Fratur Mhani Conrt Conrt Strutur - High Prforman, Fibr Rinford Conrt, Spial Loading Strutural Appliation- B. H. Oh, t al. (d) 200 Kora Conrt Intitut, ISBN 978-89-5708-82-2 Bhavior onrt mmbr ontrutd ith SHCC/GFRP prmannt formor Changli Yu, Chritophr K.Y. Lung & Qian Cao Dpartmnt Civil Environmntal Enginring, Hong Kong Univrity Sin Thnology ABSTRACT: To nhan th durability rinford onrt trutur, high prforman onrt ith lo atr/bindr ratio i tn mployd. Hovr, on raing our in th onrt ovr du to mhanial loading or hrinag, atr hlorid an pntrat aily to indu tl orroion. Th prnt tudy fou on an altrnativ approah for th ontrution durabl onrt mmbr, ith th u prmannt formor. To ma th formor, train hardning mntitiou ompoit (SHCC) i mployd. With 2% inorporatd fibr, th SHCC xhibit multipl raing bhavior in tnion, ith ra opning ontrolld to blo 60 miron at train lvl up to vral prnt. ith uh mall ra opning, th tranport proprti ar imilar to tho th un-rad matrial. n addition to SHCC, gla fibr rinford polymr (GFRP) an b inorporatd into th formor to provid flxural ritan. n om appliation, th mmbr an b mad by ating onrt dirtly on th formor. n othr, a rdud amount tl rinformnt an b addd. With tl prottd by th GFRP/SHCC formor (hih at a part th ovr), high durability an b nurd. In thi papr, ill drib th matrial mployd for maing th prmannt formor th mthod to fabriat U-hap formor for lab bam. Tt rult on omponnt mad ith th prmannt formor ill b prntd. Failur bhavior ill b diud failur load ompard to analytial valu. An xampl ill alo b providd to illutrat th u GFRP/SHCC formor in prati. INTRODUCTION SHCC, alo rfrrd to a Enginrd Cmntitiou Compoit (ECC), ar fibr rinford ompoit dignd bad on fratur mhani onpt ith th hlp miromhanial modl (Li & Lung 992, Li 993, Lung 996, Ka &Li 999). Through th propr nginring miroparamtr, th ompoit xhibit train hardning bhavior in tnion ith failur train up to vral prnt. Tnil failur th ompoit i aompanid by th formation loly-pad multipl ra that ar ontrolld to vry mall opning (normally blo 60 miron). Aording to th xprimntal rult in Wang t al. (997) Lph & Li (2005), ra ith mall opning hav littl fft on th tranport proprti th matrial. In othr ord, for SHCC mad ith a matrix ith uffiintly lo atr/bindr ratio, high durability an b maintaind vn if th mmbr urfa i ubjtd to high tnil train during rvi. A th durability a onrt mmbr i govrnd by th quality th ovr, SHCC (hih i mor otly than normal onrt) an b ud tratgially to prpar prmannt formor firt. Th mmbr i thn ontrutd by th ating normal onrt. With a urfa layr xhibiting lo prmability high raing ritan, pntration orroiv agnt an b ritd. Morovr, by rplaing oodn formor, ontrution ffiiny i improvd it at ar rdud. To furthr failitat ontrution improv mmbr durability, th onpt an b xtndd to inlud gla fibr rinford plati (GFRP) rod inid th formor. Th u GFRP rod ith SHCC rat a ynrgy btn th to matrial. If normal onrt i mployd, th lo modulu GFRP, lo bond trngth mimath in thrmal xpanion fiint btn onrt GFRP in th tranvr dirtion ill rquir a minimum ovr 35 mm to prvnt th formation unightly ra. Th formor ill thn b rlativly thi havy. With th u SHCC, a mall ovr to th GFRP i uffiint a ra opning ar ll ontrolld. Alo, a hon in Fihr & Li (2002), du to th multipl raing SHCC hih produ fin loly pad ra, th intrfaial har dformation tr indud by raing i ignifiantly rdud. Th rquird bond trngth i hn alo a lot lor. For omponnt undr light or modrat loading, th GFRP rod inid th SHCC formor ill b uffiint to arry th rquird loading. Whn th applid loading i highr, tl rinformnt an b addd to inra both th load-arrying apaity th dutility. In thi a, th tl i ll prottd from orroion
a J = it D ( i far h, T ) aay h from th mmbr urfa. A a () rult, high durability th mmbr an b aurd. Whn Th proportionality prmannt formor fiint i mployd, D(h,T) i th alld intrfaial moitur bonding prmability btn th it i at a nonlinar onrt funtion th formor th rlativ i alay humidity a onrn. h tmpratur In an arlir T (Bažant papr (Lung & Najjar & 972). Cao in Th pr), moitur hav ma foud balan on rquir th dvlopmnt that th variation flat in plat tim SHCC th atr formor, ma pr to unit b plad volum at th onrt bottom (atr lab/d. ontnt ) Whn b qual GFRP to th i not divrgn inorporatd th into moitur th formor, flux J th introdution tranvr groov on th innr urfa i found to b fftiv in prvnting dbonding. Hovr, for GFRP/SHCC = J formor, intrfaial dbonding (2) i t found to b th dominant failur mod th final omponnt. Th atr To ontnt improv an th intrfa b xprd bonding, a th a faibl um th olution vaporabl i to atr introdu a U-hap Prmannt (apillary atr, atr formor vapor, to adorbd inra atr) th total ara th non-vaporabl th intrfa. Furthrmor, (hmially a bound) th formor atr ill hav a highr n (Mill 966, momnt Pantazopoulo inrtia & Mill ith 995). th ontribution It i raonabl from th to bnd aum up that lg, th damag vaporabl during atr ontrution i a funtion hling rlativ tranportation humidity, an h, b dgr minimizd. hydration,, dgr In thi papr, ilia fum th fftivn ration, U-hapd formor, i.. = (h,, ) = ag-dpndnt rlativ to flat plat orption/dorption formor ill b iothrm tudid. In (Norling th folloing, Mjonll 997). ill Undr firt prnt thi aumption th matrial dign by ubtituting SHCC Equation th prparation into Equation U-hapd 2 on formor. obtain Thn, bnding tt rult on bam mad ith GFRP/SHCC formor ( ith or ithout additional tl rbar) ill b rportd, ith pial attntion h paid on th load apaity failur mod. + ( D h) = & + & + & n (3) Finally, h ta dign hxampl ill b givn to illutrat th faibility GFRP/SHCC formor in th ontrution latral panning d for footbridg. hr / h i th lop th orption/dorption iothrm (alo alld moitur apaity). Th govrning quation (Equation 3) mut b ompltd 2 SPECIMEN PREPARATION by appropriat boundary initial ondition. Th rlation btn th amount vaporabl 2. Matrial atr rlativ humidity i alld adorption From iothrm litratur, if maurd SHCC ith an b inraing mad ith rlativity polyvinyl humidity alohol (PVA) dorption fibr at iothrm a doag in th 2% oppoit in volum. a. Nglting Th proprti thir diffrn PVA fibr (Xi i t hon al. 994), in Tabl th folloing,. To nur orption uniform iothrm fibr ditribution ill b ud ith to in ontrol rfrn th to toughn both orption th matrix, dorption fin ondition. ilia i By ud th in ay, th matrix if th hytri no oar aggrgat th moitur ar inorporatd. iothrm ould In b thi tan tudy, into 80% aount, by ight to diffrnt th mnt rlation, a vaporabl rplad atr by fly v ah. rlativ A fly humidity, ah i a at mut matrial, b ud aording th u to a th larg ign amount th variation fly ah in th SHCC rlativity an humidity. b onidrd Th a hap grn approah th orption (Yang t iothrm al. 2007). for HPC Som i inflund th fly ah by ill many undrgo paramtr, pozzolani pially ration tho that to improv influn th xtnt long-trm rat tranport th proprti. hmial ration Hovr,, a ignifiant in turn, part dtrmin th fly por ah ill trutur not hydrat por iz an ditribution b onidrd (atr-to-mnt a inrt fillr. ratio, Aording mnt hmial to th rult ompoition, in Song SF & Van ontnt, Zijl (2004), uring tim inrad mthod, dformability tmpratur, toughn mix additiv, an b t.). obtaind In th ith litratur fly ah variou addition formulation byond 40%. an Suh b a found trnd to an drib aribd th orption to th phrial iothrm hap normal th unhydratd onrt (Xi fly t ah al. partil, 994). Hovr, hih an in rdu th prnt frition papr along th th mi-mpirial matrix-fibr intrfa xprion propod failitat fibr Norling pull-out Mjornll (rathr than (997) ruptur). i adoptd High fly bau ah on- by it tnt xpliitly ill dra aount th for ompriv th volution trngth hydration SHCC ration inra it SF poroity. ontnt. In Thi our mix, orption ilia iothrm fum alo rad addd, a mix ith ilia fum ar found to xhibit l dutility rdution in th long trm. Th mix portion hon for our tt i hon in Tabl. With high ontnt unratd fly ah, xpt a ( h,, ) = G (, ) + high ontnt ditributd por in th matrix hih 0( g ) h an failitat th formation multipl ra (4) thu improv th dutility (Wang & Li 2007). Prmability maurmnt ha 0bn ( g prformd ) h on our K (, ) SHCC mix a valu 5x0-2 m/ a obtaind. In Lph & Li (2005), a valu x0 - m/ a obtaind for a SHCC mix ith a muh lor fly ah to hr mnt th ratio. firt trm Th rult (gl iothrm) indiat that rprnt th poroity phyially in our mix bound i not (adorbd) highly onntd, atr o th it do ond not th hav trm dtrimntal (apillary fft iothrm) on th rprnt prmability. th apillary atr. Th Thi tr xprion v. train urv i valid for only fiv for SHCC lo ontnt pimn SF. ttd Th fiint at 28 day G ar rprnt hon th in amount Figur. From atr th pr unit figur, volum on an hld dfin th gl th por firt raing at 00% trngth rlativ a humidity, th point hr it an th b urv xprd xhibit (Norling a harp dra Mjornll 997) in lop a from th initial linar bhavior. Th ultimat trngth i th maximum tr arrid by th matrial th ultimat train i th train G (, ) = + (5) orrponding vgto th vg ultimat trngth. Aftr th pa load, raing tart to loaliz th rapid opning hr a ingl ra i obrvd. Th ultimat vg vg ar matrial paramtr. From th train maximum i hn amount a good atr indiator pr unit matrial volum dutility, that an a fill th all por SHCC (both an apillary b onidrd por a a gl damagd por), on homognou an alulat matrial K a on bfor obtain thi train i rahd. A hon in Figur, th SHCC mix an rah a dutility 4.4% in avrag. g 0.88 + 0.22 G Tabl. Proprti 0 th PVA Fibr. Diamtr ( ) Lngth Elongation, Young Tnil (6) K = 0 Modulu Strngth g µm mm % GPa MPa 38 2 6.5 33 530 Th matrial paramtr vg vg g an Tabl b alibratd 2. Mix Proportion by fitting th xprimntal SHCC Mix. data rlvant to Matrial fr (vaporabl) atr ontnt Proportion in onrt at Fly variou Ah ag (Di Luzio & Cuati 2009b). Cmnt Silia Fum 0.8 0.8 0.02 Silia 2.2 Tmpratur S volution 0.2 Watr Not that, at arly ag, in 0.22 th hmial ration Suprplatiizr 0.005 aoiatd ith mnt hydration SF ration PVA Fibr 2% in volum 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 hr q i th hat flux, T i th abolut Figur tmpratur,. Str v. Strain λ i th Curv hat SHCC ondutivity; Mix. in thi (7) Proding FraMCoS-7, May 23-28, 200
2.2 Fabriation th Prmannt Formor Prmannt formor a prpard ith th u oodn mould. Bfor ating SHCC, Alan GFRP rod (ith proprti hon in Tabl 3) r inrtd through hold in th nd plat th mould upportd intrmittntly ith par. Sin th ltd SHCC had high orability, th formor a fabriatd ithout intrnal vibration or tampring. Whn th matrial a till frh, latral groov r introdud on th urfa. Flat plat formor 30mm thin a prpard by dirt ating into th mould. To ma U-hap Formor, a ood mould a hon in Figur 2 a mployd. Th mould i ambld 3 plan onntd by 2 hing. Th innr urfa th mould i lind ith a rubbr ht o th joint (at th hingd loation) ar proprly ald to prvnt atr fin partil from laing out. Thr i a oodn trip plad along ah th to id plan (S Fig. 2) to maintain a rtain thin SHCC during ating. At th middl plan, an additional pair trip (alld th thin adjutr) a plad to allo th ating SHCC to a highr thin than that on th id. At a uitabl tim aftr initial tting (dtrmind by trial rror), th thin adjutr i rmovd. Sin th onrt i tiff nough, th middl part ill rmain highr than th id. Th to id plan ar foldd up to form th U- hap formor. Tranvr groov (Fig. 3a) an b introdud on th formor urfa bfor or aftr th id ar foldd up. A hon in Lung & Cao (in pr), uh a impl urfa tratmnt an fftivly improv th bonding btn th SHCC formor th onrt to b at. For a bam mad ith plain onrt SHCC formor ith no GFRP rinformnt, dirt ra in th onrt ar arrtd at th onrt/shcc intrfa turnd into multipl fin ra ithin th SHCC layr (Fig. 3b). In thi tudy, th thin at th bottom part th U-hap formor i 30mm to provid a propr ovr to th GFRP rod inid. Th to lg (formd by folding up SHCC) ar 20mm in thin. Thin th Thin Hol for Figur 2. Woodn Mould for U-hap Formor. (a) (b) With a rdud Jthin, = D ( h, T ) tranportation h han- Th proportionality fiint D(h,T) moitur prmability it i a nonlina th rlativ humidity h tmpratur & Najjar 972). Th moitur ma balan that th variation in tim th atr ma volum onrt (atr ontnt ) b q divrgn th moitur flux J t Fold- Fold- = J onrt Th atr ontnt an b xprd a th vaporabl atr (apillary a SHCC vapor, adorbd atr) th non- (hmially bound) atr Figur 3. (a) Tranvr groov on th SHCC n (Mil (b) Cra ontrol Pantazopoulo ability th & SHCC Mill layr. 995). It i ra aum that th vaporabl atr i a fu dling i failitatd rlativ by a rdud humidity, ight. h, dgr Th formor ot i alo rdud. dgr ilia fum ration,, i.. = hydration Th formor = fabriation ag-dpndnt pro orption/dorption dribd abov ha a major (Norling limitation. Mjonll If 997). th vrtial Undr lg thi aum ar ovr a rtain by hight, ubtituting lf ight Equation th SHCC into Equati obtain ill rult in a ollap aftr th ood mould i foldd up. A hort lg i uffiint for th formor lab lmnt. To ma a bam, th formor an h + ( D h) = b mad by attahing plat lmnt to th to & id + & + h t h a U-hap formor ith rlativly hort lg. A impl dmontration th ida i hon in Figur 4. Th omponnt hr an b onntd / h i th by lop ithr poxy th orption/ or bolt. iothrm (alo alld moitur apa govrning quation (Equation 3) mut b Tabl 3. Proprti by GFRP appropriat Rinformnt. boundary initial onditi Diamtr Ultimat Th rlation tnil btn Tnil th modulu amount atr trngth rlativ humidity latiity i alld mm iothrm MPa if maurd GPa ith inraing humidity dorption iothrm in th 6 825 40.8 a. Nglting thir diffrn (Xi t al. th folloing, orption iothrm ill b rfrn to both orption dorption By Prat th ay, plat if th hytri th iothrm ould b tan into aount, to rlation, vaporabl atr v rlativ humi b ud Conntd aording by poxy to or th bolt ign th varia rlativity humidity. Th hap th iothrm for HPC i inflund by many p pially tho that influn xtnt hmial ration, in turn, dtrm Prat U-hapd formor ith trutur hort lg por iz ditribution (atrratio, mnt hmial ompoition, SF uring tim mthod, tmpratur, mix Figur 4. Ambling formor for a bam. t.). In th litratur variou formulatio found to drib th orption iothrm onrt (Xi t al. 994). Hovr, in th papr th mi-mpirial xprion pro Norling Mjornll (997) i adoptd b Proding FraMCoS-7, May 23-28, 200
J = ) D ( h, T h 800 200 800 () Th proportionality fiint D(h,T) i alld moitur prmability it i a nonlinar funtion th rlativ @70 paing humidity h tmpratur @70 paing T (Bažant & Najjar 972). Th moitur (A-) ma balan rquir that th variation in tim th atr ma pr unit volum onrt (atr ontnt ) b qual to th divrgn th moitur flux J 70 20 50 = J (2) t 80 30 30 Th atr ontnt an b xprd a th um th vaporabl atr (apillary atr, atr vapor, adorbd 00 atr) th 00 non-vaporabl (hmially bound) SHCC/GFRP atr Formor n (Mill 966, Pantazopoulo & Mill 995). It i raonabl to aum that th vaporabl (A-2) atr i a funtion rlativ humidity, h, dgr hydration,, dgr ilia fum ration,, i.. = (h,, ) 300 200 = ag-dpndnt orption/dorption 300 iothrm (Norling Mjonll 997). Undr thi aumption by ubtituting Equation into Equation 2 on obtain GFRP Rinformnt SHCC Formor h + h t (B-) ( D h) = & + & + & n (3) h 20 70 hr / h i th lop th orption/dorption 50 iothrm (alo alld moitur apaity). Th 80 govrning quation (Equation 3) mut b ompltd by appropriat 30 boundary 30 initial ondition. Th rlation btn th amount vaporabl atr rlativ 00 humidity i alld 00 adorption iothrm if 750 maurd ith 300 inraing 750 rlativity humidity dorption(b-2) 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. @00paing @00paing By th ay, if th hytri (C-) th moitur iothrm ould b tan into aount, to diffrnt rlation, vaporabl atr v rlativ humidity, mut b ud aording to th ign th variation th 00 rlativity 20 humidity. Th hap th orption iothrm for HPC i inflund by many paramtr, 250 pially tho that influn xtnt rat th 50 hmial ration, in turn, dtrmin por trutur por iz ditribution (atr-to-mnt 30 30 ratio, mnt hmial ompoition, SF ontnt, uring tim 50 mthod, tmpratur, 50 mix additiv, t.). In th litratur variou (C-2) formulation an b found to drib th orption iothrm normal onrt (Xi t al. 994). Hovr, in th prnt Figur 5. Th Tting Configuration Stion Dtail Spimn papr th for mi-mpirial Slab Spimn (unit xprion all in mm). propod by Norling Mjornll (997) i adoptd bau it 2.3 xpliitly Prparation aount Tt for Spimn th volution hydration ration SF ontnt. Thi orption iothrm 2.3. Slab mad ith GFRP/SHCC Formor rad To tudy th appliation prmannt formor for lab, four pimn r prpard in to diffrnt har/pan ratio, ith both flat-plat U- hap ( h, formor., ) = G ( In ah, ) formor lmnt, 3 + GFRP rod ith 6mm diamtr r 0 mbddd. ( g Th ) h tting onfiguration tion dtail SF (lab pimn ith flat-plat formor) SU (lab p- (4) 0( g ) h imn ith U-hap K (, formor) ) ar hon in Figur 5 (A-) & (A-2). Mild tl ith diamtr 6mm r ud to prvnt har failur. Tting onfiguration tion dtail SF2 SU2 ar hr th firt trm (gl iothrm) rprnt th hon in Figur 5 (B-) & (B-2). With largr har phyially bound (adorbd) atr th ond pan-dpth ratio, no tirrup ar rquird for thi trm (apillary iothrm) rprnt th apillary a. atr. Thi xprion i valid only for lo ontnt SF. Th fiint G 2.3.2 Bam mad ith GFRP/SHCC rprnt th amount Formor atr pr unit volum hld in th gl por at 00% To tudy th appliation for bam, to additional rlativ humidity, it an b xprd (Norling pimn r prpard. Th tting onfiguration Mjornll 997) a tion dtail BF (bam pimn ith flatplat formor) BU (bam pimn ith U- hap G (, formor) ) = ar + hon in Figur 5 (C-) & (C- (5) vg vg 2). Mild tl tirrup ith diamtr 6mm r again ud to prvnt har failur. Four GFRP rod (6mm hr diamtr) vg vg r ar mbddd matrial paramtr. in ah formor; From th to maximum high yild amount tl atr bar ith pr unit diamtr volum that 0mm an r fill all ud por a (both additional apillary longitudinal por rinformnt. gl por), on In an th alulat bam lmnt, K a on th obtain vrtial lg do not xtnd all th ay to th top th mmbr, to imulat th ituation ith a lab abov th bam. If th lg ar g furthr xtndd, 0.88th + 0.22 lilihood G 0 for dbonding btn formor onrt i furthr rdud. (6) K (, ) = g 3 TEST RESULTS Th matrial paramtr vg vg g an Load b alibratd a applid by fitting ntrally xprimntal by a 500N data rlvant hydrauli to ja fr undr (vaporabl) diplamnt atr ontrol ontnt at in th onrt rat 0.5 at mm/min. variou ag LVDT (Di Luzio a ud & Cuati to maur 2009b). mid-pan diplamnt. Th tt rult for all mmbr, in trm failur load failur momnt, ar ummarizd 2.2 in Tabl Tmpratur 5. Th load volution v. diplamnt urv ar hon Not that, in Figur at arly 6. In ag, both in th th tabl hmial th ration figur, a dign aoiatd load ith i hon. mnt Thi hydration valu i alulatd SF ration from th ar xothrmi, plan-tion-rmain th tmpratur plan fild aumption i not uniform a in onvntional for non-adiabati rinford ytm onrt vn if dign. th nvironmntal Aording to tmpratur th alulation, i ontant. failur Hat our ondution by ruhing an b ompriv dribd in onrt, in at all lat a. for tmpratur not xding 00 C (Bažant & Kaplan 996), by Fourir la, hih rad 3. Spimn ith Flat-plat Formor All q = mmbr λ T mad ith flat-plat formor hod (7) ignifiant dbonding btn th onrt SHCC formor. Th phyial mhanim lading hr q i th hat flux, T i th abolut to intrfaial dbonding i illutratd in Figur 7. tmpratur, λ i th hat ondutivity; in thi Whn a flxural or har/flxural ra i arrtd Proding FraMCoS-7, May 23-28, 200
by th SHCC layr, th dirt ra bom bridgd at th bottom by th GFRP/SHCC. Conidring a fr body btn th ra th lor upport, on an obrv tnion in both th GFRP SHCC that ill indu onntratd har tr along th SHCC/onrt intrfa. Whn th har tr ovrom th intrfaial har ritan, dbonding our a a har ra propagating along th intrfa. Th failur mod th thr mmbr mad ith flat-plat formor ar hon in Figur 8. To diffrnt ind failur an b idntifid. (i) Dbonding failur Dbonding failur our hn th intrfaial ra propagat ignifiantly along th SHCC/onrt intrfa to bring along a drop in th load. Thi ind failur mod our for SF BF mmbr. A on an obrv from Figur 6, th load apaity SF rah th thortial valu dpit th dbonding, hil that BF i ignifiantly lor than th thortial dign load. If Tabl 4. Thortial Load Capaiti Tt Rult for all pimn. Sri Dignd flxural apaity Dignd load Tt momnt Tt load N*m N N*m N SF 9.5 23.7 0.3 25.8 SF2 9.5 4.6 9.6 4.7 SU 9.5 23.7 0.6 26.5 SU2 9.5 4.6 6.9 SF 35.4 94.5 27.4 73 SU 35.4 94.5 39.8 06 (a) SF&SU (b) SF2&SU2 = ) D ( h, T h = J Figur 6. Load v. Diplamnt t Curv. J Th proportionality fiint D(h,T) moitur prmability it i a nonlina th rlativ humidity h tmpratur & Najjar 972). Th moitur ma balan that th variation in tim th atr ma volum onrt (atr ontnt ) b q divrgn th moitur flux J dbonding do not Th our, atr both ontnt mmbr an hould b xprd fail a by onrt ruhing th aording vaporabl to thortial atr (apillary alulation. SF i mor vapor, ovr-rinford adorbd than atr) BF. Whn th non- a onrt ruhing (hmially our, th orrponding bound) atr GFRP n (Mil for i hn lor. Pantazopoulo Aording & to Mill th illutration 995). It in i ra Figur 7, dbonding aum i air that to th our vaporabl ith a highr atr i a fu for in th GFRP. rlativ Thi xplain humidity, hy h, dbonding dgr our pr-maturly dgr in BF, hil ilia fum it ta ration, pla at, i.. a = hydration load imilar to that = for ag-dpndnt onrt ruhing orption/dorption to our. (ii) Flxural (Norling failur aftr Mjonll dbonding 997). Undr thi aum For SF2, dbonding by ubtituting a obrvd Equation during th into tt, Equati but it rmaind tabl obtain ovr a part th intrfa adjant to th bam. With inraing loading, th mmbr vntually faild by onrt ruhing. In h thi a, dbonding i not + th ( dirt D h) au = & mmbr failur. Hovr, a dbonding our along th + & + h t h intrfa, th plan-tion-rmain plan aumption no longr hold. hr Atually, / h ompard i th lop to th th a orption/ ith full bonding, iothrm tr (alo in th GFRP alld i moitur avragd apa out ovr th dbondd govrning rgion quation bom (Equation lor 3) in mut b th tion ith by maximum appropriat momnt. boundary Thrfor, initial onditi hn onrt ruhing Th rlation our, th btn load i th mallr amount than that for mmbr atr SU2 rlativ ith no humidity intrfaial i dbonding. iothrm if maurd ith inraing alld humidity dorption iothrm in th a. Nglting thir diffrn (Xi t al. 3.2 Spimn ith U-hap Formor th folloing, orption iothrm ill b On major raon rfrn to introdu to both U-hap orption formor dorption i to inra th intrfaial By th ay, ritan, if th mainly hytri by in-oraing th intrfa iothrm ara. ould In thi b rgard, tan th into rult aount, to th hav bn vry atifatory. rlation, vaporabl A hon atr in Figur v rlativ 9, humi all pimn ith b U-hap ud aording formor to th faild ign in flxur. No ign dbonding rlativity a humidity. obrvd Th in SU&2, hap th th varia hil only limitd iothrm dbonding for (a HPC hon i inflund Fig. 9()) by many p ourrd in BU pially hn th tho ultimat that influn load a xtnt approahd. In all a, hmial th load ration apaity, mmbr in turn, dtrm mad ith U-hap trutur formor i por highr iz than ditribution that for (atrratio, mnt ith flat-plat hmial formor. ompoition, SF orrponding mmbr Th inra i mot uring ignifiant tim for mthod, th bam tmpratur, mmbr ( Fig. 7()), t.). hr In pr-matur th litratur dbonding variou ig- formulatio mix nifiantly rdud found th load to drib apaity th mmbr orption BF. iothrm Figur 9(d) ho onrt th typial (Xi t fin al. multipl 994). Hovr, ra in th ditributd along papr th pimn th mi-mpirial bid th xprion major pro Norling Mjornll (997) i adoptd b Proding FraMCoS-7, May 23-28, 200
J = ) D ( h, T h () Th proportionality fiint D(h,T) i alld moitur prmability it i a nonlinar funtion th rlativ humidity h tmpratur T (Bažant & Najjar 972). Th moitur ma balan rquir that th variation in tim th atr ma pr unit volum onrt (atr ontnt ) Dbonding b qual to th divrgn th (a) moitur SF flux J Failur t = J (2) Th atr ontnt an b xprd a th um th vaporabl atr (apillary atr, atr Dbonding vapor, adorbd atr) th non-vaporabl Failur (hmially bound) atr n (Mill 966, Pantazopoulo &(b) BF Mill 995). It i raonabl to aum that th vaporabl atr i a funtion rlativ humidity, h, dgr hydration,, Loading dgr ilia fum ration,, i.. = (h,, ) Point = ag-dpndnt orption/dorption iothrm (Norling Mjonll 997). Undr thi aumption Dbonding by ubtituting Equation into Equation 2 on obtain h + h t ( D h) = & () SF2 + h & + & n (3) Figur 8. Failur mod Flat-Plat Spimn. hr / h i th lop th orption/dorption iothrm (alo alld moitur apaity). Th ra that form hn final failur i approahd. govrning quation (Equation 3) mut b ompltd by appropriat boundary initial ondition. 3.3 Th Diuion rlation btn th amount vaporabl atr rlativ humidity i alld adorption Comparing th tt rult both lab bam iothrm if maurd ith inraing rlativity pimn, th advantag adopting th U-hap humidity dorption iothrm in th oppoit formor i obviou. By inraing th bonding btn th GFRP/SHCC formor at onrt a. Nglting thir diffrn (Xi t al. 994), in th folloing, orption iothrm ill b ud ith intrfaial dbonding i fftivly prvntd. Failur thn our by onrt ruhing in flxur, at an rfrn to both orption dorption ondition. By th ay, if th hytri th moitur inrad load. In prati, th flxural failur mod iothrm ould b tan into aount, to diffrnt i alo mor dirabl a dbonding i nitiv to rlation, vaporabl atr v rlativ humidity, mut th intrfaial ondition hih i diffiult to ontrol. b ud aording to th ign th variation th A a rult, if failur our by dbonding, on an rlativity humidity. Th hap th orption xpt a highr variability in th load apaity, a iothrm for HPC i inflund by many paramtr, highr afty fator ha to b ud. pially tho that influn xtnt rat th In addition to th prvntion dbonding failur, hmial ration, in turn, dtrmin por th ra ontrol ability thi U-hap formor i trutur por iz ditribution (atr-to-mnt alo rmarably bttr. A omparion btn flatplat U-hap Formor aftr firt raing i ratio, mnt hmial ompoition, SF ontnt, uring tim mthod, tmpratur, mix additiv, hon in Figur 0. Whn th flat-plat formor i t.). In th litratur variou formulation an b ud, although th ra i ll ontrolld at th bottom, it an till opn ignifiantly on th id in th found to drib th orption iothrm normal onrt (Xi t al. 994). Hovr, in th prnt onrt abov th formor (Fig. 0(a)). Suh ind papr th mi-mpirial xprion propod by raing i abnt abov th U-hap formor. Norling Mjornll (997) i adoptd bau it xpliitly aount for th volution hydration ration SF ontnt. Thi orption iothrm rad ( h,, ) = G (, ) (a) KSF2, + Major Cra 0( g ) h (4) 0( g ) h ( ) Major Cra hr vg vg ar matrial paramtr. From th maximum amount atr pr unit volum that an fill all por (both apillary por gl por), on an alulat K a on obtain Slight dbonnding () BU hr th firt trm (gl iothrm) rprnt th phyially bound (adorbd) atr th ond trm (apillary iothrm) rprnt th apillary Major Cra atr. Thi xprion i valid only for lo ontnt SF. Th fiint G rprnt th amount atr pr unit volum hld in th gl por at 00% rlativ humidity, it an b xprd (Norling (b) SF Mjornll 997) a G (, ) = + vg vg K (, ) = g 0.88 + 0.22 G 0 g Major Cra (5) (6) Th matrial paramtr vg vg g an b alibratd by fitting xprimntal data rlvant to fr (vaporabl) atr ontnt in onrt at variou ag (Di Luzio & Cuati 2009b). (d) Fin multipl ra bid th major ra aftr failur 2.2 Tmpratur volution Figur Not 9. that, Failur at arly Mod ag, U-hap in Spimn. th hmial ration aoiatd ith mnt hydration SF ration ar xothrmi, th tmpratur fild i not uniform ditributd for non-adiabati multipl ytm ra vn an if b th obrvd nvironmntal at th bottom tmpratur th i pimn ontant. (Fig. Hat 0()). ondution an b dribd In our in rarh onrt, program, at lat prmannt for tmpratur formor not ith xding both flxural 00 C (Bažant har rinformnt & Kaplan 996), ha alo by Fourir la, hih rad bn prpard. Suh formor i formd by a U- hap formor ith GFRP rod in th longitudinal dirtion q = λ T a pair id plat ith mbddd (7) GFRP rinformnt along th vrtial dirtion, onntd hr togthr a in Figur 3. Tting th q i th hat flux, T i th abolut mmbr tmpratur, ill b prformd λ i th hat oon. ondutivity; in thi Proding FraMCoS-7, May 23-28, 200
(a) Flat-plat pimn (b) U-hap pimn () Multipl ra at th bottom Figur 0. Cra Control by th formor. Dirt ra in onrt 4 AN EXAMPLE APPLICATION OF GFRP/SHCC FORMWORK Fin multipl ra in SHCC Fin multipl ra in SHCC Uniformly ditributd multipl ra A potntial appliation GFRP/SHCC formor i in th ontrution th d a footbridg undr aggriv nvironmnt (uh a marin nvironmnt or old rgion hr alt i ud for diing). To if th SHCC formor invtigatd abov i uitabl for uh an appliation, a footbridg 4m id 30m long i tan a xampl. W aum th u to dg bam along th longitudinal dirtion, o th onrt d i panning in th latral dirtion. Th ultimat dign momnt i alulatd aording to BS 5400 (Britih Stard: Stl, onrt ompoit bridg), hih pifi a dign load 5Pa for loadd lngth 36 m undr. For pdtrian traffi on bridg upporting footay yl tra only, th liv load hall b tratd a uniformly ditributd. For ultimat limit tat dign, th load to b onidrd ar th prmannt load, togthr ith th appropriat primary liv load. Undr thi ombination, th partial J = load D ( h, fator T ) h i.5 for dad load.5 for liv load. For th a alulation, on an onidr th Th d proportionality to b ompod fiint latrally-panning mmbr moitur 0.m prmability in idth 0.5m it i a in nonlina D(h,T) hight, hih i idntial th rlativ to humidity th bam h mmbr tmpratur ttd in our tudy. & Najjar Th rquird 972). Th momnt moitur apaity ma balan an thn b alulatd that th in th variation folloing tim ay: th atr ma G = 24 0. 0 volum.5 = 0.36 onrt N m (atr ontnt ) b q divrgn th moitur flux J Q DignLoad M = 5 0. = 0.5 N =.64 = PL N 2 m = γ G + γ q Q m t = 2.33 N m = J =.5 0.36 +.5 0.5 8 Th atr ontnt an b xprd a th vaporabl atr (apillary a All th ttd vapor, lab in thi adorbd or faild atr) at a momnt byond th th non- (hmially dign valu bound) 9.5N*m, atr hih i n (Mil about 4 tim th Pantazopoulo rquird momnt & Mill apaity 995). alulatd abov. Evn It i ra aum ith an that additional th vaporabl afty fator atr i a fu 2.0, th dign i rlativ till adquat humidity, for h, th dgr footbridg. hydration Th abov impl dgr alulation ilia thrfor fum ration, illutrat th, i.. = faibility uing = th ag-dpndnt prmannt formor orption/dorption in pratial appliation. (Norling Mjonll 997). Undr thi aum Whil mmbr by mad ubtituting ith both Equation flat-plat formor U-hap into Equati obtain formor hav nough load apaity for th abov appliation, th u U-hap formor i prfrabl for to raon. Firtly, ith U-hap formor, flxural h failur an b aurd + ( D h) = & + & + th failur load hi l t variabl h than th a ith dbonding failur. Sondly, in th U-hap formor ha a ignifiantly highr tiffn than hr th flat-plat formor, th / h i th lop th orption/ amount falor rquird to upport th formor during ontrution iothrm (alo alld moitur apa govrning quation (Equation 3) mut b an b rdud. by appropriat boundary initial onditi In th abov xampl, th GFRP ithin th Th rlation btn th amount SHCC i alrady uffiint to provid th rquird atr rlativ humidity i alld load apaity. A no additional tl rinformnt iothrm if maurd ith inraing (for both flxur har) ar rquird, th it humidity dorption iothrm in th ontrution only involv th ating onrt a. Nglting thir diffrn (Xi t al. thi an b highly ffiint. Alo, in thr i th folloing, orption iothrm ill b no tl, th orroion problm hih i a major rfrn to both orption dorption au trutural dgradation i liminatd. By th ay, if th hytri th iothrm ould b tan into aount, to rlation, vaporabl atr v rlativ humi 5 CONCLUSIONS b ud aording to th ign th varia rlativity humidity. Th hap th In thi papr, th onpt uing GFRP/SHCC iothrm for HPC i inflund by many p prmannt formor to ma durabl onrt pially tho that influn xtnt trutur i firt introdud. Tt pimn ar hmial ration, in turn, dtrm prpard ith both flat-plat U-hap formor. trutur por iz ditribution (atrratio, mnt hmial ompoition, SF Th pimn an b dividd into to group, for lab hih ar gnrally undr rlativly light or uring tim mthod, tmpratur, mix modrat loading, bam undr a highr load t.). In th litratur variou formulatio hih poibly rquir additional tl rinformnt. With th flat-plat formor, ignifiant intr- found to drib th orption iothrm onrt (Xi t al. 994). Hovr, in th faial dbonding our along th SHCC/onrt papr th mi-mpirial xprion pro intrfa. On th othr h, mmbr mad ith U- Norling Mjornll (997) i adoptd b hap formor fail in flxur, at a highr failur Proding FraMCoS-7, May 23-28, 200
load. J = D ( In h, T ) partiular, h th failur load th bam () mmbr inra by ovr 40% hn th failur mod Th hang proportionality from dbonding fiint to onrt D(h,T) i ruhing alld undr moitur flxur. prmability A impl dign it i xampl a nonlinar i thn funtion prntd th rlativ to illutrat humidity th u h tmpratur prmannt formor T (Bažant for & Najjar maing 972). th latral Th moitur panning ma d balan a footbridg rquir Th that potntial th variation th in tim GFRP/SHCC th atr prmannt ma pr formor volum for pratial onrt (atr appliation ontnt i ) hn b qual dmon- to th unit tratd. divrgn th moitur flux J REFERENCES = J t (2) Fihr, G. & Li, V.C. 2002. Influn Matrix Dutility on Tnion-Stiffning Th atr ontnt Bhaviour an b xprd Stl Rinford a th Enginrd th vaporabl Cmntitiou atr Compoit (apillary (ECC), ACI atr, Strut. atr J., um vapor, 99:04-. adorbd atr) th non-vaporabl Ka, (hmially T. & Li, bound) V.C. 999. atr A N Miromhani n (Mill Dign 966, Pantazopoulo Thory for Pudo & Mill Strain Hardning 995). It Cmntitiou i raonabl Compoit. ASCE J. Eng. Mh. 25:373-38. to aum that th vaporabl atr i a funtion Lph, M. & Li, V.C. 2005. Watr Prmability Crad rlativ Cmntitiou humidity, Compoit, h, dgr Pro. th hydration, Int. Conf. on, Fratur, ditd ilia by A. fum Carpintari, ration, CD ROM., i.. = (h,, ) dgr Lung, = ag-dpndnt C.K.Y. 996. Dign orption/dorption Critria for Strain hardning iothrm Fibr (Norling Compoit. Mjonll ASCE 997). J. Eng. Mh. Undr 22:0-8. thi aumption Lung, by ubtituting C.K.Y. & Cao, Equation Qian. in pr. into Dvlopmnt Equation 2 Strain on hardning Prmannt Formor for Durabl Conrt obtain Strutur. Li, V.C. & Lung, C.K.Y. 992. Stady Stat Multipl Craing Short Rom Fibr Compoit. ASCE J. Eng. h Mh. 8:2246-2264. + ( D h) = & + & + & n (3) Li, V.C. h t993. From h Miromhani to Strutural Enginring--th Dign Cmntitou Compoit for Civil Engi- nring Appliation. JSCE J. Stru. Mh. Earth. Eng., hr 0:37-48. / h i th lop th orption/dorption Song, iothrm G. & (alo Van Zijl, alld G.P.A.G. moitur 2004. Tailoring apaity). ECC Th For govrning Commrial quation Appliation. (Equation In: Proding 3) mut b th ompltd 6th RILEM by Sympoium appropriat on boundary Fibr-Rinford initial Conrt ondition. (FRC) - BEFIB 2004, 20-22 Sptmbr 2004, Varnna, Italy. Th rlation btn th amount vaporabl Wang, K., Jann, D., Shah, S. & Karr, A. 997. Prmability atr Study Crad rlativ Conrt. humidity Cm. i & alld Conr. adorption R., 27:38- iothrm 393. if maurd ith inraing rlativity Wang, humidity S. & Li, dorption V.C. 2007. High-Early-Strngth iothrm in th Enginrd oppoit a. Cmntitiou Nglting Compoit. thir diffrn ACI Mat. J., (Xi 03:97-05. t al. 994), in Yang, th folloing, E.H., Yang, orption Y.Z. & Li, iothrm V.C. 2007. ill U b ud High ith Volum Fly Ah to Improv ECC Mhanial Proprti rfrn Matrial to both Grnn. orption ACI Matrial dorption J., 04:620-628. ondition. By th ay, if th hytri th moitur iothrm ould b tan into aount, to diffrnt rlation, vaporabl atr v rlativ humidity, mut b ud aording to th ign th variation th rlativity humidity. Th hap th orption iothrm for HPC i inflund by many paramtr, pially tho that influn xtnt rat 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 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 hydration ration SF ontnt. Thi orption iothrm rad ( h,, ) = G (, ) + 0( g ) h 0( g ) h K (, ) (4) 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 SF. Th fiint G rprnt th amount atr pr unit volum hld in th gl por at 00% rlativ humidity, it an b xprd (Norling Mjornll 997) a G (, ) = + vg vg (5) hr vg vg ar matrial paramtr. From th maximum amount atr pr unit volum that an fill all por (both apillary por gl por), on an alulat K a on obtain K (, ) = g 0.88 + 0.22 G 0 g (6) Th matrial paramtr vg 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 FraMCoS-7, May 23-28, 200