Experimental study on the flexural behaviour of fibre reinforced concretes strengthened with steel and macro-synthetic fibres

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1 Fratur Mhani o Conrt Conrt Strutur - Amnt, Durability, Monitorg Rtroittg o Conrt Strutur- B. H. Oh, t al. (d) 2 Kora Conrt Intitut, Soul, ISBN Exprimntal tudy on th lxural bhaviour o ibr rord onrt trngthnd ith tl maro-ynthti ibr N. Buratti, C. Mazzotti & M. Savoia DISTART Strutural ngrg, Univrity o Bologna, Bologna, Italy ABSTRACT: Fibr ar idly ud to improv th lxural toughn dutility o onrt, thy may vn limat th nd or onvntional rormnt. Stl ibr ar mor ommonly ud trutural appliation hil ynthti ibr ar mor otn ud to rdu rak opng du to hrkag. Maro-ynthti ibr hav bn dvlopd ith th aim o ratg an altrnativ to tl ibr trutural appliation but thir u i till limitd. Th prnt papr drib th rult o an xprimntal vtigation on th prorman o onrt pimn rord ith ithr tl or maro-ynthti ibr undr thr pot bndg. Tt rult r ud to alulat th paramtr o tr-rak opng rlation via vr analyi. INTRODUCTION Fibr Rord Conrt (FRC), obtad by addg tl or ynthti ibr to pla onrt, i bomg idly ud ivil ngrg bau o it avourabl proprti (Ahmad t al. 24). In partiular, th trodution o ibr giv to onrt a igniiant tnil ridual trngth th rakd pha rdu th rak propagation. Fibr ar alo ud to improv th lxural toughn dutility o onrt. FRC may ra th pd o ontrution may vn limat th nd or onvntional rormnt. Th haratriti o FRC dpnd on th proprti o th onrt matrix but motly on th typ, th amount th gomtry o th ibr; th paramtr, at, ontrol th bond btn ibr onrt. Noaday dirnt typ o ibr ar availabl to ngr. Stl-Fibr Rord Conrt (SFRC) ar idly ud a rang o trutural appliation uh a: trutural aad panl, dutrial loor, prat trutural lmnt, tunnl lg, t., gnral all tho appliation hih onrt rakg ontrol i important. Synthti ibr ar uually manuaturd mallr dimnion ith rpt to tl ibr mot typially ud dutrial loor to rdu rakg dud by hrkag. Rntly, Maro-Synthti Fibr Rord Conrt (MSFRC) hav bn dvlopd ith th aim o ubtitutg tl ibr trutural appliation but th lvl o knoldg on thir mhanial bhaviour i till limitd. Thi papr drib th rult o an xtniv xprimntal ampaign prormd at Laboratory o Strutural Engrg o th Univrity o Bologna. In thi ampaign vral onrt bam r atd ug a onrt rord ith dirnt typ amount o tl maro-ynthti ibr r ttd a thr-pot bndg hm. All th bam hr atd ug th am onrt mix dign. Th mix ompoition a dd a prlimary xprimntal ampaign, ordr to hav th dird tnil trngth. Data obtad durg th tt r ud to alibrat th paramtr o a tr rakopng rlation by man o an vr analyi produr. 2 DESCRIPTION OF THE EXPERIMENTAL CAMPAIGN Th ollog tion drib th mot important atur o th xprimntal ampaign. All th tt dribd thi papr r prormd ollog th guidl givn by EN 465:25 EN 4845: Rrn onrt Th mhanial proprti o th onrt ud th prnt tudy r agrmnt ith th prription o EN 4845:26, hih pii our typ o rrn onrt ith givn lxural tnil trngth, maximum iz o th aggrgat maximum mnt ontnt. In gnral, th rrn onrt hould b ltd aordg to th typ o produt or ytm hih th ibr i to b applid, hovr th tard rquir ibr manuaturr to dlar th prorman o thir produt on o th aormntiond our mix hih thror bom matory or thi raon it a ud th prnt ork. Thi mix mut hav lxural tnil trngth o 4.3 ±.3 MPa, a thr-pot bndg tt. In ordr to obta a mix ith th rquird lxural

2 Tabl. Mix dign o th rrn onrt. Componnt Unit Amount Cmnt kg/m S (-2 mm) kg/m S (-5 mm) kg/m Gravl (8-5 mm) kg/m Gravl (5-22 mm) kg/m Watr l/m Suprplatiizr l/m tnil trngth om prlimary tt r prormd, hih pimn atd ug tlv dirnt mix dign r ttd a thr-pot bndg hm. Th mix r haratrizd by thr dirnt valu o atr/mnt ratio by our dirnt typ o aggrgat. Thi pha o th tudy ld to th dition o th rrn onrt mix ith th dird lxural tnil trngth. Tabl giv th mix dign Figur giv th aggrgat gradg. Aggrgat, mnt, atr/mnt ratio r hon ollog th guidl givn by EN 4845: Tt mthod Th tt produr adoptd i onitnt ith th guidl givn by EN 465:25 EN 4845:26, aordg to hih (hight idth lngth) mm 3 primati pimn ar to b ttd th thr-pot bndg hm hih i hon Figur 2. Th pimn r nothd at mid-pan (th hight o th noth i 25 mm), ordr to ontrol th triggrg o th rak. Th pimn r urd mould, undr polythyln htg, or 24 h atr atg thn dmouldd urd or urthr 26 day undr atr at 2 C. At th nd o th urg priod, th pimn r prpard or th tt ttd 28 day atr atg. Th tt haratrizd th tnil bhaviour o ibr rord onrt trm o om ridual lxural-tnil-trngth valu. Th valu ar dtrmd rom th load-crak Mouth Opng Diplamnt (CMOD) th lattr bg maurd by a omga diplamnt trur ( Figur 2). Th ttg mah oprat undr diplamnt ontrol ith a ontant rat o diplamnt (CMOD or dltion), ha uit t to avoid untabl zon th load-cmod urv. Durg th tt, th rat o ra o th CMOD a ontrolld:.5 mm/m or CMOD. mm.2 mm/m or CMOD >. mm. All th tt r trmatd at CMOD 4 mm. Figur 3 ho a gnri or-cmod urv obtad rom bam tt. Th or-cmod urv i haratrizd by a numbr o rrn pot: th load at th limit o proportionality, F L, hih i dd a th maximum load J D ( or h, CMOD T ) h.5 mm, F, F 2, F 3, F 4, hih aordg to EN465:25 ar dd a th load valu Th at proportionality CMOD.5 mm, oit CMOD D(h,T).5 mm, CMOD moitur 2.5 mm prmability CMOD 3.5 it i mm, a nonla rptivly. o th rlativ humidity h tmpratur & Najjar 972). Th moitur ma balan that th variation tim o th atr ma volum o onrt (atr ontnt ) b q divrgn o th moitur lux J t J Th atr ontnt an b xprd a o th vaporabl atr (apillary a vapor, adorbd atr) th non- (hmially bound) atr n (Mil Pantazopoulo & Mill 995). It i ra aum that th vaporabl atr i a u Figur. Aggrgat gradg rlativ or humidity, th rrn h, onrt. dgr Dahd o hydration l diat th boundari dgr o th ilia rrn um gradg ration, givn, by i.. EN 4845:26. ag-dpndnt orption/dorption (Norlg Mjonll 997). Undr thi aum by ubtitutg Equation to Equati obta t h & + & + hr / i th lop o th orption/ iothrm (alo alld moitur apa govrng quation (Equation 3) mut b Figur 2. Shmati rprntation o th xprimntal t-up. by appropriat boundary itial onditi Th rlation btn th amount o atr rlativ humidity i alld iothrm i maurd ith rag humidity dorption iothrm th a. Ngltg thir dirn (Xi t al. th ollog, orption iothrm ill b rrn to both orption dorption By th ay, i th hytri o th iothrm ould b takn to aount, to rlation, vaporabl atr v rlativ humi b ud aordg to th ign o th varia Figur 3. Qualitativ rprntation o a or-crak Mouth Opng Diplamnt rlativity (CMOD) humidity. urv dition Th hap o om o th important pot on iothrm urv. or HPC i lund by many p pially tho that lun xtnt Th rult o hmial th tt ar ration otn xprd, alo turn, dtrm trm o lxural trutur tnil tr; por onvntionally iz ditribution ob-(atrtad by aumg ratio, a lar mnt tr hmial ditribution ompoition, ovr SF th mid-pan ro urg tion, tim i.., σ mthod, M W, tmpratur, hr M mix i th mid-pan bndg t.). In momnt th litratur W variou i th tion modulu o ound th nothd to drib tion. th Th orption lxural iothrm ormulatio tnil trngth drivd onrt rom (Xi Ft L i al. namd 994). Hovr, t, L, th th ridual lxural papr tnil th mi-mpirial trngth drivd xprion rom pro F, F 2, F 3, F 4 ar Norlg namd,, Mjornll 2, 3, (997) 4. i adoptd b Prodg o FraMCoS-7, May 23-28, 2

3 2.3 J D ( Exprimntal h, T ) h program () In th prnt ork our dirnt typ o ibr r ud: Th thr proportionality dirnt maro-ynthti oit D(h,T) ibr i a alld tl ibr. moitur Figur prmability 4 ho th ibr it i ud a nonlar Tabl untion 2 giv dtail o th rlativ on thir humidity gomtry h (lngth, tmpratur l, diamtr, T (Bažant d ) & Najjar on thir 972). mhanial Th moitur proprti ma (lati balan modulu, rquir E, that th tnil variation trngth, tim t ). o th atr ma pr unit volum o onrt (atr ontnt ) b qual to th Tabl divrgn 2. Spiiation o th moitur o th ibr lux J ud th prnt ork (data providd by th manuaturr). Typ Cod l d l /d E t J (2) t mm mm GPa MPa Stl Th atr SFB ontnt 5 an b 5 xprd 2 a th um Synthti o th vaporabl MSB 54 atr (apillary - atr, atr vapor, adorbd atr) th non-vaporabl Synthti (hmially MS2B bound) 4.83 atr 48.3 n (Mill , Pantazopoulo & Mill 995). It i raonabl to Synthti MS3B aum that th vaporabl atr i a untion o rlativ humidity, h, dgr o hydration,, Tabl dgr 3. Fibr o ilia ontnt um th ration, pimn onidrd., i.. (h,, ) Mix od ag-dpndnt Fibr od orption/dorption Amount Volum o iothrm ibr (Norlg Mjonll 997). Undr thi aumption kg/m 3 % by ubtitutg Equation to Equation 2 on MSB_2 obta MSB 2.22 MSB_4_8 MSB MS2B ( D h) 5 & +.37 & + & n (3) t h MS2B_ MS2B.74 hr / MS3B i th lop 2 o th orption/dorption.22 iothrm (alo alld moitur apaity). Th MS3B govrng quation (Equation 3) mut b ompltd SFB_2 by appropriat SFB boundary 2 itial.26 ondition. Th rlation btn th amount o vaporabl SFB_35 SFB atr rlativ humidity i alld adorption iothrm i maurd ith rag rlativity humidity To dirnt dorption doag r iothrm ud or ah th oppoit typ o ibr. a. Ngltg Morovr, or thir ah dirn ibr-doag (Xi t ombation al. 994), vn th ollog, bam r orption atd iothrm ttd ill a b thr-pot ud ith bndg rrn hm. to both To orption ub (5 dorption x 5 mm) ondition. on yldr By th (5 ay, x i 3 th mm) hytri hr atd o th a ll moitur ud iothrm to maur ould th b ompriv takn to aount, trngth to th dirnt lati modulu rlation, o vaporabl th ibr rord atr v onrt, rlativ humidity, rptivly. mut b Giv ud aordg th doag, to th trm ign o o ma th variation pr ubi o mtr th rlativity o volum humidity. prntag, Th onidrd hap o or th ah orption typ o iothrm ibr. Tho or HPC doag i lund r ltd by many paramtr, ordr to b rprntativ, pially tho or that ah lun typ o xtnt ibr, o th rat doag o th uggtd hmial by ration th manuaturr, turn, o dtrm th maximum por doag trutur rommndd por iz to ditribution kp a good (atr-to-mnt orkability o th ratio, rh mnt onrt, hmial rptivly. ompoition, SF ontnt, urg In th tim ollog, mthod, th ombation tmpratur, doag-typ mix additiv, o ibr t.). ill In th b diatd litratur by variou th od ormulation givn th an irt b olumn ound to o drib Tabl 3. All th th orption pimn iothrm r o at normal ug th onrt onrt (Xi mix t al. givn 994). Tabl Hovr,, ith th th prnt xption papr o th th mi-mpirial uprplatiizr xprion hih ah propod a a by adjutd Norlg Mjornll ordr to obta (997) a lump i adoptd valu o bau 5-7 m. it 3 xpliitly RESULTS aount OF THE or EXPERIMENTAL th volution CAMPAIGN o hydration ration SF ontnt. Thi orption iothrm Thi rad tion drib th rult obtad durg th xprimntal ampaign. 3. ( hfrh,, onrt ) G ( proprti, ) + ( g ) h In ordr to ompar th mhanial proprti o (4) th dirnt ibr rord onrt onidrd, th tability o th proprti o th ( gonrt matrix ) h among K (, ) dirnt bath i xtrmly important. A antiipatd Stion 2., th rrn onrt a dd aordg to EN 4845:26. Durg th atg pro, om hr proprti th irt o trm th rh (gl iothrm) onrt r rprnt maurd: th lump phyially (Abram bound on), (adorbd) hydration atr tmpratur, th ond ma. trm (apillary iothrm) rprnt th apillary atr. Thi xprion i valid only or lo ontnt o SF. Th oit G rprnt th amount o atr pr unit volum hld th gl por at % rlativ humidity, it an b xprd (Norlg Mjornll 997) a G (, ) k + k vg vg (5) hr k vg k vg ar matrial paramtr. From th maximum amount o atr pr unit volum that an ill all por (both apillary por gl por), on an alulat K Figur 4. Fibr ud a on obta th prnt tudy. Tabl 4. Proprti o th rh onrt maurd durg th g atg o th dirnt t o pimn G Mix od Additiv Slump Hydration t. Dnity l/m 3 m C kg/m 3 (6) K (, ) g MSB_ MSB_ MS2B_ Th matrial 3.4 paramtr 5 k23.6 vg k vg 2445 g an b alibratd 3.4 by ittg 5 xprimntal 23.3 data 2448* rlvant to r (vaporabl) 3.38 atr 5 ontnt * onrt at variou ag 3.38 (Di Luzio 3 & Cuati b). 2426* SFB_ *; SFB_ Tmpratur 2.7 volution ; 2466* * Not With that, ibr at arly ag, th hmial ration Tabl aoiatd 5. Elati ith modulu mnt man hydration ompriv SF trngth, ration R m, maurd ar xothrmi, or pimn th tmpratur o th dirnt ild t. i not uniorm Mix or od non-adiabati ytm Elati vn i th modulu nvironmntal R m tmpratur i ontant. MPa Hat ondution MPa an b MSB_2 dribd onrt, at lat or 5.2 tmpratur not xdg C (Bažant & Kaplan 996), by MSB_4_ Fourir la, hih rad MS2B_ q λ T (7) hr q i th hat lux, T i th abolut SFB_2-4.6 tmpratur, λ i th hat ondutivity; thi SFB_ Prodg o FraMCoS-7, May 23-28, 2

4 Th o obtad valu ar litd Tabl 4 ho vry littl variability among th dirnt bath. R [MPa] Exprimntal data Man valu MSB MS2B MS3B SFB MSB_2 MSB_4_8 MS2B_ Figur 5. Conrt ompriv trngth. Figur 6. St SFB_2: or CMOD urv. Th dahd l diat th or-cmod urv or a pla-onrt pimn. For om o th ibr rord onrt, th orkability a alo maurd ug th Vb tt, hih gav rult o about 2 ond. Th proprti o th rh onrt r tabl among all th at. 3.2 Mhanial proprti o th onrt For ah ibr rord onrt mix, to ub (5 x 5 mm) hr atd, atr 28 day o atr urg, thy r ttd to obta th ompriv trngth. All th pimn, ith th xption o tho rom th MSB_2 t, gav vry imilar valu o ompriv trngth ( Figur 5), ith a man valu o 42.2 MPa a oit o variation o.3. Th lati modulu o th rord onrt a maurd a ll; it valu ar givn Tabl 5, togthr ith th ompriv trngth. Aordgly to th rult obtad th ompriv tt, th onrt o th MSB_2 t had an lati modulu highr than avrag. 3.3 Rult o thr pot bndg tt A prviouly tatd, load CMOD valu r maurd ah tt. A an xampl, Figur 6 ho th urv obtad or th pimn o th t SFB_2 (tl ibr) a or-cmod urv or a plaonrt pimn ttd durg th onrt-mix dition pha (dahd l). SFB_2 SFB_35 A idly knon, J D ( th h, T ) addition h o ibr to onrt do not igniiantly ra th tnil trngth, but gratly nhan th Th onrt proportionality toughn. oit It i orth D(h,T) moitur prmability it i a nonla o th rlativ humidity h tmpratur & Najjar 972). Th moitur ma balan that th variation tim o th atr ma volum o onrt (atr ontnt ) b q divrgn o th moitur lux J t,l [MPa] MS MS2 MS3 SF MSB_2.22%) MSB_4_8 (V.53%).37%) MS2B_ (V.74%).22%%).52%) SFB_2.26%) SFB_35.45%) 3 & + & + Figur 8. Flxural tnil trngth t at th h limit o proportional- ity (MS: Maro-Synthti ibr; SF: Stl Fibr). t,l / t,l.5.5 MS MS2 MS3 SF MSB_2 (V.22%) MSB_4_8.53%) t J Th atr ontnt an b xprd a o th vaporabl atr (apillary a Figur 7. St : vapor, or-cmod adorbd urv. atr) th non- (hmially bound) atr n (Mil 7 Pantazopoulo & Mill 995). It i ra aum that th vaporabl atr i a u rlativ humidity, h, dgr o hydration dgr o ilia um ration,, i.. ag-dpndnt orption/dorption (Norlg Mjonll 997). Undr thi aum by ubtitutg Equation to Equati obta.37%) MS2B_ (V.74%).22%%) (V.52%) SFB_2 (V.26%) SFB_35 (V.45%) hr / i th lop o th orption/ iothrm (alo alld moitur apa govrng quation (Equation 3) mut b by appropriat boundary itial onditi Th rlation btn th amount o atr rlativ humidity i alld iothrm i maurd ith rag humidity dorption iothrm th a. Ngltg thir dirn (Xi t al. th ollog, orption iothrm ill b rrn to both orption dorption Figur 9. Normalizd lxural tnil trngth at limit o proportionality (MS: Maro-Synthti ibr; SF: Stl Fibr). By th ay, i th hytri o th iothrm ould b takn to aount, to rlation, vaporabl atr v rlativ humi notg that th attr o th or-cmod urv i b ud aordg to th ign o th varia uually igniiant: a it ill b diud th ollog, thi irumtan, unavoidabl ug th tt rlativity humidity. Th hap o th iothrm or HPC i lund by many p mthod prribd by EN 465:25, i maly du pially tho that lun xtnt to th variability o th numbr o ibr rog th hmial ration, turn, dtrm rak. Th diprion o rult thr-pot bndg trutur por iz ditribution (atrratio, mnt hmial ompoition, SF bam tt trongly dpnd on th typ amount o ibr; a an xampl, Figur 7, ho th orurg tim mthod, tmpratur, mix CMOD urv or th pimn o th t t.). In th litratur variou ormulatio (maro-ynthti ibr). Comparg Figur 6 ith ound to drib th orption iothrm Figur 7 it an b aily n that th attr o th xprimntal rult th pot-pk rgion i muh onrt (Xi t al. 994). Hovr, th papr th mi-mpirial xprion pro mallr or th pimn ith th MS ibr than or Norlg Mjornll (997) i adoptd b th SF pimn. Prodg o FraMCoS-7, May 23-28, 2

5 J In D ( th h, T ) ollog, h th rult o th tt ill () b givn mor oni orm ordr to allo a bttr omparion Th proportionality among th prorman oit D(h,T) o th i dirnt alld ibr moitur rord prmability onrt. Figur it i a 8 nonlar ho th untion lxural tnil o th rlativ trngth humidity at th limit h o tmpratur proportionality, T (Bažant t,l, or & Najjar th dirnt 972). pimn. Th moitur Gray ma dot balan diat rquir atual data that th pot, variation thik blak tim l o th atr avrag ma valu, pr unit th volum blak o l onrt th ± (atr σ trval. ontnt ) It i b orth qual notg to th that divrgn th maurd o th moitur valu o lux t,l J ar quit lo thir avrag valu all to th trval 4.3 ±.3 MPa a rquird by EN 4845-:26. A prviouly obrvd Jtrm o omprivtrngth lati (2) t modulu, th pimn o th t MSB_2 had lightly bttr Th mhanial atr ontnt proprti an b alo xprd trm o a th t,l. um o In th ordr vaporabl to allo atr a bttr omparion btn th (apillary atr, atr rult, vapor, th t adorbd o variability atr) o th mhanial non-vaporabl proprti (hmially o th onrt hav bn rdud by normalizg th bound) atr n (Mill 966, Pantazopoulo t,l valu & ith rpt to th lxural tnil trngth valu, Mill 995). It i raonabl to aum that th t,l, vaporabl prditd by atr th quation i a untion propod o by rlativ Modl humidity, Cod 9, h, hih dgr i a o untion hydration, o th ompriv, dgr o trngth ilia um ( Tabl ration, 5 or ompriv trngth, i.. (h,, ) valu ag-dpndnt obtad th orption/dorption prnt ork). iothrm (Norlg Figur Mjonll 9 ho 997). th normalizd Undr thi aumption lxural tnil trngth by ubtitutg valu. It Equation i not poibl to to Equation d any 2 trnd on btn obta thi mhanial paramtr th ibr amount. Thi onirm that th ibr do not ra th onrt tnil trngth; on th ontrary an xiv amount o ibr may dra thi trngth, & + & + & n (3) a a onqun t ho a rdution o orkability. Th ridual lxural tnil trngth valu (, 2, 3, 4 ) hav bn ompard a ll. Thy hav hr / i th lop o th orption/dorption bn normalizd ith rpt to th lxural tnil iothrm trngth, (alo alld moitur apaity). Th t,l ar rportd Figur. It an b govrng quation (Equation 3) mut b ompltd obrvd by appropriat that th boundary ridual trngth itial o th ondition. t ontag tl Th ibr rlation (SF) btn ar uually th highr amount than o tho vaporabl o th bam atr ontag rlativ maro-ynthti humidity i ibr alld (MSB, adorption MS2B, iothrm MS3B). i Th maurd rlativ trngth ith rag o th dirnt rlativity t o humidity bam do not dorption igniiantly iothrm hang rom th oppoit to 4, i.. a. or Ngltg rag thir valu dirn o CMOD. (Xi Obviouly, t al. 994), th ridual th ollog, trngth orption i highr iothrm hn a highr ill b amount ud ith o ibr rrn i addd to both to th orption onrt mix. dorption ondition. By Th th attr ay, o i th th trngth hytri valu o i highr th moitur or tl ibr iothrm rord ould onrt, b takn to a prviouly aount, to antiipatd. dirnt Thi rlation, diprion vaporabl i du atr to iz v rlativ o th pimn humidity, rotion, mut b ud hih aordg i mall to th ith ign rpt o th to variation th amount o th o ibr rlativity ( Stion humidity. 3.4). Th hap o th orption Figur iothrm or ho HPC a i plot lund o th man by many normalizd paramtr, ridual pially trngth tho at that variou lun rak xtnt opng rat or o ah th t. hmial It larly ration hon that, th prorman turn, dtrm o th tl por ibr trutur ar uually por bttr iz ditribution than tho o (atr-to-mnt ynthti ibr. Nvrthl ratio, mnt hmial dign problm ompoition, haratriti SF ontnt, valu ar urg ommonly tim ud mthod, tad tmpratur, o man valu. mix additiv, Th haratriti t.). In th litratur valu tak variou to aount ormulation alo th an diprion b ound to o drib th xprimntal th orption data, iothrm thror o normal i th haratriti onrt (Xi t ridual al. 994). trngth Hovr, o th dirnt th prnt t ar papr ompard, th mi-mpirial a don xprion Figur 2, propod th bnit by givn Norlg by th Mjornll tl ibr (997) i rdud. i adoptd bau it xpliitly Fally, aount or ah or pimn th volution th toughn o hydration dx a ration alulatd SF a ll. ontnt. S Thi data orption or th pla iothrm onrt rad pimn r availabl (olltd durg th prlimary pha), th toughn dx a aumd a th ratio o th ara undr th or-cmod urv ( h,, ) G (, ) +.5 MS MS2 ( gms3 ) h SF / t,l MSB_2 (V.22%) MSB_4_8.53%).37%) MS2B_ (V.74%).22%%) (V.52%) SFB_2.26%) SFB_35.45%).5 hr th irt trm (gl iothrm) rprnt th phyially bound (adorbd) atr th ond trm (apillary iothrm) rprnt th apillary atr..5 Thi xprion i valid only or lo ontnt o SF. Th oit MS MS2 G MS3 SF rprnt th amount o atr pr unit volum hld th gl por at % rlativ humidity, it an b xprd (Norlg Mjornll 997) a 2 / t,l.5 G, k + k vg vg MSB_2.22%) MSB_4_8.53%) (V.37%) MS2B_ (V.74%).22%%).52%) SFB_2.26%) SFB_35 (V.45%) hr k vg k vg ar matrial paramtr. From th maximum.5 amount o atr pr unit volum that an MS MS2 MS3 SF ill all por (both apillary por gl por), on an alulat K a on obta 3 / t,l g G.5 (6) K (, ) g Th.5 matrial paramtr k vg k vg g MS MS2 MS3 SF an b alibratd by ittg xprimntal data rlvant to r (vaporabl) atr ontnt onrt at variou ag (Di Luzio & Cuati 29b). 4 / t,l MSB_2.22%) MSB_4_8.53%) (V.37%) MS2B_ (V.74%).22%%).52%) SFB_2.26%) SFB_35 (V.45%) 2.2 Tmpratur.5 volution Not that, at arly ag, th hmial ration aoiatd ith mnt hydration SF ration ar xothrmi, th tmpratur ild i not uniorm Figur. From top to bottom, normalizd ridual trngth or non-adiabati ytm vn i th nvironmntal at: CMOD.5 mm; CMOD.5 mm; CMOD 2.5 mm; tmpratur i ontant. Hat ondution an b CMOD 3.5 mm. dribd onrt, at lat or tmpratur not or xdg th ibr C rord (Bažant pimn & Kaplan ovr th ara 996), undr by th Fourir am la, urv hih or rad th pla onrt pimn (Gopalaratnam & Gttu, 995). Dirnt pla onrt pimn manuaturd rom th rrn mix (7) q λ T r ttd thror th avrag valu o th ara hr undr q i thir th or-cmod hat lux, urv T i a th ud. abolut Th valu o th toughn dx ar hon Figur 3. MSB_2.22%) ( g ) h K (, ) ( ) MSB_4_8.53%) (V.37%) MS2B_ (V.74%).22%%).52%) SFB_2.26%) SFB_35 (V.45%) (4) (5) tmpratur, λ i th hat ondutivity; thi Prodg o FraMCoS-7, May 23-28, 2

6 / i t,l MSB_2 MSB_4_8 MS2B_ SFB_2 SFB_ CMOD [mm] Figur. Avrag trngth at dirnt CMOD valu or th t o pimn ith dirnt typ amount o ibr. / i t,l MSB_2 MSB_4_8 MS2B_ SFB_2 SFB_ CMOD [mm] Figur 2. Charatriti trngth at dirnt CMOD valu or th t o pimn ith dirnt typ amount o ibr. Toughn dx MS MS2 MS3 SF MS_2.22%) MS_4.8 (V.53%) MS2_5.37%) Figur 3. Toughn dx. MS2_.74%) MS3_2 (V.22%%) MS3_4.8.52%) SF_2.26%) SF_35 (V.45%) Th ditribution o th valu o th toughn dx i vry imilar ith that o th ridual trngth. It i orth notg that th addition o ibr to onrt an ra it toughn rom 5 to tim. 3.4 Corrlation btn ridual trngth numbr o ibr To bttr undrt th raon o th high attr o th rult obtad or om typ o ibr, th numbr o ibr rog th rak r dtrmd. Whn CMOD rad ovr 4 mm, th trur r rmovd rom t,l / t,l.5 J ) D h T h MSB: R 2 (,.3 MS3B: R 2. MS2B: R 2.6 SFB: R 2.7 Th proportionality oit D(h,T) moitur prmability it i a nonla o th rlativ humidity h tmpratur & Najjar 972). Th moitur ma balan that th variation tim o th atr ma volum o onrt (atr ontnt ) b q divrgn o th moitur lux J Total numbr J o ibr t Figur 4. Corrlation among normalizd trngth at th limit o proportionality th total numbr o ibr th rak propagation ura. Th atr ontnt an b xprd a o th vaporabl atr (apillary a th pimn to prrv vapor, thir tgrity adorbd atr) thn th tt th non- a arrid out until (hmially th pimn bound) tor apart. atr Th ibr n (Mil on th to a o Pantazopoulo th rak r & thn Mill ountd 995). ditguihg btn brokn aum ibr that th pulld-out vaporabl ibr. atr i a u It i ra Th ro-tion rlativ o th humidity, pimn a h, dgr dividd o to hydration thr horizontal zon dgr ith o qual ilia hight um ration, th numbr, i.. o ibr a ountd ag-dpndnt ah o thm. Th orption/dorption data r thn ud to d (Norlg a orrlation Mjonll btn 997). ah Undr ridual thi aum trngth valu by th ubtitutg numbr o ibr Equation ah zon to o Equati th ro tion. For obta th ak o brvity, hr only th orrlation ith th total numbr o ibr i onidrd. Figur 4 giv th normalizd t,l valu vru th total numbr o ibr. Th ymbol rprnt obrva- tional data hil th l rprnt th rult o lar & + & + t h rgrion analyi. Thi plot onirm that ibr hav littl lun on hr lxural tnil / i trngth. th lop In partiular o th orption/ th oit o iothrm dtrmation (alo R 2, alld ho valu moitur ar apa givn th lgnd, govrng i vry quation lo to (Equation or all th 3) t mut b o pimn. by appropriat boundary itial onditi On th ontrary, Th ridual rlation trngth, btn, th..., amount 4 ar o trongly orrlatd atr ith th numbr rlativ o ibr. humidity Figur i 5, alld ho lxural trngth iothrm valu at i dirnt maurd CMOD ith valu rag vru th total numbr humidity o ibr. dorption Th valu o iothrm R 2 ar th givn th lgnd. a. Obviouly, Ngltg th thir lop dirn o th l (Xi t al. dpnd on th trngth th ollog, o th ibr orption thror iothrm i ill b highr a ar a tl rrn ibr ar to both onrnd. orption Thi orrlation xpla th By high th variability ay, i o th th hytri rult. In o th dorption at, Figur 6 ho iothrm ould total numbr takn o to ibr aount, or to all th pimn rlation, onidrd vaporabl th prnt atr tudy v rlativ humi ho that th ± σ b ud trval aordg ar id to th or tl ign o ibr th varia ror onrt rlativity pimn. humidity. Furthrmor, Th th trval hap o th or th to doag iothrm onidrd or ar HPC trongly i lund ovrlappd. by many p On th ontrary, pially a ar a tho maro-ynthti that lun ibr xtnt ar onrnd, th hmial ± σ trval ration orrpondg, to turn, th dtrm to doag onidrd trutur th prnt por iz tudy ditribution ar uu-(atrally non-ovrlappg. ratio, mnt hmial ompoition, SF Th ditribution urg o ibr tim th mid-pan mthod, tion tmpratur, obviouly dpnd on t.). ibr In doag, th litratur ibr gomtry variou ormulatio mix pimn iz (Sorouhian, ound to drib 99): thror orption th grat iothrm diprion o rult onrt an b (Xi aud t al. by 994). th at Hovr, that th th iz o th pimn papr th i too mi-mpirial mall ith rpt xprion to pro th doag o ibr Norlg to Mjornll thir dimnion. (997) i adoptd b Prodg o FraMCoS-7, May 23-28, 2

7 J ) D ( 4 h, T h MSB: R 2.5 MS3B: R 2.2 () MS2B: R 2.53 SFB: R 2.69 Th 3 proportionality oit D(h,T) i alld moitur prmability it i a nonlar untion o th 2 rlativ humidity h tmpratur T (Bažant & Najjar 972). Th moitur ma balan rquir that th variation tim o th atr ma pr unit volum o onrt (atr ontnt ) b qual to th divrgn o th moitur lux J [MPa] a) 5 5 Total numbr o ibr J t 4 MSB: R 2.62 MS3B: R 2.29 MS2B: R 2.83 SFB: R [MPa] 3 [MPa] [MPa] (2) Th atr ontnt an b xprd a th um o th vaporabl atr (apillary atr, atr vapor, adorbd atr) th non-vaporabl 2 (hmially bound) atr n (Mill 966, Pantazopoulo & Mill 995). It i raonabl to aum that th vaporabl atr i a untion o rlativ humidity, h, dgr o hydration, b), dgr o ilia um 5 ration,, i.. (h,5, ) ag-dpndnt Total orption/dorption numbr o ibr iothrm (Norlg 4 Mjonll 997). Undr thi aumption by ubtitutg MSB: Equation R 2.65 to Equation MS3B: R on MS2B: R 2.84 SFB: R 2.7 obta + t ( D h) n (3) h & + & + hr / i th lop o th orption/dorption ) iothrm (alo alld moitur apaity). Th 5 5 govrng quation Total (Equation numbr o 3) ibr mut b ompltd by appropriat boundary itial ondition. 4 Th rlation MSB: btn R 2.67 th amount MS3B: o vaporabl R 2.3 atr rlativ MS2B: humidity R 2.82 i alld SFB: adorption R iothrm i maurd ith rag rlativity humidity dorption iothrm th oppoit a. 2Ngltg thir dirn (Xi t al. 994), th ollog, orption iothrm ill b ud ith rrn to both orption dorption ondition. By th ay, i th hytri o th moitur iothrm ould b takn to aount, to dirnt d) rlation, vaporabl 5atr v rlativ humidity, 5 mut Total numbr o ibr b ud aordg to th ign o th variation o th Figur 5. Corrlation among ridual trngth at dirnt CMOD rlativity valu humidity. th total Th numbr hap o ibr o th th orption rakd ura. iothrm or HPC i lund by many paramtr, pially tho that lun xtnt rat o th hmial ration, turn, dtrm por 4 trutur STRESS CRACK-OPENING por iz ditribution RELATIONS (atr-to-mnt ratio, mnt hmial ompoition, SF ontnt, Data urg obtad tim rom mthod, xprimntal tmpratur, th tt mix r additiv, ud to t.). d, In th or litratur ah typ variou amount ormulation o ibr, th an paramtr ound to o drib a tr-rak th orption opng iothrm ontitutiv o normal dia- b gram. onrt Invr (Xi t analyi al. 994). a Hovr, ud to obta th uh prnt paramtr. papr th In mi-mpirial th ollog th xprion adoptd modl propod th by obtad Norlg ontitutiv Mjornll (997) bhaviour i ill adoptd b dribd. bau it & xpliitly 25 aount or th volution o hydration ration SF ontnt. Thi orption iothrm rad MS MS2 MS3 SF 2 Numbr o ibr 5 MSB_2.22%) MSB_4_8.53%) (V.37%) MS2B_ (V.74%) 5 ( h,, ) G (, ) + ( g ) h (V.22%%).52%) SFB_2.26%) ( g ) h K (, ) SFB_35 (V.45%) (4) Figur hr 6. th Total irt numbr trm o (gl ibr iothrm) rak rprnt propagation tion o th pimn. th phyially bound (adorbd) atr th ond trm (apillary iothrm) rprnt th apillary 4. atr. Modl Thi xprion i valid only or lo ontnt o SF. Th oit G rprnt th amount o Many atr pr modl unit dribg volum hld th mhanial th gl por bhaviour at % o rlativ FRC bhaviour humidity, ith it dirnt an b dgr xprd o auray (Norlg Mjornll omplxity 997) a an b ound th litratur. In th prnt ork, a impliid modl ha bn adoptd, ordr to hav a mor dirt a poibl onntion btn G (, th ) kxprimntal + k rult obtad rom (5) th vg vg tt pimn tho rquird or th dign o ibr rord trutural lmnt. In at, th CMOD-tr hr k vg rlationhip k vg ar matrial i not paramtr. a ontitutiv From rlationhip, th maximum i.. amount i not o an atr tri pr proprty unit volum o th that matrial, an ill all th por rlationhip (both apillary obtad por through gl por), vr on analyi an alulat dpnd K on a th on modl obta ltd. Th rakd hg modl ud th prnt ork ha bn propod by Oln g(2) drib th bndg ailur G o a FRC bam by th dvlopmnt o a ititiou rak. Th bai ida (6) o K (, ) th rakd hg i to modl th portion o th g bam lo to th propagatg rak a a layr ontitutd by horizontal trip, attahd at th to nd to rigid Th matrial boundari paramtr hih an k vg rotat. k vg Th trip g an ar thn b alibratd modlld by a ittg dpndnt xprimntal prg data lmnt rlvant ith to non r lar (vaporabl) ontitutiv atr bhaviour. ontnt With onrt thi approah, variou th ag diturban (Di Luzio & o Cuati th tra 29b). ild, aud by at th prn o th rak, i ond to tak pla btn th rigid boundari. Th to rigid boundari may tranlat rotat, o ontitutg a non 2.2 Tmpratur volution lar Not that, prg at arly hih ag, an b jod th hmial ith unrakd ration bam aoiatd modlld ith aordg mnt hydration to th laial SF bam ration thory. ar xothrmi, Th ontitutiv th tmpratur rlation o ild th prg i not uniorm layr i th or am non-adiabati a that o ytm th FRC. vn Oln i th nvironmntal modl u a bilar tmpratur tr-rak i ontant. opng Hat rlation, ondution hon an b Figur dribd 7 to drib onrt, th at prg lat layr or tmpratur bhaviour. not xdg C (Bažant & Kaplan 996), by Fourir la, hih rad 4.2 Invr analyi ormulation Th q vr λ T analyi produr ha bn ud (7) ordr to d th valu o th paramtr dg th tr-rak opng rlation - t, σ( ), hr q i th hat lux, T i th abolut 2 ( Figur 7) - that togthr ith th Oln tmpratur, λ i th hat ondutivity; thi modl, allo to bt r-produ th tt rult. Th Prodg o FraMCoS-7, May 23-28, 2

8 σ() t σ( ) σ(4 mm) Figur 7. Str-rak opng rlation ud th Oln modl (Oln, 2). lngth o th non-lar hg hould b onidrd a ittg paramtr or th alulation bau, gnral, it dpnd on th typ o trutural lmnt. In th prnt ork, aordg to Oln (2) RILEM TC 62-TDF (22), it a aumd that th lngth o th hg i.5 tim it hight; thi lattr paramtr i t qual to th nt tion hight. Th optimal valu o th aormntiond paramtr r dtrmd ug Matlab optimization algorithm. Th objtiv untion to b mimizd by th algorithm a dd a a ightd um o th quard ridual btn xprimntal numrial rult at om CMOD opng valu. In partiular th valu onidrd ar: th ara undr th or-cmod diagram th trval.5 < CMOD < 4 mm, th or at limit o proportionality th ridual trngth at CMOD valu o.5,.,.2,.5,.5, 2.5, 3.5 mm. 4.3 Rult o th vr analyi Tabl 6 giv, or ah t o pimn, th avrag valu th oit o variation o th paramtr valu obtad rom th vr analyi. S th tt r toppd at CMOD 4 mm, to mak lar th limit o validity o th rult, th lxural tnil tr at 4 mm, σ (4 mm), i givn tad o 2 ; thi lattr paramtr a alay igniiantly gratr than 4 mm. Invr analyi a ud on all th xprimntal rult, obtag gnral a good auray o th rult. In partiular, th tr-rak opng rlation obtad produ or-cmod diagram providg good approximation o all th xprimntal diagram trm o all th maur onidrd th optimization pro. Th math o numrial diagram ith xprimntal on i or th urv portion traight atr th pak: th tpr th urv th lor th math. Error th prdition o Oln modl, alulatd a rlativ dirn among xprimntal numrial valu, ar vry lo a ar a th or at limit o proportionality 2 Tabl 6. Man valu J D oit ( h, T ) h o variation o th paramtr o th tr-rak opng rlation ( Figur 7) obtad by vr analyi. Mix od Th proportionality t σ ( ) oit σ (4 mm) D(h,T) MSB_2 Man moitur.7 prmability it i a nonla o th rlativ humidity h tmpratur COV & Najjar 972). Th moitur ma balan MSB_4_8 Man that th variation tim o th atr ma COV volum o onrt (atr ontnt ) b q Man divrgn o th.29 moitur.29 lux J COV MS2B_ Man J COV.8 t Man COV.6 Th atr.3 ontnt.38 an.75 b xprd a Man o.7 th vaporabl atr.59 (apillary a COV vapor,.36.2 adorbd.22 atr).27 th non- SFB_2 Man (hmially bound).6 atr.6 n (Mil Pantazopoulo & Mill 995). It i ra COV aum that th vaporabl atr i a u SFB_35 Man rlativ humidity, h, dgr o hydration COV dgr o ilia um ration,, i.. ag-dpndnt orption/dorption 5 (Norlg Mjonll 997). Undr thi aum Tt data by ubtitutg Equation to Equati Modl obta F [kn] 5 t h & + & + hr / i th lop o th orption/.5 iothrm.5 2(alo 2.5 alld moitur 4 apa CMOD [mm] govrng quation (Equation 3) mut b Figur 8. Comparion btn an xprimntal or-cmod urv that obtad by atr appropriat th vr boundary analyi. itial onditi Th rlation btn th amount o (l than 2%) atr th ara undr rlativ th humidity diagram i (l alld than %) ar onrnd iothrm hil i maurd thy ar gratr ith rag trm o ridual humidity trngth: 5% dorption on avrag iothrm or th 5% on avrag a. or Ngltg 2, 3, thir 4. A dirn an xampl, (Xi t al. Figur 8 ho th a omparion ollog, orption btn th iothrm numri-ilal th xprimntal rrn or to both orption CMOD diagram dorption b or on pimn By o th th t ay, namd i SFB_35. th hytri In thi o th a th modl giv iothrm vry ould good b prdition takn to pially th lattr rlation, part o vaporabl th urv. atr For vry v rlativ lo humi aount, to rak opng valu b ud th aordg auray to o th ign rult o th i varia lor. Th auray rlativity might humidity. b rad Th by hap ug o th mor omplx or-rak iothrm or opng HPC rlation. i lund by many p pially tho that lun xtnt hmial ration, turn, dtrm 5 CONCLUSIONS trutur por iz ditribution (atrratio, mnt hmial ompoition, SF Th prnt ork urg vtigatd tim th mthod, lxural tmpratur, bhaviour mix o nothd bam t.). mad In o th onrt litratur ibr-rord variou ormulatio ith dirnt typ ound to amount drib o th ibr. orption Stl iothrm ibr hod gnrally onrt bttr (Xi prorman t al. 994). than Hovr, maroynthti ibr but papr ith th a gratr mi-mpirial attr o xprion or- pro th CMOD urv. Norlg Mjornll (997) i adoptd b Prodg o FraMCoS-7, May 23-28, 2

9 J Th D ( xprimntal h, T ) h data r ud a put or () vr analyi hih lad to th optimal bilar tr-rak Th proportionality opng rlation oit to b D(h,T) ud ith i alld Oln moitur modl prmability ordr to rprodu it i a nonlar th xprimntal untion bhaviour o th rlativ o th humidity bam. h tmpratur T (Bažant & Najjar 972). Th moitur ma balan rquir that th variation tim o th atr ma pr unit ACKNOWLEDGEMENTS volum o onrt (atr ontnt ) b qual to th divrgn o th moitur lux J Fanial upport o th Thnial Conortium o tl ibr produr i gratully aknoldgd. J (2) t REFERENCES Th atr ontnt an b xprd a th um o th vaporabl atr (apillary atr, atr Ahmad, A. Di Prio, M. Myr, C. Plizzari, G.A. & Shah, S.P. vapor, adorbd atr) th non-vaporabl 24. Fibr rord onrt: rom thory to prati, (hmially Brgamo, 24 - bound) 25 Sptmbr. atr n (Mill 966, Pantazopoulo & Mill 995). It i raonabl to aum that th vaporabl atr i a untion o rlativ humidity, h, dgr o hydration,, dgr o ilia um ration,, i.. (h,, ) ag-dpndnt orption/dorption iothrm (Norlg Mjonll 997). Undr thi aumption by ubtitutg Equation to Equation 2 on obta + t ( D h) n (3) h & + & + hr / i th lop o th orption/dorption iothrm (alo alld moitur apaity). Th govrng quation (Equation 3) mut b ompltd by appropriat boundary itial ondition. Th rlation btn th amount o vaporabl atr rlativ humidity i alld adorption iothrm i maurd ith rag rlativity humidity dorption iothrm th oppoit a. Ngltg thir dirn (Xi t al. 994), th ollog, orption iothrm ill b ud ith rrn to both orption dorption ondition. By th ay, i th hytri o th moitur iothrm ould b takn to aount, to dirnt rlation, vaporabl atr v rlativ humidity, mut b ud aordg to th ign o th variation o th rlativity humidity. Th hap o th orption iothrm or HPC i lund by many paramtr, pially tho that lun xtnt rat o th hmial ration, turn, dtrm por trutur por iz ditribution (atr-to-mnt ratio, mnt hmial ompoition, SF ontnt, urg tim mthod, tmpratur, mix additiv, t.). In th litratur variou ormulation an b ound to drib th orption iothrm o normal onrt (Xi t al. 994). Hovr, th prnt papr th mi-mpirial xprion propod by Norlg Mjornll (997) i adoptd bau it & D xpliitly Olivira aount Soua, J.L.A. or & th Gttu, volution R. 26. Dtrmg o hydration th ration tnil tr-rak SF ontnt. opng urv Thi o orption onrt by iothrm vr rad Analyi. Journal o Engrg Mhani 32(2): EN 465: Tt mthod or mtalli ibrd onrt - Maurg th lxural tnil trngth (limit o proportionality (LOP), ridual). EN 4845: Tt mthod or ibr onrt. ( h Gopalaratnam,,, ) G ( V.S.& Gttu,, ) R On th haratrization o lxural toughn ibr rord ( g onrt. ) h Cmnt Conrt Compoit 7(3): (4) Oln, J.F. 2. Fitiou rak propagation ibrrord onrt bam. Journal o Engrg M- ( g ) h K (, ) hani 27(3): RILEM TC 62-TDF 22. Tt dign mthod or tl ibr rord onrt. Dign o tl ibr rord onrt ug th σ- mthod: pripl appliation. hr th irt trm (gl iothrm) rprnt th Matrial Strutur 35(5): Sorouhian, phyially P. bound & L, (adorbd) C.-D. 99. Ditribution atr th ortation ond trm o ibr (apillary tl iothrm) ibr rord rprnt onrt. th ACI apillary Matrial atr. Journal Thi 87(5): xprion i valid only or lo ontnt o SF. Th oit G rprnt th amount o atr pr unit volum hld th gl por at % rlativ humidity, it an b xprd (Norlg Mjornll 997) a G (, ) k + k vg vg (5) hr k vg k vg ar matrial paramtr. From th maximum amount o atr pr unit volum that an ill all por (both apillary por gl por), on an alulat K a on obta K (, ) g G g (6) Th matrial paramtr k vg k vg g an b alibratd by ittg xprimntal data rlvant to r (vaporabl) atr ontnt onrt at variou ag (Di Luzio & Cuati 29b). 2.2 Tmpratur volution Not that, at arly ag, th hmial ration aoiatd ith mnt hydration SF ration ar xothrmi, th tmpratur ild i not uniorm or non-adiabati ytm vn i th nvironmntal tmpratur i ontant. Hat ondution an b dribd onrt, at lat or tmpratur not xdg C (Bažant & Kaplan 996), by Fourir la, hih rad q λ T (7) hr q i th hat lux, T i th abolut tmpratur, λ i th hat ondutivity; thi Prodg o FraMCoS-7, May 23-28, 2