Construction and Building Materials 23 (2009) 725–733

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Construction and Building Materials

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A model for predicting the carbonation depth of concrete containing low-calciumfly ash

Xiao-Yong Wang, Han-Seung Lee *

School of Architecture and Architectural Engineering, Hanyang University, Ansan 425-791, Republic of Korea

a r t i c l e i n f o

Article history:Received 23 November 2007Received in revised form 9 February 2008Accepted 20 February 2008Available online 9 June 2008

Keywords:CarbonationFly ashConcreteNumerical simulation

0950-0618/$ - see front matter � 2008 Elsevier Ltd. Adoi:10.1016/j.conbuildmat.2008.02.019

* Corresponding author. Tel./fax: +82 31 400 5181.E-mail address: ercleehs@hanyang.ac.kr (H.-S. Lee

a b s t r a c t

Low-calcium fly ash (FL) is a general product from the combustion of anthracite and bituminous coals andhas been widely used as a mineral admixture to produce high strength and high performance concrete.Carbonation of cement blended with fly ash is much more complex than ordinary Portland cementbecause of the pozzolanic activity in an aluminosilicate glass phase of fly ash. In this paper, based onmulti-component concept, a numerical model that can predict carbonation of low-calcium fly ash con-tained concrete was built. This numerical model includes two parts: hydration and carbonation models.The hydration model starts with a mix proportion of concrete and considers both Portland cement hydra-tion and pozzolanic activity. By applying a hydration model, the amount of hydration product that is sus-ceptible to carbonate as well as porosity was obtained as a function of curing age. Furthermore, thediffusivity of CO2 in concrete was determined and the carbonation depth of concrete was also predicted.The prediction results showed good agreement for the results of the experiment performed in this study.

� 2008 Elsevier Ltd. All rights reserved.

1. Introduction

Fly ash is the combustion residue in coal-burning electric powerplants. Viewed from significant differences in its mineralogicalcomposition and properties, the fly ash can be divided into two cat-egories based on their calcium content. The ash in the first cate-gory, low-calcium fly ash (FL), containing less than 10% ofanalytical CaO, is a general product from the combustion of anthra-cite and bituminous coals. The ash in the second category, high-calcium fly ash (FH), typically containing 15–40% of analyticalCaO, is a general product from the combustion of lignite and sub-bituminous coals. The FL is categorized as a normal type of pozzo-lan that consists of silicate glass and is modified by aluminum andiron. Also, it has long been used as a mineral admixture to producehigh strength and high performance concrete [1,2].

Steel embedded in concrete is usually protected from corrosionby a thin oxide layer that is formed and maintained on the surfaceof concrete due to the highly alkaline environment of the sur-rounding concrete (pH value around 13). However, due to the car-bonation, which is a certain physicochemical process betweencarbon dioxide and cement hydrates, such as calcium hydroxideand calcium silicate hydrate, the pH of pore water drops to a lowvalue of 9. The passive layer on the steel surface will no longer re-main stable when the alkalinity of the concrete surrounding thesteel drops to approximately 11.5. In the design of concrete struc-

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).

tures, the influence of the carbonation on their service life must beconsidered [2].

There are lots of literatures that deal with such concrete carbon-ation. From several experimental studies on the concrete carbon-ation for both outdoor conditions [3] and controlled indoorconditions [4], a carbonation front was found. The carbonationfront divides concrete into two different regions: a fully carbonatedregion and the one in which carbonation has not started at all. Thecarbonation front proportionally proceeds with a square root ofexposure time. Papadakis [5–7] proposed a fundamental mathe-matical model for the physicochemical process involved in the car-bonation of concrete containing ordinary Portland cement. Bothconcrete compositions and environment factors were consideredin his model. Jiang [8] proposed a practical mathematical modelto predict the carbonation of concrete containing ordinary Portlandcement. This model considered both concrete composition andenvironmental relative humidity. This model started with a mixproposition of concrete and estimated the influence of the degreeof hydration on carbonation.

The carbonation process indicates that the factors controllingcarbonation are the diffusivity of CO2 and the reactivity of theconcrete with CO2. The diffusivity of CO2 depends on the pore sys-tem of hardened concrete and the exposure condition. The poresystem of concrete depends on the type and content of the binder,water/binder ratio, and the degree of hydration. Due to pozzolanicactivity, the pore system of the concrete incorporating FL is differ-ent from that of the concrete without FL [9]. The reactivity of con-crete with CO2 is the amount of hydration products that are

726 X.-Y. Wang, H.-S. Lee / Construction and Building Materials 23 (2009) 725–733

susceptible to the carbonate in a unit volume, such as Ca(OH)2 andCSH. Due to pozzolanic activity, the reactivity of concrete incorpo-rating FL will also be different from that of the concrete withoutFL [9].

To predict carbonation of concrete containing mineral admix-tures, such as silica fume, fly ash and slag, the pozzolanic reactionshould be considered. By considering the influence of ‘effectivewater/binder ratio’ and cement content on carbonation, Jiang[10] predicted the carbonation of high-volume fly ash concrete.Papadakis [11–14] proposed a simplified scheme describing theactivity of silica fume and fly ash in terms of chemical reactionsand yielded quantitative expressions of the final chemical compo-sition of supplementary cementing materials (SCM) concrete.Carbonation of the SCM concrete was predicted as a furtherresult.

This paper presents a new numerical model that can predict thecarbonation of concrete containing low-calcium fly ash. Fig. 1 illus-trates this model. As shown in Fig. 1, the numerical model includeshydration and carbonation models. The hydration model startswith a mix proportion of concrete and curing conditions of con-crete. Using a hydration model that considers both the Portland ce-ment hydration and the pozzolanic activity, the hydration productsthat are susceptible to carbonate as well as porosity are obtained asaccompanied by the results of the proposed model during a hydra-tion period. Furthermore, the diffusivity of carbon dioxide in con-crete is expressed as a function of relative humidity, porosity,and its mix proportion. Finally, the carbonation depth of concreteincorporating low-calcium fly ash was determined. This proposedmodel includes some improvements from Papadakis’ model [10–14]. Papadakis’ model is not a kinetic model. The kinetic of pozzo-lanic reactions, such as the calcium hydroxide that is produced bycement hydration and consumed by pozzolanic reaction, were notreflected in his model. Papadakis’ model can compute only the finalconcentrations of the reaction products that can be applied aftercompleting hydration and pozzolanic reactions and establishing asteady state. Contrastively, the model proposed in this paper is akinetic model. By introducing a hydration model, the proposedmodel expressed the evolution of concrete properties, such as theamount of hydration products and the amount of porosity andchemically bound water as a function of curing ages. The experi-ments on the carbonation were adopted to verify the proposed

mixing proportion and curing condition

of concrete

1.evolution of Ca(OH)2 and CSH amount

with age

2.evolution of porosity and bound water

with age

Hydration model considers

pozzolanic activity

1.diffusivity of carbon dioxide

2.carbonation depth of concrete

Carbonation model

Fig. 1. The flow chart of predicting of carbonation depth of concrete containing FL.

model. The prediction results agree well with the results of theexperiments.

2. Hydration model of ordinary portland cement

2.1. Assumption of a hydration model

In a hydration model, the influences of the water to cementratio, cement particle size distribution, cement mineral compo-nents, and curing temperature on the hydration reaction of Port-land cement are considered. The assumptions of this model canbe summarized as follows:

1. Cement particles are randomly casted in a representative unitcell space as shown in Fig. 2. As proposed by Navi and Pignat[15], the length of the edge of the representative unit cell is100 lm. The amount of chemically bound water for eachcement component, C3S, C2S, C3A, and C4AF, proposed by Park[16] can be used to a simulation performed in this paper.

2. The degree of the hydration of cement components is the ratioof the volume of reacted cement components volume to thevolume of initial cement components. The degree of thehydration of cement paste can be regarded as a weightedsum of cement particles and mineral components as shownin Fig. 3.

3. The liquid phase that is assumed to be water diffused through ahydrate layer reaches the surface of the cement particle andchemically reacts with cement. The hydrate formed by hydra-tion adheres to the cement particles spherically.

4. The particle size distribution of cement can be approximatedusing the Rosin–Rammler function [17].

2.2. Hydration mechanism

In Park’s model [16], some improvements were achieved to con-sider the size distribution of cement particles and the componentof cement minerals including C3S, C2S, C3A, and C4AF. The basichydration equation for each mineral composition in cement parti-cles can be described as the following:

daji

dt¼ 3Cw1

ðvi þwagÞrj0qi

1

1kd� rj

0Dei

� �þ rj

0Deið1� aj

iÞ�13 þ 1

krið1� aj

i�23

ð1Þ

Fig. 2. Cement particles distribute randomly in cell space.

Fig. 3. The schematic of multi-component hydration model.

X.-Y. Wang, H.-S. Lee / Construction and Building Materials 23 (2009) 725–733 727

where aji denotes the hydration degree of the mineral component in

given cement particles, i is the mineral component, j is the numberof cement particles, vi is the stoichiometric ratio by the mass ofwater to mineral component, wag is the physically bound water thatis equal to 13% of the weight of reacted cement, qi is the density ofthe anhydrate cement mineral component, kd is the reaction coeffi-cient in a dormant period, rj

0 is the radius of anhydrate cement par-ticles, Dei is the effective diffusion coefficient of water in thehydration product for each mineral component, and kri is the coef-ficient of reaction rate for each mineral component. The influence oftemperature on the reaction rate can be considered by the Arrhe-nius law [16].

Whereas kd is assumed to be a function of degree in the hydra-tion during the initial reaction period and it is expressed as

kd ¼B

ðajiÞ

1:5 þ C rj0 � rj

t

� �4ð2Þ

The effective diffusion coefficient of water is affected by the tortu-osity of the gel pore as well as the radius of the gel pore in hydrate.This phenomenon can be expressed as a function of degree in thehydration and is described by

Dei ¼ Dei0 ln1

aji

!ð3Þ

when the cement is mixed with water, the hydration of each min-eral component processes according to the model described in theprevious section. The degree of the hydration of cement can be cal-culated as the following:

a ¼Pj¼n

j¼1

Pi¼4i¼1a

jigigjPj¼n

j¼1

Pi¼4i¼1gigj

ð4Þ

where gi is a weight fraction in mineral components. gj is a weightfraction for each cement particle, and n is the total number of ce-ment particles in a cell space. As shown in Eq. (4), the global degreeof the hydration of cement is a weighted average of mineral compo-nents and cement particles.

2.3. Water withdrawl mechanism

During the hydration period, in a certain time point after theinitial setting time, due to the increase in the interconnect of ce-ment particles, the contact area between cement particles and sur-rounding water will be decreased. As a result, the slower hydrationrate will be achieved. On the other hand, the available space for

packing cement hydration products will be decreased becausethe volume of hydration products is larger than the reacted cementvolume (in terms of solid volume), 2.2 times. With the increase inthe gel-space ratio, the relative hydration rate will be decreasedduring the cement hydration period [18]. By considering thesepoints, the modification of Eq. (1) can be expressed as thefollowing:

daji

dt

!0¼ daj

i

dt� freesurface

totalsurface

� �j

�w0 � 0:38 � Ce0 � aw0

ð5Þ

In Eq. (5), the item freesurfacetotalsurface

� �jis that given a certain cement par-

ticle j, the ratio between the free surface area (the area which is incontact with water) and the total surface area, w0 is the water con-tent and Ce0 is the cement content in a mixing proportion. Theitem w0�0:38�Ce0�a

w0considers the decrease in the available space for

packing cement hydration products.

3. Hydration model for the cement blended with low-calciumfly ash

3.1. Amount of CH and CSH during hydration process

As proposed by Papadakis [11–14], during the hydration period,the chemical reaction of the mineral component of Portland ce-ment can be expressed as the following:

2C3Sþ 6H! C3S2H3 þ 3CH ð6:1Þ2C2Sþ 4H! C3S2H3 þ CH ð6:2ÞC3Aþ CSH2 þ 10H! C4ASH12 ð6:3ÞC4AFþ 2CHþ 10H! C6AFH12 ð6:4Þ

By the aforementioned multi-component hydration model and Eqs.(6-1), (6-2), (6-3), and (6-4), the content of the hydration product ina unit volume of Portland cement, such as calcium hydroxide andCSH contents, can be obtained from:

CH ¼ ð1:5gc3sac3s þ 0:5gc2sac2s � 2gc4afac4afÞ � 74:1 � Ce0 ð7:1ÞCSH ¼ ð1:5gc3sac3s þ 0:5gc2sac2sÞ � 342:41 � Ce0 ð7:2Þ

Fly ash is a complex material that consists of a wide range of glassand crystalline compounds. In its reaction form, there is aluminosil-icate (A–S) glass with a high content of silicon. The hydration prod-uct of an aluminosilicate glass/hydrated lime mixture should be aCSH gel incorporating significant amounts of A. The S of A–S glassis proposed to react with the CH without additional water bindingand to form a calcium silicate hydrate described by the simplifiedformula of C3S2H3 as shown by using almost pure vitreous silica[11]. The silicon presented as quartz or in crystalline aluminosili-cate phases is inert. As proposed by Papadakis [13], the pozzolanicactivity in cement-low-calcium fly ash blends is written as thefollowing:

2Sþ 3CH! C3S2H3 ð8:1ÞAþ CSH2 þ 3CHþ 7H! C4ASH12 ð8:2ÞAþ 4CHþ 9H! C4AH13 ð8:3Þ

Based on the hydration model and pozzolanic reaction proposed inEqs. (8-1), (8-2), and (8-3), during the hydration period, the amountof calcium hydroxide, chemical bound water, and CSH can be writ-ten as the following:

CH ¼ ð1:5gc3sac3s þ 0:5gc2sac2s � 2gc4afac4afÞ � 74:1 � Ce0

� ð1:85 � cS � fS;P þ 2:907 � cA � fA;PÞ � areacted � P ð9:1ÞH ¼ Hce þmH2O � cA � fA;P � areacted � P ð9:2ÞCSH ¼ ð1:5gc3sac3s þ 0:5gc2sac2sÞ � 342:1 � Ce0

þ 2:85 � fS;P � cS � areacted � P ð9:3Þ

728 X.-Y. Wang, H.-S. Lee / Construction and Building Materials 23 (2009) 725–733

In Eqs. (9-1), (9-2) and (9-3), fS,P and fA,P are the weight fraction of Sand A in fly ash, cS and cA are its active (glass) part, areacted is the re-acted degree of the active (glass) part of fly ash, P is the fly ash con-tent in a mixing proportion, Hce is the amount of chemically boundwater of Portland cement, and mH2O is the chemically bound waterin a unit weight of the reacted active (glass) part of fly ash. In fact, asshown in Eqs. (9-1), (9-2), and (9-3), it is assumed that the active(glass) S and A, hydrate show equal rates.

3.2. simulation of pozzolanic reaction in cement-low-calcium fly ashblends

The hydration rate of pozzolanic materials depends on theamount of calcium hydroxide in hydrating cement-low-calciumfly ash blends and the degree of hydration of mineral admixtures[19,20]. Compared with the silica fume, the hydration rate of thelow-calcium fly ash is much lower levels due to the larger particlesize. In the age of 0–21 days, no traces of reaction among FL par-ticles can be detected [13]. In the simulation, it is assumed thatthe pozzolanic reaction is divided into three processes: initialdormant, reaction-control, and diffusion-control processes. Byconsidering these points, based on the method proposed by Saeki[19], the hydration equation of the active (glass) part in FL can bewritten as

dareacted

dt¼ mCH

P3

vFLrFL0qFL

11

kdFL� rFL0

DeFL

� �þ rFL0

DeFLð1� areactedÞ

�13 þ 1

krFLð1� areactedÞ

�23

ð10:1Þ

kdFL ¼BFL

ðareactedÞ1:5þ CFL � ðareactedÞ3 ð10:2Þ

DeFL ¼ DeFL0 � ln1

areacted

� �ð10:3Þ

where mCH is the calcium hydroxide content in a unit volume inhydrating cement-low-calcium fly ash blends and can be obtainedfrom Eqs. (9-1), (9-2), and (9-3), P is the low-calcium fly ash contentin a mixing proportion, vFL is the stoichiometry ratio by the mass ofCH to low-calcium fly ash, rFL0 is the radius of low-calcium fly ashparticles, qFL is the density of fly ash, kdFL is the reaction rate coef-ficients in a dormant period (BFL and CFL are coefficients), DeFL0 isthe initial diffusion coefficient, and krFL is the reaction rate coeffi-cient. Because water is consumed in a pozzolanic reaction, com-pared with the hydration rate of the plain Portland cement, thehydration rate of Portland cement in cement-fly ash blends willbe reduced. By using modified water reducing coefficients, thismechanism is considered.

The porosity of hydrating blends is reduced due to the Portlandcement hydration and pozzolanic activity during hydration period[13]. The porosity can be determined as

ec ¼w0

qw� Deh � Dep ð11Þ

where Deh is the porosity reduction due to the hydration of Portlandcement. It can be obtained from the amount of chemically boundwater that is consumed in the hydration of Portland cement. Also,Dep is the porosity reduction due to the pozzolanic activity and it

Table 1The hydration coefficients of the proposed modela

b c krc3s krc2s krc3a k

2.00 � 10�9 1.50 � 1015 2.42 � 10�5 1.82 � 10�7 1.99 � 10�6 3

a Unit for reaction coefficient of mineral component is cm/h, unit for diffusion coefficie

can be obtained from the amount of chemically bound water thatis consumed in a pozzolanic reaction.

4. Verification of the hydration model

4.1. Hydration degree of mineral components of ordinary Portlandcement

The results of this part in the experiments for regarding thehydration degree of ordinary Portland cement were used [21].The water to cement ratio was 0.5 and curing temperature was293 K. The hydration degree of mineral components was measuredon 1, 3, 7, 28, 91, 190, and 365 days. By regression experiment re-sults, the reaction coefficients of the multi-components hydrationmodel were obtained and are listed in Table 1.

Fig. 4 represents the comparison between the experiment re-sults and the prediction results. As shown in Fig. 4, the predictionresults agree well with the experiment results. By Eqs. (7-1) and(7-2), the amount of calcium hydroxide and CSH in a unit volumecan be obtained during the hydration period. In Figs. 5 and 6, theamount of calcium hydroxide and CSH are shown as a function ofdegree in the hydration. It is obvious that the amount of CH andCSH almost linearly depends on the hydration degree. By measur-ing the amount of calcium hydroxide and combined water, Saeki[21] also found that the amount of CH linearly depends on the de-gree of hydration.

4.2. Hydration process of cement blended with low-calcium fly ash

In this part, the experiment results of the hydration of cement-FL blends [13] are adopted to verify the proposed hydration model.The mixture proportions [13] for specimens are shown in Table 2. Avolume unit (1 m3) mortar was chosen as a common basis. WhenFL was added to this unit, an equal volume of another component(either cement or aggregate) was removed in order to keep thesame total volume and common comparison basis. In the controlspecimen, the water to cement ratio (W/C) was 0.5 and the aggre-gate to cement ratio (A/C) was 3. When FL replaces the volume ofaggregates, three contents of FL were selected, such as 10%, 20%,and 30%, and added to the cement weight for the specimensFLA1, FLA2, and FLA3, respectively. For the cement replaced byFL, the same contents were also selected, such as 10%, 20%, and30%, for replacing the control cement weight for the specimensFLC1, FLC2, and FLC3, respectively. The specimens were cured un-der a sealed condition with 20 �C. The CH content, chemicallybound water content and porosity on 3, 7, 14, 28, 49, 112, 182,and 364 days after casting was tested.

4.2.1. Amount of the calcium hydroxide during the hydration processIn the hydration of ordinary Portland cement, the amount of

calcium hydroxide will increase until it reaches its steady state.In the hydration of cement-low-calcium fly ash blends, the evolu-tion of the amount of CH depends on two factors, such as the Port-land cement hydration that produces CH and the pozzolanicreaction that consumes CH. Because the low-calcium fly ash repre-sents a low reaction rate, the CH content of FLA specimens in theinitial period follows the CH content of its control, but the CH ofFLA specimens is consumed at a slow rate after 14 days. Based

rc4af Dec3s0 Dec3a0 Dec2s0 Dec4af0

.76 � 10�7 6.34 � 10�10 9.57 � 10�8 6.33 � 10�10 9.57 � 10�8

nt of mineral component is cm2/h, unit for coefficient of temperature dependent is K.

Fig. 4. The comparison between experiment result and simulation result of hydration degree of cement mineral components: C3S, C2S, C3A and C4AF.

Fig. 5. The calculated CH amount as a function of degree of hydration. Fig. 6. The calculated CSH content as a function of degree of hydration.

X.-Y. Wang, H.-S. Lee / Construction and Building Materials 23 (2009) 725–733 729

on the amount of calcium hydroxide [13], the reaction coefficientsof the pozzolanic reaction in Eqs. (10-1), (10-2), and (10-3) can beobtained (as B = 1.169 � 10�12 cm/h, C = 0.0426 cm/h, krFL = 8.829� 10�8 cm/h, and DeFL0 = 2.705 � 10�11 cm2/h). The evolution ofthe amount of CH shows a function of hydration time as illustratedin Fig. 7. As shown in Fig. 7, the simulation results agree well withthe experiment results.

The reacted ratio of the total fly ash (both active and inert parts)can be obtained based on Eqs. (10-1), (10-2), and (10-3) and the

weight fractions of the constitutes in fly ash. The reacted ratio ofthe total fly ash can be calculated as the following:

aflyash ¼ ðcs � fS;P þ cA � fA;PÞ � areacted

¼ ð0:82 � 0:535þ 0:82 � 0:204Þ � areacted

¼ 0:606 � areacted ð12Þ

The reacted ratio of the total fly ash is calculated and shown inFig. 8. As shown in Fig. 8, the reacted ratio of FLA almost equalszero in the initial 500 h (3 weeks). This agrees well with the SEM

Table 2mixture proportions for mortar specimens

Specimen Cement (kg/m3) Water (kg/m3) Fly ash (kg/m3) Aggregate (kg/m3) Water to cement ratio Fly ash to cement ratio Aggregate to cement ratio

Control 515 257 0 1544 0.50 0.00 3.00FLA1 515 257 52 1483 0.50 0.10 2.88FLA2 515 257 103 1422 0.50 0.20 2.76FLA3 515 257 154 1361 0.50 0.30 2.64FLC1 463 257 52 1527 0.56 0.11 3.30FLC2 411 257 103 1509 0.63 0.25 3.67FLC3 360 257 154 1492 0.72 0.43 4.14

Fig. 7. The comparison between experiment result and simulation result of CH amount.

730 X.-Y. Wang, H.-S. Lee / Construction and Building Materials 23 (2009) 725–733

images of experiment results: in the early hydration period of 0–21 days, no traces of the reaction in FL particles can be detected[13]. The prediction results of the reacted ratio of the fly ash of10%FLA and 20% FLA at the age of one year were 0.42 and 0.34,respectively. Hanehera [22] measured the reaction ratio of flyash. The water to binder ratio of fly ash cement paste was 0.5and the fly ash substation rates were 10% and 20%, respectively.The specimens were cured at 20 �C over one year. The measuredreaction ratios of the fly ash were 0.40 and 0.36, respectively. Thesimulation results in this paper overall agree with experimentresults.

4.2.2. Amount of bound water and the porosity during the hydrationprocess

In the case of the cement-low-calcium fly ash blends, in its ini-tial three months of hydration, there are two factors that affect thebound water content. First is the selective reaction of CH with S in-

stead of its reaction with C3A and C4AF phases of cement. Second isthe high content of aluminate in fly ash the counterbalances lossesin water content. The global result is that the control specimen aswell as all FLA specimens has almost the same water content in itsinitial three months. After three months, because the remainingamounts of C3A and C4AF phases of cement have reacted andbound to additional water, the water content values for FLA spec-imens exceed those of the controls. In this proposed model, thisselective reaction is not accurately included and the water evolu-tion is simulated phenomenologically. In its initial 3 months, thecontent of the chemically bound water in a unit weight FLA spec-imen equals to that of the unit weight control specimen. Afterthree months, the contributions from both cement hydration andpozzolanic activity are considered. The evolution of porosity isshown as a function of hydration time as shown in Fig. 9. As shownin Fig. 9, the calculation results agree well with the experimentresults.

Fig. 8. The calculated reacted ratio of total fly ash versus time.

Fig. 9. Comparison between experiment result and simulation result of porosity.

X.-Y. Wang, H.-S. Lee / Construction and Building Materials 23 (2009) 725–733 731

5. Prediction of carbonation of concrete containing fly ash

The carbonation of concrete occurred in the cement pastecomponent of concrete in which the aggregates that constitutethe major part of the mass and volume of concrete are essentialinert fillers, as far as a certain carbonation is concerned. Thehydration products of the calcium hydroxide (CH) and calciumsilicate hydrate (CSH) that are susceptible to carbonation consti-

tutive typically an 85% of weight of the mass of hardened cementpastes. Other hydration products containing complex CaO, Al2O3,Fe2O3, and CaSO4 compounds are also formed, but since they con-stitute typically less than a 15% of the weight of the mass of hard-ened cement pastes and since they are susceptible only to surfaceand not bulk carbonation [7], they are not considered in this pa-per. Consequently, the carbonation reactions that must be occurare

732 X.-Y. Wang, H.-S. Lee / Construction and Building Materials 23 (2009) 725–733

CaðOHÞ2 þ CO2!kCH CACO3 þH2O ð13:1Þ

ð3CaO � 2SiO2 � 3H2OÞ þ 3CO2 !kCSHð3CaCO3 � 2SiO2 � 3H2OÞ ð13:2Þ

Concrete carbonation is a complicated physicochemical process.The process includes the diffusion of CO2 in a gaseous phase intoconcrete pores, its dissolution in the aqueous film of these pores,the dissolution of solid Ca(OH)2 in water of the pores, the diffusionof dissolved Ca(OH)2 in pore water, its reaction with dissolved CO2,and the reaction of CO2 with CSH. In addition, there is a parallel pro-cess that includes the hydration of cementitious materials and thereduction of concrete porosity. Papadakis [6] developed and exper-imentally verified a fundamental and comprehensive reaction mod-el of the process, which leads to concrete carbonation. When allhydration reaction rates are set to zero (when carbonation experi-ments were conducted with fully hydrated samples), the simplifiedmodel equations can be written as the following:

o

oxDe

o½CO2�ox

� �¼ ½CO2�ðKCH½CaðOHÞ2� þ 3KCSH½CSH�Þ ð14:1Þ

o

ot½CaðOHÞ2� ¼ �KCH½CaðOHÞ2�½CO2� ð14:2Þ

o

ot½CSH� ¼ �KCSH½CSH�½CO2� ð14:3Þ

Fig. 10. The comparison between experiment result and prediction result of carb-onation depth.

Fig. 11. The comparison between experiment result and prediction r

where De is the effective diffusivity of CO2; [CO2] is the molar con-centration of CO2, KCH and KCSH are the carbonation rate constants ofCa(OH)2 and CSH, respectively, [Ca(OH)2] and [CSH] are the molarconcentration of Ca(OH)2 and CSH, respectively. This mathematicalmodel is based on the mass-balance of gaseous CO2, solid and dis-solved Ca(OH)2, and CSH. This model accounts to the production,diffusion, and consumption of these substances. In the given initialand boundary conditions, the differential equations can be solvedby using a finite differential method or finite element methodnumerically.

For the usual range of parameters (especially for relativehumidity >50%, CO2 diffusion-controls carbonation process), cer-tain simplifying assumptions can be made and that lead to the for-mation of a carbonation front, separating completely carbonatedregions from those in which the carbonation has not yet started.For one-dimensional geometry, the evolution of the carbonationdepth xc(m) with time t(s), is given by the analytical expressionas the following:

xc ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2De½CO2�0t½CH� þ 3½CSH�

sð15:1Þ

De ¼ Aec

CqCþ P

qPþ W

qW

!a

1� RH100

� �b

ð15:2Þ

where [CO2]0 is the CO2 content in the ambient air at the concretesurface, RH is the ambient relative humidity, qC, qP, qW are the den-sity of cement, fly ash, and water, respectively, and A, a, b are theparameters which will be regressed from the carbonation experi-ment results. The influence of the concrete composition and envi-ronmental factor on the carbonation is considered in Eqs. (15-1)and (15-2).Based on the proposed hydration model, the amount ofCH, CSH, and porosity can be obtained as accompanied results dur-ing the hydration period of cement-fly ash blend concrete. Further-more, the carbonation depth can be predicted by using Eqs. (15-1)and (15-2).

Papadakis [12] performed accelerated carbonation experimentsof the concrete containing low-calcium fly ash. (Experiment de-tails: the concrete specimens containing fly ash were cured inwater (saturated with Ca(OH)2) for 1 year before the acceleratedcarbonation test was applied. In the carbonation experiment, thespecimens were placed in a chamber with a controlled 3% concen-tration of CO2 and relative humidity 61% for 100 days). The con-crete mix proportions are shown in Table 2. The comparisonbetween the prediction results and the experiment results isshown in Fig. 10 (A = 0.0001191, a = 6.326, b = 2.2). As shown in

esult about carbonation depth as a function of exposure period.

X.-Y. Wang, H.-S. Lee / Construction and Building Materials 23 (2009) 725–733 733

Fig. 10, the prediction results agree well with the experimentresults.

Sulapha [23] investigated the influence of low-calcium fly ashon the carbonation through applying accelerated carbonationexperiments (Experiment details: After a scheduled period ofwater curing and a minimum two weeks to stabilize the internalrelative humidity of concrete, the specimens are put into a cham-ber with CO2 concentration of 6.5 ± 0.2% and relative humidity65 ± 1%). In FA15 and FA30, the cements were replaced by thelow-calcium fly ash as 15% and 30% in addition to the cement mass,respectively. The carbonation depth of the specimens was moni-tored up to 12 months. The comparison between the prediction re-sults and the experiment results is shown in Fig. 11 (Furtherhydration of concrete containing fly ash during an acceleration car-bonation test period is considered by using the proposed hydrationmodel. A = 2.3326 � 10�7, a = 1.447, b = 2.2). As shown in Fig. 11,the prediction results agree well with the experiment results.

6. Conclusion

This paper proposed a numerical model for predicting the car-bonation depth of concrete incorporating the low-calcium fly ash.This numerical model includes two parts: hydration and carbon-ation models. The hydration model starts with a mix proportionof concrete and curing conditions of concrete. Both Portland ce-ment hydration and pozzolanic activity are considered in thishydration model. The hydration products that are susceptible tocarbonate as well as the porosity were obtained as accompaniedresults during the hydration period. Furthermore, the diffusivityof the carbon dioxide in concrete was expressed as a function ofrelative humidity, porosity, and mix proportion. Finally, the car-bonation depth of the concrete incorporating the low-calcium flyash was determined. Due to the similarity of the pozzolanic reac-tion between calcium hydroxide and other pozzolanic materials,such as silica fume and slag, the proposed model showed a poten-tial in the simulated carbonation of other blended materials be-sides fly ash.

Acknowledgements

The authors are grateful to the reviewers for their valuablecomments.

This work is supported by Sustainable Building Research CenterHanyang University, which is supported by the SRC/ERC programof MOST (#R11-2005-056-04003-0) and a Grant (06-CIT-A02:Standardization Research for Construction Materials) from Con-struction Infrastructure Technology Program funded by Ministryof Land, Transport and Maritime Affairs.

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