Use of Mathematical Models for Predicting the Service Life of Concrete Structures

Transcription

1 halmers Uiversiy of Techology Use of Mahemaical Models for Predicig he Service Life of ocree Srucures Tag Lupig, halmers Uiversiy of Techology oes: Service life modellig i geeral Mahemaics i modellig of chloride igress Aalyical sesiiviy of models Mechaisic modellig ompariso of differe models oclusios Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

2 halmers Uiversiy of Techology eerioraio of ocree orrosio iduced by carboaio orrosio iduced by chlorides Freeze/haw aack hemical aack (groud waer, soil, ) Abrasio (erosio, wearig) Leachig, AAR/ASR, Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

3 halmers Uiversiy of Techology eerioraio of ocree orrosio iduced by carboaio orrosio iduced by chlorides Freeze/haw aack hemical aack (groud waer, soil, ) Abrasio (erosio, wearig) Leachig, AAR/ASR, Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

4 halmers Uiversiy of Techology Service Life of ocree Srucures Eposed o hloride Evirome Fucioaliy Acual fucioaliy esiged fucioaliy Srucural failure orrosio iiiaio hloride igress orrosio propagaio esiged service life Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

5 halmers Uiversiy of Techology efiiio of Service Life There are some argumes o he defiiio of service life, especially i he cosideraio of propagaio period. From he viewpoi of srucural desig, service life is ofe defied as he ime of damage iiiaio, especially i he case of chloride iiiaed piig corrosio. Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

6 halmers Uiversiy of Techology Probabilisic Service Life esig Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

7 halmers Uiversiy of Techology Probabilisic Service Life esig Probabilisic service life desig is i fac i a saisic way o hadle eermiisic models, Key o proper predicio of service life Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

8 halmers Uiversiy of Techology Empirical Modellig Based o pheomea, observaios ad perimeal daa Much depedig o he availabiliy of represeaive daa for model buildig ad validaio Apar from cause-ad-effec bewee variables, o much requirig i erms of kowledge or udersadig A rial ad error approach Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

9 halmers Uiversiy of Techology Quesioable Empirical Modellig y.6e.8 R.95 y R.96 y.77e.9 R.9 y R.89 y y 8.43L() +.65 R.94 y y 8.48L() R.79 Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

10 halmers Uiversiy of Techology Mechaisic Modellig Based physics ad chemisry goverig he behaviour of he process No requirig much daa for model developme, ad hece o subjec o he hypersesiiviies i daa Requirig a fudameal udersadig of he physics ad chemisry goverig he process Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

11 halmers Uiversiy of Techology Modellig for hloride Igress Simple Fick s d Law Modified Fick s d Law uraree Model Mechaisic models (e.g. lioc Model) Based o physical ad chemical processes Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

12 halmers Uiversiy of Techology Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig Simple Model based o Fick s d Law Error-fucioal soluio o Fick s d Law erf i s s erf s whe i

13 halmers Uiversiy of Techology Assumpios i he simple Fick s law model for choride raspor No-charged paricles (bu l - is acually charged oes) osa diffusio coefficie (bu may chage wih may facors, such as coisig ios, cocree age, emperaure, ad i some cases wih deph) osa bidig capaciy (bu i may chage wih ph, emperaure, ec.) No effec of emperaure Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

14 halmers Uiversiy of Techology Time-depede iffusio oefficie Isaaeous (e.g. from rapid migraio es) ( ) + ' cocree age; ' age whe is esed; ' age whe cocree is posed; posure duraio Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

15 halmers Uiversiy of Techology Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig Mahemaics of Time-epede T a s erf erf a appare ( ) ( ) ( ) ( ) b a ( ) ( ) ( ) ( ) [ ] d T + + ( ) T + a

16 halmers Uiversiy of Techology Mahemaics of Time-epede ( ) a a T + ( + ) ( ) d Appare a is a average of isaaeous () uder he posure duraio from o Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

17 halmers Uiversiy of Techology Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig Mahemaical soluio o Fick s Law wih Isaaeous () ( ) + + T a s erf erf erf

18 halmers Uiversiy of Techology Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig Mahemaical soluio o Fick s Law wih Isaaeous () ( ) + + T a s erf erf erf

19 halmers Uiversiy of Techology Appare iffusio oefficie (curve-fied from he field posure daa) a ( ) a m a + m a m Impossible o obai a wihou posure ( )! Erapolaio from a umber of a ( i ) is eeded o obai a Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

20 halmers Uiversiy of Techology Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig Mahemaical soluio o Fick s Law wih Appare a () T m m a a a s erf erf erf erf ( ) m m a a a I is pracically difficul o obai a, sice i eeds rapolaio from field daa afer posure for may years.

21 halmers Uiversiy of Techology Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig Mahemaical soluio o Fick s Law wih Appare a () T m m a a a s erf erf erf erf ( ) m m a a a I is pracically difficul o obai a, sice i eeds rapolaio from field daa afer posure for may years.

22 halmers Uiversiy of Techology uraree Model for hloride Igress cl (, ) s,cl erf k e,cl k c,cl,cl cl,cl Isaaeous measured usig RM a age k e,cl, k c,cl Eviromeal ad curig facor, respecively No real mahemaical relaioship bewee,cl ad a! No a aalyical soluio o Fick s d law! Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

23 halmers Uiversiy of Techology Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig Relaioship bewee Isaaeous ad appare a () ( ) m m + a a a A age ' he posure duraio! No real mahemaical relaioship bewee ad a!

24 halmers Uiversiy of Techology a from Field Eposures (Bamforh) Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

25 halmers Uiversiy of Techology Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig Aalyical Sesiiviy of Models π z e z s l l l π e z z s l s e z e z z z s π π s s ' ' a

26 Mos Sesiive Parameer halmers Uiversiy of Techology 4 s o or k. f i f i - -4 '..5 '.5.8 ' z ('.) ('.5) ('.8) / s as i Eq (6) ' as i Eq (9) Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

27 halmers Uiversiy of Techology a from Field Eposures (Bamforh) Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

28 halmers Uiversiy of Techology Mechaisic Models for hloride Traspor The sophisicaed models cosider he ieracio bewee he followig processes: Free chlorides as drivig force, Irisic diffusio coefficie, No-liear chloride bidig Effec of co-isig ios, Effec of pore srucures, ad Effec of emperaure (Arrheius law). Numerical echiques have o be employed o simulae he above processes! Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

29 Mechaisic Model lioc TWO Procedures: halmers Uiversiy of Techology. Simulaio of free chloride peeraio hrough he pore soluio i cocree usig a geuie flu equaio based o he priciple of Fick s law wih he free chloride coceraio as he drivig poeial. alculaio of he disribuio of he oal chloride coe i cocree usig he mass balace equaio combied wih o-liear chloride bidig Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

30 halmers Uiversiy of Techology lioc Model for hloride Igress q l Mass balace equaio: Rae of accumulaio of mass i he sysem c b c f d c q l + dq l Rae of mass flow i l d Rae of mass flow ou + dq dq l ( l l ) l dc b q q c l q l Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

31 halmers Uiversiy of Techology Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig lioc Model for hloride Igress Traspor fucio: + + f b f b f o c c c c c c c q c f l o q l q l + dq l c f d c b dc b

32 halmers Uiversiy of Techology Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig hloride Igress Fucios As a egieerig pressio for a ime-depede diffusio process + ξ c c c c i i 6m 6m s erf ( ) c b + ε B c c Free chlorides Toal chlorides

33 hloride Igress Fucios As a egieerig pressio for a ime-depede diffusio process halmers Uiversiy of Techology Free chlorides c c c s c erf Toal chlorides ε i i ( c + c) b B c ξ 6m 6m + Facor bridgig he gap bewee lab es ad acual field posure akig io accou effecs of bidig, emperaure, ec. Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

34 hloride Igress Fucios As a egieerig pressio for a ime-depede diffusio process halmers Uiversiy of Techology Free chlorides c c c s c erf Toal chlorides ε i i ( c + c) b B c ξ 6m Bider coe 6m + Facor bridgig he gap bewee lab es ad acual field posure akig io accou effecs of bidig, emperaure, ec. Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

35 halmers Uiversiy of Techology ocree ad Ipu Parameers Mi No. Bider ype Bider [kg/m 3 ] w/b RM [ - m /s] s [%bider] 3 SRP % SF % FA (fly ash) % SF + % FA % SF (silica fume) Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

36 halmers Uiversiy of Techology Resuls from Modellig for ocree wih Porlad eme l [% by w of bider] 6 4 Field M M Mb M3 No. : SRP w/b.3 [No. ]: SRP, w/b.3 l [% by w of bider] 6 4 No. : SRP w/b.35 [No. ]: SRP, w/b M Simple Fick s d law M uraree equaio Mb uraree wih aalyical eq. M3 lioc model l [% by w of bider] 6 4 No. 3: SRP w/b.4 [No. 3]: SRP, w/b.4 ouble sides igress eph [mm] Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

37 halmers Uiversiy of Techology Resuls from Modellig for ocree wih Bleded eme l [% by w of bider] 6 4 Field M M Mb M3 No. 4: %SF w/b.3 [No. 4]: % SF, w/b.3 l [% by w of bider] [No. 5]: % FA, w/b.3 No. 5: %FA w/b M Simple Fick s d law M uraree equaio Mb uraree wih aalyical eq. M3 lioc model l [% by w of bider] No. 6: 5%SF+%FA w/b.35 [No. 6]: 5% SF + % FA, w/b eph [mm] Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

38 halmers Uiversiy of Techology Resuls from Modellig for ocree Bleded wih 5% Silica Fume l [% by w of bider] [No. 7]: 5% SF, w/b.5 No. 7: 5%SF w/b.5 l [% by w of bider] [No. 8]: 5% SF, w/b.3 No. 8: 5%SF w/b.3 Field M M Mb M l [% by w of bider] No. 9: 5%SF w/b.35 [No. 9]: 5% SF, w/b.35 l [% by w of bider] No. : 5%SF w/b.4 [No. ]: 5% SF, w/b.4 Field M M Mb M eph [mm] eph [mm] Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

39 halmers Uiversiy of Techology Modellig for years hloride Igress i P ocree l [% by w of bider] No. : SRP w/b.3 [No. ]: SRP, w /b.3 l [% by w of bider] No. 3: SRP w/b.4 [No. 3]: SRP, w/b.4 Field y M-y M-y Mb-y M3-y l [% by w of bider] No. 4: %SF w/b.3 [No. 4]: % SF, w /b.3 l [% by w of bider] eph [mm] No. 5: %FA w/b.3 [No. 5]: % FA, w/b.3 Field y M-y M-y Mb-y M3-y eph [mm] eph [mm] Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

40 halmers Uiversiy of Techology Modellig for years hloride Igress i ocree Bleded wih Silica Fume l [% by w of bider] No. 7: 5%SF w/b.5 [No. 7]: 5% SF, w/b.5 l [% by w of bider] [No. 8]: 5% SF, w/b.3 No. 8: 5%SF w/b.3 Field y M-y M-y Mb-y M3-y l [% by w of bider] [No. 9]: 5% SF, w/b.35 l [% by w of bider] [No. ]: 5% SF, w/b.4 Field y M-y M-y Mb-y M3-y eph [mm] eph [mm] No. 9: 5%SF, w/b.35 No. : 5%SF, w/b.4 Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig

41 halmers Uiversiy of Techology oclusios Mahemaics i a predicio model should be carefully amied i order o udersad he physical meaig of ipu parameers The acual daa from he field are very useful for verificaio of differe predicio models Mechaisic model lioc reveals good predicio for all he cases sudied The model usig simple error fucio o Fick s d law sigificaly overesimaes chloride igress uraree model seems uderesimaig chloride igress i cocree wih pozzolaic addiives Research group Buildig Maerials Belfas Workshop, 9 Jue, by Tag Lupig