carbonatacion efecto agrietamiento

7/29/2019 carbonatacion efecto agrietamiento

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P r e di c ti n g c a r bo n at i on i n e a r ly - a ge d c r ac k e d c o nc r et e

H a - Wo n So n g a,, S e un g -J u n K w on a, K eu n- Jo o B yu n a, C ha n- Ky u P ar k b

a S c h o o l o f C i v i l a n d E n v i ro n m e n t a l E n g i n e e ri n g , Y o n s e i U n i v e r s i t y, S e o u l 1 2 0 - 4 7 9 , R e p u b l i c o f K o r e ab S a m su n g C o r po r a ti o n C o ., L T D, R e pu b l ic o f K o re a

R e c ei v e d 2 A p r il 2 0 0 5; a c c ep t e d 2 2 D e c em b e r 2 0 0 5

Abstract

C a r b o n a t i o n i n c r a c k e d c o n c r e t e i s c o n s i d e r e d a s o n e o f m a j o r d e t e r i o r a t i o n s a c c e l e r a t i n g s t e e l c o r r o s i o n i n r e i n f o r c e d c o n c r e t e s t r u c t u r e s . F o r

d u r a bl e c o n c re t e s t r u c t u r es , i t i s n e c e ss a r y t o c o n t ro l c r a c k i n c o n c re t e t h r o u g h c r a c k r e s i st a n c e e v a l u a ti o n f o r e a r l y - a g ed c o n c r et e s t r u ct u r e s, b u t

o f te n u n av o id a bl e c r ac k s i n e a rl y -a g ed c o nc r et e m a y o c cu r. T h es e c r ac k s b e co m e a m a in p a th f o r C O2 p e ne t ra t io n i n si d e c o nc r et e s o t h at t h e

c a r b on a t io n i s a c c e le r a t ed i n c r a c ke d c o n c re t e .

I n t h is s t ud y, a n a n al y ti c al t e ch n iq u e f o r c a rb o na t io n p r ed i ct io n i n e a rl y -a g ed c r ac k ed c o nc r et e w a s d e ve l op e d f o r c o ns i de r in g b o th C O2d i f f u s i o n o f p o r e w a t e r i n s o u n d c o n c r e t e a n d i n c r a c k e d c o n c r e t e . T h e n , c h a r a c t e r i s t i c s o f d i f f u s i v i t y o n t h e c a r b o n a t i o n i n e a r l y - a g e d c o n c r e t e a r e

s t u d i e d t h r o u g h f i n i t e e l e m e n t a n a l y s i s i m p l e m e n t e d w i t h t h e s o - c a l l e d m u l t i - c o m p o n e n t h y d r a t i o n h e a t m o d e l a n d m i c r o - p o r e s t r u c t u r e f o r m a t i o n

m o d e l . T h e c a r b o n a t i o n b e h a v i o u r i n s o u n d c o n c r e t e a n d c r a c k e d c o n c r e t e a r e a l s o s i m u l a t e d b y u s i n g t h e d e r i v e d d i f f u s i v i t y w i t h c o n s i d e r a t i o n o f

r e a c t i o n w i t h d i s s o l v e d C O2. F i n a l l y , n u m e r i c a l r e s u l t s o b t a i n e d f o r c r a c k e d c o n c r e t e m a d e w i t h 3 d i f f e r e n t W/ C r a t i o s ( 4 5 % , 5 5 % , a n d 6 5 % ) w i t h

d i f fe r e n t c r a c k w i d t hs w e r e c o m p a r e d w i t h e x p e r i m e nt a l r e s u lt s .

2 0 05 E l se v ie r L t d. A l l r i g h ts r e se r ve d .

Keywords: Co n crete; Micro -mo d els; FEM; Carb o n atio n ; Early -ag ed crack s

1. Introduction

T he m aj or it y o f c on cr e te d et er io ra ti on i s c on ne ct ed t o

c or r os io n o f r ei nf or ce me nt d ue t o c ar bo na ti on o r c hl or id e-

i n d uc e d d e p a s si v a t io n o f s t e e l b a r s [1]. I n u r ba n a n d i n d u st r ia l

a r ea s , w h er e e n vi r on m en t al p o ll u ti o n r e s ul t s i n a s i gn i fi c an t

c o nc e nt r at i on o f c a rb o n d i ox i de , c a rb o na t io n -i n it i at e d r e in -

f or ce me nt c or r os i on p re va il s. I n t he c as e o f c ar bo na ti on ,

c he mi c al r e ac ti on b et we en c ar bo n d io xi de f ro m t he a ir a ndt h e h y d r a ti o n p r od u ct s o f c e me n t i n c o nc r et e c a us e s a r e du c -

t io n i n t h e a l ka l in i ty o f c o nc r et e a n d c o ns e qu e nt l y i n i t s a b il i ty

t o p r ot e ct t h e s t ee l r e in f o rc e me n t f r om c o rr o s io n [26]. To

prevent premat ure det eri orat i on of concret e st ruct ures, desi gn

a n d m a in t en a nc e g u id e li n es h a ve b e en i s su e d b y a n u mb e r o f

o r ga n iz a ti o ns i n cl u di n g t h e A me r ic a n C o nc r e te I n st i tu t e [7]

a n d t h e C a na d ia n S t an d ar d s A s so c ia t io n [8]. T he re f or e , r e-

s e a r c h i s c u r r e n tl y c o n d uc t e d a t v a r i ou s i n s t it u t io n s t o d e v e lo p

n e w a n d i m pr o ve d c o ns t ru c ti o n m a te r ia l s, r e ha b il i ta t io n a n d

r e pa i r t e ch n ol o gi e s, a n d a b e tt e r u n de r s ta n di n g o f t h e p h ys i ca l

a n d c h em i ca l m e ch a n is m s t h at l e ad t o d e te r io r at i on . T h e i m-

proved knowl edge wi l l enabl e desi gners not onl y t o properl y

r e ha b il i ta t e a n d m a in t ai n t h e c u rr e n t s t oc k o f c o nc r et e s t ru c -

t u re s , b u t a l s o t o i mp r o ve t h e d u r a b il i ty o f f u tu r e s t ru c tu r es b y

g i vi n g, i n t h e d e si g n s t ag e , p r op e r c o ns i de r at i on t o t h e e n vi -

r o n m en t a n d c o n d it i o n s. E x p e ri m e n ta l s t u d ie s o n c a r b o na t i o nw e re c o nd u ct e d b y v a ri o us r e se a r ch e rs [911]. I t wa s c om-

bi ned wi t h a one-di mensi onal di ffusi on model for heat , moi s-

t ur e a nd C O2 f lo w b y S ae tta e t a l. [12] w h o s u b s e qu e n t ly

proposed a t wo-di mensi onal ext ensi on [13]. T h e i d e n ti f i c a ti o n

o f c ar bo na ti on i s a n i mp or ta nt f ac to r f or d ur ab il it y o f r ei n-

f o r c e d c o n c re t e s t r u ct u r e s .

C r ac k s m a y e a si l y o c c u r i n c o nc r e te s u rf a c e d u e t o h e a t o f

h y dr a ti o n, d r yi n g s h r in k ag e a n d i m pr o pe r c u ri n g o f c o nc r et e .

D u ri n g t h e h y dr a ti o n p r oc e s s o f e a rl y -a g ed c o nc r et e , e x te r na l

h a rm f ul a g en t s l i ke c h lo r id e s a n d C O2 p e n e tr a t e s t h r o u gh t h e

c r a c k s a n d i t m a y c a u s e t h e d e t e r i o r a t i o n o f r e i n f o r c e d c o n c r e t e

C e m en t a n d C o n c r et e R e s ea r c h 3 6 ( 2 0 06 ) 9 7 99 8 9

C o r re s p on d i ng a u t ho r. T el . : + 8 2 2 2 1 2 3 2 8 0 6 .

E -mail address: so n g @y o n sei.ac.k r (H.-W. Song).

0 0 08 - 8 84 6 / $ - s e e f r o n t m a t t e r 2 0 0 5 E l s e vi e r L t d . A l l r i g h t s r e s er v e d.doi: 10.1016/j.cemconres.2005.12.019
mailto:[email protected]://dx.doi.org/10.1016/j.cemconres.2005.12.019http://dx.doi.org/10.1016/j.cemconres.2005.12.019mailto:[email protected]


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( R C ) s t r u c t u r e s . T h e e a r l y - a g e d b e h a v i o u r o f c o n c r e t e h a s t o b e

e v a l ua t e d b y c o n s id e r i n g t h e c h a r a ct e r i s ti c s o f e a r l y- a g e d c o n -

c r e t e l i k e h y d r at i o n, m o i st u r e t r a n sf e r , a n d m i c r o- p o r e s t r u c t u r ef o r ma t io n w h ic h a r e i n fl u en c ed b y c o nc r et e m i x p r op o rt i on ,

c ur in g, a nd e xp os ur e c on di ti on f or t he e va lu at io n o f c ra ck

r e s is t an c e i n c o nc r et e s t ru c tu r es [14,15]. E ve n r ea ct io n w it h

d i s s ol v e d C O2 a n d h y d r at e s ( C a ( OH )2 a n d C S H) a r e r e ce n tl y

c o ns i de r ed i n m o de l in g a n d a n al y si s o f c a r bo n at i on [1621],

t he c r ac ks a re n ot c on si de re d o r b ei ng c on si de re d i n a l ea s t

m a n n e r . I t h a s r e p o r t e d t h a t , l o n g t e r m c r a c k i n g h a s b e e n f o u n d

t o a f f ec t t h e d i ff u si v it y o f c o nc r e te [22] . S t ud i es r e ve a le d t h at ,

CaCO3 f o r m e d d u r i n g c a r b o n a t i o n e x c e e d s t h a t o f t h e h y d r a t e s

c a u s i ng d e c r e as e i n p o r o s i t y [23,24].

I n t h is s t ud y, t h e c a r bo n at i on p r oc e s s i n c r ac k ed c o nc r et e i s

s i mu l at e d b y c o ns i de r in g t h e r e ac t io n w i th d i ss o lv e d C O2, Ca

(OH)2, a nd C aC O3 b a se d o n t h e c h ar a ct e ri s ti c s o f e a r ly - ag e dc o n c r et e o b t a in e d b y t h e s o - c a ll e d m u l ti - c o m po n e n t h y d r a t i o n

m o d e l a n d m i c r o - p o r e s t r u c t u r e f o r m a t i o n m o d e l [15,19,25,26].

I n o r de r t o o b ta i n c a rb o na t io n b e ha v io u r i n c r a ck e d c o nc r e te ,

a n e q u i va l e n t d i f f u s iv i t y o f C O2 i n c r a c k e d c o n c r e t e i s d e r i v e d

a n d t h e i r r e s u l t s f o r c a r b o n a t i o n p r e d i c t i o n u s i n g F E M a n a l y s i s

a r e v e ri f ie d w i th e x pe r i me n ta l r e su l ts f o r c o nc r et e m a nu f ac -

t u re d w it h d i ff e r en t w a te r c e me n t r a t i o ( 4 5% , 5 5 % a n d 6 5 %)

a n d c r a c k w i d th s .

2. CO2 diffusion in cracked concrete

2 .1 . E nt i re f l ux f or C O2 i n s o un d a n d c r ac k ed c o nc re t e

T he C O2 d i ff u si o n i n c r ac k ed c o nc r e te c a n b e f o rm u la t ed

by averagi ng t he CO2 d i ff u si o n i n s o un d c o nc r et e v o lu m e,

w hi ch d os e n ot h av e c ra ck s, a nd t he C O2 d i f f us i o n i n c r a c k ed

c o nc r et e v o lu m e h a vi n g d i ff e r en t c r ac k w i dt h s. I n t h is p a pe r,

a n e q u i va l e n t d i f f u s iv i t y o f C O2 i n c r a c k e d c o n c r e t e i s d e r i v e d

a n al y ti c al l y w i th a n a s su m pt i on t h at l i qu i d a n d g a se o us f l ow

r a t e o f C O2 ( m o l /s ) a r e c o n s ta n t i n t h e s o - c a l l e d r e p r e s e n t at i v e

e le me nt v ol um e ( RE V) o f c r ac ke d c on cr et e. A d et ai le d d is -

c u ss i on o n m o de l in g f o r e a rl y -a g ed c o nc r e te l i ke m u lt i -c o m-

ponent hydrat i on model and mi cro-pore st ruct ure format i on

m od el a nd s ch em at ic s o f t he ir i nt er a ct io ns c an b e f ou nd i n

Refs. [15,25,26].

I sh id a a nd M ae ka wa [19] h av e p ro vi de d C O2 f lu x a nd

d if fu si vi ty a s s ho wn i n E qs . ( 1) a nd ( 2) , r es pe c ti ve ly, w hi ch

u t i l i z e s b o t h l i q u i d C O2 d i f f u s i o n i n s a t u r a t e d p o r e v o l u m e a n dg a s e o us C O2 d i f f us i o n i n n o n - s a tu r a t ed p o r e v o l u me

JCO2 /Dd0X

Zrc0

dVAqdAx

/Dg0

X

Zlrc

dV

1 NK Aqg

Ax

0@

1A 1

D CO2 /1S4 KCO2X1 NK D

g0

/S4

XDd0 2

where JCO2 i s e n t i r e f l u x o f C O2, V i s p o r e v o l u m e , i s a v e r a g e

t or tu ri ty o f s in gl e p or e (2/ 4), D0d ( 1 . 0 1 09 m2/ s) a nd D0

g

( 1 . 3 4 1 09 m2/s ) a re b as ic CO2 d i f f us i v i ti e s f o r d i s s o lv e da n d g a s e o us s t a t e, r e s p e c ti v e l y, d and g (kg/ m

3) a r e c o n c en -

t r at i on o f C O2 f o r d i s s o lv e d a n d g a s e o us s t a t e, r e s p e c ti v e l y,

i s p o r o si t y, NK i s K n ud s en n u mb e r, S i s s a t u r a ti o n , KCO2 i s

e q u i li b r iu m f a c t or f r o m H e n r y 's L a w.

I n o rd er t o d er iv e t he e qu iv al en t d if fu si vi ty o f C O2 i n

c r a ck e d c o n c r et e , a n R EV i s c o ns i de r ed a s s h ow n i n F ig . 1. It

i s a s su m ed t h at d i ff u si o n p a th s a r e c o mp o se d o f o n ly c a pi l la r y

pores and cracks. It i s al so assumed t hat each capi l l ary pore can

be model ed as each pi pe whi ch has const ant radi i ri a n d a r e a s Aia nd e ac h c r ac k i s m od el ed a s a c on e w it h d if fe r en t d ia me te r

v a r y i ng f r o m m a x i m u m c r a c k w i d th rcr t o z e ro .

To t al i o n f l ow r a te QiL

( mo l/ s ) i n t he R EV, i s e qu al t o t hes u m o f i o n f l o w r a t e i n c a p i l l a r y p o r e s Qicp

L ( m o l / s ) a n d i o n f l o w

r a te i n c ra ck s w id th QcrL ( mo l/ s) , w hi ch i s g iv en i n E q. ( 3) .

Q Li QLicp QGicr QLicp Q Licr d f/Sd KCO2 3

where f(S) i s a r e si s ta n t f u nc t io n r e pr e s en t in g t h e c h ar a ct e r-

i s ti c s o f p a th s o f t h e c r ac k s. L o ca l e q ui li b ri u m c o nd i ti o n b e -

t we en l iq ui d s ta te a nd g as eo us s ta te i s s at is f ie d i n t he p or e

v ol um e b ut n ot i n t he c ra ck w id th , s o t ha t t he f un ct io n f(S)

w ri tt en a s E q. ( 4) i s c on si de r ed f or d ec re as e i n c ar bo na ti on

process i n cracked concret e wi t h l ower W/ C rat i o.

f/S 0:002/S9:1952 4

Total Area of REV : A0Area of Capillary Pore : Acp

Area of Crack : Acr

CO2 (liquid)

CO2 (liquid)

CO2 (gas)

F i g . 1 . R E V i n c r a ck e d c o n c r et e .

9 8 0 H . - W. S o n g e t a l . / C e m en t a n d C o n cr e te R e s ea rc h 3 6 ( 2 0 0 6 ) 9 7 9989


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where S i s d e f i n e d a s E q . ( 5 ) .

/S VL0 =V0 5where V0

L i s s a t u r a t e d v o l u m e o f R E V a n d V0 i s v o l u m e o f R E V .

A l o n g w i t h t h e F i c k ' s 1 s t L a w , i o n f l o w r a t e QicpL and QcrL c a n b ee x p r e s s e d i n E q s . ( 6 ) a n d ( 7 ) .

QLicp JLcpX

Ai DCO2 FLAcp 6

QLicr JLcr X

Ai Dcrack FLAcr 7where Jcp

L and JcrL a r e a v er a ge f l ux i n c a pi ll a ry p o re a n d c r a c k,

respect i vel y, and FL (mol / m4) i s c o n c e n t r a t i o n g r a d i e n t i n p o r e

sol ut i on.

I n o r de r t o o b ta i n e q ui v al e nt d i ff u si v it y DCO2eq i n R E V, t o t a l

s a t u ra t e d a r e a A0L (= Acp + Acr) o f d i s s o l v e d C O2 i n t ot al a re a i n

t h e R E V i s c o n s i d e r ed a s E q . ( 8 ) t h e n , t h e e q u i v a le n t d i f f u s iv i t y

DCO2eq c a n b e o b ta i ne d f r om t h e d i ff u si v it y i n s o un d c o nc r e teDCO2 a n d d i ff u si v it y i n c r ac k ed c o nc r et e Dcrack a s Eq . ( 9) .

QLi JLiX

Acp Acr D eqCO2 FL AL0 8

DeqCO2

AL0 DCO2 Acp D crackAcr KCO2f/S 9

E q . ( 9 ) c a n b e r e w r i t t e n a s E q . ( 1 0 ) .

DeqCO2

DCO2 AL0Acr =Acr Dcrack KCO2f/S

AL0 =Acr 10

S i n c e t h e r a t i o o f s a t u r a t e d a r e a A0L t o t o t a l a r e a A0 i n R EV i s

g i ve n a s E q . ( 11 ) w i th a v er a ge t o rt u ri t y (= ( / 2)2) o f s i n g l e

pore, Eq. (10) becomes Eq. (12).

AL0 =A0 /S=X 11

DeqCO2

DCO2 Dcrack KCO2 f/SX

Ra/S12

where Ra i s d e f i n e d a s t h e r a t i o o f t o t a l a r e a A0 t o c r a c k a r e a Acrw h i c h i s e q u i v a l e n t t o t h e a r e a o f t h e c o n e (rcr

2 / 3 ) i n t h e R E V

a s E q . ( 1 3 ) .

Ra A0=Acr 13

I n t h e R E V, s i nc e C O2 d i ff u si o n i n c r ac k i s a l mo s t s a m e a s

CO2 di ffusi on D0g i n t h e a i r , t h e DCO2

eq i n R E V o f E q . ( 2 ) c a n b e

r e wr i tt e n a s E q . ( 1 4) .

D

eq

CO2 /

1S

4

KCO2

X1 NK Dg

0 /S4

X D

d

0 D

g0KCO2 f

/S

X

Ra/S 14E q . ( 1 4) s h ow s t h at i n cr e as e d c r ac k w i dt h rcr c o n s i de r e d i n Raa c c e le r a t e s d i f f u s i on o f C O2 i n c r a c k ed c o n c r et e .

2 . 2. Te m pe r at u re e f f ec t o n C O2 diffusion

A s t e mp e ra t ur e g o es u p , t h e s o l u bi li t y o f C O2 i s d e c r e as e d

a n d a c i d f o rm a ti o n i s a l so d e cr e as e d , b u t d i ff u si v it y o f C O2 i s

i n cr e as e d d u e t o i n cr e as e d a c ti v it y e n er g y. T h e t e mp e ra t ur e

d e pe n de n ce o n d i ff u si o n f o ll o ws A r rh e ni u s' s L a w. I t i s s h ow n

t h at a c ti v it y e n er g y o f C O2 i s a l mo s t c o ns t an t i n c e rt a in t e m-

perat ure range (204 0 C ) r e g a r d l e s s o f W/ C r a t i o s o f c o n c r e t e

[27]. B a si c al l y, t h e t e mp e ra t ur e e f fe c t s h ou l d b e c o ns i de r ed i nc a rb o na t io n r e ac t io n b e ca u se t h e s o lu b il i ty - p ro d uc t c o ns t an t

a nd H en ry 's c on st an t o f C O2 a r e d e pe n d en t o n t e mp e r at u re .

B u t w e c o ns i de r t h e t e mp e ra t ur e e f f ec t o n d i ff u si v it y o n ly t o

A rr he ni us 's L aw f or t he s ak e o f s im pl ic it y i n a na ly si s. T he

t e mp e ra t ur e e f f ec t o n d i ff u si v it y o f C O2 i s g iv en i n E q. ( 15 ).

DT Dref d exp UR

1

Tref

1

T

15

where Dref i s r e fe r e nc e d i ff u si v it y ( s am e a s DCO2eq i n c r a ck e d

c o n c re t e a n d DCO2 i n s o u n d c o n c r e t e ), U ( 8 50 0 C a l/ m ol K ) i s

0.00E+00

5.00E-08

1.00E-07

1.50E-07

2.00E-07

2.50E-07

0 2 4 6 8 10

Cover depth (cm)

Diffusivity(m2/s)

with temperature effect T : 25C

with temperature effect T : 40C

with porosity change effect (T : 25C)

F i g . 2 . D i f fu s i vi t y o f C O2 v s . e f f ec t o f p o r os i t y a t v a r i ou s t e m pe r a t ur e s .

0.00E+00

2.00E-06

4.00E-06

6.00E-06

8.00E-06

1.00E-05

1.20E-05

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.450.4

Crack width (mm)

Diffusivity(m2/s)

W/C 45%

W/C 55%

W/C 65%

F i g . 3 . D i f f us i v i t y o f C O 2 v s . c r a ck w i d t h.

0

40

80

120

160

200

Crack width (mm)

DeqCO2

/DCO2

W/C 45%

W/C 55%

W/C 65%

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.450.4

F i g . 4 . R a t i o o f DCO2eq / DCO2 v s . c r a c k w i d t h f o r v a r i ou s W / C ratio s.

9 8 1 H.-W. Song et al. / Cement and Concrete R esearch 36 (2006) 979989


4/11

a ct iv it y e ne rg y o f CO2, and Tref ( 29 8 K) is r ef er en ce

t emperat ure.

2 . 3. P o ro s it y c h an g e e f f e c t o n C O2 diffusion

I n g e ne r a l, t h e d i ff u s iv i ty c o ef f ic i en t o f C O2 i s o b ta i ne d b y

e x pe r im e nt s w i th N2 or O2 m u lt i pl i ed b y t h e m o le c ul a r m a ssr a ti o o f C O2, s o t h a t i f C O2 g a s i s u s ed , t h e d i ff u si v it y c o ef f i-

c i e n t i s c h a n g e d b y p o r o s i t y c h a n g e d u e t o c a r b o n a t i o n p r o c e s s .

I t i s w el l k no wn t ha t d is so lv ed C O2 r e ac t s w it h h y dr a t es a n d

f o r ms C a CO3 a nd t he v ol um e o f h yd ra te s i s i nc re a se d d ue t o

c a r b o na t i o n p r o c es s [1618]. I t i s a l s o r e p o r t e d t h a t t h e r e d u c -

t i o n i n p o r e v o l u m e o b s e r v e d f o r t h e c e m e n t m a t r i c e s c o u l d b e

a s so c ia t ed w i th t h e d e po s it i on o f C a CO3 f o rm e d d u ri n g c a r-

bonat i on. The vol ume of t he CaCO3 f o r m e d e x c e e d s t h a t o f t h e

h y dr a te s , t h us c a us i ng a r e du c ti o n i n p o ro s it y [23]. C ha ng e i n

porosi t y i s report ed t o be more decreased i n concret e wi t h

r e l a ti v e l y l o w e r W/ C rat i o [24].

T he d if fu si on c oe f fi ci en t o f C O2 i n c on cr e te c an no t b e

m e a s u re d e x p e r im e n t al l y, b e c a us e c a r b o na t i on t a k e s p l a c e a l -r e a d y d u r i n g t e s t in g a n d f a l s i f i e s t h e m e a s u re m e n ts . T h e r e f or e

o xy ge n i s u se d a s a n i ne rt g as t o d et er mi ne t he d if fu si on

coeffi ci ent [28]. As p er s tu dy [29] , w hi ch s ho we d 5 0% o f

d e cr e as e i n p o ro s it y b e fo r e c a r bo n at i on , i s c o ns i de r ed f o r t h is

s t u d y a s E q . ( 1 6 ) .

/R /d 1:25R 1 0:0VRV0:4/R 0:5/ 0:4bRV1:0 16

where (R) i s t h e p o ro s it y f u nc t io n f o r c a r bo n a ti o n p r oc e ss ,

i s p o r o s i t y b e f o r e c a r b o n a t i o n , a n d R i s t h e r a t i o o f t h e a m o u n t

o f C a ( O H )2 c o n s u m e d t o t o t a l a m o u n t o f C a ( O H )2( = c o n s u m e d

w e i g ht o f C a ( O H)2 / w e i g h t o f C a ( O H )2 b e f o r e c a r b o n a t i on ) . I f

t h e e f f e c t o f t e mp e ra t ur e a n d t h e e f fe c t o f p o ro s it y c h an g e a r e

a p pl i ed t o b o th s o un d c o nc r et e a n d c r a ck e d c o nc r et e , t h en t h e

e q ui v al e nt d i ff u si v it y c a n b e r e wr i tt e n a s E q . ( 1 7) .

DeqCO2

"/R1S4KCO2

X1 NK Dg0

/RS4X

Dd0

Dg0KCO2X0:002/RS9:1952

Ra/RS

#

d expU

R

1

Tref

1

T

17

F ig . 2 s h ow s t h e s i mu l at e d d i ff u si v it y c o e ff i ci e nt b y t h e

e f f ec t o f t e mp e ra t ur e a n d p o ro s it y c h an g e d u ri n g c a r bo n at i on

process. The exposure condi t i on i s 10% concent rat i on of CO2a n d 6 5 % r e l a t iv e h u m id i t y, W/ C : 6 5 % a n d c a lc u la t ed c a rb o n-

a t i o n d e p t h i s 4 c m . T h e i n c r e a s e d d i f f u s i v i t y c o e f f i c i e n t d u e t o

c h a n g e i n t e m p e r a t u r e ( 2 0 a n d 4 0 C ) a n d d e c r e a s e d d i f f u s i v i t y

c o ef f ic i en t i n c a rb o na t io n a r ea c a n b e f o un d i n t h e F i g . 2. T h e

e f f ec t o f c r ac k w i dt h o n e q ui v al e nt d i ff u si v it y i s s h ow n i n Fi g.

3. F i g . 4 s h o w s t h e b e h a v i o u r o f DCO2eq / DCO2 v s . c r a c k w i d t h f o r

di fferent W/ C rat i os.

From F i g . 2 i t i s o b se r ve d t h at , a s t h e t e mp e ra t ur e i n cr e a se s

t h e d i f f u s i v i t y a l s o i n c r e a s e d d u e t o i n c r e a s e d a c t i v a t i o n e n e r g y .

T h e t e mp e ra t ur e e f f ec t i s v e ry p r on o un c ed i n c a rb o na t io n , b e -

c a us e t h e d i ff u si v it y o f C O2 i s d e pe n de n t o n t e mp e ra t ur e . I t i s

a l so f o un d t h at a s t h e c o ve r d e pt h i n cr e a se s t h e d i ff u si v it y i s a l so

f o u n d t o d e c r e a s e s .

From F ig . 3 i t i s o bs er v ed t ha t, a s t he w at er c em en t r at io

i nc re as es t he C O2 d if f us iv it y i s a ls o f ou nd t o b e i nc r ea se d

i r re s pe c ti v e o f t h e c r a c k w i dt h . A s t h e c r a c k w i dt h i n cr e a se d

f r om 0 .0 5 t o 0 . 4 5 m m , t h e C O2 d i f f us i v i ty a l s o i n c r e as e s w i t h

[Consideration for ion equilibrium]+

+OHHOH2 +

+ OHCaOHCa 2)( 22 ++

23

23 COCaCaCO

+

+++

2

3332 2 COHHCOHCOH

F i g . 5 . M a s s b a l a n c e a n d e q u i l i b r iu m c o n d i t i on s f o r c a r b o ni c a c i d [19].

T ab l e 1

T h e t e r m s u s e d i n g o v er n i n g e q u at i o n f o r m a s s a n d e n e rg y c o n s e r va t i o n

Variab les [ X i] Pot enti al t erm Flux term Sink t erm

T [temp eratu re] C[Kcal/K.m3]: Co n stan t KHT [Kcal/m2 s ] : C o n st a n t QH[Kcal/m

3 s ] : M u l t i c o m p o n en t

h y dr a t i on m o de l o f c e m en t

P [p o re p ressu re] /qAS

A P k g=Pa m3: P a t h

dependent

mo istu re iso th erms

( Kl + Kv) P [ k g / m2 s ] : R a nd o m

g e o me t r y o f p o r es a n d K n u d s e n

v ap o u r d iffu sio n

QhydAqS /At

k g=m3 s: Wa t e r c o m bi n e d d u e t o h y dr a t i on ; b u l k p o r o s i t y

ch an g e effect

C [CO2 concentration] (1 - S) KCO2 +S [ m ol l / mo l m3]:

P a t h d e p e n de n t t r a ns p o rt o f m a s s ,

Po ro sity ch an g e d ep en d ent

DCO2eqC o r DCO2C [mo l/m

2 s]:

M a s s a n d K n u ds e n d i f f u s i on i n s o u nd a n d /o r

c r a ck e d s u r fa c e , T em p e ra t u re a n d p o r os i t y

ch an g e d ep en d en t

QCO2 [mo l/m3 s ] : C O2 co n su mp tio n

d u e t o c a r bo n a ti o n p r o ce s s

9 8 2 H . - W. S o n g e t a l . / C e m en t a n d C o n cr et e R e s ea rc h 3 6 ( 2 0 0 6 ) 9 7 9989


5/11

r e fe r e nc e t o d i ff e re n t W/ C r at io s. C ar b on at io n h as a c le ar

i n fl u en c e o n t h e p o r o s it y a n d t h is d e cr e a se i s m o re i m po r ta n t

f o r h i gh e r W/ C r a ti o s. T h e p o ro s it y d e cr e a se s a s t h e c a r bo n -

a t io n p r oc e ed s . T h is i s i n a g re e me n t w i t h t h e f i n d in g s o f o t he r

researchers [30] .

From F i g . 4 i t i s o b s e r v e d t h a t , a s t h e c r a c k w i d t h a n d W/ C

r at io i nc r ea se s, t he d if fu si on c oe f fi ci en t DCO2eq

/ DCO2 al so

i ncreases proport i onat el y.

C r ac k s i r re s pe c ti v e o f t h ei r n a tu r e , h a ve a c o ns i de r ab l e i n -

f l u e n c e o n t h e m o i s t u r e p e r m e a b i l i t y o f c e m e n t i t i o u s m a t e r i a l s .

A s a c on se qu en ce , t he t ra ns po rt o f a gg re ss iv e s ub st an ce s i s

promot ed and t he degradat i on process i s furt her accel erat ed. It

i s a l s o r e p o r t e d t h a t l o n g t e r m c r a c k i n g h a s b e e n f o u n d t o a f f e c t

t h e d i f f u s i v i t y o f c o n c r e t e [22]. I t h a s a l s o b e e n r e p o r t e d t h a t t h e

d i ff u si v it y o f t h e m a t e ri a l c a n b e i n cr e a se d b y a f a c to r r a ng i ng

f ro m 2 t o 1 0. T he p re se nc e o f c on ti nu ou s c ra ck s t en ds t o

m a r k ed l y m o d i f y t h e t r a n s p o r t c o e f f i c i en t o f t h e s o l i d . R e s u lt s

o b ta i ne d w it h t h e m o de l i n di c at e t h at t h e i n fl u en c e o f c r ac k in g

t e n d s t o b e m o r e s i g n i f i c a n t w h e n t h e r a t i o D1 / D0 i s i n c r ea s e d .

T h is e s se n ti a ll y m e an s t h e a f fe c t o f c r a ck i ng i s r e la t iv e ly m o re

i m p o r t a n t f o r d e n s e m a t e r i a l s . C o n t i n u o u s c r a c k s f a v o u r l o c a l l y

t h e p e n e t ra t io n o f i o ns . I t m a y a l so c o nt r ib u te t o a c ce l er a t e t h e

Geometrical data

- Shape

- Boundary

Mixture proportions

- Cement, binder

- Content of water and aggregate

2-D Heat Transfer Analysis

Convergence check

2-D Moisture Transfer Analysis

Finite

element

mesh

discretization

and

Solution of

governing

equation

(23)

Exposure

condition

Exterior

temperature

Convergence check

2-D Carbonation process Analysis

Exterior

CO2concentration

Potential

termSKS CO + 2)1(

Flux termCDeqCO 2

For cracked

concrete

CDCO 2For sound

concrete

Flux term ]][[ 22+ COCak

Solving ion equilibrium equation [19,31]

0201110121 2][

2)(2][ CCH

KSSSSH W ++=++++

+

+

Convergence check

FEM Analysis

DataAllocation

Hydrationrate

Amount ofCa(OH)2

Hydration

heat

Porosity

Saturation

Consumed

Ca(OH)2

pH-[H+]

Solubility ofCa(OH)2CaCO3

Reducedporosity

Previous

results

are usedin

carbonation

process

analysis

Exterior

relative

humidity

F i g . 6 . C o m pu t a ti o n al s c h e me o f c o u pl e d m o d el i n g o f c a r bo n at i o n i n c r a ck e d c o nc r e t e.

(a) Splitting test setup (b) Photo for splitting test

Bearing plate

Bearing plate

Front View Section A-A

AA

Lateral LVDT

Lateral LVDT

Loading andunloading test

30-40mm

2-3mm plywood

90-100mm

F i g . 7 . S c h em e f o r c r a ck - i nd u ci n g .



6/11

l o ca l d i ss o lu t io n o f s o li d p h as e s t h at m a y s u bs e qu e nt l y a f fe c t

t h e m a t e ri a l b e h a vi o u r.

3. Modeling for CO2 transport and reaction of carbonation

3 . 1. G o ve r ni n g e q ua t i on f o r C O2 transport

I n t hi s s ec ti on , t he m as s b al an ce c on di ti on s f or c ar bo n

d io xi de i n a p or ou s m ed iu m a r e f or mu la te d. Tw o p ha se s o f

c a r bo n d i ox i de e x is t in g i n c o nc r et e a r e c o ns i de r ed ; g a se o us

c ar bo n d io xi de a nd c ar bo n d io xi de d is so lv ed i n p or e w at er.B y s o lv i ng t h e m a s s b a la n c e e q u a ti o n u n de r g i ve n i n it i al a n d

boundary condi t i ons, t he non-st eady st at e condi t i on of carbon

d i ox i de i s q u an t if i ed a s E q . ( 1 8) .

A

At/1Sdqg /Sdqd di vJCO2QCO2 0 18

where i s t ot al p or os it y a s t ra ns f er r ou te a nd s to ra ge , S i s

sat urat i on, g and d a r e d e n s i t y o f g a s e o u s a n d d i s s o l v e d C O 2d e n s i t y ( k g / m3), respect i vel y. JCO2 i s t o t a l f l u x o f d i s s o l v e d a n d

g a s e o u s C O2 (kg/ m2 s ) . T h e f i r s t t e r m i n E q . ( 1 8 ) r e p r e s e n t s t h e

r a t e o f c h a n g e i n t o t a l a m o u n t o f C O 2 p e r u n i t t i m e a n d v o l u m e ,

t h e s e c o n d t e r m i s t h e f l u x o f C O2, a n d t h e t h i r d t e r m QCO2 i s a

s i nk t e rm . T h e a b ov e e q ua t io n g i ve s t h e c o nc e nt r at i on o f g a s-e ou s a nd d is so lv ed C O2 w it h t im e a nd s pa ce . I n p re vi ou s

st udi es [1618], t h e f o rm a ti o n o f h y dr a te a n d p o ro s it y c h a ra c -

t e ri s ti c s a r e o b ta i ne d f r om r e gr e s si o n a n al y si s a s P o we r L a w,

but i n t hi s paper, t he so-cal l ed Mul t i -Component Hydrat i on

H e at M o de l ( M CH H M) a n d M i cr o -P o re S t ru c tu r e F o rm a ti o n

M o d e l ( M P S F M ) a r e u t i l i z e d f o r s y s t e m d y n a m i c s f o r E q . ( 1 8 ) .

3 . 2. E q ui l i br i u m c o nd i ti o n f o r g a se o us a n d d i ss o l ve d C O2

T h e l o c a l e q u i l i b r i u m b e t w e e n g a s e o u s a n d d i s s o l v e d C O 2 i s

r e p r e s e n t e d b y H e n r y ' s L a w a n d D a l t o n ' s L a w , w h i c h s t a t e t h e

r e l a t i o n s h i p b e t w e e n g a s s o l u b i l i t y i n p o r e w a t e r a n d t h e p a r t i a lg a s p r e s su r e a s E q . ( 1 9 ) .

PCO2 HVCO2 dqVd; 19where PCO2 i s e q u i l i b r iu m p a r t i a l p r e s s u r e o f c a r b on d i o xi d e i n

t h e g a s p r e s s ur e ( P a) , d i s m ol e f r ac ti on ( CO2 mol / sol ut i on

mol ), HCO2 i s H en r y c on st an t ( 1. 45 1 08 P a /m ol f r a ct i on , a t

2 5 C) . F or o ne c ub ic m et er o f d il ut e s ol ut io n, t he m ol es o f

w at er i n t he s ol ut io n, nH2O wil l b e 5 .5 6 1 04 (mol / m3).

A c co r di n gl y, t h e c o nc e nt r a ti o n o f d i ss o lv e d C O2 p er c ub ic

m e te r o f s o lu t io n , d (kg/ m3 ) c an b e e xp re ss ed a s E q. ( 20 ).

qd PCO2

HVCO2d nH2 Od MCO2

PCO2HCO2

20

where MCO2 i s m ol ec ul ar m as s o f C O2 ( 0 .0 4 4 k g /m o l) . E q .

( 19 ) c an b e r ew ri tt en a s E q. ( 21 ) w it h a ss um pt io n o f p er f ec t-

g a s e q u a ti o n .

PCO2 qg RT

MCO221

where R i s g a s c o ns t an t ( J /m o l K ) , T i s a b s o lu t e t e m p er a t u r e

(K).

A f t e r t h e d i s s ol u t io n , C O 2 r e ac t s w i t h c a lc i um i o ns , a n d s o

t he c on ce nt ra ti on o f d is so lv ed C O2 c an f lu ct ua te f ro m t he

a b o v e e q u i li b r i u m c o n d i t i on . T h e e q u i li b r i u m c o n d i t i on c a n n ot

be formul at ed by Henry's Law al one; i t i s al so necessary t o

d e te r mi n e t h e a m ou n t o f d i ss o lv e d C O2 b as ed o n t he r at e o f c h em i ca l r e ac t io n s, w h ic h r e pr e s en t s k i ne t ic f l uc t ua t io n s d e -

pendent on t he di st ri but i on of CO2 c o n c e nt r a t io n . H o w ev e r , i t

i s v e r y d i f f i c u l t t o t a k e i n t o a c c o u n t s u c h k i n e t i c f l u c t u a t i o n s a s

i t is, and in f act, i t is expect ed t hat the rate of CO2 gas

d i ss o lu t io n w i ll b e f a s te r w h en t h e p a rt i al p r es s u re o f C O2 gas

becomes l arge. For t hese reasons, i n t hi s model we assume t hat

t h e a m o u nt o f d i ss o lv e d C O2 c a n b e a p p r ox i m at e l y d e s c r i be d

by Henry's Law [17,27].

3 . 3 . M o d e l i n g o f c a r b on a t i o n p r o c e s s

I s h i d a a n d M a e k a w a h a v e p r o p o s e d t h e c a r b o n a t i o n r e a c t i o nw i t h s o l u b i l i t y o f C a ( O H )2, C a C O3 [19,25,26]. T h e r a t e o f C O2c o ns u mp t io n d u e t o c a rb o na t io n c a n b e e x pr e s se d b y t h e f o l -

l ow in g d if f er en ti al e qu at io n a s E q. ( 22 ), a ss um in g t ha t t he

r e ac ti on i s t he f ir s t o rd er w it h r es pe c t t o [ Ca2+] a nd [ CO32]

concent rat i on.

Ca2 CO23 YCaCO3;ACCaCO 3

At kCa2CO23 22

where CCaCO3 ( m ol / l) i s c o nc e nt r at i on o f c a lc i um c a rb o na t e

and k ( 2 .0 4 l / mo l s ) i s r e a ct io n r a te c o ef f ic i en t . C a lc i um i o ns

T ab l e 3

C o n di t i o n o f a c c el e r a te d c a r bo n at i o n t e s t

CO2co n cen tratio n

Temperat ure R.H. Exposu re

p erio d

D u r at i o n o f

measurement

1 0% 25 0.5 (C) 65 5% 3 mont hs 2 week s F i g . 8 . C a r bo n at i o n d e p t h i n s o u nd c o nc r e t e.

T ab l e 2

M i x p r o po r t i on s o f c o n cr e t e s p e ci m e ns

W / C Slu mp

(cm)

Water

(k g /m3)

Cement

(k g /m3)

Sand

(k g /m3)

Co arse ag g reg ate

(k g /m3)

4 5 15 1 91 424 668 10 58

5 5 15 1 84 335 762 10 58

6 5 15 1 82 280 829 10 41



7/11

r es ul ti ng f r om t he d is s ol ut io n o f C a( OH )2 a re a ss um ed t o

r ea ct w it h c ar bo na te i on s, w he re as t he r ea ct io n o f s il ic ic

a ci d c al ci um h yd ra te ( CS H) i s n ot c on si de re d. T hi s i s b as ed

o n t he f ac t t ha t t he s ol ub il it y o f C SH i s q ui te l ow c om pa r ed

w it h t ha t o f C a( OH )2. I n o rd er t o c al cu la te t he r e ac ti on r at e,

t h e r e l a ti o n o f i o n e q u i li b ri u ms a n d m a s s b a la n ce a s s h ow n i n

F ig . 5 a re c on s id er ed . A d et ai le d d is cu ss i on o f t he c ar bo n-

a t io n r e a ct io n a n d c a rb o na t io n p r oc e ss c a n b e f o un d i n R e fs .

[19,25,26,31].

4. Modeling of coupled heat transfer, moisture transport

and carbonation process in cracked concrete

I n o r d e r t o s i m u l a t e c a r b o n a t i o n p r o c e s s i n c r a c k e d c o n c r e t e ,

h y d r at e s C a ( O H)2, s a tu r at i on , a n d p o ro s it y i n e a rl y -a g ed c o n-

c r e t e s h o u l d b e o b t a i n e d u s i n g g o v e r n i n g e q u a t i o n f o r m a s s a n d

e n er g y c o ns e rv a ti o n i n p o ro u s m e di a g i ve n b y E q . ( 2 3)

aiAXi

At di vJiDijXiQ i 0 23

w he re , t he f ir st t er m i s p ot en ti al t er m, t he s ec on d t er m i s

f lu x t er m a nd t he l as t t e rm i s s in k t er m o f [Xi] i n Eq . ( 23 ).

T he d et ai ls o f [Xi] a nd c om po s it io n t er ms a re e xp la in ed i n

Ta b le 1.From Ta b le 1, C i s s p ec i fi c h e at c a pa c it y, KH i s h ea t

conductivity, QH i s h e at g e ne r at i on r a te , Kl and K a r e l i q ui d

a n d v a po u r c o nd u ct i vi t ie s , Qhyd i s c om bi ne d w at er d ue t o

h yd ra ti on . I n o rd er t o a pp ly t hi s d yn am ic s ys te m t o c r ac ke d

concret e, DCO2eq c o n s id e r i n g t h e t e m pe r a t u re e f f e c t a n d p o r o s it y

c h a n g e r a t e i s c o n s i d e r e d t o f l u x t e r m i n e a c h t i m e a n d s p a c e . A

c o mp u ta t io n al s c he m e o f c o up l ed m o de l in g o f c a r bo n at i on i n

c r ac k ed c o nc r e te i s s h ow n i n F i g . 6 .

5. Verification of the test results for sound concrete and

cracked concrete

5 . 1 . E x p e r im e n t a l p r og r a m

C y li n dr i ca l c o nc r et e s p ec i me n s o f s i ze 1 0 c m d i am e te r a n d

2 0 c m h e ig h t w i th d i ff e r en t W/ C r a ti o s ( 4 5% , 5 5 %, a n d 6 5 %)

w e r e c a s t f o r a c c e l e r a t e d c a r b o n a t i o n t e s t . A f t e r 2 4 h t h e s p e c i -

m en s w er e d em ou ld ed a nd c ur ed u nd er w at er f or 2 8 d ay

( 20 C) . A ft er c ur in g, t he c on cr e te s pe ci me ns w er e k ep t i n

h um id it y c ha mb e r f or 2 w ee k s a t 6 5% R .H . c on di ti on . F or

1 - D c a r b o na t io n p r oc e ss , e x ce p t t h e t o p s u rf a c e o t h e r s i de s o f

t h e s p ec i me n s a r e c o at e d w i th w a x.

F or c ar bo na ti on i n c ra ck ed c on cr et e, t he c ra ck s a re i n-

d uc ed i nt o t he s pe ci me ns b y s pl it ti ng t es t. To m ea su re t he

0

20

40

60

80

100

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

crack width(mm)

carbonation

depth(mm)

0

20

40

60

80

100

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

crack width(mm)

carbonationdepth(mm)

0

20

40

60

80

100

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

crack width(mm)


2 weeks exposed

4 weeks exposed

6 weeks exposed

(a) Carbonation depth in cracked concrete (W/C 45%)

2 weeks exposed

4 weeks exposed

6 weeks exposed

(b) Carbonation depth in cracked concrete (W/C 55%)

2 weeks exposed

4 weeks exposed

6 weeks exposed

(c) Carbonation depth in cracked concrete (W/C 65%)

F i g . 9 . C a r bo n at i o n d e p t h i n c r a ck e d c o n c r e te .

Table 4

C a r bo n at i o n r e s u lt i n s o u nd a n d c r a ck e d c o n cr e t e

Co n d itio n Y Affiffiffiffi

Tp

: mm=week 0:5W / C 4 5 % W / C 5 5 % W / C 6 5 %

C r a ck w i d t h A R2 A R2 A R2

0 (s ound su rface) 1.8 56 0.84 59 2.70 5 0.84 59 4 .472 0. 9057

0 .00.1 mm 8.9 84 0.87 10 12.1 58 0.99 55 22 .283 0. 9288

0 .10.2 mm 13.7 98 0.93 63 18.2 65 0.97 05 22 .283 0. 9887

0 .20.3 mm 18.7 67 0.99 01 23.6 58 0.95 48 25 .904 0. 9982

Over 0.3 mm 24.1 07 0.97 64 29.5 62 0.99 98 30 .671 0. 9939



8/11

F i g . 10 . M o d el l i n g f o r c a r bo n a ti o n p r oc e s s a n d F E M .

(a) Experimental results in sound concrete (b) Experimental results in cracked concrete (W/C 45%)

(c) Experimental results in cracked concrete (W/C 55%)

0

20

40

60

80

100

120

0 10 20 30 40 50

exposed period (days)

0 10 20 30 40 50


0

Experiment

Analysis

Analysis

Analysis

(55%)

(55%)

(65%)

(65%)

(45%)

(45%)

Experiment

Experiment

2010 30 40 50 60 70 80 90


0 10 20 30 40 50


carbonationdep

th(mm)

0

20

40

60

80

100

120


0

20

40

60

80

100

120


0

2

4

6

8

10

12

16

14

18

carbonationd

epth(mm)

EXP (sound)

EXP (0.0-0.1mm crack)



EXP (over 0.3mm crack)

NUM (sound)

NUM (0.0-0.1mm crack)



NUM (over 0.3mm crack)

EXP (sound)




EXP (over 0.3mm crack)NUM (sound)





(d) Results in cracked concrete (W/C 65%)

EXP (sound)




EXP (over 0.3mm crack)

NUM (sound)





F i g . 1 1 . E f f e c t o f c r a ck s a n d W / C r a t i o i n c a r bo n a ti o n p r o ce s s .

i nd uc ed c r ac k w id th , LV DT i s i ns ta ll ed o n t he s ur f ac e o f

s p ec i me n s, p e rp e nd i cu l ar t o d i re c ti o n o f c r ac k p r op a ga t io n .

T he c r ac k w id th m ea s ur e d i n l oa di ng s te p i s w id er t ha n i n

unloadi ng step so we measured crack wi dt h in fully

u nl oa de d s ta te . I t i s v e ry d if f ic ul t t o o bt ai n r e qu ir e d c r ac k

w id th s o t ha t w e h av e t ri ed t o s or t o ut t he c ra ck w id th b y0 . 1 m m- d iv i si o n a f te r s p li t ti n g t e st . T h e s p li t ti n g t e st s e tu p i s

s h ow n i n F ig . 7. M i x p r op o rt i on s o f c o nc r et e s p ec i me n s a r e

s h ow n i n Ta b l e 2, a n d p r oc e du r es o f a c ce l er a te d c a rb o na t io n

t es t a re s ho wn i n Ta b le 3.

5 . 2. E x pe r i me n t al r es u l ts o f c a rb o na t i on d e pt h i n s o un d a n d

c r a c k ed c o n c re t e

T he f r es h- cu t s ur f ac es o f e ac h s li ce ( s ou nd a nd c r ac ke d)

w e r e c l e a n e d a n d s p r a y e d w i t h a p h e n o l p h t h a l e i n p H - i n d i c a t o r .

T h e r e su l ts o f c a rb o na t io n t e st i n s o un d a n d c r ac k ed c o nc r et ea r e s h o w n i n F i g s . 8 a n d 9 ( a , b a n d c ) , r e s p e c t i v e l y . F r o m Fi g.

8 i t i s o b se r ve d t h at t h e c a r bo n a ti o n d e pt h i n cr e as e s w it h t h e

e x p o s u r e p e r i o d . T h e e x p e r i m e n t a l r e s u l t i n s o u n d c o n c r e t e a r e

r e g r e s se d w i t h, s o - c a ll e d , t h e s q u a r e r o o t -t e q u a t i o n a n d t h o s e



9/11

i n c r a c k e d c o n c r e t e a r e p l o t t e d w i t h c r a c k w i d t h s . T h e c i r c l e s i n

F ig . 9 c l ea r ly s h ow t h at t h e c a rb o na t io n p r oc e s s i s f a st e r w i th

hi gher W/ C r a ti o s a n d l a rg e r c r ac k w i dt h . T h e d e ta i le d r e su l ts

i n c ar bo na ti on t es t a re s ho wn i n Ta b le 4. F or s im pl ic it y a nd

c o nv e ni e nc e o f e x pr e s si o n, t h e c r ac k w id t hs o f s p ec i me n s a r e

s o r t ed o u t i n 0 . 1 m m - i n t e rv a l .

From F i g . 9 i t i s o b se r ve d t h at , a s t h e c r a c k w id t h i n c r ea s est h e c a r b o n a t i o n d e p t h a l s o i n c r e a s e s w i t h i n c r e a s e i n W/ C rat i o

a nd e xp os ur e p er io d. I t i s a w el l k no wn f ac t t ha t, a s t he c ra ck

w id th i nc re a se s, a tm os ph er ic ( ga se ou s a nd d is so lv ed ) C O2e nt er s t hr ou gh t he c ra ck a nd i t d et er io ra te t he c on cr et e i n

t er ms o f c ar bo na ti on b y f or mi ng C aC O3 a nd r e du ci ng t he

a lk al in it y o f t he c on cr et e, w hi ch r e du ce s t he d ur ab il it y o f

concret e. Ta b le 4 r e pr e s en t s t h e c a r bo n at i on r e su l ts i n s o un d

a n d c r a c k ed c o n c r et e .

5 . 3 . Ve r i f i c at i o n a n d c o m p a ri s o n

M es h f or F EM a na ly si s i s s ho wn i n F i g. 1 0 a n d n u m e r ic a lr e su l ts a r e c o mp a re d w i th e x pe r im e nt a l r e s ul t s i n F i g . 1 1. T h e

d ep th o f c ar bo na ti on o n s ou nd a nd c r ac ke d c on cr et e c an b e

predi ct ed wel l by t he proposed scheme. Bot h experi ment al and

n u m e r i c a l r e s u l t s s h o w t h e t r a d i t i o n a l t r e n d o f c a r b o n a t i o n w i t h

t i m e . I n t h e c a s e o f l o w W/ C r a t i o, r e l a ti v e l y s l o w c a r b o na t i o n

i s m e a s u r e d . W i t h t h e i n c r e a s e i n c r a c k w i d t h s a n d W/ C rat i os,

r a pi d c a r bo n at i on i s o b ta i ne d . T h e e f f e c t o f c r a ck s o n c a r bo n -

a t io n p r oc e s s i s o b ta i ne d t o b e m o re c r it ic a l f o r c o nc r et e w i th

hi gher W/ C rat i o.

5 . 4. A p pl i c at i on e x am p le s f o r l o ng t e rm e x po s ur e c o nd i ti o n

5 . 4. 1 . P a r a me t er s f o r l o n g t e r m e f f e c t i n t h e m o d e l

A p pl i ca t io n e x am p le s o f l o ng t e rm e x po s ur e c o nd i ti o n a r e

performed t hrough t he proposed model . In cont rast wi t h accel -

e r at e d c a rb o na t io n t e st , C O2 c o nc e nt r at i on i s s o s m al l ( a bo u t

0.030 . 0 6 5% ) t h a t t h e c a r b o ni c r e a c t io n c o n s ta n t , i s c o n s i d-

e r e d t o b e m o d i f i e d f o r r e a s o n a b l e a c c u r a c y [ 24] . T h e E q . ( 2 2 )

f o r c a r b o n i c r e a c t i o n i s m o d i f i e d t o E q . ( 2 4 ) .

ACCaCO3 At

kdkd Ca2CO23 24

where i s c on st an t ( = 52 0) f or l ow c on c en tr at io n o f C O2.

F ur th e rm or e, t he C O2 d if fu si vi ty i n c r ac ke d c on cr et e i s

d e p e n d e n t o n e n v i r o n m e n t a l c o n d i t i o n s u c h a s l o c a l s a t u r a t i o n ,a u to h e al i ng ( c r ac k -c l os i ng ) a s w e ll a s c o nc e nt r at i on o f C O2.

B u t i t i s v e ry d i ff i cu l t t o p e rf o r m q u a n ti ta t iv e m od e li n g f o r t h e

phenomena so equi val ent di ffusi vi t y of CO2 c a n b e m o di f ie d

f o r r e as o na b le a c cu r ac y a s E q . ( 2 5 ) f o r t h e s a k e o f s i mp l ic i ty.

DeqCO2

"/R1S4KCO2

X1 NK Dg0 /RS

4

XD d0

Dg0KCO2X0:002/RS9:1952

Ra/RS dj#

d expU

R

1

Tref

1

T

25

where i s c r ac k p a ra m et e r c o ns i de r in g l o ng t e rm e x po s ur e

c o nd i ti o n a s E q . ( 2 6) .

j 0:1d CCO2 26w h er e i s CCO2 part i al vol ume pressure of CO2, i . e . , c o n c e n tr a -

t i o n o f C O2 (%).

5 . 4. 2 . C a rb o na t i on i n s o un d a n d c r ac k ed c o nc re t e u n de r l o ng

t e r m e x p o s ur e c o n d i t io n

F or v er if ic at io n o f t he p ro po s ed m od el , f ie ld d at a o f a n

u nd er gr ou nd s tr uc tu re i s s el ec te d. F or t he a na ly s is o f f ie ld

d a ta t h e f o ll o wi n g m i x p r op o r ti o ns a n d e n vi r on m en t al c o nd i -

t i o n s a r e a d o p t e d a s s h o w n i n Ta b l e 5.

Table 5

Mix tu re p ro p o rtio n an d en v iro n men tal co n d itio n

W / C(%) C (k g /m3) G (k g /m3) S (k g /m3) Slu mp (cm)

55 335 1058 762 15

U nd er gr ou nd E xt er io r t em pe ra tu re :

1 8 C

CO2 co n cen tratio n :

6 7 0 p p m

R e la t iv e h um i di t y : 65 . 3% E x po s ed p e ri o d : 20 . 0 y e ar s

A bo v eg r ou nd E x te r io r t e mp e ra t ur e :

1 8 C

CO2 co n cen tratio n :

3 4 0 p p m

R e la t iv e h um i di t y : 80 . 0% E x po s ed p e ri o d : 18 . 3 y e ar s

0

5

10

15

20

0 5 10 15 20 25 30

exposed period (year)

Analysis

Field data

Carb

onationdepth(mm)

F i g . 1 2 . C o m p a r i s o n o f n u m e r i c a l d a t a w i t h f i e l d d a t a ( u n d e r g r o u n d s t r u c t u r e o f

so u n d co n crete).

0

2

4

6

8

0 5 10 15 20 25 30

Exposed period (year)

Carbonationdepth(mm)

Analysis : sound

Field data : sound

Analysis : 0.1mm crack

Field data : 0.1-0.2mm crack

F i g . 1 3 . C o m p a r i s o n o f n u m e r i c a l r e s u l t s w i t h f i e l d d a t a ( a b o v e g r o u n d s t r u c t u r eo f so u n d /cracked co n crete).



10/11

T h e n u m e ri c al r e su l t w i t h f i e l d d a t a i s s h ow n i n F i g . 1 2 and

t he p ro po s ed m od el c an p re di ct t he c ar bo na ti on d ep th w it hreasonabl e accuracy. F i g. 1 3 s h ow s t h e n u me r ic a l r e s ul t s w i th

f ie ld d at a o f c ar bo na ti on d ep th f or R C c ol um n l oc at ed i n

o u td o or c o nd i ti o n ( a bo v eg r o un d ) . T h e f i el d d a ta s h ow s s l ow

c a r bo n at i on d e pt h b e ca u se o f l o w h u m i di t y d u e t o v a ri a ti o n o f

e n vi r on m en t al c o nd i ti o n s u ch a s r a in o r d r ai n ag e w a te r. T h e

e xp os ed p er io d o f t he s tr uc tu re s i s 1 8. 3 y ea rs a nd e xt er io r

c o nc e nt r at i on o f C O2 i s a ss um ed t o b e 3 40 p pm f or n or ma l

c o n d it i o n . T h e s l o w c a r b o n a t io n v e l o ci t y i n o u t do o r c o n d it i o n

i s a l so r e po r te d b y p r ev i ou s s t ud i es [6,32] .

F o r c o m p a r i s o n o f n u m e r i c a l d a t a w i t h f i e l d d a t a o f c r a c k e d

c o n c r et e , p r e v i ou s w o r k [33] i s r ef er r ed b ut i t i s a ss um ed t ha t

f or c ar bo na te d c on cr et e t he c om pr es s iv e s tr en gt h w as 2 0

2 4 M pa a nd e xp os ur e p er io d i s 2 02 5 y e ar s . T h e n u me r i ca lr e su lt s f or c ar bo na ti on i n c ra ck ed c on cr et e i s s ho wn i n Fi g.

14 w it h f i el d d a ta .

A s s h o w n i n F i g . 1 4, t h e n u m e r i c a l a n a l y s i s c a n w e l l p r e d i c t

t h e c a r bo n at i on d e pt h e x ce p t t h at t h e c a r bo n at i on d e pt h s f r o m

n um er ic al a na ly si s f or t he c as e o f s ma ll c ra ck w id th ( 0. 0

0 .1 m m) a r e s li gh tl y o ve r e st im at e d t ho se f r om f ie ld d at a.

T hi s d if fe re nc e i s t ho ug ht t o b e b as ed o n t he f ac t t ha t t he

i nc re as ed f lu x t er m w it h c ra ck i n p ro po se d t ec hn iq ue i s

a ss um ed t o b e i n p ro po r ti on t o s qu ar e d c ra ck w id th .

6. Conclusions

T he f ol lo wi ng c on cl us io ns w er e d ra wn f ro m t he a bo ve

i nvest i gat i on:

T h e c a r b o n a t i o n p r e d i c t i o n t e c h n i q u e a l o n g w i t h m u l t i c o m -

ponent hydrat i on model and mi cro-pore st ruct ure format i on

m o de l i s c a pa b le o f h a nd l in g d i ff u si v it y o f C O2, b y c o n s i d -

e r in g t h e m a te r ia l b e ha v io u rs l ik e p o ro s it y, s a tu r at i on , a n d

t e mp e ra t ur e e f fe c ts a s w e ll a s p o ro s it y c h an g e d u ri n g c a r-

bonat i on process i n earl y-aged concret e.

C o mp a r is o n o f e x pe r im e nt a l d a ta w it h n u me r i ca l r e su l ts

o bt ai ne d s ho ws t ha t t he p ro po se d m od el c an p re di ct t he

c ar bo na ti on d e pt h i n c ra ck ed c on cr et e w it h r ea so na bl e

accuracy.

T he d ev el op ed m od el c an b e u se d a s a t oo l t o e va lu at e t he

d u ra b il i ty r a ti n g o f r e in f or c ed c o nc r et e s t ru c tu r es a n d t h usm a y h e lp a v oi d in g d a ma g e d u e t o c a rb o na t io n .

Acknowledgment

T h e a u th o rs w is h es t o a c kn o wl e dg e P r of . K o ic h i M a ek a wa

o f t h e U n i v. o f To k yo f o r t h e v a l u ab l e a d v i ce a n d S A MS U NG

C o r p or a t i o n C o . , LT D . f o r f i n a n ci a l s u p p or t .

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d e te r io r at i on o f c o nc r et e s t ru ct u re s , C o ns t r. B u il d . M a te r. 1 0 ( 1 99 6)

2 73 7 .

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C o nc r e t e, S P - 49 , A C I , 1 9 7 5 , p p . 2 13 8 .

[ 3 ] L . J . P a r r o t t, C a r bo n a ti o n , m o i s t u re , a n d e m p ty p o r es , A d v. C e m . R e s . 4

(1 5 ) (1 9 9 1 ) 1 1 1118.

[ 4 ] R . J . C u r r i e , C a r b o na t i o n D e p t h s i n S t r u ct u r al Q u a li t y C o n cr e t e , B u i l d i ng

R e s ea r c h E s t a b l i s hm e n t R e p o r t Wa t f or d , U K , 1 9 86 , 1 9 p p .

[ 5 ] D . W. S . H o , R . K . L e w i s , C a r b o na t i on o f c o nc r e t e a n d i t s p r e di c t i on , C e m .

C o nc r. R e s . 1 7 ( 1 9 87 ) 4 8 9504.

[ 6 ] H . J. W ie r ig , L o ng t i me s t ud i es o n t h e c a rb o na t io n o f c o nc r et e u n de r

n or ma l o ut d oo r e xp os ur e, R IL EM S ym po si um o n D ur ab il i ty o f

C o nc r e t e u n d er N o r ma l O u t do o r E x p os u r e, H a n ov e r, G e r ma n y, 1 9 8 4,

p p . 1 9 2196.

[ 7 ] A C I C o m m i t t ee 2 0 1 , G u i d e t o D u r ab l e C o n c r et e ( A C I 2 0 1 . 2R - 9 2) .

[8 ] CAN/CSA-A2 3 .1 /A2 3 .2 -0 0 , Co n crete Materials an d Meth o d s o f Co n crete

Co n stru ctio n/Meth o d s o f Test fo r Co n crete, 2 0 0 0 .

[ 9 ] L . J i an g , B . L i n, Y. C a i, A m od e l f o r p r ed i ct i ng c a rb o na t io n o f h i gh -

v o l um e f l y a s h c o n c r e te , C e m . C o n c r. R e s . 3 0 ( 2 00 0 ) 6 9 9702.

[ 10 ] W. P. S. D ia s , R ed uc ti on o f c on cr et e s or pt i vi t y w it h a ge t hr ou gh

c a r bo n a ti o n , C e m . C o n c r. R e s . 3 0 ( 2 0 00 ) 1 2 5 51261.

[ 1 1] S . K . R o y , K . B . P o h , D . O . N o r t hw o o d, D u r ab i l i t y o f c o n cr e t e- a c ce l e ra t e d

c a r bo n a ti o n a n d w e a t he r i ng s t u d ie s , B u i l d. E n v ir o n . 3 4 ( 1 99 9 ) 5 9 7606.

[ 1 2 ] A . V. S a e tt a , B . A . S c h r e fl e r, R . V i ta l i a ni , T h e c a r b o na t i o n o f c o n cr e t e a n d

t h e m e c h a n i sm o f m o i s t ur e , h e a t a n d c a r b o n d i o x i d e f l o w t h r ou g h p o r o u s

m a t er i a l s , C e m . C o nc r. R e s . 2 3 ( 1 9 93 ) 7 6 1772.

[ 1 3 ] A . V. S a e t ta , B . A . S c h r e fl e r, R . V it a l i a ni , 2 - D m o d e l f o r c a r b o na t i o n a n d

m oi s t ur e /h ea t f l ow i n p or o us m a te r ia l s, C e m. C on c r. R e s. 2 5 ( 1 99 5)

17031712.

[ 1 4 ] H . - W. S o n g, H . - J . C h o , S . - S . P a r k , K . - J . B y un , K . M a e ka w a , E a r l y- a g e

c r a ck i n g r e s i s t a n ce e v a lu a t i on o f c o nc r e t e s t r u c t u re , C o n cr . S c i . E n g . 3

(2 0 0 1 ) 6 27 2 .

(a) carbonation depth with time (b) carbonation depth with crack width (after 25years)

0

10

20

30

40

50

60

70

0 10 15 20 25 30

exposed period (year)

carbonat

iondepth(mm)





Analysis : over 0.3mm crack

0.00

10.00

20.00

30.00

40.00

50.00

60.00

0.00 0.10 0.20 0.30 0.40 0.50

crack width (mm)

carbonat

iondepth(mm)

field data [33]

Analysis

5

F i g . 1 4 . N u m er i c al r e s ul t s w i t h f i e l d d a t a i n c r a ck e d c o n c r et e .



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carbonatacion efecto agrietamiento