Crack propagation analysis due to rebar corrosion

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1 Fraur Mani Conr and Conr Sruur - Amn, Durabiliy, Monioring and Rriing Conr Sruur- B. H. O, al. (d) 2 Kora Conr Iniu, Soul, ISBN Crak propagaion analyi du o rbar orroion H. Nakamura, K.K.Tran, K.Kaamura & M. Kunida Dparmn Civil Enginring, Nagoya Univriy, Japan. ABSTRACT: Craking bavior du o rbar orroion or onr pimn i ingl rbar a valuad xprimnally and analyially. In xprimn, propagaion rak a obrvd by lri orroion. Tr-dimnional Rigid- Body-Spring-Mod (RBSM) i r pa marial orroion xpanion modl a applid o imula inrnal raking parn, ura rak id propagaion and inrnal rak propagaion. T orroion produ propri and pnraion orroion produ ino rak during orroion pro r invigad and raking bavior du o rbar orroion a imulad raonably. A rul, manim ura rak id propagaion i inrnal rak propagaion a lariid. INTRODUCTION Craking onr du o rbar orroion i on major drioraion bavior and i au palling onr ovr or alraion drioraion. I i nary o prdi inrnal damag rom obrvabl ura ondiion during mainnan pro. Tror, i i dirabl o abli a prdiion mod o quaniaivly a inrnal rak propagaion bavior and rbar orroion ra rom ura rak. T inrnal rak parn du o rbar orroion onidring dirn ovr ikn or diamr rinoring bar r lariid (Andrad al., 993, Cabrra 996). Hovr, rlaionip bn propagaion ura and inrnal rak a ll a progr ura rak id av no bn lar. In i udy, rak propagaion bavior i invigad bo analyially and xprimnally. In xprimn, propagaion rak i obrvd by lri orroion. Tn, ura rak id ar maurd and inrnal rak parn ar obrvd a vral rbar orroion ra. On or and, rak propagaion bavior i imulad uing Rigid-Body-Spring-Mod i rdimnional Voronoi paril. In analyi, r pa marial modl i oni rbar, orroion produ layr and onr i propod. For orroion produ layr, in orroion produ i onidrd by iniial rain problm du o orroion xpanion. Morovr, pnraion orroion produ ino rak during orroion pro i onidrd. T appliabiliy modl i vriid by omparing i rul. A rul, progr ura rak id, propagaion bavior inrnal rak, and inrnal rak o ura rak id and o on ar lariid. 2 EXPERIMENTAL STUDY 2. Ting mod Dimnion pimn i ingl rbar ar on in Figur. To yp pimn ar arrid ou. Typ C3 a onr ovr ikn 3mm. Typ C a mm ovr ikn. Tr ar ix pimn in yp C3 and on pimn in yp C. 5 C3 C D9 D9 3 5 Figur. Spimn up. Crak id maurmn Cuing ion Unimm In ordr o alra orroion pro, an xrnal dir lri urrn dniy 9µA/m 2 i applid ar 32 day rom aing. Smai lri orroion i on in Figur 2. A ing im, onr ompriv rng and nil rng ar 8.5 MPa and.53 MPa rpivly. During, ura rak id ar rordd uing rak gaug and rak id ar loggd in ompur il. Ting im i varid or ix pimn yp C3 o inviga

2 orroion J D (, T ) ra o rak parn and rak id () propagaion. Wn a bn inid, pimn T ar proporionaliy u along iin poiion D(,T) on i in alld Figur moiur o obrv prmabiliy inrnal and rak i i parn a nonlinar and maur union inrnal rlaiv rak id umidiy and lng. and mpraur T (Bažan & Najjar 972). T moiur ma balan rquir a variaion in im - ar ma pr uni volum onr (ar onn ) b qual o divrgn moiur lux J J rinormn onr T ar onn an b xprd a um NaCl 3% vaporabl ar (apillary ar, ar vapor, and adorbd ar) and non-vaporabl (mially bound) ar Corroion ra W r (mg/m 2 n (Mill 966, Panazopoulo & Mill 995). ) during I i raonabl ing o i alulad aum a by dividing ma lo W(mg) by ura rbar (m 2 vaporabl ar i a union rlaiv umidiy, )., dgr ydraion,, and dgr W ilia um raion,, i.. (,, ) W r ag-dpndn orpion/dorpion iorm () π D L (Norling Mjonll 997). Undr i aumpion and r by ubiuing D and L ar Equaion bar diamr ino (m) Equaion and bar lng 2 on (m) obain rpivly. Ma lo W(g) i alulad by uing olloing mpirial ormula bad on rul a on in Figur 3: ( D ) & & & n (3) Woodn pakr Coppr pla Figur 2. Smai orroion. W.235I T (I.T < 66) W.67I T (I T > 66) r / i lop orpion/dorpion r iorm I and (alo T ar alld urrn moiur inniy (A) apaiy). and ing T im govrning (our) quaion rpivly. (Equaion 3) mu b ompld by appropria boundary and iniial ondiion. T rlaion bn amoun vaporabl ar and 2rlaiv umidiy i alld adorpion iorm i maurd i inraing rlaiviy umidiy and dorpion W.67 IT iorm in oppoi a. Ngling 8 ir dirn (Xi al. 994), in olloing, 6 orpion iorm ill b ud i rrn o bo orpion and dorpion ondiion. 4 By ay, i yri moiur Exprimn iorm 2 ould b akn ino aoun, o dirn rlaion, vaporabl W.235 IT ar v rlaiv umidiy, mu b ud aording 5o ign 5 2 variaion 25 rlaiviy umidiy. Aumulad T urrn ap amoun (A.r) orpion Figur iorm 3. Rbar or HPC ma lo i inlund ompuaion. by many paramr, pially o a inlun xn and ra 2.2 mial Exprimnal raion rak and, parn in urn, drmin por ruur and por iz diribuion (ar-o-mn Figur raio, mn 4 india mial dind ompoiion, inrnal SF rak onn, yp on uring in im rak and parn. mod, mpraur, mix addiiv,.). Inrnal In rak liraur parn variou a vral ormulaion orroion an ra b ound yp o C3 drib ar on in orpion Figur 5. iorm normal onr Iniiaion (Xi viibl al. 994). rak Hovr, our on in ura prn onr papr ovr mi-mpirial (vrial rak). xprion Wn propod orroion by produ Norling inra, Mjornll (997) rak i propaga adopd bau inid i Ma lo (g) onr ovr. Ar a, laral rak appar and ir xpliily lng aoun inra. or Wi urr voluion amoun ydraion orroion raion produ, and SF inid onn. rak iniia Ti orpion and propaga iorm inid rad pimn rom rbar. (,, ) G ( ) Vrial rak, Laral rak g Inid rak 6mg/m 2 ( ) T marial paramr k vg and k vg and g an b alibrad by iing xprimnal daa rlvan o r (vaporabl) ar onn in onr a Figur 6. Typ C rak parn. variou ag (Di Luzio & Cuai 29b). 2.3 Sura rak id propagaion 2.2 Tmpraur voluion In a 3mm ovr ikn (yp C3), propagaion No a, a arly ura ag, rak in id mial again orroion raion ra aoiad a dirn i mn rbar ma ydraion lo lvl and i SF on raion in Figur ar xormi, 7. I an b n mpraur a opning ild i ura no uniorm rak iniia or non-adiabai ar a ym igniian vn amoun i nvironmnal orroion produ mpraur ar ormd. i onan. I an Ha b xplaind onduion a an a riial b dribd orroion in onr, amoun a orroion la or mpraur produ i no rquird xding o build C up noug (Bažan xpanion & Kaplan r 996), and by o au Fourir raking la, i in onr rad a B.H.O diud abou valu (O al. 29). Ar iniiaion, q λ T ura rak id propaga rapidly up o valu.4mm. Ar a, pd propagaion (7) rdu r q i i ourrn a lux, laral T rak i and abolu mpraur, pnraion and λ orroion i a produ onduiviy; ino rak in i i i diud in lar par prn pa- ( g ) K (, ) Figur 4. Inrnal rak yp. r ir rm (gl iorm) rprn pyially bound (adorbd) ar and ond rm (apillary iorm) rprn apillary ar. Ti xprion i valid only or lo onn SF. T iin G rprn amoun ar pr uni volum ld in gl por a % 8mg/m 2 435mg/m 2 749mg/m rlaiv umidiy, and i an b xprd (Norling 2 Mjornll Sura rak 997) id a Sura rak id Sura rak id.35mm.78mm.mm Figur 5. Typ C3 rak parn. G (, ) k k vg vg In a mm ovr ikn (yp C), o rak appar on onr ura and propaga r k vg and k vg ar marial paramr. From o rbar. Tn, laral rak our n amoun maximum amoun ar pr uni volum a an orroion produ inra a on in Figur 6. ill all por (bo apillary por and gl por), on an alula K a on obain K (, ) g G g (6) Proding FraMCoS-7, May 23-28, 2

3 pr. Morovr, pd propagaion inra again i propagaion inid rak Sura rak id (mm) Corroion ra (mg/m 2 ) Figur 7. Typ C3 ura rak id propagaion. 3 ANALYTICAL MODEL 3. Tr- dimnional RBSM Rigid- Body-Spring-Mod (RBSM) i on dir approa, i ar ud a ruural analyi, in i i ay o dal i rak propagaion onr dirly. T mod rprn a oninuum marial a an amblag rigid paril lmn inronnd by zro pring along ir boundari (Fig. 8). In i udy, rdimnional RBSM i applid. Ea lmn a ix dgr rdom a nr poin. Boundary bn o lmn i dividd ino riangl ormd by nr and vri boundary. A a nr poin riangl, r pring, on normal and o ar pring ar. T analyial modl i dividd ino lmn uing Voronoi random polygon. In RBSM modl, rak id an b auomaially maurd during analyi. T r-dimnional modl i poibl o imula ompliad problm. 3.2 Marial modl Figur 9 o onr marial modl i ar ud in analyi. In ompriv modl, i ompriv rng onr, G ompriv raur nrgy, E i Young modulu onr. T nil bavior onr up o rng i modld by uing linar lai. Wil bilinar ning bran /4 modl i aumd ar raking a on, in i i nil rng, G i nil raur nrgy and i dian bn nr Voronoi lmn. Tangnial pring rprn ar ranrring manim onr. T ar rng i aumd o ollo Mor- Coulomb yp ririon i nion Jand D ( omprion, T ) ap. T ar raur ririon i xprd a ollo (Saio. 999): T proporionaliy iin D(,T) τ 2 moiur prmabiliy and i i a nonlina rlaiv umidiy and mpraur (3) τ 2 & Najjar 972). T moiur ma balan a variaion in im ar ma r volum onr (ar onn ) b q divrgn σ an φ, orσ.5 ' moiur lux J τ.5 an φ, orσ <.5 ' J Rbar i modld a linar lai. T ar onn an b xprd a Zro pring vaporabl ar (apillary a vapor, and adorbd ar) and non- (mially bound) ar n (Mil Panazopoulo & Mill 995). I i ra aum a vaporabl ar i a u rlaiv umidiy,, dgr ydraion dgr ilia um raion,, i.. Triangl nr poin Nular ag-dpndn Voronoi orpion/dorpion paril (Norling Mjonll 997). Undr i aum Figur 8. RBSM Voronoi polygon. by ubiuing Equaion ino Equai obain σ E E G / σ l.25 ε l.75 G F / ε u 5. G ( D ) F / E GF/ ε ε ε ε u & & ε ε ε ε / 2 u r / i lop orpion/ Conr ompriv modl Conr nil modl iorm (alo alld moiur apa govrning quaion (Equaion 3) mu b.38 by appropria boundary φ 37 o and iniial ondii T rlaion bn amoun ar and rlaiv umidiy i alld iorm i maurd i inraing umidiy and dorpion iorm in Conr ar modl- Mor-Coulomb ririon i nion and a. omprion Ngling ap ir dirn (Xi al. Figur 9. Conr marial olloing, modl. orpion iorm ill b rrn o bo orpion and dorpion By ay, i yri 3.3 Corroion xpanion iorm modl ould b akn ino aoun, o Modling xpanion rlaion, orroion vaporabl produ ar i v on rlaiv umi in Figur. Tr b ud pa aording marial modl o ign inluding varia rbar, orroion rlaiviy produ and umidiy. onr T i applid. ap T mri iorm modl i or a HPC propri i inlund orroion produ pially u a ikn o a (H) inlun and lai xn and by many p modulu (E r ) ar mial aumd dirly. raion T and, modl in i urn, iin o inviga ruur and por orroion iz diribuion produ. (ar- drm In modl, iniial raio, rain mn i gradually mial inrad ompoiion, in SF normal pring load uring on im boundary and mod, mpraur, orroion mix produ layr bad.). on In iniial rain liraur problm. variou ormulaio Ludgrn K.(22), ound O o drib al. (29) orpion uggd iorm a modl dormaion onr around (Xi rbar al. du 994). o orroion Hovr, in produ i an papr b dribd mi-mpirial a on in xprion Figur pro, in i r, x, Norling U and UMjornll or ar iniial (997) radiu i adopd r- b Proding FraMCoS-7, May 23-28, 2

4 bar, J D ( orroion, T ) pnraion dp, r inra () radiu and ral inra radiu rpivly. T T proporionaliy rain in orroion iin produ D(,T) i i alld moiur U prmabiliy or U and i i a nonlinar union ε or rlaiv ε ral ε r x U umidiy and mpraur T (Bažan & Najjar 972). T moiur ma balan rquir a In RBSM variaion modl, in im iniial ikn ar ma orroion pr uni produ volum layr onr i modld (ar onanly onn ) a b H qual o o divrgn U moiur lux J ε r (6) H Ti paramr J i inpu daa in analyial program roug inraing orroion ra. U i om- pud T rom ar onn orroion an ra b a xprd olloing a quaion (Mauo vaporabl al. 997) ar (apillary ar, ar um vapor, W r ( and U dv ) adorbd ar) and non-vaporabl (mially (7) ρ bound) ar n (Mill 966, Panazopoulo & Mill 995). I i raonabl o r aum Wa r i orroion vaporabl ra (mg/m ar 2 i ),dv a union i volum xpanion rlaiv umidiy, raio orroion, dgr produ ydraion, (2.5, in i udy), ρ i rbar dniy (7.85x 3 mg/m 3, and dgr ilia um raion,, i.. (, )., ) ag-dpndn orpion/dorpion iorm (Norling Conr Mjonll 997). Undr i aumpion and by ubiuing Equaion ino Equaion 2 on obain Corroion produ Rbar ( D ) n (3) & & Expanion r rain / i lop orpion/dorpion iorm (alo alld moiur apaiy). T Figur govrning. RBSM quaion orroion (Equaion xpanion 3) modl. mu b ompld by appropria boundary and iniial ondiion. T rlaion bn amoun vaporabl ar and rlaiv umidiy i alld adorpion iorm i maurd Ui inraing rlaiviy umidiy and dorpion iorm in oppoi a. Ngling ir dirn (Xi U or al. 994), in olloing, orpion iorm r ill b ud i rrn Iniial o rbar bo orpion and dorpion ondiion. By radiu ay, i yri moiur iorm ould b akn x ino aoun, o dirn rlaion, vaporabl ar v rlaiv umidiy, mu b ud aording o ign variaion rlaiviy umidiy. T ap orpion iorm or HPC i inlund by many paramr, pially o a inlun xn and ra Figur. Dormaion around rbardu o orroion produ. mial raion and, in urn, drmin por ruur and por iz diribuion (ar-o-mn I may no b ay o maur propri orroion produ u a ikn and linar lai raio, mn mial ompoiion, SF onn, uring im and mod, mpraur, mix addiiv, modulu by xprimn. W av rid o analyz.). In liraur variou ormulaion an b pimn i variou valu iniial ikn and linar lai modulu orroion ound o drib orpion iorm normal onr (Xi al. 994). Hovr, in prn produ layr. A rul, iniial ikn papr mi-mpirial xprion propod by (H).mm and lai modulu (E r ) 5MPa an Norling Mjornll (997) i adopd bau i imula raonabl raking bavior in rm & rak xpliily parn aoun and ura or rak voluion id propagaion ydraion in raion omparion and i SF onn. xprimnal Ti orpion rul. iorm rad 4 ANALYTICAL RESULTS (,, ) G (, ) In analyi, m iz Voronoi ( g paril ) ar 5mm in ovr ara and mm in or. Anor arrangmn Voronoi paril i alo rid ( g ) o onirm imilariy analyial rul. K (, ) 4. Simulaion inrnal rak parn Analyial r rak ir parn rm (gl a vral iorm) valu rprn ura pyially rak id bound (adorbd) ar obaind ar or yp and C3 ond pi- mn. rm (apillary T analyi iorm) don i rprn o valu apillary linar ar. lai Ti modulu xprion i orroion valid only produ or lo 5MPa onn and SF. MPa T iin o ompar G rprn i propry amoun o inrnal ar pr rak uni parn. volum ld Figur in 2 o gl por a inrnal % rak rlaiv parn umidiy, n and Ei r i an 5MPa b xprd and Figur (Norling 3 o Mjornll 997) parn a n E r i MPa. G (, ) k k vg vg Figur 2. Typ C3 rak parn (Er5Mpa). g G Figur 3. Typ C3 rak parn (ErMpa). 2.2 Tmpraur voluion Wi dirn valu lai modulu No a, a arly ag, in mial raion E r, rak parn ar dirn bu dirn ar mall. In omparion i xprimn- aoiad i mn ydraion and SF raion ar xormi, mpraur ild i no uniorm al rul in Figur 5, valu 5 MPa an imula br rak parn inid rak n or non-adiabai ym vn i nvironmnal mpraur i onan. Ha onduion an b ura rak id i.78mm and.mm. T dribd in onr, a la or mpraur no rak parn vrial rak and laral rak ar xding C (Bažan & Kaplan 996), by imilar. Fourir la, i rad In a yp C, alo analyz pimn i o valu 5MPa and MPa q λ T lai modulu E r. Analyial rak parn (7) a ura rak id.5mm ar on in Figur 4. A r ll q a i in a a lux, yp T C3 i pimn, abolu valu mpraur, 5MPa and lai λ i modulu a onduiviy; orroion in produ an imula rak parn mor loly i o r k vg and k vg ar marial paramr. From maximum amoun ar pr uni volum a an ill all por (bo apillary por and gl por), on an alula K a on obain K (, ) g (6) T marial paramr k vg and k vg and g an b alibrad by iing xprimnal daa rlvan o r (vaporabl) ar onn in onr a variou ag (Di Luzio & Cuai 29b). Proding FraMCoS-7, May 23-28, 2

5 xprimnal rul (Fig. 6) i o rak apparing in onr ovr. ErMPa Er5MPa Figur 4. Typ C rak parn (ura rak id.5mm). 4.2 Simulaion ura rak id propagaion Analyial rul in a yp C3 ar ompard i xprimnal rul a on in Figur 5. T analyial rul appar raonably agrmn i xprimnal rul, i.. iniiaion rak id ourring i a rain amoun orroion produ and n rak opning propagaing pdily up. Hovr, analyial valu o largr ura rak id an xprimnal rul, pially n orroion ra inra. Sura rak id (mm) Er 5MPa ErMPa Exprimn Corroion ra (mg/m 2 ) Figur 5. Analyial ura rak id propagaion (Typ C3). Wi a igr valu linar lai modulu orroion produ, E r 5MPa, orroion xpanion prur indud by orroion produ i largr and i au iniiaion ura rak id quikr an mallr a, E r MPa. In arly ag orroion, ura rak id in a E r 5 MPa i lor o xprimnal rul an on in a E r MPa. 4.3 Pnraion orroion produ ino rak During orroion pro, i i knon a orroion produ an pnra ino rak in onr o i may rdu orroion xpanion prur on onr aordingly a on in Figur 6 (Val al. 29, J D ( Toongonong, T ) & Makaa. 24). T proporionaliy iin D(,T) moiur prmabiliy and i i a nonlina rlaiv umidiy and mpraur Vrial rak & Najjar 972). T moiur ma balan a variaion in im ar ma volum onr (ar onn ) b q divrgn Iniial moiur lux J rbar radiu Laral rak J Figur 6. Pnraion orroion produ ino rak. T ar onn an b xprd a Ti a bn imulad vaporabl in ar RBSM (apillary analyial program. vapor, On and adorbd advanag ar) RBSM and non- a modl i a rak (mially id and volum bound) ar rak an n (Mil b alulad dirly Panazopoulo during & analyi Mill (Fig. 995). 7). I I i ra i ror onvnin aum o a alula vaporabl rduion ar volum orroion rlaiv produ umidiy, i, pnra dgr ino ydraion i a u rak. T rduion dgr orroion ilia um xpanion raion, prur du o pnraion ag-dpndn orroion orpion/dorpion produ ino, i.. rak i alulad (Norling by rduing Mjonll 997). r inra Undr i U aum in orroion xpanion by ubiuing modl a Equaion on in Figur ino Equai 8. obain W av aumd olloing n onidring i in analyi: Corroion produ an only pnra ino ( D ) & & rak i rak id xd rold valu rak id. Corroion r produ ully / i ill in lop rak orpion/ T r iorm inra U (alo i uniormly alld moiur rdud apa around govrning rbar. quaion (Equaion 3) mu b Wi a r inra by appropria U, boundary orrponding and iniial or-ondiroion produ volum T V or rlaion i (Figur bn 8a): amoun ar and rlaiv umidiy i alld V or [ π ( r U ) 2 iorm πr 2 ] i maurd i inraing L πu (2r U ) L (8) umidiy and dorpion iorm in in U 2, quaion a. (7) Ngling an b approximad ir dirn a (Xi al. olloing, orpion iorm ill b Vor 2 πr U L (9) rrn o bo orpion and dorpion r L i lng By rbar. ay, i yri Wn pnraion iorm ould orroion b akn produ ino aoun, ino o rak i onidrd, rlaion, vaporabl iv orroion ar v rlaiv produ volum V or, umi b i: ud aording o ign varia rlaiviy umidiy. T ap V or, Vor V iorm rk or HPC i inlund by many p () pially o a inlun xn and mial raion and, in urn, drm r V rk i volum ruur rak and a por ompud iz diribuion in Figur (arraio, mn mial ompoiion, SF 7. I iv uring r inra im and i mod, U, mpraur, iv mix volum orroion.). produ In liraur in Figur variou 8b ill ormulaio b (imilar o (9)) ound o drib orpion iorm V or, 2π. r. U onr. L (Xi al. 994). Hovr, in papr mi-mpirial xprion pro () Norling Mjornll (997) i adopd b Proding FraMCoS-7, May 23-28, 2

6 rom J D ( (9),(), T ) and (): 2π. rt. U proporionaliy. L 2π. r. U. L V iin D(,T) i rk alld moiur prmabiliy and i i a nonlinar union rlaiv umidiy and mpraur T (Bažan V U & Najjar U rk 972). T moiur ma balan rquir (3) a variaion 2π. r. L in im ar ma pr uni volum onr (ar onn ) b qual o divrgn moiur lux J Normal pring i ε n,i : rain J normal pring i () T ar onn an b xprd Inra ura a i um vaporabl ar (apillary S i i ara ar, ura ar i vapor, and adorbd ar) and non-vaporabl (mially bound) ar n (Mill 966, Panazopoulo & Mill 995). I i raonabl o aum a vaporabl ar i a union rlaiv umidiy, i, dgr ydraion,, and dgr V rk i ilia oal volum um raion, rak, i.. (,, ) ag-dpndn NSPG orpion/dorpion iorm (Norling VMjonll rk n ε 997).,. i i. Si Undr i aumpion and by ubiuing Equaion ino Equaion 2 on obain r NSPG i numbr pring i ε n,i. i i rak id a inra ura i Figur 7. Compuaion ( D ) volum & rak in RBSM & & modl. n (3) r / U i lop Uorpion/dorpion iorm (alo alld moiur apaiy). T govrning quaion r (Equaion 3) mu b ompld by appropria Iniial boundary and iniial ondiion. T rlaion bn amoun vaporabl rbar ar and rlaiv umidiy i alld adorpion radiu iorm i maurd i inraing rlaiviy umidiy and dorpion iorm in oppoi a. Ngling ir dirn (Xi al. 994), in olloing, a) No pnraion orpion iorm b) Pnraion ill b ud i rrn ino rak o bo orpion and ino dorpion rak ondiion. Figur By 8. ay, Compuaion i rduion yri r inrau moiur du o pnraion iorm ould orroion b akn produ ino ino aoun, rak. o dirn rlaion, vaporabl ar v rlaiv umidiy, mu b Figur ud aording 9 o o propagaion ign variaion ura rak id rlaiviy n umidiy. i T i onidrd ap or yp orpion C3 pimn. iorm or Trold HPC i inlund.mm by and many.2mm paramr, rak id pially ar onidrd. o a inlun T valu xn 5MPa and ra i ud or mial lai raion modulu and, in orroion urn, drmin produ. por ruur I an and b por n iz a diribuion propagaion (ar-o-mn ura rak raio, id mn i mial raonably ompoiion, agrmn i SF onn, xprimnal uring im rul and mod, n mpraur, pnraion mix addiiv, orroion.). In produ liraur ino rak variou i ormulaion onidrd. an b ound Wn o drib rold orpion.mm iorm id normal or pnraion onr (Xi orroion al. 994). produ Hovr, ino rak, prn propagaion papr mi-mpirial pd ura xprion rak propod id i rdud Norling n Mjornll ura (997) rak i adopd id gro bau up o by i.4mm xpliily bau aoun laral or rak voluion av ourrd ydraion and raion oal volum and SF onn. rak bom Ti orpion larg i iorm indu rad a igniian rduion on orroion xpanion prur on onr. For a.2mm rold, anging poin propagaion i a valu.8mm (,, ) G (, ) ura rak id. T ndny rak id ( g ) propagaion i imilar i a.mm rold. ( g ) K (, ).6 Sura rak id (mm).4.2 r ir rm (gl iorm) rprn pyially bound (adorbd) ar and ond D rm (apillary iorm) rprn apillary.8 ar. Ti xprion i valid only C or lo onn SF..6 T iin G rprn amoun ar No pnraion.4pr uni volum ld in gl por a % B Trold.mm rlaiv umidiy, and i an b Trold xprd.2mm (Norling Mjornll.2 997) a Exprimn A, k G ( ) k Corroion ra (mg/m 2 ) vg vg Figur 9. Sura rak id propagaion i pnraion orroion produ ino rak. r k vg and k vg ar marial paramr. From maximum amoun ar pr uni volum a an In omparion i xprimnal rul, i ill all por (bo apillary por and gl por), on rold rak id i bn.mm an alula K a on obain and.2mm, i an raonably imula ura rak id propagaion a on in Figur 9. Hovr, i i nod a in xprimn, g orroion produ may no ully G pnra ino rak and pd pnraion alo dpnd on rak (6) K (, ) id and propri g orroion produ. In analyi, av aumd a and bigg pnraion i indu larg rduion on orroion T marial xpanion. paramr k vg and k vg and g an b T alibrad rold by iing pnraion xprimnal graly daa a rlvan o propagaion r (vaporabl) ura ar rak onn id. in T onr abov aumpion variou ag ar (Di alo Luzio impl & Cuai a or 29b). analyi in a i udy and i ill dinily rquir urr ork o 2.2 imula Tmpraur voluion o orroion pro. Epially, i ill nd urr xprimnal rul o vriy No a, imulaion arly rul. ag, in mial raion aoiad i mn ydraion and SF raion ar xormi, mpraur ild i no uniorm 4.4 or non-adiabai Simulaion inrnal ym rak vn propagaion i nvironmnal I mpraur i nary i o onan. imula inrnal Ha onduion rak propagaion an b o dribd prdi inrnal onr, raking a la bavior or mpraur rom ura xding rak. C Analyial (Bažan rul & Kaplan propagaion 996), by no rak Fourir id la, nar i rad rbar, laral rak lng and laral rak id ar ompard i xprimnal q λ T rul. T pnraion orroion (7) produ ino rak r rak id i largr an.mm r q i onidrd. i a lux, T i abolu mpraur, and λ i a onduiviy; in i Proding FraMCoS-7, May 23-28, 2

7 4.4. Propagaion rak id vrial rak nar rbar T rak id vrial rak nar rbar a on in Figur 2 i mallr an ura rak id a am lvl orroion ra a on in Figur 9. T propagaion rak id nar rbar alo appar raonably agrmn i xprimnal valu n pnraion orroion ino rak i akn ino aoun Crak id (mm) No pnraion Wi pnraion Exprimn Corroion ra (mg/m 2 ) Figur 2. Propagaion vrial rak id narrbar Propagaion laral rak lng T analyial laral rak lng propagaion i on in Figur 2. T ndny analyial rul i imilar o ing rul. T propagaion laral rak lng i lor o xprimn n pnraion i onidrd. Laral rak lng(mm) No pnraion Wi pnraion Exprimn Corroion ra (mg/m 2 ) Figur 2. Propagaion laral rak lng Propagaion laral rak id Analyial rak id laral rak a om poiion rom rbar ar ompard i xprimnal rul a on in Figur 22a and 22b. Again, n orroion produ pnraion i onidrd, analyial rul appar loly o xprimnal rul. Crak id (mm) mm rom rbar (Analyial) 2mm rom rbar (Analyial) 4mm rom rbar (Analyial) mm rom rbar ( Exp.) 2mm rom rbar ( Exp.) 4mm rom rbar ( Exp.) J Corroion ra (mg/m 2 ) Figur 22a. Propagaion laral rak id (no pnraion). Crak id (mm) J ) D (, T T proporionaliy iin D(,T) moiur prmabiliy and i i a nonlina rlaiv umidiy and mpraur & Najjar 972). T moiur ma balan a variaion in im ar ma volum onr (ar onn ) b q divrgn moiur lux J T ar onn an b xprd a vaporabl ar (apillary a vapor, and adorbd ar) and non- (mially bound) ar n (Mil mm Panazopoulo rom rbar ( Exp.) & Mill 995). I i ra 2mm aum rom rbar a ( Exp.) vaporabl ar i a u 4mm rlaiv rom rbar umidiy, ( Exp.), dgr ydraion mm dgr rom rbar ilia (analyial) um raion, 2mm rom rbar (analyial), i.. 4mm rom ag-dpndn rbar (analyial) orpion/dorpion (Norling Mjonll 997). Undr i aum by ubiuing Equaion ino Equai obain Corroion ra (mg/m 2 ) Figur 22b. Propagaion laral rak ( Did ) (i pnraion). & & 4.5 Manim ura rak id propagaion r i inrnal rak propagaion / i lop orpion/ iorm (alo alld moiur apa From ura govrning rak id quaion propagaion (Equaion (Figur 3) mu b 9) and inrnal by appropria rak propagaion boundary (Figur and iniial 2, ondii 2,22a and 22b), a T manim rlaion bn ura rak amoun id propagaion ar i and inrnal rlaiv rak umidiy propagaion i alld an b imad a iorm on in i Figur maurd 23: i inraing a) Vrial umidiy rak iniia and dorpion rom onr iorm ura (Figur a. Ngling 23a.) and propaga ir dirn o (Xi al. in rbar orrponding olloing, o orpion ag iorm A o B in ill b Figur rrn 9. In i o bo ag, orpion ura and rak dorpion id rapidly By inra. ay, i yri b) Tn, laral iorm rak ould iniia b akn (Figur ino 23b.) aoun, o and inra rlaion, in vaporabl ir id ar and v lng rlaiv umi i au b ud roaion aording on o onr ign par varia a on rlaiviy in Figur umidiy. 23. Inid T rak ap inii-oa (Figur iorm 23.). or HPC Corroion i inlund produ by many p pnra pially ino inrnal o rak. a inlun In i ag, xn and ura mial rak raion id alo and, inra urn, bu drm pd ruur ura and por rak iz id diribuion propaga-(arion rdu raio, (ag mn B o mial C in Figur ompoiion, 9). SF ) Wi a uring urr im amoun and mod, orroion mpraur, produ,.). inid In rak liraur propaga variou rom ormulaio mix rbar and ound au o drib roaion on orpion onr iorm par a onr on in (Xi Figur al. 23d. 994). T pd Hovr, in ura papr rak id mi-mpirial propagaion xprion in i pro Norling Mjornll (997) i adopd b Proding FraMCoS-7, May 23-28, 2

8 J ) D (, Tag (C o D in Figur 9) i ligly () igr an prviou ag (B o C). T proporionaliy iin D(,T) i alld moiur prmabiliy and i i a nonlinar union rlaiv umidiy and mpraur T (Bažan & Najjar 972). T moiur ma balan rquir a variaion in im ar ma pr uni (a) (b) volum onr (ar onn ) b qual o divrgn moiur lux J J T ar onn () an b xprd (d) a um vaporabl ar (apillary ar, ar Figur 23. Inrnal raking manim. vapor, and adorbd ar) and non-vaporabl (mially bound) ar n (Mill 966, Panazopoulo & Mill 995). I i raonabl o 5 CONCLUSIONS aum a vaporabl ar i a union rlaiv umidiy,, dgr ydraion,, and Exprimn dgr ilia and um 3D- raion, RBSM analyial, i.. modl (, a, ) udid ag-dpndn o valua raking orpion/dorpion bavior iorm onr pimn (Norling Mjonll i ingl 997). rbar. Undr i aumpion and by T ubiuing r pa Equaion marial ino orroion Equaion xpanion 2 on modl obain a applid in analyi. T valu iniial ikn and linar lai modulu orroion produ r rommndd. Inrnal rak parn, ura rak ( D ) & & id & propagaion n (3) and inrnal rak propagaion r imulad quaniaivly and qualiaivly and ompard i r xprimnal / i lop rul. Morovr, orpion/dorpion iorm orroion (alo produ alld pnraion moiur ino apaiy). rak during T orroion govrning pro quaion a (Equaion invigad 3) mu and b i ompld a onirmd by appropria a boundary imulaion and rul iniial r ondiion. quaniaivly agrd T i rlaion xprimnal bn rul amoun n vaporabl i a ar onidrd. and rlaiv umidiy i alld adorpion iorm Manim i maurd ura i rak inraing id propagaion rlaiviy a umidiy lariid and and dorpion i a rongly iorm dpndn in oppoi on inrnal a. Ngling rak propagaion. ir dirn Tror, (Xi al. in 994), ordr o in valua olloing, ura orpion rak iorm propagaion, ill b ud inrnal i rak rrn propagaion o bo orpion mu b and lariid. dorpion ondiion. By ay, i yri moiur iorm ould b akn ino aoun, o dirn rlaion, vaporabl ar v rlaiv umidiy, mu b ud aording o ign variaion rlaiviy umidiy. T ap orpion iorm or HPC i inlund by many paramr, pially o a inlun xn and ra mial raion and, in urn, drmin por ruur and por iz diribuion (ar-o-mn raio, mn mial ompoiion, SF onn, uring im and mod, mpraur, mix addiiv,.). In liraur variou ormulaion an b ound o drib orpion iorm normal onr (Xi al. 994). Hovr, in prn papr mi-mpirial xprion propod by Norling Mjornll (997) i adopd bau i REFERENCES xpliily aoun or voluion ydraion raion and SF onn. Ti orpion iorm Andrad, rad C., Alono,C.,Molina,F.J.,993.Covr raking a a union bar orroion: Par I-Exprimnal, Marial and Sruur, 26: Cabrra,J.G.,996.Drioraion Conr Du o Rinormn l Corroion, Cmn & Conr Compoi (,, ) G (, ) 8: ( g ) Kaamura,K.,Nakamura,H.,Kunida,M.,Uda,N.,29.A undamnal udy abou valuaion rak propagaion in onr indud by rbar orroion ( g (in Japan), ) Prod- ing JCI ming, K (, Japan ) Conr Iniu, CD:75-8. Lundgrn,K.,22, Modling orroion on bond in rinord onr, Magazin Conr Rar,54,No.3: ir rm (gl iorm) rprn r Mauo, pyially T., Niiui, bound (adorbd) T., Maumura, ar T.,997.Crak and Propagaion ond rm (apillary Analyi in Conr iorm) indud rprn by Rbar Corroion apillary Expanion (in Japan), Conr Journal, Japan Conr ar. Iniu,9:99-4. Ti xprion i valid only or lo onn Nguyn,Q.T.,Millard,A.,Car,S.,L Hoi,V.,Braud,Y.,26 SF. T iin G rprn amoun ar.fraur pr uni onr volum aud ld by in rinormn gl por a orroion % rlaiv produ, umidiy, J.Py.IV and Fran i 36:9-2. an b xprd (Norling O,B.H., Mjornll Kim,K.H.,Jang, 997) a B.S.,29.Criial orroion amoun o au raking rinord onr ruur, ACI Marial Journal,V,6,No.4: Saio, S.,999.Fraur analy G ruural onr uing (, ) k k pring nork vg i random vg gomry, Dooral i, Kyuu Univriy. Toongonong,K.,Makaa,K. 25.Simulaion oupld r k vg and k vg ar marial paramr. From orroiv produ ormaion, migraion ino rak and maximum propagaion amoun in rinord ar ion, pr uni Journal volum Advand a an ill Conr all por Tnology, (bo apillary Vol.3, No.2: por and gl por), on Tran,K.K., an alula Kaamura,K.,Nakamura,H.,Kunida,M.,29. K a on obain Prdiion O Craking O Conr Du To Rbar Corroion Uing 3D- RBSM, Proding Elvn Inrnaional Summr Sympoium, JSCE: g Val,V. D., Crnin,L.,.88 Sar,G.M.,29.Exprimnal.22 G and Numrial Invigaion Corroion-Indud Covr (6) K ( ) Craking, in Rinord Conr Sruur, Journal Sruural Enginring, ASCE, g 35: T marial paramr k vg and k vg and g an b alibrad by iing xprimnal daa rlvan o r (vaporabl) ar onn in onr a variou ag (Di Luzio & Cuai 29b). 2.2 Tmpraur voluion No a, a arly ag, in mial raion aoiad i mn ydraion and SF raion ar xormi, mpraur ild i no uniorm or non-adiabai ym vn i nvironmnal mpraur i onan. Ha onduion an b dribd in onr, a la or mpraur no xding C (Bažan & Kaplan 996), by Fourir la, i rad q λ T (7) r q i a lux, T i abolu mpraur, and λ i a onduiviy; in i Proding FraMCoS-7, May 23-28, 2