Fraur Mhani Conr and Conr Sruur - Rn Advan in Fraur Mhani Conr - B. H. Oh, al.(d) 200 Kora Conr Iniu, Soul, ISBN 978-89-5708-80-8 Fraur analyi rain hardning mniiou ompoi by man dir modling hor fibr M. Kunida, K. Kozaa, N. Uda & H. Nakamura Dp. Civil Enginring, Nagoya Univriy, Nagoya, apan ABSTRACT: Thr ar a id variy hor fibr rinford mn ompoi, uh a rain hardning and mulipl fin raking in nion. Quaniaiv marial dign mhod onidring h propri marix, fibr and hir inrfa hould b ablihd. Thi papr inrodu numrial modl by man hrdimnional mo-al analyi (i.. marix, fibr and hir inrfa ar dirizd rpivly.), o imula h nil fraur inluding rain hardning and mulipl fin raking. Th fibr ih pifi lngh and diamr hav bn arrangd ihin h pimn, and loading in analyi hav bn alo arrid ou o ompar ih xprimnal rul. I a larifid ha h propod modl an b roughly imulad h nil failur high rngh Srain Hardning Cmniiou Compoi (SHCC) inlud rak parn. And h ff marix rngh, i variaion and fibr diribuion on h nil fraur r numrially invigad. INTRODUCTION Th prforman hor fibr rinford mniiou ompoi ha bn nhand in rn yar, ih a variy marial dign mhod bing propod o ahiv h rquird mhanial prforman. Typial marial i Srain Hardning Cmniiou Compoi (SHCC), uh a Enginrd Cmniiou Compoi (ECC) dvlopd by Li, V.C. (993). Th marial a dignd bad on miro mhani prinipl. Th ff fibr orinaion and hrogniy du o h fibr diribuion anno b, hovr, invigad in ordinary marial dign onp dirly. And a n marial uing hybrid fibr (i.. ombinaion diffrn fibr lngh or fibr yp) ha bn alo propod. Bolandr & Saio (997), for inan, ondud 2-D analyi in hih hor fibr r dirizd a bam lmn o xamin nil fraur fibr rinford onr paramrially, h ff h fibr diribuion on h mhanial prforman h ruling ompoi. Kunida al. (2008) propod hr-dimnional mo-al analyi for SHCC bad on a Rigid-Body-Spring Modl (RBSM) (Kaai 978) o luida h nil fraur ordinary SHCC (ECC) ih PVA fibr. And h propod modl an ll imula h nil fraur SHCC. Hovr, h appliabiliy h modl o ohr yp SHCC (.g. high rngh) hould b larifid. Thi papr prn h analyial rul high rngh SHCC by man dir modling hor fibr. In ordr o inrpr h fraur mhanim (rngh and rain apaiy, rak parn), paramri analy onrning variaion marix rngh and fibr diribuion a ondud. 2 OUTLINE OF PROPOSED MODEL 2. Oulin RBSM Figur ho an xampl a pair lmn (Voronoi ll in h Fig.) ompoing h lmn iffn marix in h RBSM (Bolandr & Bron 2004). Th lmn r aumd o b rigid bodi, hil ing 6 dgr frdom for ah rigid lmn. Six pring r plad on ah boundary plan ah ll, in h normal ( pring) and angnial (2 pring) o h boundari and roaional dirion (3 pring). Th marial propri (nil rngh, lai modulu, and fraur nrgy) h marix r adopd a h mhanial propri h normal and angnial pring, hra h mhanial propri h roaional pring r aumd bad on h liraur (Bolandr & Bron 2004). No ha fraur a valuad uing h rak band bad on h dian bn ah lmn h o minimiz h ff h dirizaion on h raking propri (Thomur al. 200).
D ( h, T h () Th proporionaliy fiin D(h,T) i alld moiur prmabiliy and i i a nonlinar funion h rlaiv humidiy h and mpraur T (Bažan & Najjar 972). Th moiur ma balan rquir ha h variaion in im h ar ma pr uni Figur volum. Elmn onr and dfind (ar dgr onn ) frdom. b qual o h divrgn h moiur flux = (2) Th ar onn an b xprd a h um h vaporabl ar (apillary ar, ar vapor, and adorbd ar) and h non-vaporabl Figur (hmially 2. Fibr loaion bound) and zro-iz ar pring. n (Mill 966, Panazopoulo & Mill 995). I i raonabl o aum ha h vaporabl ar i a funion 2.2 Modling fibr aion bfor raking rlaiv humidiy, h, dgr hydraion,, and mn marix dgr ilia fum raion,, i.. = (h,, ) Bfor = ag-dpndn raking mn orpion/dorpion marix, h r iohrm born by (Norling fibr Mjonll a alulad 997). bad Undr on hi h aumpion har lag hory by by ubiuing Cox (952). Equaion Cox xprd ino h Equaion nil 2 r on and diribuion obain aing on fibr in h marix a Equaion. Th auhor hrfor xprd h rinforing ff fibr bfor raking by alulaing h h nil + r ( D hfibr ) = uing & + Equaion & +. & n (3) h h oh β ( l / 2 x) σ hr f = E f ε m /h i h lop h orpion/dorpion () oh β ( l / 2) iohrm (alo alld moiur apaiy). Th govrning quaion (Equaion 3) mu b ompld hr by appropria σ f = nil boundary r and fibr iniial (MPa), ondiion. E f = lai modulu Th rlaion fibr bn (MPa), εh m = amoun rain marix vaporabl in h dirion ar and rlaiv h fibr, humidiy l = fibr i lngh alld (mm), adorpion x = dian iohrm from if h maurd nd fibr ih (mm), inraing and β = rlaiviy onan drmind humidiy and by dorpion marial onan iohrm marix in h and oppoi fibr (.0 a. in Ngling hi udy). hir diffrn (Xi al. 994), in h folloing, orpion iohrm ill b ud ih 2.3 rfrn Modling o boh fibr orpion aion and afr dorpion raking ondiion. By mn h marix ay, if h hyri h moiur iohrm ould b akn ino aoun, o diffrn 2.3. rlaion, Oulin vaporabl modling ar v rlaiv humidiy, mu Shor b ud fibr aording ih h o pifi h ign lngh h variaion r randomly h arrangd rlaiviy in humidiy. lmn auming Th hap h pimn h orpion iz o b iohrm analyzd, for HPC o a i o inflund aain h by pifid many paramr, fibr onn pially by volum. ho ha A hon influn Figur xn and 2, a ra zro-iz h pring hmial a raion plad on and, a poin, urn, hr drmin a fibr ro por o ruur lmn and por boundary, iz diribuion and h bonding (ar-o-mn r h raio, fibr mn a ad hmial on h ompoiion, pring. Th SF mbdmn onn, lngh uring im l and and h mhod, angl o mpraur, h normal mix dirion addiiv, o rak.). In plan h (orinaion liraur variou angl) formulaion φ r alo an alulad found for o ah drib fibr. h No orpion ha h iohrm orinaion normal angl b a onr drmind (Xi from al. 994). h innr Hovr, produ in h normal prn vor papr and h h mi-mpirial vor in h xprion dirion propod fibr orinaion. Norling Mjornll (997) i adopd bau by i xpliily aoun for h voluion hydraion raion and SF onn. Thi orpion iohrm rad ( h,, ) = G (, ) + 0( g ) h 0( g ) h K (, ) Figur 3. Pullou diplamn obaind from rak idh (bfor ning in pullou bhavior). (4) hr h fir rm (gl iohrm) rprn h phyially bound (adorbd) ar and h ond rm (apillary iohrm) rprn h apillary ar. Thi xprion i valid only for lo onn SF. Th fiin G rprn h amoun ar pr uni volum hld in h gl por a 00% rlaiv humidiy, and i an b xprd (Norling Mjornll 997) a G (, ) = k + k vg vg (5) hr k vg and k vg ar marial paramr. From h maximum amoun ar pr uni volum ha an fill all por (boh apillary por and gl por), on an alula K a on obain K (, ) = g 0.88 + 0.22 G 0 g (6) Th marial paramr k vg and k vg and g an Figur 4. Produr for alulaion fibr bridging for. b alibrad by fiing xprimnal daa rlvan o fr (vaporabl) ar onn in onr a variou Afr ag raking, (Di Luzio h r & Cuai ranfr 2009b). by fibr aro a rak plan in h mn marix (hrafr rfrrd o a h marix ) a alulad by h p hon 2.2 Tmpraur in Figur 3 voluion and 4 (Kunida al. 2008). Half No h ha, alulad a arly rak ag, idh in W h 0 a hmial aumd raion o b h aoiad lngh ih fibr mn pull-ou hydraion diplamn and SF bfor raion ning ar xohrmi, bond r h mpraur lip rlaion. fild Afr i no h uniform ning, for non-adiabai i a alo aumd ym ha vn h if fibr h having nvironmnal horr mbdmn mpraur lngh i onan. a pulld Ha onduion ou. Pull-ou an diplamn b dribd in a onr, aumd a o la b qual for mpraur o oal rak no idh. xding Th hap 00 C (Bažan lip diribuion & Kaplan a drmind 996), by hrough Fourir h la, analyi hih rad ingl fibr pull-ou. If h hap lip diribuion i knon, hn h bond r q diribuion i drmind from h bond = λ T r-lip rlaionhip. Th bridging for fibr (7) aro rak an hn b alulad by ingraing h hr bond q r i h diribuion ha flux, in h T dirion i h abolu h fibr mpraur, axi. Uniaxial and λ bond i h r-lip ha onduiviy; urv a hon in hi in Figur 5 a idnifid hrough h rul ingl Proding FraMCoS-7, May 23-28, 200
fibr pull-ou (Kozaa al. 2008). No ha h ar o bindr raio (W/B) ud marix a 0.8, and high rngh Polyhyln (PE) fibr a ud in h. D ( h, T h Th proporionaliy fiin D(h,T) moiur prmabiliy and i i a nonlina h rlaiv humidiy h and mpraur & Najjar 972). Th moiur ma balan ha h variaion in im h ar ma volum onr (ar onn ) b q divrgn h moiur flux = Figur 5. Bond r-lip rlaion (PE fibr, W/B=0.8). Figur 6. Bridging inlind fibr o rak plan. Figur 7. Shap dumbbll-hapd pimn. Evnually, normal for o rak plan du o bridging fibr a modld. Hovr, h ff raking on ion har rian i no onidrd. 2.3.2 Inra bond rngh du o orinaion angl A hon in Figur 6, a fibr a no alay arrangd prpndiular o rak plan, ha man h fibr ha orinaion angl φ. Li al. (990) rvald h inra bond rngh in h inlind fibr pull-ou, and drivd h folloing Equaion; Figur 8. Tnil r-rain Th ar urv onn pimn an ih b diffrn fibr onn. h vaporabl ar (apillary a xprd a vapor, and adorbd ar) and h non- (hmially bound) ar n (Mil Panazopoulo & Mill 995). I i ra aum ha h vaporabl ar i a fu rlaiv humidiy, h, dgr hydraion dgr ilia fum raion,, i.. = = ag-dpndn orpion/dorpion (Norling Mjonll 997). Undr hi aum by ubiuing Equaion ino Equai obain h + ( D h) = h h & + & + Figur 9. Final rak parn afr nil. hr /h i h lop h orpion/ fφ iohrm (alo alld moiur apa F = F 0 govrning quaion (Equaion 3) (2) mu b by appropria boundary and iniial ondii hr F = pull-ou load Th (N), rlaion F 0 = bn pull-ou load h amoun a an orinaion angl ar 0 rad.(n), and rlaiv φ = orinaion humidiy angl i alld fibr (rad.), f = iohrm paramr if on maurd nubbing ff. ih inraing Rgarding h paramr humidiy f, 0.5 and a dorpion idnifid iohrm hrough in h numrial rul a. (Kozaa Ngling 2009). hir diffrn (Xi al. h folloing, orpion iohrm ill b 2.3.3 Dra rfrn rupur rngh o boh orpion fibr and du dorpion o orinaion angl By h ay, if h hyri h Thr ar xprimnal iohrm finding ould b ha akn h ino rupur aoun, o rngh fibr rlaion, nd o vaporabl b lor han ar h v valu rlaiv humi givn in h manufaurr b ud aording aalogu o in h h ign a h varia PVA fibr (Kanda rlaiviy & Li 998). humidiy. Th orinaion Th hap angl h ah fibr o iohrm rak for HPC plan i aff inflund rupur by many p rngh fibr ilf, pially a dribd ho ha in influn h folloing xn and Equaion; hmial raion and, in urn, drm ruur and por iz diribuion (arraio, mn hmial ompoiion, (3) SF n f ' φ σ σ fu = fu uring im and mhod, mpraur, mix hr σ fu = rupur.). rngh In h liraur fibr (MPa), variou σ n formulaio fu = apparn rupur rngh found o a drib an orinaion h orpion angl iohrm 0 rad.(mpa), φ = orinaion onr (Xi angl al. fibr 994). (rad), Hovr, f = in h rngh rduion papr faor. h In mi-mpirial h prviou rarh xprion pro ih PVA fibr, Norling 0.3 a adopd Mjornll a a (997) f valu. i adopd b Proding FraMCoS-7, May 23-28, 200
D h T h (, () I ha alo bn xprimnally onfirmd ha h pull-ou Th proporionaliy fibr a obrvd fiin in h D(h,T) a i PE alld fibr having moiur ulra prmabiliy high rngh. and In i hi a udy, nonlinar h apparn funion fibr h rngh rlaiv valu humidiy a ud h and for mpraur h analyi. T (Bažan & Najjar 972). Th moiur ma balan rquir ha h variaion in im h ar ma pr uni volum onr (ar onn ) b qual o h divrgn h moiur flux = (2) Th ar onn an b xprd a h um h vaporabl ar (apillary ar, ar vapor, and adorbd ar) and h non-vaporabl (hmially bound) ar n (Mill 966, Panazopoulo & Mill 995). I i raonabl o Figur 0. Diriizd mn marix and fibr. aum ha h vaporabl ar i a funion rlaiv humidiy, h, dgr hydraion,, and dgr ilia fum raion,, i.. = (h,, ) 3 = ANALYSIS ag-dpndn FOR CRACKING orpion/dorpion OF iohrm (Norling COMPOSITES Mjonll WITH 997). STRAIN Undr hi HARDENING aumpion and by ubiuing Equaion ino Equaion 2 on 3. obain Oulin marial rpon for analyi Th arg hi analyi i Ulra High Prforman- Srain Hardning Cmniiou Compoi (UHP h SHCC) dvlopd + ( D by h) Kunida = & + al. (2007) & + and & n Kamal (3) h h al. (2008). Th marial xhibi high rngh ovr 8MPa in nion, high rain apaiy in nion mor han hr 2%, ih /h i xrmly h lop highr h durabiliy. orpion/dorpion Uniaxial nil iohrm (alo pimn alld onaining moiur 0.5%, apaiy)..0% Th and.5% govrning PE fibr quaion (6 mm (Equaion in lngh 3) and mu 0.02 b ompld mm in diamr) by appropria r arrid boundary ou. and A iniial hon ondiion. in Figur 7, dumbbll-hapd Th rlaion bn pimn h having amoun a ro-ion vaporabl 30 ar x 3 and mm rlaiv r ud humidiy in h i o alld maur adorpion h rain iohrm zon if maurd 00 mm in lngh. ih inraing rlaiviy humidiy and dorpion iohrm in h oppoi Tabl a.. Ngling Marial propri hir diffrn for analyi. (Xi al. 994), in h folloing, orpion iohrm ill b ud ih rfrn o boh orpion and dorpion ondiion. By h ay, if h hyri h moiur iohrm ould b akn ino aoun, o diffrn rlaion, vaporabl ar v rlaiv humidiy, mu b ud aording o h ign h variaion h rlaiviy humidiy. Th hap h orpion iohrm for HPC i inflund by many paramr, pially ho ha influn xn and ra h hmial raion and, in urn, drmin por ruur and por iz diribuion (ar-o-mn raio, mn hmial ompoiion, SF onn, uring im and mhod, mpraur, mix addiiv, 3.2.). Oulin In h liraur analyi variou formulaion an b found o drib h orpion iohrm normal Th onr analyi (Xi modl, al. 994). hih Hovr, ar dirizaion in h prn mn papr marix h mi-mpirial and fibr inluding xprion an inrfa, propod ar by hon Norling in Figur Mjornll 0. (997) Th i zon adopd mauring bau 30 x 3 i xpliily aoun for h voluion hydraion x raion 00 mm and a SF akn onn. ou Thi h orpion pimn iohrm for modling, rad and h rain a drmind in h ara 00 mm in lngh imilarly o h xprimn. Whn uing a RBSM, h rak parn, hih govrn h rain apaiy dirly in hi udy, i affd by ( h,, ) = G (, ) + h mh iz and hap. For impliiy, hovr, 0( g ) h h rangl-hapd lmn a ud and h mh (4) iz a mm in h dirion h longiudinal axi h pimn, hih 0( g i l han ) h xprimnal K (, ) rak paing, and 3mm in h dph dirion, o a o horn h alulaion im (a o-dimnional- lik diviion). Fibr r modld by randomly dipring hr h hm fir in rm h (gl pimn iohrm) a hon rprn in Figur h 0. phyially A for h bound boundary (adorbd) ondiion, ar ford and h horizonal rm diplamn (apillary a iohrm) givn o rprn h righ id h lmn, apillary ond hil ar. omplly Thi xprion fixing i h valid lf only id for lmn lo onn h pimn. SF. Th fiin G rprn h amoun ar Tabl pr uni giv volum h phyial hld in propri h gl por h a fibr, 00% marix, rlaiv and humidiy, fibr-marix and i inrfa an b xprd for h analyi. (Norling Mjornll 997) a 3.3 Trial analyi for pimn ih diffrn fibr Gonn (, ) = k + k vg vg (5) Figur ho h r-rain rlaionhip hn h hr nil k vg and rngh k vg ar h marial marix paramr. a aumd From o h b 7.5MPa. maximum Th amoun nil ar rngh pr uni a volum drmind ha an hrough fill all por h flxural (boh apillary rngh por and marix gl por), ilf, on in hih an alula h flxural K a on rngh obain a 7.5MPa. Th xprimnal rul ar alo rprnd in h figur. In h a 0.5%, h fir rak ourrd a g r 7.5MPa, and r inra up o 0.88 + 0.22 G 3MPa 0 afr uddn drop in r. Finally, ning bhavior K ( a, ) (6) obrvd. = In hi a, oal rpon an b 0 ll imulad. g Thi modl alo prdi h ning bhavior in h Th a marial.0%, paramr alhough k xprimnal rul vg and k vg and g an ho lighly rain hardning up o.0% in rain. b alibrad by fiing xprimnal daa rlvan o fr Rgarding (vaporabl) h analyial ar onn rul for in.5% onr a, h a analyi variou ag rprodud (Di Luzio h & Cuai rpad 2009b). r gain and lo bginning afr h fir rak on and h larg ulima nil rain xding 5%, alhough h 2.2 Tmpraur rul hod voluion only rain apaiy ranging from 2.0% o 2.5%. No inra in h r up o h No ha, a arly ag, in h hmial raion poin aoiad 2.0% ih in mn rain hydraion r obrvd and SF bau raion raking ar xohrmi, rngh h mpraur 7.5MPa. Afr fild ha, i no i uniform xhibi rain hardning up o 5.2% in rain. Th oal rpon for non-adiabai ym vn if h nvironmnal mpraur anno i b onan. imulad Ha quaniaivly. onduion Figur an 2 b ho dribd analyial in onr, rak parn a la a for rain mpraur.0%, 2.0% no and 4.0%, rpivly. In rain hardning marial xding 00 C (Bažan & Kaplan 996), by ih Fourir mulipl la, fin hih rak, rad numbr rak rongly aff h rain apaiy in nion. A hon in rak parn hi analyi, mo inrfa lmn, hih r orrponding o rak ponially, (7) q = λ T r opnd, and i a indud onan rak paing hr in ah q rain i h lvl. ha I m flux, ha T hi bhavior h abolu gav muh mpraur, rain valu and λ in i h h analyi. ha onduiviy; in hi Proding FraMCoS-7, May 23-28, 200
D ( h, T h Th proporionaliy fiin D(h,T) moiur prmabiliy and i i a nonlina h rlaiv humidiy h and mpraur & Najjar 972). Th moiur ma balan ha h variaion in im h ar ma volum onr (ar onn ) b q divrgn h moiur flux = Figur 3. Eff marix rngh (.5% a). Th ar onn an b xprd a In ah a, r h valu vaporabl ju bfor ar loalizaion (apillary a (failur) in h xprimn vapor, and a adorbd roughly ar) imulad and by h non- h analyi. Thi (hmially man ha fibr bound) bridging ar rngh, n (Mil hih onrol h Panazopoulo rngh ompoi & Mill in 995). hi marial, i alo valuad aum in ha ah h ri, vaporabl and h ar mod- i a fu I i ra ling in hi udy rlaiv i appropria humidiy, in h, rm dgr fibr hydraion bridging rpon. dgr Hovr, ilia oal fum rpon raion, rprnd by r = rain ag-dpndn urv a no orpion/dorpion imulad, i.. = quaniaivly. On (Norling h raon Mjonll i 997). xiing Undr marial ha diribuion by ubiuing rngh Equaion marix and ino fibr Equai hi aum orinaion, obain h au qunial raking ihin a pimn. In h folloing ion, paramri udi rlad o diribuion marix h rngh and fibr diribuion + r ( D ondud. h) = & + & + h h Figur. Sr-rain urv pimn ih diffrn fibr onn. Figur 2. Analyial rak parn (.5% a). 4 PARAMETRIC hr ANALYSIS /h i h lop h orpion/ iohrm (alo alld moiur apa 4. Eff marix govrning rngh quaion (Equaion 3) mu b by appropria boundary and iniial ondii Figur 3 ho h analyial rul ih diffrn marix rngh, pially in h a fibr onn Th rlaion bn h amoun ar and rlaiv humidiy i alld.5%. Thr kind marix rngh (5.0MPa, 7.5MPa iohrm if maurd ih inraing and 0MPa) r adopd a a main paramr. A humidiy and dorpion iohrm in h hon in Figur 3, a h marix rngh bam a. Ngling hir diffrn (Xi al. lor, h rain apaiy bam highr ih rain h folloing, orpion iohrm ill b hardning bhavior. Bau h fibr bridging rngh rfrn o boh orpion and dorpion a l han 0MPa in h a.5%, i m ha By h ay, if h hyri h marix rngh lor han 0MPa i rquird o xhibi iohrm ould b akn ino aoun, o ignifian rain hardning bhavior. rlaion, vaporabl ar v rlaiv humi b ud aording o h ign h varia rlaiviy humidiy. Th hap h iohrm for HPC i inflund by many p pially ho ha influn xn and hmial raion and, in urn, drm ruur and por iz diribuion (arraio, mn hmial ompoiion, SF uring im and mhod, mpraur, mix.). In h liraur variou formulaio found o drib h orpion iohrm onr (Xi al. 994). Hovr, in h papr h mi-mpirial xprion pro Figur 4. Eff diribuion Norling Mjornll marix rngh (997) (.5% i a). adopd b Proding FraMCoS-7, May 23-28, 200
D ( h, T h () Th proporionaliy fiin D(h,T) i alld moiur prmabiliy and i i a nonlinar funion h rlaiv humidiy h and mpraur T (Bažan & Najjar 972). Th moiur ma balan rquir ha h variaion in im h ar ma pr uni volum onr (ar onn ) b qual o h divrgn h moiur flux = (2) Th ar onn an b xprd a h um h vaporabl ar (apillary ar, ar Figur 5. Changing rak idh up o final failur (.5% vapor, and adorbd ar) and h non-vaporabl a). (hmially bound) ar n (Mill 966, Panazopoulo & Mill 995). I i raonabl o 4.2 aum Eff ha h diribuion vaporabl marix ar rngh i a funion along rlaiv pimn humidiy, axi h, dgr hydraion,, and dgr ilia fum raion,, i.. = (h,, ) Figur = ag-dpndn 4 ho h orpion/dorpion analyial rul ih iohrm diffrn (Norling propry Mjonll marix. 997). Undr No ha hi aumpion diribuion and marix by ubiuing rngh Equaion along h pimn ino Equaion axi i 2 on aumd obain o b normal diribuion, and hr kind andard dviaion (S.D.=0MPa,.0MPa and 2.0MPa) r analyzd undr h avragd rngh 0.0MPa. h + ( D h) = & + & + & n (3) Th h rul ih h S.D. 0MPa hod only o rak, bau r rahd up o 0MPa i, a dribd in prviou. Afr ha, ning bhavior hr /h i h lop h orpion/dorpion a obrvd. Hovr, onidring andard dviaion (S.D.) hangd fraur pro dramaially iohrm (alo alld moiur apaiy). Th govrning quaion (Equaion 3) mu b ompld from rain ning o rain hardning, a hon by appropria boundary and iniial ondiion. in Figur 4. In a phyial bhavior, fir rak our a ak ro ion in a pimn, and - Th rlaion bn h amoun vaporabl ar and rlaiv humidiy i alld adorpion ond rak our a ondly ak ro ion. iohrm if maurd ih inraing rlaiviy Squnial raking along pimn axi m o b humidiy and dorpion iohrm in h oppoi rongly affd by diribuion marix rngh. a. Ngling hir diffrn (Xi al. 994), in Rgarding analyial rul, largr andard dviaion marix rngh produd highr rain apa- h folloing, orpion iohrm ill b ud ih rfrn o boh orpion and dorpion ondiion. iy in hi analyi, undr h aumpion onan By h ay, if h hyri h moiur bridging rngh fibr. iohrm ould b akn ino aoun, o diffrn rlaion, vaporabl ar v rlaiv humidiy, mu b ud aording o h ign h variaion h rlaiviy humidiy. Th hap h orpion iohrm for HPC i inflund by many paramr, pially ho ha influn xn and ra h hmial raion and, in urn, drmin por ruur and por iz diribuion (ar-o-mn raio, mn hmial ompoiion, SF onn, uring im and mhod, mpraur, mix addiiv,.). In h liraur variou formulaion an b found o drib h orpion iohrm normal onr (Xi al. 994). Hovr, in h prn papr h mi-mpirial xprion propod by Figur 6. Crak parn pimn onidring diribuion marix rngh (.5% a). Norling Mjornll (997) i adopd bau i xpliily aoun for h voluion hydraion raion and SF onn. Thi orpion iohrm rad ( h,, ) = G (, ) + 0( g ) h 0( g ) h K (, ) (4) hr h fir rm (gl iohrm) rprn h phyially bound (adorbd) ar and h ond rm (apillary iohrm) rprn h apillary ar. Thi xprion i valid only for lo onn SF. Th fiin G rprn h amoun ar pr uni volum hld in h gl por a 00% rlaiv humidiy, and i an b xprd (Norling Mjornll 997) a G (, ) = k + k vg vg (5) hr k vg and k vg ar marial paramr. From h maximum amoun ar pr uni volum ha an fill all por (boh apillary por and gl por), on an alula K a on obain Figur 7. Sr rain urv onidring andard dviaion marix rngh. g 0.88 + 0.22 G 0 (6) KTablG (, 2. ) = Avragd numbr fibr in a ro ion and i andard dviaion. g Avragd numbr fibr Sandard dviaion in a ro ion Ca Th marial 28830 paramr k vg and k52 vg and g an b Ca2 alibrad 28858 by fiing xprimnal 565 daa rlvan o Ca3 28834 396 fr (vaporabl) ar onn in onr a variou ag (Di Luzio & Cuai 2009b). 2.2 Tmpraur voluion No ha, a arly ag, in h hmial raion aoiad ih mn hydraion and SF raion ar xohrmi, h mpraur fild i no uniform for non-adiabai ym vn if h nvironmnal mpraur i onan. Ha onduion an b dribd in onr, a la for mpraur no xding 00 C (Bažan & Kaplan 996), by Fourir la, hih rad q = λ T (7) hr q i h ha flux, T i h abolu mpraur, and λ i h ha onduiviy; in hi Figur 8. Numbr fibr along pimn axi. Proding FraMCoS-7, May 23-28, 200
Figur 5 ho avragd rak idh during fraur pro in h a.5% a. Th analyial modl imula ady a raking bhavior ha man no ignifian inra rak idh up o final fraur, and hi bhavior i imilar o xprimnal rnd (Li 2003). Figur 6 ho rak parn in h a.5% ih S.D.=.0MPa. Alhough prviou analyi ihou onidring S.D. marix rngh indiad onan rak paing a hon in Figur 2, h analyi onidring S.D. marix rngh ho non uniform rak paing in ah p bau randomly diribud marix rngh along pimn axi. Bad on hi onp onidring diribuion marix rngh, diffrn fibr onn a an b alo imulad. Epially, lighly rain hardning hon in Figur 7(b) a rprodud, hil h prviou analyi imad ning bhavior.0% a, a hon in Figur (b). Figur 9. Sr ain urv pimn ih diffrn fibr diribuion. 4.3 Eff fibr diribuion along pimn axi In ordr o a h ff fibr diribuion in h pimn, analyi a ondud by hanging h andard dviaion numbr fibr aro h ah ro ion, hih i orrponding o ponially rak plan. In hi modl, ah fibr i randomly poiiond ihin h pimn, and avragd numbr fibr aro ah ro ion a abou 28,800, a abulad in Tabl 2. Thr kind analyi ih diffrn andard dviaion numbr fibr in ah ro ion (SD=0, 52, 565 and 396) r ondud, a hon in Figur 8. Figur 9 ho h r-rain rlaionhip h pimn having diffrn fibr diribuion. Th analyial rul ho ha largr diribuion fibr having ro ion ih l fibr ignifianly rdu rain apaiy. Sin l fibr impar draing bridging rngh a a ro ion o a ompoi, rduion no only rain apaiy = D ( h, T ) bu halo ulima rngh a obrvd a hon in Figur 9. Th proporionaliy fiin D(h,T) moiur prmabiliy and i i a nonlina 5 CONCLUSIONS h rlaiv humidiy h and mpraur & Najjar 972). Th moiur ma balan In hi udy, a hr-dimnional ha h variaion in analyi im mhod h ar ma ih dirizd volum hor fibr onr a ad (ar onn hrough ) b q h analyi high divrgn rngh rain h hardning moiur flux mniiou ompoi (UHP-SHCC). Th finding ob- aind inlud h folloing: = () By analyi ondud on a marial ih high rngh rain Th hardning ar onn and mulipl an b xprd fin a rak in nion (UHP-SHCC), h vaporabl hi ar modl roughly (apillary a imulad mhanial vapor, rpon and adorbd rprnd ar) by and r h non- rain urv and (hmially rak parn. bound) ar n (Mil (2) Paramri Panazopoulo analyi a & ondud Mill 995). o inrpr fraur mhanim aum ha h rain vaporabl hardning ar and i a fu I i ra mulipl fin rak rlaiv in UHP-SHCC. humidiy, h, Srain dgr apaiy hydraion a inrad du dgr o largr ilia diribuion fum raion, marix, i.. = rngh. Srain apaiy, = ag-dpndn hovr, drad orpion/dorpion ih inraing diribuion (Norling Mjonll fibr. 997). Undr hi aum by ubiuing Equaion ino Equai Th auhor innd obain o nhan h modl o a o b uful for h dvlopmn fibr rinforing marial. h + ( D h) = & + & + h h REFERENCES hr /h i h lop h orpion/ Bolandr,.E. & Saio, S. 997.Dir modling horfibr rinformn iohrm in mniiou (alo ompoi, alld moiur Advand apa Cmn Bad Marial, govrning 6, 76-86. quaion (Equaion 3) mu b Bolandr,.E. & Bron, by appropria S. 2004. Cohiv boundary Zon and Modling iniial ondii Fraur in Irrgular Th Lai, rlaion Fraur bn Mhani h amoun Conr Sruur, Pro. ar and FRAMCOS-5, rlaiv 989-994. humidiy i alld Cox, H. 952. Th Elaiiy and Srngh Papr and Ohr iohrm if maurd ih inraing Fibrou Marial, Briih. Applid Phyi, 3. Kamal, A., Kunida, humidiy M., Uda, and N. dorpion & Nakamura, iohrm H. 2008. in h Evaluaion Crak a. Opning Ngling Prforman hir diffrn a Rpair Marial ih Srain h Hardning folloing, Bhavior, orpion Cmn iohrm and Con-ill b (Xi al. r Compoi, rfrn 30(0), 863-87. o boh orpion and dorpion Kanda, T. & Li, V. C. 998. Inrfa Propry and Apparn By h ay, if h hyri h Srngh High-Srngh Hydrophili Fibr in Cmn Marix, ournal iohrm Marial ould in Civil b Enginring, akn ino ASCE, aoun, o 0(), 5-3. rlaion, vaporabl ar v rlaiv humi Kaai, T., 978. N b Dir ud aording Modl and o Thir h ign Appliaion h varia o Simi Rpon rlaiviy Analyi humidiy. Sruur, Th Nular hap Engi-onring Dign, 48, iohrm 207-229. for HPC i inflund by many p h Kozaa, K. 2009. Sudy on Tnil Fraur Mhanim Ulra High Prforman-Srain Hardning Cmniiou pially ho ha influn xn and Compoi and hmial I Modling, raion Mar Thi and, in Nagoya urn, drm Univriy. (in apan) ruur and por iz diribuion (arraio, E. Brühilr, mn E hmial &Nakamura, ompoiion, H. 2007. SF Kunida, M., Dnarié, Challng for Srain uring Hardning im and Cmniiou mhod, mpraur, Compoi mix Dformabiliy Vru Marix Dniy, Pro. h fifh.). In h liraur variou formulaio Inrnaional RILEM Workhop on HPFRCC, 3-38. Kunida, M., Kozaa, found K., Uda, o drib N., Nakamura, h orpion H. & Ogura, iohrm H. 2008. Thr-dimnional onr (Xi Mo-al al. Analyi 994). for Hovr, Srain in h Hardning Cmniiou papr Compoi, h mi-mpirial Crp, Shrinkag xprion and pro Durabiliy Mhani Norling Conr Mjornll and Conr (997) Sruur, i adopd b Pro. CONCREEP8, 745-75. Proding FraMCoS-7, May 23-28, 200
Kozaa, = D ( hk.,, T ) Kunida, h M., Kanda, T. & Nakamura, H. 2008. () Bond Propri Organi Fibr Embddd in Ulra High Srngh Marix, Proding h apan Conr Iniu, Th 30(), proporionaliy 23-236. (in apan) fiin D(h,T) i alld Li, moiur V.C., Wang, prmabiliy Y. & Bakr, and S. i 990. i a Eff nonlinar Inlining funion Angl, h rlaiv Bundling, humidiy and Surfa h and Tramn mpraur on Synhi T (Bažan Fibr & Najjar Pull-ou 972). from a Th Cmn moiur Marix, ma Compoi, balan 2(2), rquir 32-40. ha h variaion in im h ar ma pr uni Li, V.C. 993. From Miromhani o Sruural Enginring volum Th Dign onr Cmniiou (ar onn Compoi ) b for qual Civil o Engi- h divrgn h moiur flux = (2) Th ar onn an b xprd a h um h vaporabl ar (apillary ar, ar vapor, and adorbd ar) and h non-vaporabl (hmially bound) ar n (Mill 966, Panazopoulo & Mill 995). I i raonabl o aum ha h vaporabl ar i a funion rlaiv humidiy, h, dgr hydraion,, and dgr ilia fum raion,, i.. = (h,, ) = ag-dpndn orpion/dorpion iohrm (Norling Mjonll 997). Undr hi aumpion and by ubiuing Equaion ino Equaion 2 on obain h + h ( D h) = n (3) h & + & + hr /h i h lop h orpion/dorpion iohrm (alo alld moiur apaiy). Th govrning quaion (Equaion 3) mu b ompld by appropria boundary and iniial ondiion. Th rlaion bn h amoun vaporabl ar and rlaiv humidiy i alld adorpion iohrm if maurd ih inraing rlaiviy humidiy and dorpion iohrm in h oppoi a. Ngling hir diffrn (Xi al. 994), in h folloing, orpion iohrm ill b ud ih rfrn o boh orpion and dorpion ondiion. By h ay, if h hyri h moiur iohrm ould b akn ino aoun, o diffrn rlaion, vaporabl ar v rlaiv humidiy, mu b ud aording o h ign h variaion h rlaiviy humidiy. Th hap h orpion iohrm for HPC i inflund by many paramr, pially ho ha influn xn and ra h hmial raion and, in urn, drmin por ruur and por iz diribuion (ar-o-mn raio, mn hmial ompoiion, SF onn, uring im and mhod, mpraur, mix addiiv,.). In h liraur variou formulaion an b found o drib h orpion iohrm normal onr (Xi al. 994). Hovr, in h prn papr h mi-mpirial xprion propod by Norling Mjornll (997) i adopd bau i & xpliily nring Appliaion, aoun for ournal h voluion Sruural Mhani hydraion raion and Earhquak and SF Enginring, onn. Thi SCE, orpion 0(2), 37-48. iohrm Li, rad V. C. 2003: On Enginrd Cmniiou Compoi(ECC) A Rvi h Marial and I Appliaion,. Advand Conr Thnology, (3), 25-230. Thomur,. & Bolandr,.E. & Kunida, M. 200. Rduing Mh Bia on Fraur ihin Rigid-Body Spring Nork,,, ) = G ( ) ( h ournal Sruural, + Mhani and Earhquak Enginring, SCE, No.682/I-56, 05-23. ( g ) h (4) 0( g ) h K (, ) hr h fir rm (gl iohrm) rprn h phyially bound (adorbd) ar and h ond rm (apillary iohrm) rprn h apillary ar. Thi xprion i valid only for lo onn SF. Th fiin G rprn h amoun ar pr uni volum hld in h gl por a 00% rlaiv humidiy, and i an b xprd (Norling Mjornll 997) a G (, ) = k + k vg vg (5) hr k vg and k vg ar marial paramr. From h maximum amoun ar pr uni volum ha an fill all por (boh apillary por and gl por), on an alula K a on obain K (, ) = g 0.88 + 0.22 G 0 g (6) Th marial paramr k vg and k vg and g an b alibrad by fiing xprimnal daa rlvan o fr (vaporabl) ar onn in onr a variou ag (Di Luzio & Cuai 2009b). 2.2 Tmpraur voluion No ha, a arly ag, in h hmial raion aoiad ih mn hydraion and SF raion ar xohrmi, h mpraur fild i no uniform for non-adiabai ym vn if h nvironmnal mpraur i onan. Ha onduion an b dribd in onr, a la for mpraur no xding 00 C (Bažan & Kaplan 996), by Fourir la, hih rad q = λ T (7) hr q i h ha flux, T i h abolu mpraur, and λ i h ha onduiviy; in hi Proding FraMCoS-7, May 23-28, 200