratur, and λ i th hat ondutivity; in thi Proding of FraMCoS-7, May 23-28, 2
f q(-.6) i th quivalnt pot-raking trngth alulatd for a CTOD rang varying from to.6 mm (SLS) inludd in th UNI Standard. f q(.6-3.6) i th quivalnt pot-raking trngth alulatd for a CTOD rang varying from.6 to 3 mm (ULS) inludd in th UNI Standard. Othr orrlation r alo dtrmind btn panl (mall and larg) and bam (CEN and UNI). Figur 8 and Figur 9 rport th orrlation btn UNI bam tt and Small Round Panl, obtaind uing 2 xprimntal point. Th offiint of variation i again onidrably good and th linar approximation i alo onitnt, lading to th folloing rlation: E E S,3.7 S,3 E S,3.7 RPS [J] 7 6 4 3 2 =. f = 7.84 f q(.6) q(.63) Rlation Small Round Panl - UNI Bam; SLS ( Only Strain-Softning Matrial Undr Flxur) E S,3.7 RPS =. f q (-.6) UNI R 2 =.97.. 2. 3. 4.. f q (-,6) UNI Bam [MPa] (2) Figur 8. Corrlation btn nrgy aborption and quivalnt pot raking trngth: Small Round Panl tt v. Bam Tt UNI, rviability limit tat. E S,3 RPS [J] 3 2 2 Rlation Small Round Panl - UNI Bam; ULS ( Only Strain-Softning Matrial Undr Flxur) E S,3 RPS = 7.84 f q (.6-3) UNI R 2 = 9.. 2. 3. 4. f q (.6-3) UNI Bam [MPa] Figur 9. Corrlation btn nrgy aborption and quivalnt pot raking trngth: Small Round Panl tt v. Bam Tt UNI, ultimat limit tat. Figur 2, Figur 2 and Figur 22 xhibit th orrlation btn th ridual trngth and quivalnt pot-raking J = tr D ( h, T ) dfind h in th CEN and UNI tandard bam tt. Evn though a mallr databa i availabl (only Th proportionality 7 xprimntal offiint point ar D(h,T) plottd, ah on moitur rfrring to prmability th avrag and valu it i of a at nonlina lat thr bam of tt th pr rlativ ri), humidity th offiint h and tmpratur of variation i quit & good Najjar and 972). th rlation Th moitur alrady ma onitnt. Furthr omparativ that th variation tudi in or tim olltion of th atr of ma balan xprimntal omparativ volum of xprimntal onrt (atr data ontnt orld-id ould b uful divrgn for a rfinmnt of th moitur of th flux rla- J b q tionhip. Not that all orrlation r t a lin and for to ro th ax origin. Thi in fat m to b in good agrmnt = ith J th xprimntal rult. t f r CEN Bam [MPa] f r4 CEN Bam [MPa] 7. 6.. 4. 3. 2.. Th atr ontnt an b xprd a Rlation CEN of th Bam vaporabl - UNI Bam; atr SLS (apillary a vapor, and adorbd atr) and th non- (hmially bound) atr n (Mil Pantazopoulo & Mill 99). It i ra aum that th vaporabl atr i a fu rlativ humidity, h, dgr of hydration dgr of ilia fum ration,, i.. = = ag-dpndnt orption/dorption (Norling Mjonll 997). Undr thi aum by ubtituting f r CEN Equation =.98 f q(-.6) UNI into Equati R 2 =.83 obtain. h.. 2. 3.+ 4. ( D h. ) = 6. + 7. f q (-.6) h UNI t Bam [MPa] h & & + Figur 2. Corrlation btn ridual tr and quivalnt pot raking trngth: Bam Tt CEN v. Bam Tt UNI, rviability limit tat. hr /h i th lop of th orption/ iothrm (alo alld moitur apa 4. govrning quation (Equation 3) mut b Rlation by CEN appropriat Bam - UNI boundary Bam; and ULSinitial onditi 3. Th rlation btn th amount of 3. atr and rlativ humidity i alld iothrm if maurd ith inraing 2. humidity and dorption iothrm in th 2. a. Nglting thir diffrn (Xi t al. th folloing, orption iothrm ill b. rfrn to f r4 both CEN = orption.78 f q(.6-3) UNI and dorption R 2 =.7. By th ay, if th hytri of th iothrm ould b takn into aount, to. rlation, vaporabl atr v rlativ humi b ud aording to th ign of th varia... rlativity 2. humidity. 3. Th 4. hap. of th iothrm f q (.6-3) for UNI Bam HPC [MPa] i inflund by many p Figur 2. Corrlation pially btn ridual tho that tr influn and quivalnt xtnt and pot raking trngth: hmial Bam Tt ration CEN v. Bam and, Tt in turn, UNI, dtrm ultimat limit tat. trutur and por iz ditribution (atrratio, mnt hmial ompoition, SF On th orrlation ar found, it i poibl to uring tim and mthod, tmpratur, mix dtrmin, for xampl, bam toughn proprti t.). In th litratur variou formulatio from panl tt, uing th orrponding lor diprion. A an xampl, th haratriti valu of found to drib th orption iothrm onrt (Xi t al. 994). Hovr, in th th quivalnt pot-raking trngth, uitabl for dign purpo, r alulatd by uing th orr- papr th mi-mpirial xprion pro Norling Mjornll (997) i adoptd b ponding xprimntal attr rptivly of UNI Proding of FraMCoS-7, May 23-28, 2
bam, J = D ( larg h, T ) (ASTM) h and mall (our propoal) round () panl. In doing o, Figur 23 and Figur 24 xhibit a omparion Th proportionality btn th offiint avrag and D(h,T) th haratri- alld ti moitur valu prmability of th fratur and paramtr it i a nonlinar f q(-.6), for funtion FRC ith of th 2 rlativ (Fig. 23) humidity and 3 h and kg/mtmpratur 3 of tl fibr T (Bažant (Fig. 24). & Najjar Du to 972). a rathr Th high moitur attr, ma uing balan th bam rquir tt th that haratriti th variation valu in tim turn of th out atr to b ma at lat pr 4% unit lor volum than of onrt th avrag (atr on ontnt hra, ) b in qual th a to th of panl divrgn tt, th of th rdution moitur vari flux from J to 3%; thi lor diffrn rprnt a bnfiial fft on th valu adoptd in th dign pro and, onquntly, = on J th trutural dimnion. Th dign (2) ad- t vantag ar, thrfor, doubtl. Th atr ontnt an b xprd a th um 4. of th vaporabl Rlation CEN atr Bam (apillary - UNI Bam; atr, ULSatr vapor, 4. and adorbd atr) and th non-vaporabl (hmially 3. f r3 CEN bound) =.9 f q(.6-3) atr UNI n (Mill 966, R 2 =.69 Pantazopoulo & Mill 99). It i raonabl to aum 3. that th vaporabl atr i a funtion of f r3 CEN Bam [MPa] rlativ 2. humidity, h, dgr of hydration,, and dgr of ilia fum ration,, i.. = (h,, ) 2. = ag-dpndnt orption/dorption iothrm (Norling. Mjonll 997). Undr thi aumption and by ubtituting Equation into Equation 2 on. obtain.. h + D h) = & + & + & n h. t. h 2. 3. 4.. UNI Bam [MPa] f q (.6-3) Figur 22. Corrlation btn ridual tr and quivalnt pot hr raking /h trngth: i th Bam lop Tt of th CEN orption/dorption v. Bam Tt UNI, ultimat iothrm limit (alo tat. alld moitur apaity). Th govrning quation (Equation 3) mut b ompltd by appropriat Comparion boundary and f q(-.6),m initial -f ondition. q(-.6),k Th rlation Stl btn fibr th Vamount f =.2% of vaporabl Proprti dtrmind at SLS atr and rlativ humidity i alld adorption iothrm 3. if maurd ith inraing rlativity 2.7 2.6 humidity and 2.3 dorption iothrm in th oppoit 2. 2.26 a. Nglting thir diffrn (Xi t -8% al. 994), in.96 th folloing, orption iothrm ill b ud -26% ith 2. rfrn to both orption and dorption ondition..39 By.th ay, if th hytri -4% of th moitur iothrm ould b takn into aount, to diffrnt. rlation, vaporabl atr v rlativ humidity, mut UNI RPL RPS UNI RPL RPS 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 f q(-.6),m that influn xtnt fand q(-.6),k rat of th Figur hmial 23. Avrag ration v. haratriti and, in turn, f q(-.6) dtrmin uing th attr por of trutur diffrnt tandard: por Round iz ditribution Panl tt v. (atr-to-mnt Bam Tt UNI. ratio, mnt hmial ompoition, SF ontnt, uring On tim hould and noti mthod, that tmpratur, th thr avrag mix additiv, valu ar t.). almot In th idntial, litratur a a variou furthr proof formulation of th trngth an b and found onitny to drib of th aformntiond orption iothrm orrlation. of normal onrt A a furthr (Xi t onfirmation al. 994). Hovr, of th abovmntiond in th prnt trnd, papr on th hould mi-mpirial alo look xprion at th rult propod plottd by in Figur Norling 2 Mjornll and Figur (997) 26, hoing i adoptd th alulation bau of it [MPa] ( (3) th xpliitly haratriti aount valu for th of volution th quivalnt of hydration potraking ration trngth and SF f q(.6-3) ontnt. for Thi th to orption fibr iothrm ontnt onidrd. rad Th attr of round panl, mall in th a, i vn lor than that of laial panl ASTM, vn though, a a gnral obrvation, bad on th total xprimntal program (mor than ( h,, ) = G (, ) + panl tt) arrid out during th lat 4 yar in Bria, th diprion of rult in rathr imilar ( g ) h (4) btn th to panl. ( g ) h K (, ) Comparion f q(-.6),m -f q(-.6),k Stl fibr V f =.38% Proprti dtrmind at SLS hr th firt trm (gl iothrm) rprnt th 3. 3.27 phyially 3.8 bound (adorbd) 3.6 atr and th ond 3. 2.7 trm (apillary iothrm) rprnt th apillary -% atr. Thi xprion i valid only for 2.28 lo ontnt 2. -3% of SF. Th offiint G rprnt th amount of [MPa].78 atr 2. pr unit volum hld in th -42% gl por at % rlativ humidity, and it an b xprd (Norling. Mjornll 997) a. UNI RPL RPS UNI RPL. G (, ) = k + k vg vg. f q(-.6),m f q(-.6),k RPS hr k vg and k vg ar matrial paramtr. From th Figur 24. Avrag v. haratriti f q(-.6) uing th attr of maximum diffrnt tandard: amount Round of atr Panl pr tt unit v. volum Bam Tt that UNI. an fill all por (both apillary por and gl por), on an alulat K Comparion a on obtain f q(.6-3),m -f q(.6-3),k Stl fibr FF V f =.2% Proprti dtrmind at ULS g.88 +.22 G 3. 2.76 (6) K (, ) = 2. 2.4 2. g h [MPa] 2.. 2.2.Tmpratur volution f q(.6-3),m.74-29%.72-38%. -6% fr. (vaporabl) atr ontnt in onrt at UNI RPL RPS UNI RPL RPS f q(.6-3),k () Th. matrial paramtr k vg and k vg and g an b alibratd by fitting xprimntal data rlvant to Figur Not that, 2. Avrag at arly v. ag, haratriti in th f q(.6-3) hmial uing th ration attr of aoiatd diffrnt tandard: ith mnt Round Panl hydration tt v. and Bam SF Tt ration UNI. ar xothrmi, th tmpratur fild i not uniform for non-adiabati ytm vn if th nvironmntal 3 tmpratur CONCLUDING i ontant. REMARKS Hat ondution an b dribd in onrt, at lat for tmpratur not A xding omparativ C tudy (Bažant btn & bam Kaplan and panl 996), tt by a Fourir diud la, in hih th prnt rad papr. Rult ho that th high xprimntal attr gnrally prnt in bam q = λtt T i dfinitly aud by th mall gomtry (7) and fratur ara involvd in th tt. It do not rprnt, hr q in i gnral, th hat th flux, atual T trutural i th bhavior abolut hr tmpratur, muh largr and λ fratur i th hat ara ondutivity; ar involvd in and, thi onquntly, a lor diprion our. variou ag (Di Luzio & Cuati 29b). Proding of FraMCoS-7, May 23-28, 2
Panl tt ar thrfor mor uitabl for rprnting th atual bhavior of FRC matrial. Providd that th tt i prformd undr a lo-loop ontrol ith rak idth maurmnt, th round panl tt an b adoptd for th haratrization of FRC a it impli muh lor diprion of xprimntal rult. [MPa] 4. 3. 3. 2. 2..... Comparion f q(.6-3),m Stl fibr FF V f =.38% Proprti dtrmind at ULS 3.4 3. 3.37 -f q(.6-3),k.98-43% 2. -42% UNI RPL RPS UNI RPL f q(.6-3),m f q(.6-3),k 2.86 -% RPS Figur 26. Avrag v. haratriti f q(.6-3) uing th attr of diffrnt tandard: Round Panl tt v. Bam Tt UNI. Th propod mallr pimn for panl tt do not afft th lo attr of th tandard ASTM panl; morovr, it allo for an air plaing and handling (lor ight and mallr gomtry that fit ith many rvo-ontrolld tting mahin). In fat, rult from round panl ith a diamtr of 6 mm and a thikn of 6 mm, ar onitnt, rliabl and provid a rpatabl and prditabl rak pattrn ith a onitntly lor diprion than laial bam tt. Th orrlation among fratur paramtr found in th xprimntal program ar in gnral vry promiing and allo nginr to analytially dtrmin th fratur paramtr of diffrnt tt from prforming only on or f tt typologi. Th orrlation, that r omho xptd in tandard tt alay rfr to fratur proprti of th am matrial, may b uful in prati in thy an giv immdiat indiation of th fratur proprti ithout prforming xpniv tt. In addition, thy ar uful for xhanging rult from a broad databa of bam and panl tt availabl orldid form diffrnt laboratori and univriti. Finally, th round panl tt ould b onidrd a a omplt tt for th haratrization of FRC on uitabl rang of rak idth ill b dfind. From th rang, th orrponding quivalnt (or ridual) pot-raking trngth an b dfind (from σ- plot) folloing th am produr a don for bam tt. Th ond part of th papr ill fou on th dfinition of a implifid ohiv ontitutiv la. 4 ACKNOWLEDGMENTS J = ( h, T ) Th rarh a partially Th proportionality o-fundd ithr offiint by Mag- D(h,T) ntti Building (Carvio, moitur Italy) prmability and Offiin and Maafrri (Bologna, Italy) of th ho rlativ upport humidity i gratfully h and tmpratur a- it i a nonlina knoldgd. & Najjar 972). Th moitur ma balan Th Author ould that th lik variation to thank in tim alo Enginr of th atr ma Moira Conti, Giovanni volum Fllli, of onrt Yuri Marinoni, (atr ontnt Raoul ) b q Martin Milla and divrgn Niola Vzzoli of th for moitur thir aitan flux J in prforming th xprimnt and in data proing. REFERENCES D h t = J Th atr ontnt an b xprd a ASTM C-4, Standard tt mthod for flxural toughn of fibr rinford of th vaporabl onrt (uing atr ntrally (apillary loadd a round panl), pp. vapor, 9, 24. and adorbd atr) and th non- CEN/TC 229 - PrEN (hmially 46-, Prat bound) Conrt atr Produt n (Mil Tt mthod for Pantazopoulo mtalli fibr onrt & Mill Mauring 99). It th i ra flxural tnil trngth, aum Europ. that th Standard, vaporabl 23, pp.. atr i a fu CNR DT 24/26. 26. "Guidlin for th Dign, Contrution and Prodution Control of Fibr Rinford Con- rlativ humidity, h, dgr of hydration rt Strutur", dgr National of Rarh ilia fum Counil ration, of Italy., i.. = di Prio, M., Failla, = C., ag-dpndnt Plizzari, G.A. and orption/dorption Toniolo, G. (24), Italian guidlin (Norling Mjonll SFRC, 997). in Fibr Undr Rinford thi aum Conrt: from thory by ubtituting to prati, di Equation Prio, M. and into Plizzari, G.A. Ed., Proding Equati obtain of th Intrnational Workhop on advan in Fibr Rinford Conrt, Brgamo (Italy), Sptmbr 24-2, pp. 39-72. di Prio, M., Flitti, R. and Plizzari, G.A. Ed. (24b), h Proding of th 6th RILEM + Sympoium ( D h) = on Fibr & + Rinford Conrt, BEFIB 24, RILEM PRO 39, & + h t h 4 pp. Eurood 2. 23. Dign of Conrt Strutur, pren 992 Vr. Dmbr 23. fib SAG. 2. Draft hr propoal /h th i n th fib lop Modl of Cod, th orption/ in prparation. iothrm (alo alld moitur apa Lambrht, A.N., Th govrning variation quation of tl fibr (Equation onrt 3) haratriti. Study by on appropriat toughn rult boundary 22-23, and initial Pro-onditding of th Intrnational Th rlation Workhop btn Fibr th Rinford amount of mut b Conrt. From thory to prati, Brgamo, Sptmbr atr and rlativ humidity i alld 24-2, 24, pp. 3-48. Marinoni, Y., Minlli, iothrm F., Plizzari, if maurd G.A., and Vzzoli, ith inraing N.: Prov di frattura humidity u altruzzi and dorption fibrorinforzati in iothrm aordo in th on l prinipali a. normativ Nglting intrnazionali, thir diffrn Thnial (Xi t al. Rport, Univrity th of folloing, Bria, Dpartmnt orption DICATA, iothrm 27. ill b Mda, A., Minlli, F., rfrn Plizzari, G.A. to both and orption Riva, P. 2. and dorption Shar Bhavior of Stl Fibr Rinford Conrt Bam. Matrial and Strutur, 38, 343-3. By th ay, if th hytri of th Minlli, F. 2. Plain iothrm and Fibr ould Rinford b takn Conrt into Bam aount, to undr Shar Loading: rlation, Strutural vaporabl Bhavior atr and Dign v rlativ Apt. Ph.D. Thi, b ud Dpartmnt aording of to Civil th Enginring, ign of th varia humi Univrity of Bria, rlativity Starrylink humidity. Editor, pp. Th 43. hap of th Minlli, F. & Plizzari, iothrm G.A. 26. for Stl HPC Fibr i inflund a Shar Rinformnt for Bam. Proding of Th Sond Fib by many p Congr, Napl, pially Italy, -8 Jun, tho 26, that abtrat influn on xtnt pag and 282-283, full lngth hmial papr availabl ration aompanid and, in turn, CD, dtrm pp.2. trutur and por iz ditribution (atrratio, F.J. mnt 26. Comprion hmial Fild ompoition, Modl- SF Minlli, F. & Vhio, ing of Fibr Rinford uring tim Conrt and Mmbr mthod, undr tmpratur, Shar mix Loading. ACI Strutural Journal, 3(2), 244-22. t.). In th litratur variou formulatio Minlli, F., Cominoli, L., Mda, A., Plizzari, G.A., and Riva, P. 2. Full Sal found Tt to on drib HPSFRC th Prtrd orption Roof iothrm Elmnt Subjtd onrt to Longitudinal (Xi t al. Flxur. 994). Proding Hovr, in th of th Intrnational papr Workhop th mi-mpirial on High Prforman xprion Fibr pro Rinford Cmntitiou Norling Compoit Mjornll in (997) Strutural i Appli- adoptd b Proding of FraMCoS-7, May 23-28, 2
J = ation, D ( h, THonolulu, ) h Haaii, USA, May 23-26, 2, 323- () 332. PrEN 4488--CEN/TC 4, Tting prayd onrt Part : Th Dtrmination proportionality of nrgy offiint aboprtion apaity D(h,T) of i fibr alld rinford prmability lab pimn, and Europ. it i Standard, a nonlinar 24, funtion pp.-7. moitur RILEM of th rlativ Final Rommndation humidity h and TC-62-TDF, tmpratur Tt T (Bažant and Dign Mthod 972). for Th Stl moitur Fibr Rinford ma balan Conrt; rquir σε D- & Najjar ign Mthod, Matrial and Strutur, Vol 36, Otobr that th variation in tim of th atr ma pr unit 23, pp. 6-67. RILEM volum TC62-TDF: of onrt Tt (atr and ontnt Dign Mthod ) b qual for Stl to th Fibr Rinford of th moitur Conrt: flux Rommndation. J Bnding divrgn tt, Matrial and Strutur, 33, (22), (2) 3-. Shumahr, P., Rotation apaity of lf-ompating tl fibr = rinford J onrt, Ph.D Thi, Dlft Univrity (2) of Thnology, t Th Nthrland, 26 Sorlli, L., Mda, A. and Plizzari, G.A., Bnding and uniaxial Th tnil atr tt ontnt onrt an b rinford xprd ith a hybrid th um tl of fibr, th vaporabl ASCE Matrial atr Journal, (apillary Vol.(), atr, 2, pp. atr 9- vapor, 27. and adorbd atr) and th non-vaporabl UNI (hmially 39, Stl bound) Fibr Rinford atr Conrt - Part I: Dfinition, Claifiation Spifiation and n (Mill 966, Conformity - Part II: Pantazopoulo Tt Mthod for & Mauring Mill 99). Firt Crak It i Strngth raonabl and Dutility Indx, that th Italian vaporabl Board for atr Standardization, i a funtion 23. of to aum Vandall, rlativ humidity, L., Tt and h, dgr dign mthod of hydration, for tl fibr, rinford of onrt ilia fum propod ration, by RILEM, i.. TC 62-TDF, = (h, and dgr Proding ag-dpndnt of th Intrnational orption/dorption Workhop Fibr Rinford iothrm, ) = Conrt. From thory to prati, Brgamo, Sptmbr (Norling Mjonll 997). Undr thi aumption and 24-2, 24, pp. 3-2. by ubtituting Equation into Equation 2 on obtain h + h t ( D h) = n (3) h & + & + hr /h i th lop of th orption/dorption iothrm (alo alld moitur apaity). Th govrning quation (Equation 3) mut b ompltd by appropriat boundary and initial ondition. Th rlation btn th amount of vaporabl atr and rlativ humidity i alld adorption iothrm if maurd ith inraing rlativity humidity and 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 and 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 and rat of 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 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 & xpliitly aount for th volution of hydration ration and SF ontnt. Thi orption iothrm rad ( h,, ) = G (, ) + ( g ) h ( g ) h K (, ) (4) hr th firt trm (gl iothrm) rprnt th phyially bound (adorbd) atr and 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 % rlativ humidity, and it an b xprd (Norling Mjornll 997) a G (, ) = k + k vg vg () hr k vg and k vg ar matrial paramtr. From th maximum amount of atr pr unit volum that an fill all por (both apillary por and gl por), on an alulat K a on obtain K (, ) = g.88 +.22 G g (6) Th matrial paramtr k vg and k vg and g an b alibratd by fitting xprimntal data rlvant to fr (vaporabl) atr ontnt in onrt at variou ag (Di Luzio & Cuati 29b). 2.2 Tmpratur volution Not that, at arly ag, in th hmial ration aoiatd ith mnt hydration 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 C (Bažant & Kaplan 996), by Fourir la, hih rad q = λ T (7) hr q i th hat flux, T i th abolut tmpratur, and λ i th hat ondutivity; in thi Proding of FraMCoS-7, May 23-28, 2