Fratur Mhani Conrt Conrt Strutur - Amnt, Durability, Monirg Rtrittg Conrt Strutur- B. H. Oh, t al. (d) 200 Kora Conrt Intitut, Soul, ISBN 978-89-5708-8-5 Covr rakg RC olumn ubjtd rformnt orroion undr utad load S. Jabbour Halall Aoiat Limitd, Univrity Ottaa, Canada B. Martín-Pérz Univrity Ottaa, Ontario, Canada ABSTRACT: Thi papr prnt rult an xprimntal tudy hr irular pirally-rford onrt olumn r ubjtd alratd orroion hil utag a ontant rvi ompriv load. To typ pimn r ud xprimntal program: typ CV, hr vrtial rformnt a orrodd iolatd from non-onfg piral rformnt, typ CS hr piral rformnt a orrodd iolatd from vrtial rformnt tudy fft onfmnt. Th rakg itiation, pattrn, idng onrt ovr r monird for tn month, rlation obtad btn rak idng propagation lati hortng olumn tl ma lo r tablihd. Th rakg pattrn a found b idr form longitudal rak along vrtial bar typ CV olumn, but mor rom ditributd ovr urfa not a id typ CS olumn. INTRODUCTION On major au dtrioration North Amrian rford onrt (RC) fratrutur day i orroion rformnt. Th xtniv u d-ig alt on highay tr tim brg onrt urfa an xiv upply hlorid ion, hih pntrat onrt ovr vntually dtroy paiv layr that prott rformnt from orroion. Th brak-don thi paiv layr, hih i a film that form around rformnt du high alkality onrt rdu orroion ngligibl lvl, lad itiation orroion pro. Th aumulation orroion produt around rformnt rult xpaniv for hih, on y xd tnil trngth onrt ovr, lad rakg onrt urfa. Th rakg onrt ovr itiat a dgradation pro that orn ith propagation orroion vntually lad furr dtrioration form dlamation pallg onrt ovr. Th ma orroion-dud damag mhanim RC ar: (i) dra rformnt ro-tional ara, (ii) poibl lo tl dutility, (iii) rakg pallg onrt ovr, (iv) lo bond along tl/onrt trfa. Thr ha bn an rag ffort rnt yar quantify damag progr RC du advan tl rformnt orroion. Partiularly, quantifyg onrt rakg propagation ith rpt rformnt orroion propagation i grat rlvan rviability amnt dtrioratd RC trutur ith orrodd rformnt, it mut b ludd timation ridual rvi lif (Andrad &Alono 996, Liu & Wyr 998). Thr hav bn limitd tudi on fft rformnt orroion on rviability trutural prforman RC olumn (L t al. 2000, Rodriguz t al. 996, Sai t al. 2007). A major obrvation from tudi i that load arryg apaity orrodd olumn i lor than that non-orrodd olumn. Thi rdution ritan apaity i attributd : (a) ra load ntriity du unvn orroion longitudal rformnt; (b) buklg longitudal rforg bar hn olumn ti ar orrodd;, () atual dtrioration onrt tion du rakg, pallg /or dlamation onrt ovr. Hovr, non abov tudi r ondutd on RC olumn that r ubjtd utad axial load rformnt orroion imultanouly. Thi papr prnt rult an xprimntal program hih tn RC irular olumn r ubjtd alratd rformnt orroion hil utag -rvi load. Th objtiv thi rarh a vtigat imultanou fft
-rvi J = D ( h, T ) load h orroion-dud damag () on RC olumn rviability. To that nd, rak itiation Th proportionality propagation a fit ll a longitudal D(h,T) i alld irumfrntial moitur prmability dformation it r i a nonlar monird funtion durg ttg. rlativ humidity h tmpratur T (Bažant & Najjar 972). Th moitur ma balan rquir that variation tim atr ma pr unit 2 volum EXPERIMENTAL onrt (atr PROGRAM ontnt ) b qual divrgn moitur flux J 2. Tt pimn Th RC olumn pimn ud thi tudy onit = J (2) a t 260-mm diamtr irular ro-tion rford ith 6-5M longitudal bar (φ = 6.0 mm) Th 0M atr piral ontnt (φ =.3 an mm). b xprd Th onrt a ovr um piral vaporabl rformnt atr a (apillary 20 mm. atr, Th rotion vapor, adorbd olumn atr) i illutratd non-vaporabl Figur. Th atr ompriv (hmially trngth bound) atr onrt ud n (Mill dign 966, a Pantazopoulo 25 MPa, & Mill tl 995). yild It trngth i raonabl ud a 400 aum MPa. that To typ vaporabl olumn atr dign i a r funtion ud rlativ xprimntal humidity, vtigation, h, dgr ith hydration, fiv pimn, dgr ah typ ilia bg fum built. ration, Th diffrn, i.. = btn (h,, ) to = dign ag-dpndnt a pag orption/dorption piral rformnt, (Norlg hih Mjonll a pifid 997). Undr 220 thi mm aumption for typ CV iorm olumn, by ubtitutg 80 Equation mm for typ CS olumn, Equation rptivly. obta Th diffrn piral pith allod vti- 2 on gatg fft onfmnt on bhaviour orrodd olumn. Figur 2 ho rformnt h ag ud + ( DRC h) pimn. = & + & + & n (3) h t h hr /h i lop orption/dorption iorm (alo alld moitur apaity). Th govrng quation (Equation 3) mut b ompltd by appropriat boundary itial ondition. Th rlation btn amount vaporabl atr rlativ humidity i alld adorption iorm if maurd ith rag rlativity Figur humidity. Dtail dorption RC olumn iorm ro-tion. oppoit a. Ngltg ir diffrn (Xi t al. 994), follog, orption iorm ill b ud ith rfrn both orption dorption ondition. By ay, if hytri moitur iorm ould b takn aount, to diffrnt rlation, vaporabl atr v rlativ humidity, mut b ud aordg ign variation rlativity humidity. Th hap orption iorm for HPC i flund by many paramtr, pially tho that flun xtnt rat hmial ration, turn, dtrm por trutur por iz ditribution (atr--mnt ratio, mnt hmial ompoition, SF ontnt, urg tim mthod, tmpratur, mix additiv, t.). In litratur variou formulation an b found drib orption iorm normal Figur 2. Rformnt ag ud RC olumn. onrt (Xi t al. 994). Hovr, prnt papr mi-mpirial xprion propod by Column nd r furr onfd ith tlvmm thik tl ollar, ordr limit Norlg Mjornll (997) i adoptd bau it damag propagation xpliitly aount middl for zon volution olumn hydration tad ration at anhorag SF ontnt. rgion. Thi Eah orption ap plat iorm had four rad 300-mm long anhor bnt at ir nd allo appliation ntri loadg through ap plat futur ttg. High-trngth non-hrk grout a ud for a dpth 50 mm at both nd ( h,, ) = G (, ) + olumn mak ur olumn r fully adhrd ir ap at atg. Th tl ap 0( g ) h a ll (4) a or tl aori r all patd ith zbad prottiv oatg 0( ordr g mimiz ) h K (, ) propagation orroion outid olumn rformnt. S onrt proprti ar ruial dtrmg hr rat firt natur trm (gl futur iorm) propagation rprnt orroion phyially bound amount (adorbd) orroion-du atr rakg, ond trm matrial (apillary quantiti iorm) proprti rprnt apillary onrt mix atr. ud Thi xprion xprimntal i valid ork only for r lo arfully ontnt xamd. SF. Th Th fit onrt G mix rprnt dign a amount didd bad atr on pr to unit ma volum onpt: hld (i) a gl pratial por at raliti 00% onrt rlativ humidity, ompriv trngth it an b a xprd ud rprnt (Norlg a Mjornll ral lif 997) ituation, a (ii) a rlativly high atr ontnt a ud ra onrt poroity prmability, hih allod it at a an fftiv ltrolyt vgmdium vgdurg alratd orro- G (, ) = k + k (5) ion mhanim. Th onrt mix dign ud i prntd hr k Tabl. Th atr-mnt ratio thi vg k vg ar matrial paramtr. From mix maximum a 0.75, amount 20mm atr aggrgat pr unit r volum ud, that an antiipatd fill all por onrt (both apillary ompriv por trngth gl por), f a on 25 MPa. an alulat 3% hlorid K a by on ma obta mnt a addd onrt mix ordr dpaivat rformnt itiat orroion pro. 0 g 0.88 + 0.22 G Tabl. Conrt 0 mix dign. Matrial kg/m 3 (6) K (, ) = Cmnt 0 275 g Watr 205 Coar aggr. 992 Th matrial paramtr k vg k vg g an F aggr. 838 b alibratd by fittg xprimntal data rlvant Total fr (vaporabl) atr 230 ontnt onrt at variou ag (Di Luzio & Cuati 2009b). A onrt a mixd at Univrity Ottaa Conrt Laborary, a tal 5 bath 0.2 2.2 Tmpratur m 3 ah r volution produd, from hih tard onrt Not that, yldr at arly ampl ag, r takn hmial for omprion aoiatd tt. ith Th mnt avrag hydration onrt ompriv SF ration ration trngth ar xormi, at 7 28 tmpratur day obtad fild r i 2 not MPa uniform 27 for MPa, non-adiabati rptivly. ytm vn if nvironmntal tmpratur In addition i ontant. onrt Hat ompriv ondution trngth an b tt, dribd high-trngth onrt, non-hrk at lat for grout tmpratur ud not p xdg botm 00 C tl (Bažant ap a & alo Kaplan ttd. At 996), ah by Fourir 5 onrt la, hih atg, rad atg grout ok pla bfor onrt atg at botm yldr q = λ T aftr onrt atg at p yldr. Stard ub ampl r takn (7) at ah grout atg ttd omprion at 7 28 hr day. q Th i avrag hat ompriv flux, T i trngth abolut grout tmpratur, i 53 MPa. Figur λ i 3 ho hat ondutivity; formork ud thi prodution olumn pimn. Prodg FraMCoS-7, May 23-28, 200
J = D (load h, T ) h 220 kn on ah oltal axial omprion umn. Thi load rprnt 30 40% dign axial apaity Th olumn, imulatgfit -rvi D(h,T) proportionality ondition. moitur prmability it i a nonla rlativ humidity h tmpratur & Najjar 972). 2.3 Alratd orroion tup Th moitur ma balan that variation tim atr ma In ordr du orroion on (atr rformnt, volum onrt ontnt ) b q olumn r ltrially onntdfluxj a divrgn moitur Figur 3. Formork ud prodution olumn. Figur 4. RC olumn pimn aftr formork rmoval. Curg a ahivd by ug moit burlap fabri, hih turn r rappd ith plati ht mimiz vaporation. Th pimn r prayd ith atr at lat on pr day ordr nur uffit moit ondition for hydration. Th urg rgim latd for 4 day aftr formork rmoval. Figur 4 ho fal olumn ith p botm tl ap. 2.2 Sutad loadg tup To 332 332 38-mm tl plat plad at p botm nd onntd ith four 25-mm diamtr tl rod r ud kp olumn undr a utad axial omprion load. Th olumn itlf a mountd btn to tl plat ith a ntral high-trngth 6-mm thik irular tl plat, hih a fully ldd quar plat but not ldd olumn ap plat, ordr imulat an axial p onntion. By ubjtg four tl rod a tnil for, RC olumn r ubjtd a ontant axial ompriv load. Th tnion tl rod ud apply load r alo patd ith a orroion ritant primr. A tnion for 55 kn a applid at ah rod, ith a PGSTAT00 potntiotat. A ontant anodi urrnt dnity a imprd on tl rforg bar, tl = Jht (25-mm id by hil four tal t 400-mm long) r plad dirtly at olumn xtrior rvg a ountr-ltrod. Th tal Th atr ontnt an b xprd a tl ht rplad durg atg on t (apillary a vaporabl atr onrt urfa nur ontat. rvapor, optimum adorbd atr) Th non- forg bar r onntd ltrial ir (hmially bound) atr n (Mil potntiotatpantazopoulo by man & ldd r ith Mill 995). It i ra nut ovrd ithaum ltrial tap limit fft that vaporabl atr i a fu orroion at nitiv pot. Th onnrlativ humidity, h, dgr hydration tion r alo z-pat oatd for maximum prodgr ilia fum ration,, i.. = ttion. Th pimn r furr xpod t= ag-dpndnt orption/dorption tg dryg yl tad ompltly bg (Norlg Mjonll 997).a Undr thi aum immrd atr, ordr nur uffit by ubtitutg Equation Equati upply moitur oxygn for ltrohmiobta al ration. Th t-dry yl r applid at ontant tim trval ith a pump that prayd a h tr through a prforatd ho plad around ol & + & + ( D h ) = + h umn. h t Thr out fiv CV pimn (pimn CV, CV2, CV3) had ir piral rformnt rformnt /h i lop orption/ iolatd from hr vrtial ug tmiorm (alo alldurrnt moitur pratur hrk tub, ltrial a apa govrng quation (Equation 3) mut b applid longitudal rformnt. For by appropriat boundary itial rmag to pimn undr ri, on onditi Th rlation btn orroamount olumn (pimn CVG) undrnt gnral atr rlativ humidity i alld ion ntir rformnt ag, hil or iorm if maurd ith rag on rvd a ontrol (or unorrodd) pimn. humidity dorption iorm Similarly for CS ri, thr olumn (pi- th Ngltg ir diffrnr(xi t al. mn CS, CS2, a. CS3) had ir longitudal follog, orption iorm formnt iolatd from piral rformntill b rfrn both orption ug ltri tap, ltrial urrnt adorption apby ay, if hytri plid rformnt ud for onfmnt. iorm ould b orroion takn aount, to Spimn CSG undrnt gnral rlation, vaporabl atr v rlativ humi ntir rformnt ag, rmag on b ud aordg ignfigur varia rvd a ontrol pimn for thi ri. rlativity humidity. Th hap 2 ho ho vrtial rformnt a ltri- iorm forrformnt HPC i flund by many p ally iolatd from piral by ovrpially tho that flun xtnt g longitudal rforg bar ith tap at ontat pot. hmial ration, turn, dtrm trutur por izthat ditribution Th PGSTAT00 i a potntiotat imulat (atrratio, hmial ompoition, SF an ltrohmial ll mnt ith thr ma ltrod: urg tim mthod, tmpratur, orkg ltrod onntd rforg mix In litratur variou formulatio tl, ountr t.). ltrod onntd tal found drib orption iorm tl ht, rfrn ltrod that maonrt (Xi t al.ltrial 994). Hovr, ur potntial. Galvani-ll urrnt th papr mi-mpirial xprion pro maurmnt r alo takn by potniotat Norlg Mjornll (997) i adoptd b ordr monir orroion rat RC olumn Prodg FraMCoS-7, May 23-28, 200
J = D ( h, T ) Th h urrnt dnity applid on () pimn. pimn rangd btn 280 35 µa/m2. Th dniti fit ar muh highr tho Thurrnt proportionality D(h,T)than i alld rordd fild (Rodriguz t al. 2000); homoitur prmability it i a nonlar funtion vr, du a rta lvltmpratur damag T(Bažant a rla y rlativ humidity h tivly hort priod tim. Figur 5 ho to & Najjar 972). Th moitur ma balan rquir pimn ir fal tup undr load ubthat variation tim atr ma pr unit jtd orroion. In thi volumalratd onrt (atr ontnt ) bfigur, qualorro ion tag, appard divrgn hih moitur flux5 J day aftr itiation alratd orroion pro, an alrady b obrvd at om xitg hrkag (2) = on J onrt urfa. rak t Th atr ontnt an b xprd a um vaporabl atr (apillary atr, atr vapor, adorbd atr) non-vaporabl (hmially bound) atr n (Mill 966, Pantazopoulo & Mill 995). It i raonabl aum that vaporabl atr i a funtion rlativ humidity, h, dgr hydration,, dgr ilia fum ration,, i.. =(h,,) = ag-dpndnt orption/dorption iorm (Norlg Mjonll 997). Undr thi aumption by ubtitutg Equation Equation 2 on obta Figur 5. Fal load alratd orroion tup. h + ( D h ) = n h h t &+ & + & (3) hr /h i lop orption/dorption iorm (alo alld moitur apaity). Th govrng quation (Equation 3) mut b ompltd by appropriat boundary itial ondition. Th rlation btn amount vaporabl atr rlativ humidity i alld adorption iorm if maurd ith rag rlativity humidity dorption iorm oppoit a. Ngltg ir diffrn (Xi t al. 994), follog, orption iorm ill b ud ith rfrn both orption dorption ondition. Figur 6. Eltrod LVDT xprimntal ytm. By ay, if hytri moitur iorm ould b takn aount, to diffrnt rlation, vaporabl atr v rlativ humidity, mut 2.4 Stra & dformation b ud aordg ign variation Stra gaug r plad on tl tnion rod rlativity humidity. Th hap orption ordr monir omprion load applid iorm for HPC i flund by many paramtr, olumn. Eah four rod had to tra pially tho that flun xtnt rat gaug attahd at it ntr, ith a tal 8 tra hmial ration, turn, dtrm por gaug radg. In addition, thr LVDT r ud trutur por iz ditribution (atr--mnt monir dformation olumn. To ratio, mnt hmial ompoition, SF ontnt, LVDT r ud vrtially maur tal urg tim mthod, tmpratur, mix additiv, hortng olumn a a rult omprt.). In litratur variou formulation an b iv load, rmag LVDT a ud horifound drib orption iorm normal zontally at olumn mid-hight (plad at an xponrt (Xi t al. 994). Hovr, prnt abl irular th mtal ht rappd around papr mi-mpirial xprion propod by olumn) maur irumfrntial xpanion. Norlg6 Mjornll i adoptd bauhoit Figur ho (997) ltrod, prforatd Prodg FraMCoS-7, May 23-28, 200 xpliitly aount for tra volution hydration ud pray atr, gaug, rationon SF olumn ontnt.pimn. Thi orption iorm LVDT an RC rad Stra dformation maurmnt r takn at approximatly vry thr k ith a dataaquiition tar. Aftr alibration tra radg takn at tl rod, it a dtrmd (ha, tra G (, )730 0 + -6 55 that orrpond, ) =radg h r0(g )a load kn tnion load on tl rod. Th (4) for adjutd aftr maurmnt kp it )h 0(g ontant at 55 kn at ah rod. K ( ), 3 EXPERIMENTAL RESULTS hr firt trm (gl iorm) rprnt ond trm (apillary iorm) rprnt apillary Crakg onrt ovr RC olumn atr. Thi xprion i valid only for lo ontnt a monird ovr ttg priod. On rak SF. Th fit G rprnt amount g a viually obrvd, rak idth r maatr pr unit volum hld gl por at 00% urd vry to month ug fdr blad rt. rlativ humidity, it an b xprd (Norlg Th firt round ttg latd for 0 month, it Mjornll 997) a ludd appliation alratd orroion on phyially bound (adorbd) atr 3. Crak propagation ovr tim olumn pimn CVG, CV, CSV, CS. Th + k latd ond ) = k ttg G (, round only 4 month, (5)it vg vg ludd olumn pimn CV2, CV3, CS2, CS3. Thrfor, data for pimn CVG, CV, kgo paramtr. hr kvg CS vg ar CSV, upmatrial 0 month, hilfrom data for maximum amount atr volum pimn CV2, CV3, CS2,pr unit CS3 go that up an 4 fill all por (both apillary por gl por), on month. on obta aninalulat a CV, olumnktyp motly longitudal rakg along vrtial rformnt a obrvd. On or h, olumn typ CS, pat g rakg + orrpondd trn that a obrvd that G mallr mor attrd rak along piral r (6) K ( ) = Thi a xptd ltrial formnt. g vrtial urrnt a applid only rfor mnt for olumn CV, hil ltrial urrnt ath applid onlyparamtr piral kvg forgolan matrial kvgrformnt umn CS. Exption olumn CVG CSG, b alibratd by fittgr xprimntal data rlvant hih ntir rformnt ag a ubjtd fr (vaporabl) atr ontnt onrt at an ltrial variou ag (Diurrnt. Luzio & Cuati 2009b). Corroion damag tartd bom viibl ard nd ond k ttg for all 2.2 Tmpratur volution olumn pimn. All pimn hod itial diolourg at rom potaro ration onrt Not that, at arly ag, hmial ovr urfa, orroion gl lakg through xaoiatd ithith mnt hydration SF ration itg rak void onrt. ar xormi, tmpratur fild itoard not uniform third k ttg, all olumn pimn tartd for non-adiabati ytm vn if nvironmntal ho hairl rak. Spimn typ CV hod tmpratur i ontant. Hat ondution an b longitudal hairl rakg along loadribd vrtial onrt, at lat for tmpratur not tion 00 C vrtial(bažant rformnt. By ond xdg & Kaplan 996), by month, rak had an opng btn 0.083 Fourir la, hih rad mm 0.4 mm id. Figur 7 plot ra q =longitudal rak idth ovr tim for olumn λ T (7) CV. Th figur ho avrag rak idth maurd for ah pimn. Crak idth maurhr atqara i that appard hat flux, T pallg i orabolut mnt b almot tmpratur, λ i hat ondutivity; thi pallg r idr than mm ar not ludd 0 0 0.88 0.22, 0
Figur 7. A obrvd from figur, although all pimn xprd an ra rak idth ovr tim, pimn CVG, ho rformnt ag a all ubjtd alratd orroion, diplayd highr valu rak idth aftr 0 month xpour. Longitudal Crak Width (mm). 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0. 0.0 CVG CV CV2 CV3 0 2 4 6 8 0 Tim (Month) Figur 7. Longitudal rakg idth ovr tim olumn typ CV. Latral Crak Width (mm)... 0.5 0.0 0.05 0.00 CSG CS CS2 CS3 0 2 4 6 8 0 Tim (Month) Figur 8. Latral rakg idth ovr tim olumn typ CS. Spimn typ CS hod mor hairl rak gog latrally attrd at variou pot aro onrt ovr. Although rak r ontuouly lakg orroion rut produt, y r o mall diffiult maur until about ond month ttg. Toard that tim, it bam poibl rt 0.038 mm fdr blad mot rak. Figur 8 ho ra latral rak idth ovr tim for olumn CS. Figur 8 plot avrag rak idth obtad for pimn CSG CS for a priod 0 month for pimn CS2 CS3 for a priod 4 month. A hon figur, latral rak ar a lot l id than vrtial rak obrvd olumn typ CV: J = D ( 0.083 h, T ) mm h a rordd a maximum latral rak idth for olumn typ CS a oppod 0.72 Th mm proportionality a maximum fit longitudal rak idth moitur for olumn prmability typ CV. Figur it i a nonla 9 D(h,T) ho typial urfa rakg rlativ humidity a obrvd h tmpratur to lo-up pho & Najjar a longitudal 972). Th moitur rak at ma olumn CV takn that 0 variation month, tim om latral atr ma balan rak at olumn volum CS3 takn onrt at 4 month. (atr ontnt ) b q divrgn moitur flux J t = J Th atr ontnt an b xprd a vaporabl atr (apillary a vapor, adorbd atr) non- (hmially bound) atr n (Mil Pantazopoulo & Mill 995). It i ra aum that vaporabl atr i a fu rlativ humidity, h, dgr hydration dgr ilia fum ration,, i.. = = ag-dpndnt orption/dorption (Norlg Mjonll 997). Undr thi aum Figur 9. Covr urfa by rakg ubtitutg (longitudal). Equation Equati obta 3.2 Corroion dud damag h S onrt rakg i + partly ( Ddu h) = rut & + formation produd by oxidation rfor- & + h t h mnt, rakg propagation i onidrd b dirtly rlatd hr lo /h i rformnt lop ro orption/ tion. Th tl iorm ma lo (alo M du alld rformnt moitur apa orroion i rlatd govrng ltrial quation urrnt (Equation I through 3) mut b Faraday la a follo: by appropriat boundary itial onditi Th rlation btn amount I t A M = atr rlativ humidity i alld [g] iorm if maurd ith rag () z F humidity dorption iorm th a. Ngltg ir diffrn (Xi t al. hr, I = urrnt (A); t = tim (); A = ami follog, orption iorm ill b ight (55.85 g/mol); z = valny, hih qual 2; rfrn both orption dorption F = Faraday ontant (96500 oulomb/quivalnt ma). By ubtitutg orro- By ay, if hytri iorm ould b takn aount, to ion urrnt dnity i (ltrial urrnt pr urfa ara rbar) rlation, Equation vaporabl, diamtr atr rdution v rlativ humi x(t) rforg b ud bar aordg aftr tim t an ign b alulatd from: varia rlativity humidity. Th hap iorm for HPC i flund by many p pially tho that flun xtnt A x() t = i t z F ρ hmial ration, turn, (2) dtrm trutur por iz ditribution (atrratio, mnt hmial ompoition, SF hr ρ = dnity urg iron tim (7.85 g/m mthod, 3 ). By tmpratur, ubtitutg valu t.). A, z, In F litratur ρ, alulatg variou formulatio mix rat thikn found rdution drib mm/yr ith orption i givn iorm µa/m 2, follog onrt xprion (Xi t al. rult: 994). Hovr, th papr mi-mpirial xprion pro x( t) = 0.06 i tnorlg Mjornll (997) i adoptd (3) b Prodg FraMCoS-7, May 23-28, 200
hr J = Dx(t) i givn mm, i i givn µa/m 2 ( h, T ) h, () t i givn yar. In Th thi proportionality vtigation, fit potntiotat D(h,T) urrnt i alld applid moitur varid prmability btn 280 it i 35 a nonlar µa, hih funtion tranlatd rlativ a urrnt dnity approximatly 00 µa/m 2 humidity h tmpratur T (Bažant & Najjar applid 972). Th moitur olumn ma pimn. balan Equation rquir 3 that a ud variation alulat tim rdution atr ma pr rformnt volum diamtr onrt (atr ovr ontnt priod ) b imulatd qual a- unit lratd divrgn orroion. moitur Figur flux 0 J plot avrag rak idth for ah olumn typ rlativ rdution rbar diamtr du orroion. Th rak = idth J rportd Figur 0 ha bn alulatd a avrag olumn pimn CV, (2) t CV2, CV3, avrag olumn pimn CS, CS2, CS3 ovr 0-month priod. Th atr ontnt an b xprd a um vaporabl atr Th graph ho an approximatly (apillary atr, atr lar variation vapor, adorbd atr) non-vaporabl rak idth for both olumn typ rlativ (hmially bound) atr bar diamtr rdution. Th n (Mill 966, ortial maximum bar rdution a alulatd b 0.322 mm at Pantazopoulo & Mill 995). It i raonabl aum that vaporabl atr i a funtion nd 0 month priod; thi impliitly aum that all ltrial urrnt a ud rlativ humidity, h, dgr hydration,, dgr ilia fum ration, orroion pro that r r, i.. no = lo. (h, Thi, ) = ag-dpndnt orption/dorption iorm rdution rformnt diamtr ill hav (Norlg Mjonll 997). Undr thi aumption b vrifid through forni analyi orrodd by ubtitutg Equation Equation 2 on rforg bar. It an b n from Figur 0 that obta rak idth ra approximatly lar ith tim for both olumn typ. A imilar trnd ha bn prviouly obrvd by Rodriguz h t al. (2000). + ( D h) = & + & + & n (3) h t h 0.7 hr /h i CV Column lop orption/dorption iorm 0.6 (alo (not alld onfd) moitur apaity). Th govrng quation 0.5 CS Column (Equation 3) mut b ompltd by appropriat boundary (onfd) itial ondition. Th 0.4 rlation btn amount vaporabl atr rlativ humidity i alld adorption iorm 0.3 if maurd ith rag rlativity humidity dorption iorm oppoit 0.2 a. Ngltg ir diffrn (Xi t al. 994), follog, orption iorm ill b ud ith 0. rfrn both orption dorption ondition. By 0.0 ay, if hytri moitur iorm 0.0 ould b 0.takn 0.2 aount, 0.3 to diffrnt 0.4 rlation, vaporabl Bar Diamtr atr v Rdution rlativ (mm) humidity, mut b ud aordg ign variation Figur 0. Avrag rak idth vru bar diamtr rdution. rlativity humidity. Th hap orption iorm for HPC i flund by many paramtr, 3.3 pially Column tho rviability that flun xtnt rat Maurmnt hmial ration, olumn turn, vrtial dtrm hortng por trutur irumfrntial por iz xpanion ditribution r (atr--mnt alo rgularly monird ratio, mnt rordd hmial through ompoition, data SF aquiition ontnt, on urg LVDT. tim Figur mthod, tmpratur, ho avrag mix additiv, valu for t.). In vrtial litratur irumfrntial variou formulation dformation an b mm found durg drib ttg priod orption for iorm olumn typ normal CV. From onrt (Xi figur, t al. it 994). an b Hovr, obrvd that olumn prnt CVG, papr ho mi-mpirial ntir rformnt xprion a propod ubjtd by Norlg Mjornll (997) i adoptd bau it Crak Width (mm)... orroion, xprd mot it vrtial dformation xpliitly aount firt to month for volution tabilizd aftr hydration that, hil ration olumn CV SF ontnt. diplayd Thi a ontuou orption iorm ra rad it axial dformation durg ntir ttg priod. Although olumn CV2 CV3 r only xpod alratd orroion for four month, ir rat olumn dformation ra i imilar ( h,, ) = G (, ) + olumn CV. Th rat ra irum- frntial xpanion a vry lo for a priod 0( g ) h (4) 0 month. 0( g ) h K (, ) Column Dformation (mm)... 0.40 0.35 hr firt trm (gl iorm) rprnt 0.30 phyially bound (adorbd) atr ond trm 0.25 (apillary iorm) rprnt apillary atr. Thi xprion i valid only for lo CVG ontnt 0.20 SF. Th fit G rprnt amount CV atr 0.5 pr unit volum hld gl por at CV200% rlativ humidity, it an b xprd (Norlg CV3 0.0 Mjornll 997) a Cirumf. 0.05 G ( 0.00, ) = k + k (5) vg vg 0 2 4 6 8 0 Tim (Month) hr k vg k vg ar matrial paramtr. From Figur maximum. Column amount dformation atr ovr pr tim unit for volum olumn that CV. an fill all por (both apillary por gl por), on an alulat 0.35 K a on obta CSG Column Dformation (mm)... 0.30 0.25, 0.20 K ( ) = 0.5 0.00 CS CS2 0 g 0.88 + 0.22 G 0 CS3 Cirumf. 0 g 0 2 4 6 8 0 2.2 Tmpratur volution Tim (Month) Figur Not 2. that, Column at arly dformation ag, ovr tim hmial for olumn ration CS. aoiatd ith mnt hydration SF ration ar It xormi, hould alo b notd tmpratur that fild dformation i not uniform lud for non-adiabati fft ytm rp vn hrkag if nvironmntal onrt. tmpratur Crakg i annot ontant. b onidrd Hat ondution a primary an b au dribd dformation onrt, pially at lat for durg tmpratur itial not tag xdg 00 C ttg produr. (Bažant & Kaplan 996), by Fourir la, hih rad Figur 2 plot dformation vru tim olumn typ CS. By omparg Figur 2, q = λ T it i obrvd that dformation olumn CV (7) a ll a rat ir ra ovr tim r highr hr than q i olumn hat CS. For flux, T lattr i group, abolut vrtial tmpratur, dformation appar λ i hat platau ondutivity; lightly aftr thi 3 month ttg, bfor y tart rag aga (6) Th matrial paramtr k vg k vg g an 0.0 b alibratd by fittg xprimntal data rlvant fr 0.05 (vaporabl) atr ontnt onrt at variou ag (Di Luzio & Cuati 2009b). Prodg FraMCoS-7, May 23-28, 200
at 8 month. Th irumfrntial xpanion a rlativly mallr than that olumn CV. In fat, it i onludd from rult that olumn xpanion i furr rad a ara longitudal rformnt partiipatg ritan axial load i drad du orroion. Figur 3 ho vrtial hortng obtad mm for both olumn typ vru rak idth. Although dformation obtad for olumn CV r highr than tho obtad for olumn CS, ra vrtial dformation a a funtion rak opng i mor pronound for olumn CS. Th ombd fft orroion piral rformnt onrt ovr rakg onidrably rdu onfmnt ation olumn CS. Thi typ olumn rquir l rak opng ahiv a imilar lvl axial dformation than olumn CV. Column Dformation (mm)... 0.35 0.30 0.25 0.20 0.5 0.0 0.05 0.00 CV Column (not onfd) CS Column (onfd) 0.0 0. 0.2 0.3 0.4 0.5 0.6 Crak Width (mm) Figur 3. Vrtial hortng vru rak idth. 4 DISCUSSION 4. Efft utad load on rak propagation Load r kpt ontant on olumn pimn durg orroion imulation. Thi had a ignifiant impat on latral rak propagation. Although rdution rforg bar diamtr for ttg priod a imilar for both typ olumn ( Fig. 0), latral rak idth olumn CS r ignifiantly l than idth longitudal rak olumn CV. Thi a mot likly du vrtial prur utad loadg that i prpndiular dirtion latral rak, unlik longitudal rak that had littl ountr-prur. Thrfor, trm rak idth, fft orroion on piral rformnt ha a l vr impat on ovr rakg than fft orroion vrtial rformnt a olumn. Th idth longitudal rak along vrtial J = bar D ( h, a T ) happroximatly 6 8 tim idth latral rak. Hovr, latral rak along Th piral proportionality ti ontitut fit pot D(h,T) potntial futur pittg moitur prmability onrt ovr. it i a nonla rlativ humidity h tmpratur 4.2 Efft t-dry & Najjar yl 972). Th moitur ma balan that variation tim atr ma Th ontuou diolourg volum onrt olumn (atr ontnt urfa ) b q a an diation divrgn that rut produt moitur r flux bg J ontantly ahd aay diolvd atr through rak. Prhap a mthod moitur upply diffrnt from = prayg J ith atr uh a t humidity or fog hambr ould hav a diffrnt impat on ovr rakg. Not allog rut produt diolv atr might lad furr a- Th atr ontnt an b xprd a vaporabl atr (apillary a umulation around rbar urfa mor vr vapor, adorbd atr) non- rakg onrt. (hmially bound) atr n (Mil Pantazopoulo & Mill 995). It i ra 4.3 Efft ovr aum rakg that on olumn vaporabl atr i a fu rviability rlativ humidity, h, dgr hydration dgr ilia fum ration, Rult ho that fft ovr rakg up, i.. = = ag-dpndnt orption/dorption orroion lvl vtigatd hav an impat on (Norlg Mjonll 997). Undr thi aum olumn rviability, partiularly du ra olumn vrtial dformation ard by ubtitutg Equation Equati obta ond half tn month orroion ttg. Thi larly ho that furr olumn dtrioration form ovr rakg i an h diation + ( D h) = & + & + a rdution holumn t trutural h prforman rgard rviability ritria. hr /h i lop orption/ iorm (alo alld moitur apa 5 CONCLUSIONS govrng quation (Equation 3) mut b by appropriat boundary itial onditi Thi papr ha prntd xprimntal rult rlatd Th rlation btn amount onrt rakg longitudal latral dformation RC irular olumn that r imul- atr rlativ humidity i alld iorm if maurd ith rag tanouly ubjtd axial load alratd rformnt orroion. Whil on t olumn humidity dorption iorm th a. Ngltg ir diffrn (Xi t al. only longitudal rformnt a ubjtd follog, orption iorm ill b orroion, or t olumn it a piral rformnt dignd provid olumn on- rfrn both orption dorption By ay, if hytri fmnt that a orrodd. Th rakg pattrn iorm ould b takn aount, to obrvd a quit diffrnt for to t olumn. Column ho longitudal rformnt rlation, vaporabl atr v rlativ humi b ud aordg ign varia a orrodd xhibitd vrtial rakg paralll rlativity humidity. Th hap longitudal rforg bar. On or h, iorm HPC i flund by many p olumn ho piral rformnt a orrodd pially tho that flun xtnt diplayd a mor rom rakg pattrn ditributd latral dirtion. In gnral, olumn hmial ration, turn, dtrm ho longitudal trutur rformnt por uffrd iz ditribution from orroion xprd (atrratio, highr mnt axial hmial latral ompoition, dformation, aoiatd SF urg tim rak idth mthod, r tmpratur, ix mix ight tim highr t.). magnitud In litratur than variou or t formulatio olumn. Thi xprimntal found drib tudy ill b orption ompltd iorm ith ttg olumn onrt pimn (Xi t al. up 994). failur Hovr, by th ubjtg m papr ntri axial mi-mpirial loadg. xprion pro Norlg Mjornll (997) i adoptd b Prodg FraMCoS-7, May 23-28, 200
REFERENCES J = D ( h, T ) h () Andrad, Th C. proportionality & Alono, C. 996. fit Progr on D(h,T) dign i alld ridual lif alulation ith rgard rbar orroion rford onrt. prmability In N.S. Brk, it E. i Ealant, a nonlar C.K. funtion Nmai & moitur D. Whitg rlativ (d), humidity Thniqu h tmpratur A Corroion T (Bažant Ativity 972). Stl Rford Th moitur Conrt ma Strutur, balan ASTM rquir STP & Najjar that 276: 23-40. variation tim atr ma pr unit L, volum C., Bonai, onrt J.F., (atr Thoma, ontnt M.D.A., ) Maalj, b qual M., Khajhpour, S., Harn, N., Pantazopoulou, S., & Shikh, S. divrgn moitur flux J 2000. Alratd orroion rpair rford onrt olumn ug arbon fibr rford polymr ht. Canadian Journal Civil Engrg 27(5): 94-948. = J (2) Liu Y. t & Wyr R.E. 998. Modlg tim--orroion rakg hlorid ontamatd rformnt onrt trutur. ACI Matrial Journal 95(6): 675-68. Rodriguz, Th atr J., Ortga, ontnt L. M., & an Aragonillo, b xprd J. 2000. a Corroion um rat vaporabl trutural prforman. atr (apillary In C. Andrad, atr, C. Alono, atr vapor, J. Fulla, J. adorbd Polimon, atr) & J. Rodriguz (d), non-vaporabl Maurmnt (hmially Intrprtation bound) On-it atr Corroion n (Mill Rat: 9-23. 966, RILEM Publiation S.A.R.L. Pantazopoulo & Mill 995). It i raonabl aum that vaporabl atr i a funtion rlativ humidity, h, dgr hydration,, dgr ilia fum ration,, i.. = (h,, ) = ag-dpndnt orption/dorption iorm (Norlg Mjonll 997). Undr thi aumption by ubtitutg Equation Equation 2 on obta h + h t ( D h) = n (3) h & + & + hr /h i lop orption/dorption iorm (alo alld moitur apaity). Th govrng quation (Equation 3) mut b ompltd by appropriat boundary itial ondition. Th rlation btn amount vaporabl atr rlativ humidity i alld adorption iorm if maurd ith rag rlativity humidity dorption iorm oppoit a. Ngltg ir diffrn (Xi t al. 994), follog, orption iorm ill b ud ith rfrn both orption dorption ondition. By ay, if hytri moitur iorm ould b takn aount, to diffrnt rlation, vaporabl atr v rlativ humidity, mut b ud aordg ign variation rlativity humidity. Th hap orption iorm for HPC i flund by many paramtr, pially tho that flun xtnt rat hmial ration, turn, dtrm por trutur por iz ditribution (atr--mnt ratio, mnt hmial ompoition, SF ontnt, urg tim mthod, tmpratur, mix additiv, t.). In litratur variou formulation an b found drib orption iorm normal onrt (Xi t al. 994). Hovr, prnt papr mi-mpirial xprion propod by Norlg Mjornll (997) i adoptd bau it & Rodríguz, xpliitly J., aount Ortga, L. for M., & Caal, volution J. 996. Load hydration barg ration apaity onrt SF ontnt. olumn ith Thi orrodd orption rformnt. iorm rad In C. L. Pag, J.W. Figg, & P.B. Bamforth (d), Corroion Rformnt Conrt Contrution: 220-230. Royal Soity Chmitry. Sai, Y., Mihiaki, O., Kanakubo, T., & Yamamo, Y. 2007. Strutural prforman orrodd RC olumn undr uniaxial ( h, omprion, ) = G ( load., ) Firt + Intrnational Workhop on Prforman, Prottion & Strngng 0( g Strutur ) h undr Extrm Loadg, Whitlr, Canada. (4) aknoldgmnt 0( g ) h Fanial upport providd by Natural S Engrg Rarh Counil K (, ) Canada, by Halall Aoiat Limitd i gratfully aknoldgd. hr firt trm (gl iorm) rprnt phyially bound (adorbd) atr ond trm (apillary iorm) rprnt apillary atr. Thi xprion i valid only for lo ontnt SF. Th fit G rprnt amount atr pr unit volum hld gl por at 00% 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 maximum amount atr pr unit volum that an fill all por (both apillary por gl por), on an alulat K a on obta K (, ) = 0 g 0.88 + 0.22 G 0 0 g (6) Th matrial paramtr k vg k vg g an b alibratd by fittg xprimntal data rlvant fr (vaporabl) atr ontnt onrt at variou ag (Di Luzio & Cuati 2009b). 2.2 Tmpratur volution Not that, at arly ag, hmial ration aoiatd ith mnt hydration SF ration ar xormi, tmpratur fild i not uniform for non-adiabati ytm vn if nvironmntal tmpratur i ontant. Hat ondution an b dribd onrt, at lat for tmpratur not xdg 00 C (Bažant & Kaplan 996), by Fourir la, hih rad q = λ T (7) hr q i hat flux, T i abolut tmpratur, λ i hat ondutivity; thi Prodg FraMCoS-7, May 23-28, 200