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The Effect Of Temporal And Spatial Variability
Of Ambient Carbon Dioxide Concentrations On
Carbonation Of RC Structures
MG Stewart 1 B Teply2 H Králová 3
1
Centre for Infrastructure Performance and Reliability Department of Civil
Surveying and Environmental Engineering, University of Newcastle, NSW Australia
2
Department of Structural Mechanics Brno University of Technology, 3Department
of Landscape Water Management Brno University of Technology, Czech Republic
Summary: Ambient carbon dioxide (CO2) is an environmental stressor that can lead to the
carbonation and deterioration of RC structures. In the present paper a useful model to predict
carbonation depths is reviewed. The model uses CO2 concentration as an input parameter, but
there appears to be a lack of quantitative data on existing CO2 concentrations in typical urban or
industrial cities. Hence, the paper reports on CO2 concentrations collected from the city of Brno in
the Czech Republic. It was found that the ambient CO2 concentration attributable to a typical
urban environment is approximately 5-10 % higher than CO2 concentrations in a rural
environment. Carbonation depths were calculated for RC structures with service lives of up to 100
years. It was seen that the increase in urban and global CO2 concentrations have little influence on
these predicted carbonation depths. Using a minimum (worldwide rural) CO2 concentration of 370
ppmv for exterior exposures and assuming that material and environmental properties are known,
will provide a lower bound on the actual depth of carbonation. Finally, a probabilistic analysis
showed that variability in carbonation depths can he high due to uncertainty and variability of
environmental and material properties.
Keywords. Carbonation, Probabilistic Analysis, Concrete, Deterioration, Variability
1
INTRODUCTION
The durability of reinforced concrete (RC) structures is, not surprisingly, adversely affected by environmental stressors. A
rather common and serious stressor is carbon dioxide (CO2) which can cause depassivation of the protective film of steel
reinforcement (known as carbonation). Carbon dioxide is always present in the atmosphere and its concentration is higher in
the vicinity of its sources – in industrial and densely populated regions which tend to have the highest proportion of built
infrastructure. Being heavier than air higher concentrations of CO2 may be expected to vary with height above ground level.
When the carbonation depth reaches the reinforcement the reduction in alkalinity destroys the passivity of the protective film corrosion may then occur. The time interval to this situation is normally referred to as the initiation period. During the
following time (propagation) period the corroding steel sections are gradually reduced, leading to cracking and finally spalling
of concrete thus reducing the structural and serviceability reliability of structural members. An appropriate definition of service
life would most likely be the time to significant corrosion-induced cracking and spalling [e.g., Stewart and Rosowsky, 1998;
Stewart, 1999, 2001]. However, the present study will focus on a more conservative measure of service life performance,
namely, the time to corrosion initiation.
The measurement of CO2 concentrations are seldom reported or readily accessible, are rarely based on continuous monitoring
and are more likely to be recorded in non-urban (remote) environments so as to monitor the background level of CO2
concentrations needed to help assess the magnitude of “global warming”. Therefore the aim of the present paper is (i) to report
about actual CO2 measurements recorded in typical urban environments and (ii) to show the damaging effect of CO2 on RC
structures and the variability of predicted carbonation depths.
2
PREDICTIVE MODEL FOR CARBONATION OF CONCRETE
The time to corrosion initiation (carbonation) depends on many parameters: concrete quality, concrete cover, relative humidity,
ambient carbon dioxide concentration and others. The impact of carbonation has been studied by several researches and
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various mathematical models have been developed with the purpose of predicting carbonation depths. Most models predict that
carbonation depths increase as a function of the square root of time. Some of the carbonation models are listed and compared
in Kersner, et.al. (1996) and others are described in Papadakis, et.al. (1992), Bickley (1990), Ho and Lewis (1987), Richardson
(1990), Schliessl (1976), etc. However, the model proposed by Papadakis, et.al. (1992) considers the widest range of
influencing parameters and is the only model where the CO2 concentration is directly involved as an input parameter. The
mathematical model is based on differential mass-balances of gaseous CO2, solid and dissolved Ca(OH)2, CSH and unhydrated
silicates, which account for the production, diffusion and consumption of these substances. The carbonation depth (xc in m) is
thus
1/ 2
 2 CO 0 D
[ 2 ] e, CO2 

xc = 
t
 [CH] + 3[CSH] 
[CO2 ]
0
= 42y CO 2 10
RH ≥ 50%
(1)
−6
(2)
D e, CO 2 (m yr ) = 51.8ε p [1− (RH /100)]
(3)
 ρ  (w / c)− 0.3
ε p ≈  c 
 ρ w  1+ (ρ c /ρ w )(w / c)
(4)
2
−1
[CH] + 3[CSH] ≈ 1+ (ρ
1.8
2.2
33000
c /ρ w )(w / c)+ (ρ c /ρ a )(a / c)
(5)
where [CO2]0 is the molar concentration of ambient CO2 (mol m-3); De,CO2 is the effective diffusity of CO2 in concrete;
[CH]+3[CSH] is the total molar concentration of carbonable constituents of concrete (mol m-3); t is time in years; yCO2 is the
ambient CO2 content by volume (ppmv); RH is the relative humidity (%); εp is the porosity of fully hydrated and carbonated
cement paste; ρc, ρw and ρa are the densities of cement, water and aggregates respectively (kg/m3); and c, w and a are the
contents of cement, water and aggregates respectively (kg). The aggregate content is the sum of sand and gravel (sizes 4-8mm,
8-16mm) contents. Clearly, relative humidity and ambient CO2 content are long-term averages (ie. time-invariant) values, say
measured over a year or more.
Papadakis, et.al. (1992) then proposed a “simplified” expression for carbonation depth, namely,
 ρ  (w/ c)− 0.3
f(RH)
x c ≈ 350 c 
 ρ w 1+ (ρ c /ρ w )(w / c)
 p 
  
1+  c (w/ c)+  pc  a  y CO 10−6 × t
2
  pw 
 pa  c 
(
)
(6)
where f(RH) is a function of relative humidity equal to 1-(RH/100). However, Novák, et.al. (1996) have proposed a step-wise
linear relationship for f(RH) extracted from field data of a cooling tower in Bohemia. Note that Eqn. (6) is somewhat nonconservative since it underestimates carbonation depths by approximately 5-10%. For this reason, Eqns. (1)-(5) are the
preferred expressions for the calculation of carbonation depths to be used in this paper, for indoor conditions or outdoor
concrete sheltered from rain.
3
TEMPORAL AND SPATIAL VARIABILITY OF CO2 CONCENTRATIONS
3.1
Temporal Variability and Global Warming
It has been recognised for some time that CO2 concentrations are subject to temporal and spatial variability. The average CO2
concentrations recorded in the South Pole and other unpolluted atmospheres have steadily increased from 330ppmv in 1971 to
approximately 370 ppmv in 2000 [e.g., Keeling and Whorf, 2000]. This represents an annual increase of over 1.4 ppmv per
year. As a comparison, the pre-Industrial Revolution level of CO2 concentration was between 265 and 290 ppmv [Engelfried,
1985]. However, this increase in average CO2 concentrations might just be an increase in the “global average” CO2
concentration and may not be representative of increases in previously established urban environments. In other words, the
increase in “global average” CO2 concentrations may be due more to development of new and expanding urban and industrial
regions (e.g., in the developing world), rather than an increase in CO2 concentrations within existing urban boundaries (e.g.,
within a city whose level of inter-decadal CO2 emissions would be relatively time-invariant). There appears to be little data to
confirm this hypothesis. However, Fig. 1 shows that annual average CO2 concentrations in Calgary (Canada) measured from
1992 to 1999 vary from 390 ppmv to 400 ppmv (mean is 394 ppmv with an annual increase of 1.4 ppmv) [CASA, 2001]. It is
unclear whether the increase in annual average CO2 concentrations during this period is statistically significant or not. The
considerable temporal variability within a year is shown in Fig. 2. Longer term records are needed, but unfortunately,
collection of CO2 concentration data in Calgary seems to have ceased in 2000.
9DBMC-2002 Paper 246 Page 2
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450
400
350
2
CO Concentration (ppmv)
500
300
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
Year
Figure 1. Average Annual CO2 Concentrations for Calgary, Canada [CASA, 2001].
3
600
1100
550
2
CO Concentration (ppmv)
CO Concentration (mg/m )
2
1200
1000
500
900
450
800
400
700
350
600
300
500
1-Jan-1999
1-Apr-1999
1-Jul-1999
1-Oct-1999
31-Dec-1999
Date
Figure 2. Temporal Variability of Hourly CO2 Concentrations for Calgary [CASA, 2001].
3.2
Measurements from Meteorological Station, Brno University of Technology
Long-term CO2 concentration measurements in urban environments are relatively scarce. For this reason, the Meteorological
Station of the Faculty of Civil Engineering, Brno University of Technology started to monitor hourly CO2 concentrations in
April 1999. Carbon dioxide is measured by a Multi Gas Monitor Type 1302 (Bruel&Kjaer) using the photo-acoustic infra-red
detection method.
Carbon dioxide concentrations were initially measured from the sixth floor (30m above a relatively busy street 2km from the
city centre) of the Meteorological Station. Because of the reconstruction of the building containing the Meteorological Station
in September 2000 the CO2 monitor was moved to an external location on the ground floor (2m above street level). Monitoring
is still continuing at this location, although the Meteorological Station will eventually be relocated to its original position. For
example, Fig. 3 shows hourly monitored CO2 concentrations for a typical day for (i) 30m above street level and (ii) 2 m above
street level. It is observed that the CO2 concentration varies quite significantly over a 24 hour period. The Meteorological
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Station is not located near any industries so it is expected that hourly changes in CO2 levels are attributable mainly to exhaust
emissions, especially with morning temperature inversion and during peak hours.
From all the measured data collected to date the minimum hourly CO2 concentration was 350 ppmv and the maximum
recorded value being 575 ppmv. These results are consistent with individual hourly measurements made in Calgary (see Fig.
2). The daily average CO2 concentration (in year 2000) is 390 ppmv for the sixth floor and 408 ppmv for 2m above street level.
In Phoenix (Arizona) CO2 concentrations measured at a height of 2m varied from 555 ppmv in the city centre to 370 ppmv in
outlying rural areas [Idso, et.al., 1998]. This suggests the presence of “urban CO2 domes” where intensive urbanisation can
increase local CO2 concentrations. It might be noted that the average CO2 concentrations recorded in the South Pole, Pacific
Islands, Alaska and other unpolluted atmospheres are approximately 370 ppmv (725 mg/m3). This suggests that the minimum
average CO2 concentration is 370 ppmv for exterior exposures.
The concentration of CO2 in urban environments are influenced by combustion of fossil fuels from traffic, domestic heating,
power generation, etc. Carbon dioxide concentrations at higher levels could also be influenced by wind velocity and wind
direction, together with air turbulence. During calm weather CO2 produced by traffic is concentrated close to ground level and
CO2 has a density 50% greater than air which helps explain the higher CO2 concentrations in Brno recorded at 2m above street
level. Concentrations of CO2 are increased also by air temperature inversion. This occurs especially in low lying urban
localities during morning hours (see Fig. 3). Note that the CO2 concentration for indoor environments can be considerably
higher than exterior CO2 concentrations.
500
CO Concentration (ppmv)
2m above street level
30m above street level
450
400
2
350
300
0:00:00
4:00:00
8:00:00
12:00:00
16:00:00
20:00:00
24:00:00
Time (hours)
Figure 3. Hourly CO2 Concentrations Recorded for a Typical Day in Brno.
More extensive predictive and statistical analyses will be feasible when more data is collected from the Meteorological Station
of the Faculty of Civil Engineering, Brno University of Technology. This will allow, for example, analysis of seasonal CO2
changes as well as investigating the relationship between CO2 concentrations and other meteorological (environmental) factors.
It is hoped that additional CO2 monitoring stations can be commissioned so as to allow for greater understanding of the
temporal and spatial variability of CO2 concentrations.
4
4.1
PREDICTED CARBONATION DEPTHS
Deterministic Modelling
The influence of CO2 concentration on the carbonation front (xc) as calculated from Eqns. (1)-(5) is shown in Fig. 4; for typical
concrete of class C30/37, RH equal to 65%, and CO2 concentrations of 370 ppmv, 400 ppmv and 450 ppmv. The impact of
CO2 concentration is clearly observable – e.g. a carbonation depth of a low cover (10mm) could be reached in only 32 years for
a known CO2 concentration of 400 ppmv (0.04% CO2 by volume). It was shown earlier that the minimum CO2 concentration is
370 ppmv for exterior exposures and so this may be deemed a “best case” scenario for durability. In other words, using a CO2
concentration of 370 ppmv (725 mg/m3) in Eqn. (1), and assuming that material and environmental properties are known, will
provide a lower bound on the actual depth of carbonation. The present analysis assumes that CO2 concentration is modelled as
a stationary (time-invariant) process. However, if CO2 concentrations are increasing with time then CO2 concentration needs to
be modelled as a non-stationary process [e.g., Fukushima, et.al., 1996].
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20
c
Carbonation Depth x in mm
25
15
10
y
5
=370 ppmv
CO2
yCO2=400 ppmv
yCO2=450 ppmv
0
0
10
20
30
40
50
60
70
80
90
100
Time (years)
Figure 4. Function of Carbonation Depth with Time
If it is assumed that annual CO2 concentrations increase at 1.4 ppmv then the average CO2 concentration over 100 years will be
470 ppmv. In this case, the carbonation depths for this CO2 concentration are about 8% higher than the present urban CO2
concentration (400 ppmv). This represents an approximation of carbonation depths since a more accurate analysis would model
CO2 concentration as a non-stationary process increasing linearly from 400 ppmv to 540 ppmv over the next 100 years.
The collected data shows that the additional ambient CO2 concentration attributable to a typical urban environments is
approximately only 20-40 ppmv. For a “best case” scenario of 370 ppmv this represents an increase in CO2 concentration of 510%. This change in CO2 concentration will cause less than a 5% increase in carbonation depths. This suggests, that for
carbonation, changes in relative humidity and concrete quality have a greater influence on durability of RC structures than the
additional CO2 concentration experienced in typical urban environments or that expected from global warming. This later
observation is supported by Engelfried (1985) who stated that the additional carbonation caused by “polluted” atmospheres is
minor.
4.2
Probabilistic Modelling
It is widely recognised that many parameters involved in determining carbonation depth are uncertain or random in nature. So
it is useful to adopt a probabilistic analysis by treating input parameters as random variables or processes [e.g., Stewart and
Melchers, 1997]. This approach, for carbonation depths, was initiated probably by Hergenroder (1988) and later utilised by
Teply, et.al. (1993), Holicky and Mihashi (1999), and others. A probabilistic analysis propagates the uncertainty and variability
of these parameters to provide an indication of the variability of the final result, in this case, the mean and variance of
carbonation depths. Monte Carlo simulation is useful for such a probabilistic analysis.
Statistical parameters (mean, coefficient of variation, distribution type) for class C30/37 concrete exposed to an exterior
environment are described in Table 1. The model error is modelled as an annual random process with a correlation coefficient
of 0.5. Considering model error as a random process will help account for the temporal variability of the accuracy of predictive
models. Relative humidity and CO2 concentrations might also be considered to be non-stationary and highly correlated annual
random processes; however, these are not considered herein.
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Table 1. Statistical Paramters of Carbonation Variables.
Variable
Symbol
Mean
Coefficient of
Variation
(COV)
Distribution
ME(to)
1.0
0.1
Normal
RH
65%
0.05
Normal
Cement Content
c
370kg
0.03
Lognormal
Water Content
w
181kg
0.02
Lognormal
Sand Content
s
644kg
0.03
Lognormal
Gravel (4-8) Content
g4-8
262kg
0.03
Lognormal
Gravel (8-16) Content
g8-16
925kg
Random Processes:
Model Error
Random Variables:
Relative Humidity
0.03
Lognormal
3
0.03
Normal
Cement Density
ρc
3100kg/m
Sand Density
ρs
2590kg/m3
0.03
Normal
3
0.03
Normal
0.03
Normal
Gravel (4-8) Density
ρg4-8
2540kg/m
Gravel (8-16) Density
ρg8-16
2660kg/m3
20
c
Carbonation Depth x in mm
25
95% confidence limit
15
mean
5% confidence limit
10
5
0
0
10
20
30
40
50
60
70
80
90
100
Time (years)
Figure 5. Variability of Carbonation Depth (yCO2=400ppmv)
Fig. 5 shows the variability of carbonation depths for a CO2 concentration of 400 ppmv. The scatter in carbonation depth is
quite large (COV=0.14), as is also usually observed in reality. In the present case, CO2 concentration is treated as a
deterministic variable. However, if the variability of carbonation depth is needed for a population of structures exposed to
different CO2 concentrations (e.g., different building heights) then a moderate variability of CO2 concentration (COV less than
0.15) will produce little influence on carbonation depths. If such an analysis was conducted then the probabilistic model of
CO2 concentrations would need to be truncated at 370ppmv. Not surprisingly, a sensitivity analysis has found that the most
significant variables are relative humidity and model error.
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4.3
Chloride-Induced Corrosion
It should be noted that chloride ingress also jeopardises the passivation layer on reinforcing bars. The modelling of this effect
can be done using a number of predictive models [e.g., Papadakis, et.al., 1996; Vu and Stewart, 2000] and have been utilised
for probabilistic assessment of time to corrosion initiation of concrete structures [Teply, et.al., 1998; Weyers, 1998; Vu and
Stewart, 2000]. There is evidence to suggest that chloride action is accelerated by carbonation (and SO2, NOx) because
carbonation disturbs the equilibrium between free and bound chlorides in the concrete, thereby increasing the free chloride
concentration in the pore solution. The interaction between carbonation and chloride-induced corrosion may be significant;
unfortunately, a suitable predictive model is not available.
5
CONCLUSIONS
Continuous monitoring of carbon dioxide concentrations in Brno has shown that the ambient CO2 concentration
attributable to a typical urban environment is approximately 5-10% higher than CO2 concentrations in a rural
environment. Measurements from Calgary in Canada confirm this observation. Carbonation depths were calculated
for RC structures with service lives of up to 100 years and it was seen that increased urban CO2 concentrations have
little influence on these predicted carbonation depths. Using a minimum (worldwide) CO2 concentration of
370ppmv for exterior exposures will represent a “best case” scenario or lower bound for durability. A probabilistic
analysis showed that variability in carbonation depths can he high due to uncertainty and variability of
environmental and material properties. Monitoring is continuing and should be extended to include other localities
to gain a better understanding of the spatial characteristics of CO2 concentrations, and hence, the extent of
carbonation in new and existing RC structures.
6
ACKNOWLEDGMENTS
The authors gratefully acknowledge the partial subsidy provided by research project No. CEZ:J22/98:261100007
(Czech Ministry of Education) and grant No. 103/97/K003 (Grant Agency of the Czech Republic).
7
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