Fracture mechanics of early-age concrete

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1 Fraur Mhani Conr Conr Sruur - Rn Advan in Fraur Mhani Conr - B. H. Oh, al.(d Kora Conr Iniu, Soul, ISBN Fraur mhani arly-ag onr V.T.N. Dao, P.H. Morri & P.F. Dux Shool Civil Enginring, Th Univriy Qunl, Auralia ABSTRACT: In hi papr, h fraur mhani onr ruur i fir rvid. Thi larly dmonra ha, dpi h uful appliaion fraur mhani o udy h fraur bhavior maur onr, i appliaion o h raking vry arly-ag onr (i.. ihin vral hour afr mixing i ill in i infany, ih vry limid liraur availabl. Thi i blivd prinipally o b h rul diffiuli ha ari in h xprimnal drminaion h propri xrmly fragil onr a vry arly ag. In a rn rarh a h Univriy Qunl, a apparau xprimnal produr hav bn dvlopd ha nabl h ompl nil r-diplamn bhavior onr pimn a vry arly ag o b apurd rliably. Bad on h daa obaind, h papr ho ha urrn modl h r-paraion rlaionhip maur onr may no apply onr a vry arly ag. Rvid mahmaial modl h r-paraion rlaionhip arly-ag onr ar propod. REVIEW OF FRACTURE MECHANICS OF CONCRETE STRUCTURES Th rik failur du o h groh rak an b rad uing h in knon a fraur mhani, hih aro iniially from h ork Griffih (9 on h fraur bril marial uh a gla. I mo ignifian appliaion, hovr, hav bn in onrolling h bril failur faigu failur malli ruur uh a prur vl, airplan, hip. Conidrabl dvlopmn ha akn pla in h la vral dad o aoun h duiliy ypial mal. Porl mn onr i a rlaivly bril marial a a rul, i mhanial bhavior i riially inflund rak propagaion. Many amp hav bn mad o apply fraur mhani onp o mn-bad ompoi, uh a morar maur-ag onr. Th fir appliaion fraur mhani o onr appar o hav bn mad (Nvill 959a, b,, hil Kaplan (96 appar o hav publihd h fir xprimnal udy h appliaion fraur mhani o onr. Exlln rvi h appliaion fraur mhani o maur mn onr ar availabl in h liraur, i i hu no ovrd in dail hr. Thr ar fundamnal diffrn bn h fraur bhavior onr, a quai-bril marial, ha bril duil-bril marial. Whil h nonlinar zon i praially abn in bril marial, mo h nonlinar zon in fron a rak ip in a duil-bril marial (uh a a mal involv hardning plaiiy or prf yilding (Fig.. In duil-bril marial, h fraur pro zon (FPZ, hih i h zon in hih h marial undrgo ning damag, i qui mall. In quai-bril marial (uh a maur onr, rok, rami, hovr, plai flo i almo nonxin h FPZ fill almo nirly h nonlinar zon (Fig.. I ha bn uggd ha h idh lngh h FPZ in maur onr ar h ordr hr lv im h maximum aggrga iz, rpivly (Bazan & Oh 983, Ouka & Da. Th dvlopmn a izabl FPZ nia h appliaion nonlinar fraur mhani (Bazan, hih diffr ignifianly from h fraur mhani radiionally applid o duil-bril marial. Linar lai fraur mhani i appliabl only o rlaivly larg-al ruur in hih h ff h nonlinar FPZ an b ngld. Figur. Fraur pro zon in mal onr (Bazan. Variou modl hav bn dvlopd o drib h FPZ in fron a rak in onr, inluding noably h fiiiou rak modl (FCM propod Hillrborg al. (976 h rak b modl propod Bazan & Oh (983 (Fig.. Th -

2 mr D ( modl h, T h h pro zon a a gomrially dioninuou rak ih hararii afr raking ( ha Th ar dribd proporionaliy a r-rak fiin opning D(h,T i rlaionhip. moiur Th prmabiliy lar imagin h i i pro a nonlinar zon funion o xi alld ihin h rlaiv a rain humidiy fini bidh h mpraur in hih T h (Bažan mirorak & Najjar 97. ar unimly Th moiur diribud ma balan drib rquir h bhavior ha h variaion afr raking im a h r-rain ar ma rlaionhip. volum Figur onr ho (ar h r onn diribuion b qual o - h pr uni ning divrgn r-paraion h moiur (or flux quivaln rain urv ah modl. Th o modl ar nially quivaln (Karihaloo 995, Bazan 3, ar omim rfrrd o ollivly a ohiv modl or fraur pro modl. In hi papr, h ( FCM Th i ar applid onn o udy an h b fraur xprd paramr a h um arly-ag h vaporabl onr. ar (apillary ar, ar vapor, adorbd ar 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,, dgr ilia fum raion,, i.. (h,, ag-dpndn orpion/dorpion iohrm (Norling Mjonll 997. Undr hi aumpion ubiuing Equaion ino Equaion on obain h + h ( D h n (3 h & + & + Figur. Sr diribuion ning urv: (a, b ohiv hr rak modl /h i h duil-bril lop h marial; orpion/dorpion (, d ohiv rak iohrm modl (alo quai-bril alld marial; moiur (, f apaiy. rak b modl Th govrning quai-bril quaion marial (Equaion (Bazan. 3 mu b ompld appropria boundary iniial ondiion. Th ara rlaion undr bn h nir h ning amoun r- vaporabl rak opning ar urv rlaiv (Fig. humidiy d rprn i alld h oal adorpion nrgy diipad iohrm if fraur maurd pr ih uni ara inraing rak, rlaiviy i dfind humidiy a h fraur dorpion nrgy, iohrm G F. Tha in i, h oppoi a. Ngling hir diffrn (Xi al. 994, in h folloing, orpion iohrm ill b ud ih rfrn G σ ( d ( F o boh orpion dorpion ondiion. By h ay, if h hyri h moiur iohrm ould b akn ino aoun, o diffrn hr rlaion, F vaporabl i h rak ar opning v rlaiv zro humidiy, r. Thi mu i obviouly b ud aording alo h xrnal o h ign nrgy h rquird variaion o ra h rlaiviy fully brak humidiy. a uni Th urfa hap ara rak. h orpion Th G F iohrm maur onr, HPC i inflund drmind many ihr paramr, dir or indir pially nil ho, ha influn normally xn rang bn ra h 4 /m hmial 5 raion /m (Elfgrn, in 989, urn, Karihaloo drmin 995. por I ruur i inflund por o iz varying diribuion dgr (ar-o-mn boh miroruural raio, mn nvironmnal/ing hmial ompoiion, faor, SF onn, inlud- uring h im aggrga mhod, iz mpraur, qualiy, ar-mn mix addiiv, raio,.. ag In h onr, liraur variou loading mulaion ra (Pron an b 98a, found o b, drib Wimann h orpion al. 987, iohrm Karihaloo normal 995. Gnrally, onr (Xi h highr al h rngh Hovr, in h h onr, prn h papr highr h h mi-mpirial fraur nrgy. xprion Thi i in propod ark onra Norling o lai-plai Mjornll (997 mal i ho adopd fraur bau nrgy i & dra xpliily ih aoun inraing h nil voluion rngh. hydraion raion Hovr, h SF inra onn. in Thi h fraur orpion nrgy iohrm onr rad ih i rngh hould no b onfud ih an inra in i duiliy. Th fraur nrgy alon anno diinguih duiliy from briln, nor do h rvr apply. Addiional paramr ( h,, G (, + mu b valuad o mak hi diinion. I ha ( g h bn uggd ha h hararii lngh, (4 l h, hih i dfind ( g h K (, EG F l ( h f hr h fir rm (gl iohrm rprn h an phyially b ud bound a an invr (adorbd maur ar h h briln ond rm h (apillary onr. iohrm Th mallr rprn h hararii h apillary lngh, ar. Thi h mor xprion bril i h valid marial, only lo vi onn vra (Hordijk SF. Th al. fiin 989, Karihaloo G rprn 995, D h Shur amoun & Tar ar pr 997. uni volum Th hararii hld in h gl lngh por l h a i % alo h rlaiv lngh humidiy, h FPZ. i For an mo b xprd onr, (Norling l h appar Mjornll o 997 rang a bn mm 4 mm (Hordijk al. 989, bu an omim hav valu grar han mm (Hillrborg 985. Ohr ypial G ( valu, k h hararii + k vg vg lngh maur-ag (5 onr ohr marial ar lid in Tabl. hr k vg k vg ar marial paramr. From h Tabl. Typial hararii lngh maur onr ohr maximum marial amoun (Karihaloo ar 995. pr uni volum ha an fill Marial all por (boh apillary por gl por, l h (mm on an Gla alula K a on obain -6 Cmn pa dnifid ilia fum Hardnd mn pa 5-5 g Morar G - High rngh onr (5- MPa 5-3 (6 K (, Normal onr (agg. iz mallr han - 5 g mm Dam onr (agg. iz 38 mm 7 Th marial paramr k vg k vg g an b I alibrad i noiabl fiing from xprimnal Tabl ha normal daa rlvan onr o i fr l (vaporabl bril han high ar rngh onn onr in onr bu mor a variou ag (Di Luzio & Cuai 9b. bril han dam onr, hih ompri largr aggrga. Tha i, h briln dra ih inraing aggrga iz bu inra ih inraing. Tmpraur voluion onr rngh. Alo, a omparion h daa hardnd No ha, mn a arly pa, ag, in pa h dnifid hmial raion ilia fum, aoiad high ih rngh mn onr hydraion ih ha SF raion normal ar xohrmi, rngh onr h mpraur india ha fild h i no mor unim ompa non-adiabai h miroruur ym vn h mix, if h h nvironmnal mor bril h mpraur marial. i onan. Ha onduion an b dribd Dpi in h onr, uful a appliaion la mpraur fraur mhani xding o udy C h (Bažan fraur bhavior & Kaplan maur 996, on- no r, Fourir i la, appliaion hih rad o h arly-ag raking onr i ill in i infany, ih vry limid liraur q λ T availabl. A ummary rlvan liraur (7 on h fraur bhavior arly-ag onr i prnd hr in q Tabl i h (Dao ha flux, al. 9. T i In h h abolu nmniond mpraur, a--h-ar λ i h rpor ha onduiviy; on h propri in hi onr a arly ag (RILEM ommi 4-CEA Proding FraMCoS-7, May 3-8,

3 Tabl. Summary liraur on fraur bhavior arly-ag onr (Dao al. 9. D ( h, T h Sudy Ting Conluion (Orgaard al. 4 Wdg-pliing o drmin r-rak Tnil rngh, Young modulu, fraur opning rlaionhip o high-prman nrgy r found Th proporionaliy o inra ih ag. fiin Hovr, D(h,T onr mix ih /.3.48 a ag duiliy xprd moiur in prmabiliy rm hararii i lngh i a nonlina bn 8 h 8 day. a found o h dra rlaiv ih humidiy ag. h mpraur (Zollingr al. 993 Thr-poin bnding onr agd bn h 8 day. riial ffiv rak lngh or pro zon iz Inra & in boh Najjar riial 97. r Th inniy moiur faor ma balan ha h variaion in im h ar ma ih ag r obrvd, indiaing ha arly-ag onr i volum mor bril onr han maur (ar onr. onn b q (Kim al. 4 Wdg-pliing onr ag from Boh riial divrgn r inniy h faor moiur fraur flux nrgy inra ih ag, pially a arly ag, day o 8 day. onvrg o a limi a 8 day. Similar rnd r nod (Zollingr al (D Shur & Tar Thr-poin bnding unnohd prim Rul imilar o ho mo ohr rarhr mm x 5 mm x 6 mm; pan 5 mm; r obrvd. onr agd bn day 8 day Th ar onn an b xprd a (Morri & Dux 5 Uing LEFM o ima fraur nrgy mn morar agd up o 8 h from mixing, hih uggd vapor, ha plai adorbd raking ar mn h non- Fraur nrgy h a vaporabl imad abou ar 73 N/m, (apillary a mauring h oal uion auming rak morar involv a ignifian zon plai raining or miroraking adjan o h rak ip. (hmially bound ar dph. n (Mil Panazopoulo & Mill 995. I i ra aum ha h vaporabl ar i a fu 98, nohing an b found onrning fraur nrgy. Evn a a rlaivly rn major inrnaional vry arly ag ar dribd in Dao al. (9. ha ar ruial h udy onr a h rlaiv humidiy, h, dgr hydraion dgr ilia fum raion,, i.. onfrn onrning arly-ag onr (Kovlr ag-dpndn orpion/dorpion al. 4, lil anion a paid o h xprimnal udy h voluion h ning bhavior. STRESS-SEPARATION RELATIONSHIPS (Norling Mjonll 997. Undr hi aum ubiuing Equaion ino Equai Th darh availabl liraur on h fraur bhavior arly-ag onr i prinipally h rul Variou modl, inluding linar, bi-linar non- obain diffiuli in h xprimnal drminaion linar funion (Hillrborg al. 976, Gopalaranam & Shah 985, Rinhard h 985, Foo al. h nil r-paraion urv arly-ag onr (Dao al. 9. Conqunly, a n ap- 986, Lia al. 99, h Karihaloo h995, Eli al. + ( D h & + & + parau xprimnal produr hav bn dvlopd a h Univriy Qunl (Dao 7, rlaionhip maur onr. Bad on h, hav bn propod h r-paraion hr hih hav nabld h ollion rliabl daa on modl maur onr /h i h lop h orpion/ on h arly-ag nil rngh fraur nrgi in (Dao al. iohrm (alo alld moiur apa h ompl nil r-diplamn bhavior govrning quaion (Equaion 3 mu b onr pimn a ag.5 h or mor afr 9 (Fig. 4, h folloing modl h ning bhavior onr a vry arly ag hav appropria boundary iniial ondii mixing. Th variaion h fraur nrgy ih h Th rlaion bn h amoun ag h nil rngh arly-ag onr ar bn dvlopd. In all a, b fi r obaind ar rlaiv humidiy i alld plod in Figur 3-4, rpivly. Ohr propri ordinary la-quar mhod. 8 6 /m 4 ( G F Mix Mix Mix 3 : :3 3: 4:3 6: 7:3 Ag (h Figur 3. Fraur nrgy vru ag onr. /m ( G F Mix Mix Mix Tnil rngh (kpa Figur 4. Fraur nrgy vru nil rngh onr. iohrm if maurd ih inraing humidiy dorpion iohrm in h a. Ngling hir diffrn (Xi al. h folloing, orpion iohrm ill b rfrn o boh orpion dorpion By h ay, if h hyri h iohrm ould b akn ino aoun, o rlaion, vaporabl ar v rlaiv humi b ud aording o h ign h varia Figur 5. Idalizd r-paraion rlaiviy humidiy. rlaionhip. Th hap h iohrm HPC i inflund many p pially ho ha influn xn. Linar modl hmial raion, in urn, drm Th ning funion ruur linar por iz r-paraion diribuion (arraio, i mn hmial ompoiion, SF bhavior (Fig. 5a uring im mhod, mpraur, mix.. In h liraur variou mulaio σ f found o drib h orpion (3 iohrm onr (Xi al Hovr, in h Th fraur nrgy papr h dfind mi-mpirial in Equaion xprion hu pro bom Norling Mjornll (997 i adopd b Proding FraMCoS-7, May 3-8,

4 D h T h (, f G ( d F σ (4 ( Th proporionaliy fiin D(h,T i alld moiur prmabiliy i i a nonlinar funion Th h rlaiv b-fi humidiy valu h obaind mpraur T h (Bažan daa plod & Najjar in 97. Figur Th 4 i moiur.3 mm, ma abou balan o ordr rquir magniud ha h variaion highr in han im ypial h ar valu ma bn pr uni. volum mm onr. mm (ar onn maur onr b qual (Hillrborg divrgn al h I moiur i, morovr, flux ignifianly mall- o h r han h valu abou 5 mm obaind from h xprimnal udy arly-ag onr Dao al. (Dao al. 9. Conqunly, h linar modl, ( hih i alo inonin ih h orrponding xprimnal Th ar r-paraion onn an b rlaionhip, xprd a i h inappropria h vaporabl onr ar vry arly ag. um (apillary ar, ar vapor, adorbd ar h non-vaporabl. (hmially Bi-linar modl bound ar n (Mill 966, Panazopoulo & Mill 995. I i raonabl o Th aum ning ha h funion vaporabl ar h bi-linar i a funion rparaion rlaiv humidiy, bhavior h, (Fig. dgr 5b i hydraion,, dgr ilia fum raion,, i.. (h,, ag-dpndn f f orpion/dorpion iohrm (5 (Norling Mjonll 997. Undr hi aumpion σ ( σ ubiuing Equaion ino Equaion on obain h σ ( σ σ + ( ( < & + & + & (6 n (3 h D h h hr Th fraur /h i nrgy h lop (Equaion h orpion/dorpion i hu iohrm (alo alld moiur apaiy. Th govrning quaion (Equaion 3 mu b ompld G ( f σ + σ ( + σ F appropria (7 boundary iniial ondiion. Th rlaion bn h amoun vaporabl ar Adoping rlaiv h xprimnally humidiy i drmind alld adorpion valu 5 iohrm mm (Dao if al. maurd 9 ih, h inraing b-fi valu rlaiviy humidiy ar.88 mm, dorpion.558 mm, iohrm.38 in mm h oppoi valu a. Ngling σ.f, hir.5f diffrn,.f (Xi rpivly. al. 994, Thi in rang h folloing, valu orpion σ i iohrm onin ill ih b ud boh ih h horial rfrn o modl boh orpion (Fig. 5b dorpion h xprimnal ondiion. r-paraion By h ay, if rlaionhip h hyri arly-ag h onr moiur obaind iohrm ould (Dao b akn al. 9. ino aoun, Obviouly, o hn diffrn σ qual rlaion, zro, vaporabl h modl ar bom v rlaiv linar humidiy, (Equaion mu 3 b ud 4. For aording valu o h ign σ grar h han variaion.5f, bom h rlaiviy vry humidiy. mall or vn Th ngaiv. hap h orpion iohrm Th rul HPC india i inflund ha h many bi-linar paramr, modl, hih pially ha ho h viru ha influn impliiy, xn an modl ra h h r-paraion hmial raion urv, uffiinly in urn, drmin auraly por praial ruur purpo. por iz diribuion (ar-o-mn raio, mn hmial ompoiion, SF onn, uring im mhod, mpraur, mix addiiv,.3.. Non-linar In h liraur modl variou mulaion an b A found numbr o drib non-linar h orpion funion iohrm h normal rparaion onr (Xi bhavior al (Fig. 5 Hovr, hav bn in h uggd prn (Gopalaranam papr h mi-mpirial & Shah 985, xprion Rinhard propod 985, Foo Norling al Mjornll Hr, (997 h folloing i adopd o bau non-linar i funion xpliily ar aoun invigad: h voluion hydraion raion SF onn. Thi orpion iohrm rad m f σ (8 ( h,, G (, + n ( g h σ f hr < n < (9 (4 ( g h K (, Combining Equaion 5 9 ih Equaion hil adoping h xprimnally drmind valu 5 mm (Dao al. 9, giv b-fi valu m n , rpivly. hr h fir rm (gl iohrm rprn h phyially bound (adorbd ar h ond Th lar i lo o h orrponding valu n rm (apillary iohrm rprn h apillary maur onr, hih rang bn..4 ar. Thi xprion i valid only lo onn (Rinhard 985. SF. Th fiin G rprn h amoun ar pr uni volum hld in h gl por a % rlaiv humidiy, i an b xprd (Norling 3 SUMMARY AND CONCLUSIONS Mjornll 997 a In hi papr, h fraur mhani onr ruur G (, ha k bn + brifly k rvid. Thi ha highlighd larly h limiaion h appliaion (5 vg vg fraur mhani o h arly-ag raking onr, hr dpi k vg i k vg uful ar marial appliaion paramr. in h From udy h maximum h fraur amoun bhavior ar maur pr uni onr. volum ha an fill Mahmaial all por (boh modl apillary por h r-paraion gl por, on rlaionhip an alula Karly-ag a on obain onr hav bn drivd bad on rn xprimnal daa onr a ag.5 h or mor afr mixing. I ha bn dmonrad ha g.88 no all + xiing. Gr-paraion rlaionhip maur onr ar appliabl o on- (6 K (, r a vry arly ag, h rvid modl g propod in hi papr hould b prfrrd. Th bilinar modl appar o b h b h hr modl Th invigad. marial paramr Hovr, furhr k vg ork k vg i bing g arrid b alibrad ou h auhor fiing xprimnal o oll mor daa daa rlvan r- o an fin fr h (vaporabl rvid r-paraion ar onn rlaionhip. in onr a variou ag (Di Luzio & Cuai 9b. REFERENCES. Tmpraur voluion No ha, a arly ag, in h hmial raion Bazan, Z.P.. Conr fraur modl: ing prai. aoiad Enginring ih mn Fraur hydraion Mhani/Fraur SF raion Conr Rok 69(: ar xohrmi, h mpraur fild i no unim Bazan, Z.P. 3. Rminin on four dad ruggl non-adiabai progr in ning ym damag vn if h iz nvironmnal ff. Conr ournal i (Tokyo onan. 4(: Ha 6-8. onduion an b mpraur Bazan, dribd Z.P. in & Oh, onr, B.H a Crak la b mpraur hory fraur no xding onr. C Marial (Bažan Sruur/Mariaux & Kaplan 996, Conruion 6(93: Fourir la, hih rad Dao, V.N.T. 7. Early-ag raking onr. Briban: Univriy Qunl, Auralia. Dao, q V.N.T. λ T al. 9. Tnil propri arly-ag onr. ACI Marial ournal 6(6: -. (7 D Shur, G. & Tar, L Fraur nrgy onr a hr q arly i ag. h Marial ha flux, Sruur/Mariaux T i h abolu mpraur, Conruion 3(: λ i h ha onduiviy; in hi Proding FraMCoS-7, May 3-8,

5 Elfgrn, L. (989. Fraur Mhani Conr Sruur: From Thory o Appliaion (Rpor h Thnial Commi 9-FMA Fraur Mhani o Conr - Appliaion. London: Chapman Hall. Eli, M. al.. Th ohiv zon modl: Advanag, limiaion hallng. Enginring Fraur Mhani 69(: Foo, R.M.L. al Crak groh rian urv in rain-ning marial. ournal h Mhani Phyi Solid 34(6: Gopalaranam, V.S. & Shah, S.P Sning rpon plain onr in dir nion. ACI ournal 8(3: Griffih, A. A. 9. Th phnomna rupur flo in olid. Philoophial Tranaion h Royal Soiy London Sri A : Hillrborg, A Rul hr omparaiv ri drmining h fraur nrgy G F onr. Marial Sruur/Mariaux Conruion 8(7: Hillrborg, A. al Analyi rak maion rak groh in onr man fraur mhani fini lmn. Cmn Conr Rarh 6(6: Hordijk, D.A. al Marial propri. In L. Elfgrn (d, Fraur Mhani Conr Sruur: From Thory o Appliaion (Rpor h Thnial Commi 9-FMA Fraur Mhani o Conr - Appliaion, London: Chapman Hall. Kaplan, M.F. 96. Crak propagaion h fraur onr. ournal h Amrian Conr Iniu 58(: Karihaloo, B.L Fraur Mhani Sruural Conr. Harlo: Longman. Kim,.-K. al. 4. Fraur hararii onr a arly ag. Cmn Conr Rarh 34(3: Kovlr, K. al. 4. Early ag onr-propri prman. Cmn Conr Compoi 6(5: Lia, B.M. al. 99. Improvd D ( h, T nonlinar h modl onr fraur. ournal Enginring Mhani 6(: Morri, P.H. & Dux, P.F. Th 5. proporionaliy Suion, fraur fiin nrgy, D(h,T plai raking moiur mn morar prmabiliy onr. ACI i i Ma-rial ournal (6: h rlaiv humidiy h mpraur nonlina Nvill, A.M. 959a. & Som Najjar ap 97. h Th rngh moiur onr ma balan - Par. Civil Enginring (London 54(639: ha h variaion in im h ar ma Nvill, A.M. 959b. Som ap h rngh onr - Par. Civil Enginring volum (London onr 54(64: (ar onn b q Nvill, A.M divrgn Som ap h h moiur rngh flux onr - Par 3. Civil Enginring (London 54(64: Orgaard, L. al. 4. Early-ag r-rak opning rlaionhip high prman onr. Cmn Con- r Compoi 6(5: Ouka, K. & Da, H.. Fraur pro zon in onr nion pimn. Enginring Th ar Fraur onn Mhani an b 65(: xprd a -3. h vaporabl ar (apillary a Pron, P.E. 98a. vapor, Fraur nrgy adorbd onr: ar Mhod h non- drminaion. Cmn Conr Rarh (: 79- (hmially bound ar 89. n (Mil Pron, P.E. 98b. Panazopoulo Fraur nrgy & Mill onr: 995. Praial I i ra prman aum xprimnal ha rul. h vaporabl Cmn ar Conr Rarh (: rlaiv 9-. humidiy, h, dgr hydraion i a fu Rinhard, H.W dgr Crak ning ilia fum zon in raion, plain onr, i.. undr ai loading. Cmn Conr Rarh 5(: ag-dpndn orpion/dorpion 4-5. RILEM ommi 4-CEA (Norling 98. Mjonll Propri 997. Undr onr hi a aum arly ag: Sa--h-ar ubiuing rpor. Marial Equaion Sruur/Mariaux obain Conruion 4(84: ino Equai Wimann, F.H. al Influn ag loading, armn raio ra loading on fraur nrgy onr. Marial Sruur/Mariaux h Conruion + ( D h & + & + (6: 3-. h h Zollingr, D.G. al Fraur oughn onr a arly ag. ACI Marial ournal 9(5: hr /h i h lop h orpion/ iohrm (alo alld moiur apa govrning quaion (Equaion 3 mu b appropria boundary iniial ondii Th rlaion bn h amoun ar rlaiv humidiy i alld iohrm if maurd ih inraing humidiy dorpion iohrm in h a. Ngling hir diffrn (Xi al. h folloing, orpion iohrm ill b rfrn o boh orpion dorpion By h ay, if h hyri h iohrm ould b akn ino aoun, o rlaion, vaporabl ar v rlaiv humi b ud aording o h ign h varia rlaiviy humidiy. Th hap h iohrm HPC i inflund many p pially ho ha influn xn hmial raion, in urn, drm ruur por iz diribuion (arraio, mn hmial ompoiion, SF uring im mhod, mpraur, mix.. In h liraur variou mulaio found o drib h orpion iohrm onr (Xi al Hovr, in h papr h mi-mpirial xprion pro Norling Mjornll (997 i adopd b Proding FraMCoS-7, May 3-8,