Fracture properties of high-strength steel fiber concrete

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1 Fratur Mhani of Conrt and Conrt Strutur - High Prforman, Fibr Rinford Conrt, Spial Loading and Strutural Appliation- B. H. Oh, t al. (d) 200 Kora Conrt Intitut, ISBN Fratur proprti of high-trngth tl fibr onrt W.-J. Kim, M.-S. Kak & J.-C. L Kyungpook National Univrity,Kora ABSTRACT: Thi tudy prnt th fratur proprti of tl fibr onrt. Th ratio and noth lngth of tl fibr in onrt bam pimn, ith dimnion of 0m 0m 40m, r ltd a indpndnt paramtr for th idntifiation of th proprti. Th volum ratio of tl fibr in th onrt pimn a hangd from 0% to 0.5%, 0.75% and %. Th noth lngth a hangd from 0 mm to 5, 30 and 45 mm. By applying thr-point bnding tt, J-intgral (J I ), K I, G F, dfltion trngth, and fratur nrgy r obtaind. Snitivity analyi a prformd to idntify th bhavior of th dpndnt variabl by hanging th volum ratio of tl fibr in th onrt pimn. INTRODUCTION Ordinary onrt ha many mirorak, hih dgrad and damag th onrt trutur along ith th rak that appar during rvi. Suh rak onquntly au many problm to th ntir trutur. In partiular, tr-rlatd onrt fraturing i dirtly rponibl for trutural ollap, and tudi ar rquird to addr thi problm. Thrfor, th afty prforman of th trutur annot b raonably valuatd only by onrt trngth, but rquir th valuation of th final limit tat bhavior, hih i th oftning bhavior. Randomly ditributd mirorak initially form upon th appliation of load to th onrt trutur or matrial. Suh mirorak ho nonlinar bhavior ith tabl rak groth ara bfor th load rah it maximum and hav th fratur haratriti that th fratur pro zon i big rlativ to th fratur lngth. Evn aftr th appliation of maximum load, th fratur ha oftning bhavior ith uffiint load tranfr apability. Thi an b xplaind via th fratur mhani bad on th nrgy onpt, intad of on th xiting trngth thory. In thi tudy, th fratur nrgy, hih i th paramtr for th rprntation of th fratur haratriti in th virtual fratur modl, a mainly ud. Th virtual fratur modl a propod by Hillrborg t al. Th RILEM quation a ud a th onrt fratur mhani xprimnt mthod. 2 RESEARCH SIGNIFICANCE Whn tnil tr i applid to SFRC, it tnil trngth and dutility ignifiantly inrad ompard ith tho of normal onrt. For onrt ith tl fibr ontnt of.5%, th tnil trngth of SFRC i about % highr than that of normal onrt. Th SFRC ha high tnil trngth and dutility bau of th pullout-ritant mhanim of tl fibr hrin th tl fibr in th onrt ontrol th rak propagation du to th tnil tr and rit th tnil tr aro th rak. In addition, inraing th tl fibr ontnt and th ubqunt inra in th numbr of tl fibr pr unit ara ontrol th rak propagation. Aordingly, th tnil trngth, train undr maximum tnil tr, dutility and fratur nrgy inra. 2. Virtual Crak Modl Figur. Dtrmination of fratur nrgy GF. Thi tudy mainly ud fratur nrgy, hih i th paramtr for th rprntation of th fratur haratriti in th virtual fratur modl. Th virtual fratur modl a propod by Hillrborg t al. Th mthod rommndd by RILEM a ud a th onrt fratur mhani

2 xprimnt mthod. Th virtual rak modl involv thr paramtr: fratur nrgy (G F ), matrial tnil trngth (f t ), and ritial rak diplamnt ( ). In th rommndd mthod, hovr, th dtrmination of fratur nrgy i motly addrd. Th haratriti lngth (lh), hih i dtrmind by ombining G F and f t, i knon to b a pur matrial haratriti and i rportdly proportional to th lngth of th fratur pro zon. In th virtual rak modl, th fratur nrgy an b alulatd by dividing th ara blo th load diplamnt urv in Figur by th pimn ro-tion, aording to Equation. () 3 EXPERIMENT AND MATERIAL CHARACTERISTIC EVALUATION METHOD In thi tudy, th onrt pimn a manufaturd ith ordinary Portland mnt and fibr-rinford onrt (0.5%, 0.75% and %). From th load CMOD urv obtaind from th thr-point bnding tt, Young modulu (E), ritial fftiv rak lngth (a ), ritial tr intnity fator (K IC), ritial rak tip opning diplamnt (CTOD ), fratur nrgy (G F ) and haratriti lngth (Q) r alulatd and thir orrlation r xamind. 3. Matrial Domti la- ordinary Portland mnt a ud in thi xprimnt. Tabl 3. and 3.2 ho th mnt phyial and hmial matrial proprti. Tabl 3. Chmial ompoition of th mnt. Componnt Sio 2 Al 2 O 3 F 2 O 3 MgO SO 3 CaO K 2 O Na 2 O Compoition Ratio (%) Tabl 3. 2 Phyial proprti of th mnt. Spifi Gravity Fitn (m2/g) Stting Tim Compriv Strngth (Kgf/m2) Ini Fin 3d 7d 28d Tabl 3. 3 Phyial proprti of th aggrgat. Unit Spifi Gmax Clat Wight Aborption(%) Gravity (mm) (Kg/m 2) F.M F.A C.A Rivr and from J Hapyongan, D ( h, T ) h Gyongbuk, and ruhd aggrgat from Pyongunan r ud a aggrgat in thi xprimnt. Th proportionality Th phyial offiint proprti D(h,T) r rvid aording moitur prmability to th tt mthod and it i KS a F nonlina Tabl of 3.3 th ho rlativ th humidity rult. h and tmpratur Th tl fibr & onrt Najjar 972). of domti Th moitur manufaturr ma balan S a ud in thi that tudy. th variation Th tl in fibr tim a of ud th atr ma volum ratio of 0.5%, volum 0.75% of onrt and % (atr of th ontnt bindr. ) b q Tabl 3.4 ho th divrgn phyial of proprti. th moitur flux J Tabl 3. 4 Phyial proprti of tl fibr. J t Spifi Tnil Diamtr Lngth Apt Typ gravity trngth (mm) (mm) ratio Th atr ontnt (g/ m3 ) an (MPa) b xprd a of th vaporabl atr (apillary a Doubl 0.7 vapor, 50 and 7.43 adorbd 7.85 atr),00 and th non- Hook (hmially bound) atr n (Mil Pantazopoulo & Mill 995). It i ra Tabl 3. 5 Conrt ontnt tabl. aum that th vaporabl atr i a fu Unit Wight (kg/m 3 ) Typ W/B Fibr rlativ humidity, h, dgr of hydration (%) Aggrgat Air Watr dgr Bindr of ilia Sand fum ration, (Kg) Entring, i.. ag-dpndnt orption/dorption NF 0 (Norling Mjonll 997). Undr thi aum SFC % 626 by ubtituting Equation g into Equati SFC obtain SFC3 Bindr Cmnt + Silia + Fly ah S/A(%) 33%, Noth 0,5,30,45mm h & + & + h t h Cmnt Dry mix Conrt + Coar Aggrgat hr onrt /h Admixtur i th lop of Diharg th orption/ Fin Aggrgat iothrm + (alo + alld moitur apa Watr Admixtur govrning Fibr quation (Equation 3) mut b by appropriat boundary and initial onditi Figur 2. Conrt mixtur. Th rlation btn th amount of atr and rlativ humidity i alld Conrt a mixd in manufaturing th tt iothrm if maurd ith inraing pimn uing a ford mixr, aording to th humidity and dorption iothrm in th qun hon in Figur 2. Aftr th dry mixing, a. Nglting thir diffrn (Xi t al. fibr a manually and uniformly attrd and dry th folloing, orption iothrm ill b mixing a prformd again. To idntify th rfrn to both orption and dorption unhardnd onrt haratriti, th lump and By th ay, if th hytri of th flo r maurd. In addition, th Φ50 00 mm iothrm ould b takn into aount, to pimn a manufaturd and urd in atr at rlation, vaporabl atr v rlativ humi 23±2, and it ompriv trngth a maurd on th 28 th b ud aording to th ign of th varia day. rlativity humidity. Th hap of th Th tt pimn for th thr-point bnding tt iothrm for HPC i inflund by many p on a nothd bam a a 00mm 00mm 400mm pially tho that influn xtnt and rtangular paralllpipd ith noth 5 mm, 30 hmial ration and, in turn, dtrm mm and 45 mm dp and 5 mm id, hih r trutur and por iz ditribution (atrratio, mnt hmial ompoition, SF mad uing an ltri a. Tabl 3.5 ho th onrt ompoition uring tim and mthod, tmpratur, mix Th ompriv trngth, tnil trngth and t.). In th litratur variou formulatio lati modulu r maurd a th bai found to drib th orption iothrm mhanial haratriti of th ylindrial onrt onrt (Xi t al. 994). Hovr, in th tt pimn. Eah tt a prformd aording to papr th mi-mpirial xprion pro KS F 2405, KS F 2423 and KS F Norling Mjornll (997) i adoptd b Proding of FraMCoS-7, May 23-28, 200

3 3.2 J D ( Exprimnt h, T ) h Mthod Figur 3. Thr-point J bnding tt on a nothd bam. t () 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 (2) Th atr ontnt an b xprd a th um of th vaporabl atr (apillary atr, atr vapor, and adorbd atr) and th non-vaporabl (hmially bound) atr n (Mill 966, Pantazopoulo & Mill 995). It i raonabl to aum that th vaporabl atr i a funtion of rlativ humidity, h, dgr of hydration,, and dgr of ilia fum ration,, i.. (h,, ) ag-dpndnt orption/dorption iothrm (Norling Mjonll 997). Undr thi aumption and 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 Figur govrning 4. Shap quation of th (Equation nothd bam 3) mut tt b pimn ompltd and diplamnt by appropriat maurmnt boundary poition. and initial ondition. Th rlation btn th amount of vaporabl atr In and th rlativ thr-point humidity bnding i alld tt, adorption th motor onntd iothrm to if th maurd r jak ith a inraing rotatd at a rlativity ontant pd humidity to and maintain dorption th diplamnt iothrm in of th th oppoit for appliation a. Nglting had thir attahd diffrn to th (Xi r t al. jak 994), at in mm/min. th folloing, A balan orption ith iothrm an alloabl ill b load ud of ith 0 ton rfrn a ud to both to maur orption th and load. dorption ondition. By Vrtial th ay, diplamnt if th hytri a maurd of th moitur uing a.0 0 iothrm -6 m-nitivity ould b takn diplamnt into aount, mtr to that diffrnt a attahd rlation, to vaporabl th ntr atr of th v pimn rlativ humidity, pan, and mut th CMOD b ud a aording maurd to th uing ign a of th variation -6 m-nitivity of th lip rlativity gaug humidity. attahd to Th th thikn-i hap of th nd orption of th bam iothrm pan for ntr HPC i noth. inflund A loal by many fraturing paramtr, of th tt pially pimn tho ould that influn afft xtnt atual and diplamnt rat of th during hmial vrtial ration diplamnt and, in maurmnt, turn, dtrmin a fram por for trutur mauring and por th iz diplamnt ditribution a (atr-to-mnt manufaturd. (Fig. ratio, 3) mnt hmial ompoition, SF ontnt, uring tim and mthod, tmpratur, mix additiv, t.). In th litratur variou formulation an b 3.3 Matrial Proprty Evaluation Mthod found to drib th orption iothrm of normal From onrt th (Xi thr-point t al. 994). bnding Hovr, tt on in th a nothd prnt bam, papr th load dfltion mi-mpirial xprion urv and load CMOD propod by urv Norling r Mjornll obtaind. (997) i adoptd bau it & xpliitly Figur 5 aount ho th for rprntativ th volution graph of hydration for ah tt ration pimn. and SF From ontnt. th load diplamnt Thi orption iothrm urv, fftiv rad bnding trngth, lati modulu and fratur nrgy r alulatd aording to th folloing quation. σ ( h,, ) G (, ) () Efftiv bnding trngth 3L p S 0( g ) h nt 2 2W ( D K a( ) 0), (2) D:dpth, W:idth W:idth, σ0initial noth lngth, S:pan, Lppak Load hr (2) Elati th firt modulu trm (gl iothrm) rprnt th phyially bound (adorbd) atr and th ond trm 6Sa (apillary 0 v ( ) iothrm) rprnt th apillary atr. E Thi 2 xprion i valid only for lo ontnt (3) Id b of SF. Th offiint G rprnt th amount of C atr I Initial pr loading unit volum omplian hld in th gl por at 00% Vrlativ ( ) 0.76 humidity, and 2.04it an + 2 ( b ) xprd a 0 / D(Norling Mjornll 997) a (3) Fratur nrgy (G F ) Th fratur nrgy G (, ) k + k i alulatd by dividing (5) th ara blo th vg load diplamnt vg urv until th load rah zro by fraturd ara. Th ara blo th hr urv k vg i and alulatd k vg ar by matrial intgration. paramtr. From th maximum amount of atr pr unit volum that an fill all por (both U apillary por and gl por), on G F an alulat K a on obtain (4) A + 0( g ) h (4) (4) Spifi fratur nrgy (G F ) 0 g G 0 W G (5) F (6) K (, ) A lig 0 g W F-CMOD Curv intgration A lig Crak ara 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 4 TEST RESULTS AND ANALYSIS variou ag (Di Luzio & Cuati 2009b). Graph in Figur 5 2 ho th rlationhip btn 2.2 Tmpratur th CMOD volution and dfltion aording to th load and noth lngth (0, 5, 5, 30 and 45 mm). Not that, at arly ag, in th hmial ration CMOD and dfltion r maurd by th unit of aoiatd ith mnt hydration and SF ration.0 mm. ar xothrmi, th tmpratur fild i not uniform for non-adiabati ytm vn if th nvironmntal 4. tmpratur Tt Rult i ontant. of th Cylindrial Hat ondution Tt Spimn an b dribd Matrial in Charatriti onrt, at lat for tmpratur not xding 00 C (Bažant & Kaplan 996), by Th folloing ar th tt rult of th ompriv Fourir la, hih rad trngth, tnil trngth and lati modulu of th ylindrial tt pimn. q λ T (7) 4.2 Thr-Point Bnding Tt Rult hr q i th hat flux, T i th abolut Tabl tmpratur, 4. ho and λ th i th rult hat ondutivity; of th thr-point thi bnding tt on a nothd bam. Proding of FraMCoS-7, May 23-28, 200

4 J ) D ( h, T h Th proportionality offiint D(h,T) moitur prmability and it i a nonlina of th 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 Figur 5. CMOD Load Curv (noth 0mm). Figur 6. Dfltion Load Th Curv atr (noth ontnt 0mm). an b xprd a of 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 of hydration dgr of ilia fum ration,, i.. ag-dpndnt orption/dorption (Norling Mjonll 997). Undr thi aum by ubtituting Equation into Equati obtain Figur 7. CMOD Load Curv (noth 5mm). Figur 9. CMOD Load Curv (noth 30mm). Figur. CMOD Load Curv (noth 45mm). h Figur 8. Dfltion Load h Curv t (noth h 5mm). Proding of FraMCoS-7, May 23-28, 200 & + & + 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 Figur 0. Dfltion Load iothrm Curv ould (noth b 30mm). takn into aount, to rlation, vaporabl atr v rlativ humi b ud aording to th ign of th varia rlativity humidity. Th hap of th iothrm for HPC i inflund by many p 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 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 Figur 2. Dfltion Load Curv (noth 45mm).

5 JTabl D4. ( h, TCharatriti ) h valu of th ylindrial tt pimn. () xpliitly aount for th volution of hydration Typ D ration a 0 and SF ontnt. 0 Thi orption d- a 0 iothrm Noth Th proportionality Typ offiint D(h,T) (mm) i alld rad (mm) (a 0 /d) (mm) moitur prmability NF and it i a nonlinar 00 funtion of th rlativ humidity SFC h and tmpratur 0 T (Bažant & 0mm Najjar 972). Th SFC2 moitur ma balan 00 rquir 0 ( h,, ) G ( 0, ) 00 + that th variation in tim SFC3 of th atr ma 02 pr unit 0 0 0( g 02 ) h volum of onrt (atr ontnt ) b qual to th NF (4) divrgn of th moitur flux J SFC ( g 86 ) h 5mm K ( SFC2 99 5, 0.5 ) 84 J SFC3 0 (2) t NF Th atr ontnt SFC an b xprd 00 hr a th um 30 th firt trm 0.3 (gl iothrm) 70 rprnt th 30mm phyially bound (adorbd) atr and th ond of th vaporabl atr SFC2 (apillary 0 atr, atr trm (apillary iothrm) rprnt th apillary vapor, and adorbd SFC3 atr) and th non-vaporabl atr. Thi xprion i valid only for lo ontnt (hmially bound) NF atr n (Mill , of 45 SF. Th offiint 0.44 G 57 Pantazopoulo & Mill SFC 995). It i raonabl 0 to rprnt th amount of aum 45mm atr pr unit volum hld in th gl por at 00% that th vaporabl atr i a funtion of SFC2 00 rlativ 45 humidity, and it an b xprd 55 (Norling rlativ humidity, h, dgr of hydration,, and SFC3 0 Mjornll ) a dgr of ilia fum ration,, i.. (h,, ) ag-dpndnt orption/dorption iothrm Tabl 4. 2 Charatriti valu of th ylindrial tt pimn. (Norling Typ Mjonll Numbr 997). C.S. Undr (MPa) thi T.S. (MPa) aumption E. (GPa) and by ubtituting Equation into Equation 2 on obtain NF (Plain) SFC h 0.5% & & + & 26.2 n (3) h t h SFC2 hr 0.75% /h 2 i th lop 67 of th 6.8 orption/dorption 33.2 iothrm (alo 3 alld 54.2 moitur 5.52 apaity) Th govrning SFC3 quation (Equation 3) mut b ompltd by % appropriat 2 boundary 63.2 and initial 6.42 ondition. 3.2 Th rlation 3 btn 67.3 th amount 6.85 of vaporabl 33.3 C.S atr : Compriv and rlativ Strngth, humidity T.S : Tnil i alld Strngth 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 Figur ratio, 4. mnt Fratur hmial nrgy by mixd ompoition, fibr ontnt. SF ontnt, uring tim and mthod, tmpratur, mix additiv, 4.3 t.). Rult In th and litratur Rvi variou formulation an b found to drib th orption iothrm of normal Th onrt avrag (Xi valu t al. 994). from th Hovr, tt r in ud th prnt for th rult papr th graph, mi-mpirial and th folloing xprion rult propod r by obtaind. Norling Mjornll (997) i adoptd bau it Proding of FraMCoS-7, May 23-28, 200 Th gratr amount of fibr ontnt (0%, 0.5%, G (, ) k + k (5) 0.75% or %) vgrultd vgin highr fratur nrgy, a hon in Figur 3. A hon in th figur, th longr hr noth k lngth rultd in l fratur nrgy. vg and k vg ar matrial paramtr. From th maximum Th dviation amount of btn atr pr th unit fratur volum that nrgy an obtaind fill all por from (both th apillary thr-point por bnding and gl por), tt on on a nothd an alulat bam Kand a on th nominal obtain fratur nrgy a omhat high, but thy r roughly proportional to ah othr. 0 g G 0 5 K ( CONCLUSION, ) AND FUTURE STUDIES 0 g To valuat th fratur nrgy haratriti of th onrt aording to th mixd fibr ontnt, th Th matrial paramtr k vg and k vg and g thr-point bnding tt on a nothd bam an a b alibratd by fitting xprimntal data rlvant to prformd ith varying fibr ontnt (0%, 0.5%, fr (vaporabl) atr ontnt in onrt at 0.75% and %) and diffrnt noth lngth (0, 5, variou ag (Di Luzio & Cuati 2009b). 30 and 45) a variabl. Th tt rult hod that th fibr ontnt inra th onrt fratur nrgy. 2.2 Tmpratur volution Th folloing ar th rult of thi tudy and Not that, at arly ag, in th hmial ration furthr tudi rquird in th futur. aoiatd ith mnt hydration and SF ration () It a dtrmind that fibr mixd ith ar xothrmi, th tmpratur fild i not uniform onrt inrad th onrt fratur nrgy. It for non-adiabati ytm vn if th nvironmntal m that th SFRC ha high tnil trngth and tmpratur i ontant. Hat ondution an b dutility du to th pullout-ritant mhanim of dribd in onrt, at lat for tmpratur not tl fibr hrin th tl fibr in th onrt xding 00 C (Bažant & Kaplan 996), by ontrol th rak propagation du to th tnil Fourir la, hih rad tr and rit th tnil tr aro th rak. (2) Th onrt fratur nrgy inrad for q λ T th highr fibr ontnt and hortr noth lngth. (7) Thi m to hav bn du to th inra in tl fibr hr ontnt q i and th th hat ubqunt flux, T i inra th abolut in th numbr tmpratur, of tl and fibr λ i th pr hat unit ondutivity; ara that ontrolld in thi th rak propagation, and thrfor, th tnil (6)

6 trngth, train undr maximum tnil tr, dutility and fratur nrgy inrad. In addition, it m that th longr noth lngth a, th lor th fratur nrgy du to th alration of rak propagation. (3) In th futur, furthr tudi involving fibr typ and apt ratio ill b rquird. 6 ACKNOWLEDGMENTS Th ork prntd in thi papr a upportd by th Minitry of Eduation & Human Rour Dvlopmnt through th Sond Stag of BK2. REFERENCES Alford, N. M., Grov, G. W., and Doubl, D. D"Phyi al Proprti of High-Strngth Cmnt Pat", Cmnt and Conrt Rarh, V.2, No.2, May 982, pp B. trunk. G. Shobr, A.K. Glbing. F.H. Wittmann Fratur mhani paramtr of autolavd aratd onrt Cmnt and Conrt Rarh , pp Bazant, Z. P. & Cldolin. L. Blunt Crak band Propagation in Finit Elmnt Analyi, Journal of Eng. Mhani. DIV. ASEC vol. 05. No. EN2, 979 pp Choi, Sin-Ho Th Fratur of Conrt aording to th Maximum Siz of Coar Aggrgat by 3PBT and WTT, Arhittural Intitut of Kora. No. 74, 2003 pp nrgy and train oftning of AAC. RILEM Thnial Rommndation for th tting and u of ontrution matrial E & FN Spon,994, pp Griffth, A. A., Th Phnomna of Ruptur and Flo in Soild Philoophial Tranation, Royal Soity of London Vol. A22, 92, pp Hillrbor. A., M.Modr & P.E. Ptron Analyi of Crak Formulation and Crak Groth in Conrt by man of Fratur Mhni Finit Elmnt, Cmnt and Conrt Rarh Vol. 6, 976, pp K.K. Sidri, P. Manita, E. Chaniotaki, Prforman of thrmally damagd fibr-rinford onrt, Contrution and Building Matrial 23 (2009), pp Muhammad N.S. Hadi, "Bhaviour of ntri loading of FRP onfind fibr tl rinford onrt olumn", Contrution and Building Matrial 23 (2009), pp Qingduo Hao, Yanli Wangb, Zhng H, Jinping Ou "Bond trngth of gla fibr rinford polymr ribbd rbar in normal trngth onrt", Contrution and Building Matrial, 23 (2009), pp RILEM Rommndation AAC3.. Dtrmination of th pifi fratur J ) D ( h, T h Th proportionality offiint D(h,T) moitur prmability and it i a nonlina of th 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 995). 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 h h t h & + & + 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 b ud aording to th ign of th varia rlativity humidity. Th hap of th iothrm for HPC i inflund by many p 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 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 of FraMCoS-7, May 23-28, 200