Carbonation of concrete in relation to CO2 permeability and degradation of coatings

Construction and Building

MATERIALS

Construction and Building Materials 22 (2008) 2260–2268

www.elsevier.com/locate/conbuildmat

Carbonation of concrete in relation to CO2 permeability and degradation of coatings D.C. Park

*

Division of Architecture and Ocean Space, Korea Maritime University, Dongsam-Dong, Yeongdo-Ku, Pusan 606-791, Republic of Korea Received 30 May 2007; received in revised form 17 July 2007; accepted 20 July 2007 Available online 27 September 2007

Abstract In relation to concrete carbonation as a cause of problems in concrete buildings, we have constructed a diffusion-reaction carbonation model using the finite element method to estimate the depth of carbonation. Input data for analysis using this model were obtained by measuring both the diffusion coefficient and the solubility coefficient of carbon dioxide in various coatings by studying the permeation of carbon dioxide using a differential pressure method. The validity of the model has been verified by comparing results obtained from this model with experiments on accelerated carbonation using coated concrete specimens. The diffusion coefficient of carbon dioxide in various coating materials increased in the following order: polyvinyl chloride, polyurethane, epoxy, and acrylic. The effects of the degradation of coatings and of the number of coatings have also been examined.  2007 Elsevier Ltd. All rights reserved. Keywords: Coated film; CO2 permeability; Concrete carbonation; Diffusion-reaction carbonation model

1. Introduction Although concrete buildings are considered semipermanent, in many cases they have to be repaired or reconstructed in less than several decades, owing to environmental, constructional, and material problems. As the proportion of maintenance in the total investment in construction has increased in recent years, and most reinforced concrete buildings built in the period of high growth in reinforced concrete construction are expected to be replaced in the near future, it is very important to control the useful lifetime of such buildings. In addition, many reinforced concrete buildings use paints, tiles, stones, etc. as exterior materials, not only for decorative reasons, but also to prevent degradation. Therefore, more effective

*

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maintenance can be planned if we can evaluate the protective effects of finishing materials on architectural structures. Research on salt damage in the field of concrete durability has advanced sufficiently far that we can estimate such damage accurately by experiment and calculation, whereas studies on carbonation have depended on approximating the results obtained from a colorimetric method using phepffi nolphthalein by a square-root ( t) law [1,2]. However, actual buildings consist of composite materials combined with exterior finishing materials, and it is difficult to apply this square-root law to two- or three-dimensional objects. We have measured the permeability coefficient and diffusion coefficient of carbon dioxide in some coating materials that are used as exterior finishing materials in buildings. Using these data as inputs, a diffusion-reaction carbonation model has been constructed and an accelerated carbonation experiment has been conducted to verify the validity of the model by comparing the results. In addition, the effects of degradation of coatings and of the number of coatings have been examined theoretically.

D.C. Park / Construction and Building Materials 22 (2008) 2260–2268

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2. Overview of model and experiments 2.1. Overview of diffusion-reaction carbonation model

Fig. 2. Overview of permeation-measuring (differential pressure method) experiment for carbon dioxide.

Steady State Pressure

The reaction between concrete and carbon dioxide that has permeated the coating is depicted conceptually in Fig. 1. The carbon dioxide contacts the surface of the coating (1), dissolution occurs (2), and the carbon dioxide then permeates the coating (3, 4) [3]. Once the carbon dioxide reaches the concrete, it generates calcium carbonate by carbonating calcium hydroxide, which is a cement hydration product. As calcium hydroxide is consumed by this reaction, the pH in the concrete declines, neutralization progresses, and eventually the reinforcing steel bars become corroded. In this study, the diffusion coefficient of carbon dioxide, to be used as input data for the analysis, was measured by use of an apparatus for measuring air permeation by a differential pressure method [4], so that we could obtain a model for the carbonation of concrete that took account of permeation and diffusion of carbon dioxide and also the degradation of coatings. The depth of concrete carbonation was measured by use of a colorimetric method with phenolphthalein reagent (1%) and differential scanning calorimetry (DSC). 2.2. Measuring the permeation and diffusion coefficients of carbon dioxide in coatings The permeation coefficient and diffusion coefficient of carbon dioxide in the coating were used to calculate the initial condition and the boundary condition (solubility) of the model constructed. The permeation and diffusion coefficients were measured by an apparatus for measuring gas permeation using a high-vacuum differential pressure method with a mass spectrometer as a detector. A schematic diagram of the permeation-measuring apparatus is shown in Fig. 2. The curve in Fig. 3 was obtained by injecting carbon dioxide (at 100–120 kPa) from one side of the specimen and measuring the change in concentration (pres-

dP/dt

Unsteady State P2 θ

2θ Time

Fig. 3. Permeation curve of carbon dioxide [4].

sure) over time as the carbon dioxide passed through the specimen. The permeation coefficient of carbon dioxide can be obtained by inserting the slope of this curve in the steady state into Eq. (1) below, and the diffusion coefficient can be obtained from Eq. (2), using the delay time in the nonsteady state [3]. 273 V 1 1  l  T A P 1 760 dP 2 ðcm3 ðSTPÞ  cm=cm2  s  cmHgÞ  dt l2 ðcm2 =sÞ; D¼ 6h

P¼

Fig. 1. Diffusion of carbon dioxide and concrete carbonation.

ð1Þ ð2Þ

where D is the diffusion coefficient of the gas in the coating, P is the gas permeation coefficient of the coating, T is the measured temperature (in units of K), V is the volume at the low-pressure side (ml), P1 is the gas pressure at the high-pressure side (cmHg), P2 is the gas pressure at the low-pressure side (cmHg), dP2/dt is the slope of the curve of the gas pressure (cmHg/sec), STP means the temperature and pressure in the standard state, l is the coating thickness (cm), and h is the delay time (s).

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D.C. Park / Construction and Building Materials 22 (2008) 2260–2268

In this experiment, four kinds of coating, namely polyurethane, polyvinyl chloride, epoxy, and acrylic, as shown in Table 1, were tested.

hydroxide and C–S–H in the concrete to generate calcium carbonate. The analysis was performed on the basis of the following assumptions:

2.3. Accelerated carbonation experiments

 The surface finishing materials of concrete structures are limited to organic coatings, and carbon dioxide in the atmosphere permeates through these coatings.  Carbon dioxide diffuses in concrete according to Fick’s first law.  The reaction between calcium hydroxide and carbon dioxide in concrete is a first-order reaction.  Concrete becomes denser and the diffusion coefficient decreases as a result of carbonation.

2.3.1. Carbonation of concrete without a coating The mixture proportions of the concrete specimen are shown in Table 2. The specimen was demolded 24 h after casting, and cured in water for 28 days and then in air (20 C, 60% R.H.) for 92 days. The concentration of carbon dioxide in the experimental apparatus for accelerated carbonation was 20% (with 60% R.H.). The concentration distributions of calcium hydroxide and calcium carbonate in the depth direction from the surface were measured by DSC, and the carbonation depth at the 8th and 16th weeks was measured by use of phenolphthalein. 2.3.2. Carbonation of concrete with coatings The mixture proportions of the concrete substrate were the same as in Table 2. Four types of organic paint, namely polyurethane, polyvinyl chloride, epoxy, and acrylic, were used, as in the measurement of diffusion coefficients in the coatings. After being applied, the coatings were dried for three days under conditions of 20 C and 60% R.H., and then accelerated carbonation was performed. The concentration of carbon dioxide in the accelerated carbonation test was 20% (with 60% R.H.), as before. The depth of carbonation was measured at the 8th, 16th, 32nd, and 48th weeks by use of phenolphthalein. 2.4. Model of concrete carbonation taking account of diffusion and reaction of carbon dioxide 2.4.1. Assumptions about concrete carbonation Concrete carbonation is a process in which carbon dioxide, after permeating the coating, reacts with calcium

2.4.2. Basic differential equation Since it has been proven that one half of carbon dioxide in concrete reacts with calcium hydroxide while the other half reacts with C–S–H [5,6], we established a basic differential equation to analyze the reaction between half of the carbon dioxide and calcium hydroxide. In addition, the rate of decrease of the porosity caused by the reaction product calcium carbonate and thus the reaction between C–S–H and carbon dioxide were also considered. Eq. (3) represents the diffusion of carbon dioxide through the coating, Eq. (4) represents the diffusion and consumption of carbon dioxide in the concrete, Eq. (5) represents the diffusion and the consumption of calcium hydroxide, and Eq. (6) represents the generation of calcium carbonate. The finite element method was used for numerical analysis. oCCO2 o2 CCO2 ¼ DCO2 Suf ; ot ox2 2 oCCO2 o CCO2 t ¼ DCO2  R½CCO2 =2½CCaðOHÞ2 ; o ox2 oCCaðOHÞ2 o2 CCaðOHÞ2 ¼ DCaðOHÞ2  R½CCO2 =2½CCaðOHÞ2 ; ot ox2

ð3Þ ð4Þ

ð5Þ oCCaCO3 ¼ R½CCO2 =2½CCaðOHÞ2 ; ot

Table 1 Ingredient of the coatings Polymer (molecular structure)

Hardening agent

Reaction style

Polyurethanes Polyvinyl chloride

– –

Epoxy

Polyamide

Acryl

Melamine resin

One-component moisture cure Two-component heat hardening cure Two-component heat hardening cure Two-component heat hardening cure

ð6Þ

where t is the time, x is the distance from the surface of the concrete, DCO2 is the diffusion coefficient of carbon dioxide, DCaðOHÞ2 is the diffusion coefficient of calcium hydroxide, DCO2 suf is the diffusion coefficient of the exterior material, CCO2 is the concentration of carbon dioxide, DCaðOHÞ2 is the concentration of calcium hydroxide, CCaCO3 is the concentration of calcium carbonate, and R is the rate constant of the reaction.

Table 2 Mix proportion of concrete W/C (%)

W (kg/m3)

Cement (kg/m3)

Fine aggregate (kg/m3)

Aggregate (kg/m3)

F/A (%)

Slump (cm)

Air (%)

AE water reducing agent (g/m3)

65

185

285

798

954

46

18

4.5

500

D.C. Park / Construction and Building Materials 22 (2008) 2260–2268

x > 0 : CCO2 ¼ 0; CCaðOHÞ2 ¼ CCaðOHÞ2 Init ;  lsuf < x < 0 : CCO2 ¼ 0:

ð7Þ ð8Þ

Eqs. (7) and (8) represent the initial conditions for the concrete and coating. Generally, when the hydration ratio a of Portland cement is 100%, the amount of calcium hydroxide generated is about 30% of the cement mass [7]. Therefore the molar concentration of calcium hydroxide in concrete can be represented in terms of the unit amount of cement Q and the hydration ratio as follows: Ca ¼

0:3  Q  a ðmol=m3 Þ 74

ð9Þ

It is hard to measure the diffusion coefficient of carbon dioxide in concrete in an accelerated carbonation experiment, since carbon dioxide in concrete reacts with calcium hydroxide and C–S–H and is consumed as soon as it has diffused in. Furthermore, the pore structure changes. Papadakis et al. [8] and Wittmann et al. [9] suggested formulas for the diffusion coefficient of carbon dioxide with the porosity and the relative humidity as variables. To measure the diffusion coefficient in cement mortar, one can use a sufficiently thin, disk-type cell such that concentrations of carbon dioxide and oxygen can be assumed to be homogeneous in the concrete specimen. In this study, we performed an analysis based on the following equation proposed by Papadakis et al., 2:2

DCO2 ¼ 1:64  106 e1:8 ð1  RH =100Þ ;

ð10Þ

where e is the total porosity (%) and RH is the relative humidity (%). Hukujima’s study [10] discovered that the diffusion coefficient D CaðOHÞ2 (cm2/s) of calcium hydroxide and the percentage of water in concrete have the form of exponential functions. This phenomenon was also confirmed by Saeki [11] in experiments on concrete either immersed in a liquid or exposed to air. Presumably the diffusion of calcium hydroxide is influenced by moisture, because carbonation of concrete in the immersed state is reduced more compared with the air-exposed state. In our study, the diffusion coefficient of calcium hydroxide was determined by a sensitivity analysis, in which the experimental results for the concentration distributions of calcium hydroxide and calcium carbonate were compared with the values obtained from the model. As calcium hydroxide and carbon dioxide react to form calcium carbonate, the porosity declines according to the increase in molecular weight (Eq. (11)). However, it is not appropriate to consider the change of porosity on the basis of only a calculation of the molecular weight, because research has shown that about 50% of the carbon dioxide reacts with calcium hydroxide while the remainder of the carbon dioxide reacts with C–S–H, which also changes

the porosity [6,12]. Therefore, it is not currently possible to compute the change of porosity from a calculation of the molecular weight. Instead, we took account of the change of porosity by forming a regression curve (Eq. (12)) on the basis of existing experimental data. e0 ¼ c  e0 ;

ð11Þ

0

where e is the total porosity after carbonation, c is the reduction coefficient of porosity, and e0 is the total porosity before carbonation. c is given by c ¼ 0:92  3:95  0:94WC ;

ð12Þ

where WC is the water/cement ratio (%) (Fig. 4). (2) Boundary conditions Eq. (8) was used to calculate the carbon dioxide concentration on the surface of the coating as a function of the partial pressure of carbon dioxide and the solubility coefficient. We obtain x ¼ lsuf : CCO2 suf ¼ S  p;

ð13Þ

where CCO2 suf is the carbon dioxide concentration on the surface of the coating, S is the solubility coefficient, and p is the partial pressure of carbon dioxide. At t > 0, x ¼ 0 : CCaðOHÞ2 ¼ 0;

CCO2 ¼ e  CCO2 Out ;

x ! þ1 : CCaðOHÞ2 ¼ CCaðOHÞ2 Init ;

ð14Þ

CCO2 ¼ 0

ð15Þ

Eqs. (14) and (15) represent the initial conditions and boundary conditions for the concrete. Eq. (14) was applied to the carbon dioxide concentration CCO2 on the surface of concrete without a coating, in relation to the porosity of the concrete. The concentration of carbon dioxide that had permeated through the coating was used as a boundary condition in the case of concrete with a coating. 2.4.4. Carbonation criteria It is known that calcium hydroxide and calcium carbonate coexist in the boundary area around the depth of neutralization determined by use of phenolphthalein, and the amount of calcium hydroxide retained in the carbonated

Total Porosity Reduction Coefficient

2.4.3. Initial conditions and boundary conditions (1) Initial conditions At t = 0,

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1.0 0.8 0.6

Analysis by Lee Experimental Data by Page Experimental Data by Wittmann

0.4

Equation: y = a-b*c^x R^2 = 0.99392 a 0.91699 b 3.94668 c 0.94253

0.2

± 0.02869 ± 1.6457 ± 0.01105

0.0 40

50

60 W/C (%)

70

80

Fig. 4. Changes on porosity due to carbonation [9,12,13].

D.C. Park / Construction and Building Materials 22 (2008) 2260–2268

region has not yet been examined. In our study, the position at which the amount of calcium hydroxide was reduced to half of the initial value was assumed to be the boundary of the carbonation region, on the basis of the results of previous experiments [14].

tion of calcium hydroxide becomes half is the discoloration depth. In addition, to verify the accuracy of the estimation of long-term carbonation shown in Fig. 7, the results were compared with the Kishitani formula [15], based on the

3. Experimental results and FEM analysis 3.1. Carbonation of concrete without a coating A sensitivity analysis using the measured and calculated values was performed to calculate the carbonation reaction rate and the diffusion of calcium hydroxide in the model for estimating carbonation constructed in this study. The concentrations of calcium hydroxide and calcium carbonate measured at the 8th and 16th weeks and also the calculated values are shown in Fig. 5. The depth of discoloration observed with phenolphthalein turns out to be almost same as the position at which the concentration of calcium hydroxide becomes half of its initial value, as found in previous research [14]. If the reaction rate constant was varied from 5 · 104 m3/mol/s to 5 · 106 m3/mol/s while the diffusion coefficient of calcium hydroxide was fixed at 1 · 1012 m2/s, the measured and calculated values turned out to be identical to the values obtained when the input condition for the reaction rate constant was 5 · 105 m3/ mol/s. The difference between the measured and calculated values in the concentration distribution of calcium carbonate is generated mainly by the reaction between C–S–H and carbon dioxide. As it has been verified that the calculated value (for reaction between carbon dioxide and calcium hydroxide) is about half of the measured value (for reaction between carbon dioxide and both calcium hydroxide and C–S–H), the same result as in previous research can be inferred. The measured and calculated values of the discoloration depth obtained with phenolphthalein are presented in Fig. 6. These values are almost identical to those calculated by assuming that the position where the overall concentra-

1200 1000 800 636.5 600 400 200

FEM Analysis Experiment

0.030 0.025 0.020 0.015 0.010 0.005 0.000

0 2 4 6 8 10 12 14 16 18 Time (week)

0 0.00

0.02 0.04 0.06 Depth from the Surface (m)

Ca(OH)2_R=5e-4 Ca(OH)2_R=5e-5 Ca(OH)2_R=5e-6 CaCO3_R=5e-4 CaCO3_R=5e-5 CaCO3_R=5e-6 Ca(OH)2_Experi. CaCO3_Experi.

3500 3000 2500

Color Change by Phenolphthalein Reagent

2000

2

D(Ca(OH)2)=1e-12(m /s) Time = 8 (week)

1500 1000 500 0 0.00

0.01

0.02

0.03

0.04

Depth from the Surface (m)

0.05

0.08

Kishitani Model FEM Analysis

Carbonation Depth (m)

0.08

0.06

0.04

0.02

0.00 0

10

20

30

40

Time (year)

Fig. 7. Depth of long-term carbonation.

3

4000

4 (week) 8 (week) 12 (week) 16 (week)

Fig. 6. Depth of carbonation.

Concentration of Ca(OH)2 & CaCO3 (mol/m )

3

Concentration of Ca(OH)2 & CaCO3 (mol/m )

2 (week) 6 (week) 10 (week) 14 (week)

3

Concentration of Ca(OH)2 (mol/m )

1400

Carbonation Depth(m)

2264

4000

Ca(OH)2_R=5e-4 Ca(OH)2_R=5e-5 Ca(OH)2_R=5e-6 CaCO3_R=5e-4 CaCO3_R=5e-5 CaCO3_R=5e-6 CaCO3_Experi. Ca(OH)2_Experi.

3500 3000 2500

Color Change by Phenolphthalein Reagent

2000

D(Ca(OH)2)=1e-12(m /s)

1500

Time = 16 (week)

2

1000 500 0 0.00

0.01

0.02

0.03

0.04

Depth from the Surface (m)

Fig. 5. Concentration distributions of calcium hydroxide and calcium carbonate.

0.05

50

D.C. Park / Construction and Building Materials 22 (2008) 2260–2268

pffi square-root of the time ( t). The carbonation reaction rate in the Kishitani formula was computed on the basis of Table 3 and Eq. (16). The input condition for the diffusion-reaction carbonation model was also identical to that in Table 3.

Table 3 Carbonation reaction rate in Kishitani formula

a2

a3 b1 b2 b3

The coefficient of W/C The coefficient of temperature The coefficient of humidity The coefficient of carbon dioxide concentration

1.0 1.0

A ¼ k  a1  a2  a3  b1  b2  b3 ;

a3 = W/C  0.38 1.0 (Annual average (1971–2000): 15.9 C) 1.0 (Annual average (1971–2000): 63%) 1.0

Tokyo Tokyo Outdoor (0.05%)

Table 4 Results of carbon dioxide permeation test S (·105 kmol/ m3 kPa) 2.62 1.39

0.66 0.19

1.73 0.26

5.72 10.37

0.72 6.15

4.12 63.8

1200

4 (week) 12 (week) 20 (week) 28 (week) 36 (week) 44 (week)

3

Concentration of Ca(OH)2 (mol/m )

Polyurethanes Polyvinyl chloride Epoxy Acryl

P (·1017kmol/ s m kPa)

D (·1012 m2/ s)

1000

Carbonation Depth(m)

800 600 400 200

0.010

0.02

The solubility coefficient, calculated using Eq. (17) from the permeation coefficient and diffusion coefficient for the 8 (week) 16 (week) 24 (week) 32 (week) 40 (week) 48 (week)

0.006 0.004 0.002 0.000 0

0 0.00

3.2. Carbonation of concrete with coatings

Analysis Experiment

0.008

8

0.04

16 24 32 40 48 Time (week)

0.06

1200

800 600 400 200

Carbonation Depth(m)

400 200

0.010

0 0.00

0.02

0.008 0.006 0.004 0.002 0.000

0.04

8

16 24 32 40 48 Time(week)

0.06

Depth from the Surface (m)

Epoxy(coating film:83 μ m )

0.006 0.004 0.002 0.000 8

0.04

0.08

1200

16 24 32 40 48 Time (week)

0.06

4 (week) 12 (week) 20 (week) 28 (week) 36 (week) 44 (week)

3

8 (week) 16 (week) 24 (week) 32 (week) 40 (week) 48 (week)

Analysis Experiment

0

Analysis Experiment

0.008

0.08

Depth from the Surface (m)

Concentration of Ca(OH)2 (mol/m )

3

Concentration of Ca(OH)2 (mol/m )

600

0.02

8 (week) 16 (week) 24 (week) 32 (week) 40 (week) 48 (week)

Ppolyvinyl chloride(coating film:95 μ m ) 4 (week) 12 (week) 20 (week) 28 (week) 36 (week) 44 (week)

800

0.010

0

0 0.00

0.08

Polyurethane(coating film:97 μ m)

1000

4 (week) 12 (week) 20 (week) 28 (week) 36 (week) 44 (week)

1000

Depth from the Surface (m)

1200

ð16Þ

where A is the carbonation reaction rate. It has been verified that the results obtained from our analysis for a period of 50 years reproduce results obtained from the Kishitani formula on the basis of experimental measurements with very high accuracy. Using the diffusion-reaction carbonation model constructed, the changes in the concentrations of calcium hydroxide and calcium carbonate during concrete carbonation, and also the results for long-term carbonation, can be reproduced with high accuracy. Presumably this model can be validly used to transfer the results of accelerated carbonation measurements to long-term carbonation.

Carbonation Depth(m)

The coefficient of concrete type The coefficient of cement type

1.72

1000 800 Carbonation Depth(m)

a1

Kishitani formula Ordinary concrete Ordinary Portland cement

3

Constant

Concentration of Ca(OH)2 (mol/m )

k

2265

600 400 200

0.010

Analysis Experiment

0.008 0.006 0.004 0.002 0.000 0

0 0.00

0.02

8 (week) 16 (week) 24 (week) 32 (week) 40 (week) 48 (week)

0.04

8

16 24 32 40 48 Time(week)

0.06

0.08

Depth from the Surface (m)

Acryl(coating film:89 μ m )

Fig. 8. Experiment results from accelerated carbonation and analysis results from diffusion-reaction carbonation model for concrete with coatings.

D.C. Park / Construction and Building Materials 22 (2008) 2260–2268

3.3. Carbonation of concrete in relation to degradation of the coating From the experiments on carbonation of concrete with coatings, it was inferred that carbonation of concrete does not occur in the case of healthy coatings. However, under real circumstances, organic coatings degrade naturally as a result of heat, moisture, ultraviolet radiation, etc. As a consequence of long-term carbonation, degradation of concrete buildings may occur very deeply, depending on the degradation state of the surface finishing materials. An analysis with the diffusion-reaction carbonation model was performed to evaluate the effects of time and of degradation of coatings on concrete carbonation. On the basis of Eq. (18) [16], which represents the increase with time in the concentration of carbon dioxide in the atmosphere, the concentration of carbon dioxide for the 30 years from Jan. 2007 to Dec. 2036 was used as the boundary condition. The thickness of the coating was 70 lm, and an acrylic coating was assumed. Although the degradation of coatings shows various patterns according to regions and circumstances, in this study we performed the analysis using the assumptions described by Eq. (19) [17].

where t (months) is the time (from February 1958).   F ¼ 2  expðk  tN Þ ;

ð19Þ

where F is a measure of the performance of the coating, t is the time, and k and N are material constants.

1.4 Performance (F)

where S is the solubility coefficient of carbon dioxide (kmol/m3 kPa), P is the permeation coefficient of carbon dioxide (m2/s), and D is the diffusion coefficient of carbon dioxide (kmol/s m kPa). The permeation coefficient increased in the following order for the various coatings: polyvinyl chloride, polyurethane, epoxy, and acrylic. Mostly the values were in the region of 1017 kmol/s m kPa. The diffusion coefficient increased in the same order, and was in the region of 1012 m2/s. Accelerated carbonation was performed with these coatings applied to the concrete substrate as described in Table 2. The conditions for accelerated carbonation were carbon dioxide 20% and 60% R.H., which were the same as the experimental conditions for the concrete carbonation test in Section 3.1. The depth of discoloration obtained with phenolphthalein and the value calculated from the diffusion-reaction carbonation model are depicted in Fig. 8. In the case of polyvinyl chloride, polyurethane, and epoxy, a carbonation region discolored by phenolphthalein did not appear until the 48th week. However, the analysis using the diffusion-reaction carbonation model demonstrated that the concentration of calcium hydroxide declined slightly. In the case of acrylic, a carbonation region was observed from the 32nd week onwards, and its behavior could be predicted with high accuracy from the carbonation model.

ð18Þ

Case 1

1.2 1.0 0.8 0.6 0.4 0.2 0.0 0

5

10

15

20

25

30

1.4 Performance (F)

ð17Þ

1.2

Case 2

1.0

N

F=[2-exp(λ*t )]

0.8 0.6 0.4 0.2 0.0 0

5

10

15

20

25

30

1.4 Performance (F)

S ¼ P =D;

CCO2 Out ¼ 14:41 expð0:00357tÞ þ 1:99 sinð1:99 þ 0:54tÞ þ 300:79;

1.2

Case 3

1.0 0.8 0.6 0.4 0.2 0.0 0

5

10

15

20

25

30

1.4 Performance (F)

coatings measured by use of the apparatus for carbon dioxide permeation, is shown in Table 4.

1.2

Case 4

1.0 0.8 0.6 0.4 0.2 0.0 0

5

10

15

20

25

30

1.4 Performance (F)

2266

1.2

Case 5

1.0 0.8 0.6 0.4 0.2 0.0 0

5

10

15

20

25

30

Time (year) Fig. 9. Decline of coating performance and coating application time.

D.C. Park / Construction and Building Materials 22 (2008) 2260–2268

2267

Fig. 10. Changes on the concentration of calcium hydroxide and the depth of carbonation according to the number of application times of coating in the case of long-term carbonation.

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D.C. Park / Construction and Building Materials 22 (2008) 2260–2268

Regarding the effects of time after the application of the coating, five cases, depicted in Fig. 9, were compared. The analysis period was 30 years. In case 1 the concrete had no coating, in case 2 the concrete was coated once, in case 3 the concrete was coated twice, in case 4 the concrete was coated three times, and in case 5 the concrete was coated every 5 years for a total of six times. The analysis was performed on the assumption, based on Hasegawa’s study [18], that the performance of the coating (F) eventually becomes 0 after 10 years of degradation, ending up with only the performance of the remaining concrete. The changes in the concentration of calcium hydroxide and the depth of carbonation while the carbonation is occurring are shown in Fig. 10. The results show that more coatings are better in preventing the concentration of calcium hydroxide from declining. After the coating has been applied twice or more, the depth of carbonation is reduced by a slight recovery in the concentration of calcium hydroxide due to diffusion toward the carbonated region where the concentration of calcium hydroxide has previously declined. The depth of carbonation after 30 years is about 0.028 m in case 1 with no coating, but it is no more than 0.008 m in case 5, where the coating was applied six times. On the basis of the measured and calculated results, the diffusion-reaction carbonation model that we have constructed has been validated. To estimate the depth of carbonation in concrete with a coating, it is necessary to collect highly reliable data regarding the change in the performance of the coating. 4. Conclusion A concrete carbonation model has been constructed that takes account of the diffusion of carbon dioxide through a coating and reaction with calcium hydroxide, and this model has been validated by an accelerated carbonation experiment. Also, an analysis of long-term carbonation considering five cases has been performed to evaluate the effects of degradation of the coating and the number of coatings on the depth of concrete carbonation. From experiments and modeling, the following results have been obtained. (1) The diffusion coefficient of carbon dioxide was measured by means of a permeation-measuring apparatus using a differential pressure method, and the protection performance of the coating materials tested was graded in the following order: acrylic, epoxy, polyurethane, polyvinyl chloride. (2) By using values for the coatings calculated on the basis of a diffusion–permeation theory as input data for the analysis of diffusion-reaction carbonation in an unsteady state, the effect of the coatings in reducing carbonation can be represented with high accuracy. (3) Through a sensitivity analysis of the diffusion-reaction carbonation model and the experimental results, we found that the diffusion coefficient of calcium

hydroxide could be calculated to high accuracy as 1 · 1012 m2/s. The reaction rate constant for carbonation could be calculated to high accuracy as 5 · 105 m3/mol/s. (4) With the diffusion-reaction carbonation model that we have constructed, it is possible to estimate longterm carbonation, taking account of the degradation with time of surface finishing materials, especially organic coatings. References [1] Japan Concrete Institute, Report of the committee for Concrete Carbonation, 1993. [2] Ying-yu L, Qui-dong W. The mechanism for carbonation of mortars and the dependence of carbonation on pore structure, concrete durability, SP-100, Vol. 2, American Concrete Institute, Detroit, 1987; p. 1915–43. [3] Kuwano Eiji, Nakai Noboru, Fujitani Toshihide. A study on relationship between oxygen-permeability and anticorrosive function of coating films(3)-The control of oxygen permeability by characteristics of coating films-. Res Coat 2000;134(April):2–7. [4] Miyaki Hiroaki, et al. Study on gas permeability of exterior wall coatings, Summaries of technical papers of annul meeting architectural institute of Japan. Materials and Construction 1986;635–6. [5] Chang Cheng-Feng, Chen Jing-Wen. The experimental investigation of concrete carbonation depth. Cement Concrete Res 2006;36:1760–7. [6] Shirakawa Toshino, Shimazoe Yoji, Saeki Minoru, Nagamatsu Seiki. Investigation of carbonation mechanism by hardened cement paste. Proc Jpn Concrete Inst 2001;23(2):493–8. [7] Masuda Yoshihiro, Tanano Hiroyuri. Mathematical model on process of carbonation of concrete. Concrete Res Technol 1991;2(1):125–34. [8] Papadakis VG, Vayenas CG, Fardis MN. Physical and chemical characteristics affecting the durability of concrete. ACI Mater J 1991;9(2):186–96. [9] Houst Yves F, Wittmann Folker H. Influence of porosity and water content on the diffusivity of CO2 and O2 through hydrated cement paste. Cement Concrete Res 1994;24(6):1165–76. [10] Fukujima Toshio. Theoretical predictive methods and numerical analysis for the progress of neutralization of concrete. J Constr Engng AIJ 1991;428:1–15. [11] Saeki Tatsuhiko, Ohga Hiroyoki, Nagataki Shigeyoshi. Mechanism of carbonation and prediction of carbonation process of concrete. J Jpn Soc Civil Eng 1990;414(12):99–108. [12] Li Chunhe, ISHIDA Tetsuya. Carbonation model of cement hydration products based on micro-pore structure and mass transport. Proc Jpn Concrete Inst 2006;28(1):701–6. [13] Ngala VT, Page CL. Effects of carbonation on pore structure and diffusional properties of hydrated cement paste. Cement Concrete Res 1997;27(7):995–1007. [14] Fukushima Toshio, Yosizaki Yoshiro, Tomosawa Fuminori, Takahashi Koichi. Relationship between neutralization depth and carbonation front depth-consideration from accelerated carbonation test, outdoor exposure test, field-research and theoretical research. Proc Jpn Concrete Inst 1997;19(1):805–10. [15] Architectural Institute of Japan, Recommendations for durability design and construction practice of reinforced concrete, 2004. [16] The Global 2000 Report to the President, Entering the twenty-first century, Vol. 2, Superintendent of Documents, US Government Printing Office, 1981. [17] Concrete Library 119, Recommendation for concrete repair and surface protection of concrete structures, 2006. [18] Takuya Hasegawa. A study on carbonation control effect of finishing materials for reinforced concrete components, Hokkaido University Thesis for Ph.D. degree. 2003.