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PROBABILISTIC ASSESSMENT OF THE EFFECT OF CLIMATE CHANGE
ON THE CARBONATION OF CONCRETE STRUCTURES
IN THE CARPATHIAN BASIN
Árpád Rózsás
Budapest University of Technology and Economics, Budapest, Hungary,
rozsas.bme@gmail.com
Nauzika Kovács
Budapest University of Technology and Economics, Budapest, Hungary, nauzika@vbt.bme.hu
Abstract
Due to mainly human activity in the following decades we are facing increasing mean global
temperature and rising CO
2
concentration. This paper investigates the effect of these
changing environmental parameters on the durability of concrete structures. We restrict our
attention to the examination of carbonation process and to environmental data applicable
for the Carpathian Basin. The carbonation model is based on the internationally recognized
CEB-fib model. The climatic parameters are considered through 6 climate change scenarios
according to the recommendation of the Intergovernmental Panel on Climate Change. Full
probabilistic approach utilizing Monte Carlo simulation technique is used to analyze the
reliability of currently applied concrete covers against depassivation of reinforcement. A
numerical method is proposed to efficiently take into account the time-varying atmospheric
CO
2
concentration. This method is used to assess the error of widely applied constant CO
2
level approximation. The calculations indicate that climate change could have a significant
effect; the carbonation depth may increase by 15-20% until the end of this century compared
to year 2000 as a reference. The risk of depassivation of reinforcement could increase by 60%
over time to 2100. The results suggest that the effect of climate change should be considered
in design codes.
Keywords: climate change, concrete carbonation, Eurocode, Monte Carlo simulation,
reliability.
1. INTRODUCTION
Climate change is an ongoing process which already affects our life and may lead to
devastating effects in the future [IPCC, 2007]. It is estimated that in 2012 climate change has
contributed to 1-2% GDP loss on a global scale [DARA, 2012]. This paper deals with a process
which in the following decades could deepen this burden, i.e. carbonation of concrete which
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ultimately may lead to the failure of structures. This phenomenon has great importance since
buildings and civil infrastructure comprise about 80% of the national wealth of developed
countries [Sarja, 2005] and the majority of these are made of reinforced concrete which is
the most widely used construction material on Earth. The designers of these structures bear
great responsibility since their creations will be used by future generations and have
significant effects on our natural and built environment. Therefore, decisions made today
could have harsh effects within 50-100 years which are the typical design lives of buildings
and bridges.
Previous studies showed that climate change considerably accelerates the carbonation
process [Yoon et al., 2007; Stewart et al., 2011; Talukdar et al., 2012] and could have
significant effects on the durability of concrete structures [Stewart et al., 2012; Talukdar
and Banthia, 2013]. These studies are dealt with the Australian continent and with major
cities around the world. There is a lack of analysis for Continental Europe and for the
region of the Carpathian Basin. To realistically assess the effect of climate change reliability
analysis has to be carried out. Previous probabilistic studies did not take into account the
time-varying CO
2
concentration and typically used average values; the associated degree of
error is not known. Moreover, the current standardized specifications are based on
historical data not on full probabilistic analysis and do not take into account the effect of
climate change.
Based on the above considerations and unanswered questions the main goals of this paper
are the followings: (i) Evaluation the effect of climate change on the carbonation of concrete
structures in the Carpathian Basin and (ii) the investigation the increase in risk of
depassivation considering the provisions of Eurocode. (iii) Quantitative assessment of the
time-varying CO
2
level on the carbonation process. For the analysis carbonation model
coupled with global climate change scenarios is used and full probabilistic reliability analysis
is applied to calculate the effect of uncertainties.
2. MODEL DESCRIPTION
2.1. Carbonation Model
The carbonation model recommended by CEB-fib Model Code for Service Life Design (MC
SLD) is used which has relatively broad internationally acceptance [CEB-fib, 2006]. A further
advantage of this model is that the stochastic properties of the parameters are also provided.
The applied carbonation model is based on Fick’s laws of diffusion; these are widely used to
describe the CO
2
or chloride ion transportation in concrete. Fick’s second law describes the
concentration change in time and expresses the mass conservation, Eq. (1):
2
2
CC
D
tx
∂∂
=
∂∂
(1)
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The solution of this parabolic partial differential equation (pde) in one dimension with
constant concentration at the air-concrete boundary is given by Eq. (2).
0
(,) 2
x
Cxt C erfc
D
t
=⋅ ⋅⋅
⎛⎞
⎜⎟
⎝⎠
(2)
Where x is the distance from the boundary, C
0
is the constant CO
2
level (C(x=0,t) = C
0
), D is
the diffusion coefficient, t is time and erfc is the complementary error function. Using Eq. (2)
the carbonation front in concrete can be expressed in the following form:
2
()
c
x
Dt
t
=⋅⋅
(3)
The CEB-fib carbonation model has the same square root of time form (Eq. (4)) as the above
solution with additional factors to take into account the effect of environmental conditions,
period of curing, etc. [CEB-fib, 2006].
1
() 2 ()
cecNACS
x
tkkRCtWt
−
= ⋅⋅⋅ ⋅ ⋅
(4)
where:
k
e
environmental function [-], Eq. (5);
k
c
execution parameter [-], Eq. (6);
1
NAC
R
− inverse carbonation resistance
2
3
myr
kg m
⎡
⎤
⎢
⎥
⎣
⎦
, Eq. (7);
C
S
CO
2
concentration of atmosphere [kg/m
3
], Eq. (8);
t time [yr];
W(t) weather function [-], Eq. (9).
()
()
()
2
0
,,
11
1 (5), (6), (7),
7
1
(8), ( ) (9)
e
ec
e
bw
SR
g
fb
real c
ectt
f
ref
pToW
SSatmSemi
NAC ACC
RH t
kkk
RH
t
CC C Wt t
RR
ε
⋅
−−
−
===⋅+
−
=+ =
⎡⎤ ⎛⎞
⎢⎥ ⎜⎟
⎝⎠
⎢⎥
⎣⎦
⎛⎞
⎜⎟
⎝⎠
The names and values of these variables are summarized in Section 3, Table 1. Previous
studies demonstrated that urban environments have an elevated CO
2
level compared to rural
areas [Stewart et al., 2002]. Since most reinforced concrete structures are located in urban
areas and the most unfavorable situation should be considered the C
S,emi
term is taken as 15%
of atmospheric concentration (C
S,atm
) with 0.15 coefficient of variation (COV) [Stewart et al.,
2011]. The main drawback of Eq. (4) is that it provides a point-in-time estimation and cannot
take into account the time-varying manner of CO
2
concentration which is the most important
parameter in the diffusion process [Stewart et al., 2011]. To circumvent this problem the
following numerical procedure is proposed which takes advantage of the particular character
of governing pde and boundary conditions. Since the differential equation is linear the
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principle of superposition is valid and a mathematically sound approach is to solve the
equation with the sum of basic solutions for constant concentration (Eq. (10), Figure 1). The
advantage of this approach is that the previously conducted researches and experiments
which are based on constant CO
2
concentration can be directly applied.
[0, [ 0,
1[,[
(, ) 2
i
n
tot i
iit
x
Cxt Cerfc Dt
∞
=∞
=⋅⋅⋅
⎛⎞
⎜⎟
⎜⎟
⎝⎠
∑
(10)
The above formulation makes it possible to consider time-varying diffusion coefficient as
well. To determine the carbonation depth a CO
2
threshold value is needed at which the pH of
concrete drops below about 9 and depassivation happens. This threshold value is determined
by using the known, experimentally calibrated constant CO
2
level solutions.
Figure 1: Graphical representation of the applied numerical procedure.
The method is verified against examples with constant CO
2
concentration published in CEB-
fib MC SLD. Moreover, the time-varying case is checked by solving the differential equation
by MATLAB’s built-in pde solver (this is a more general and robust solver therefore requires
considerably higher computational time). The calculations showed that the described
method converges quickly to the exact solution and they are used to tune the parameters,
i.e. the discretization of time and depth space, to get efficient algorithm with desired
accuracy.
It should be noted that the used carbonation resistances are determined by accelerated
carbonation tests with unloaded and completely sound specimens. The effect of real in-
service conditions is not yet comprehensively analyzed, but it is clear that cracks lower the
durability.
predicted concentration
approximation
2010
C
0,i
CO
2
concentration in atmosphere [ppmv
]
Time [year]
2020 2030 2040 2050 2060 2070 2080 2090 2100
400
500
600
700
800
900
1000
2000
300
t
[ti,inf[
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2.2. Climate Change Predictions
Following the recommendation of the Intergovernmental Panel on Climate Change (IPCC)
multiple scenarios are selected [IPCC, 2007]; one scenario from every SRES (Special Report on
Emission Scenarios) family which represent a wide range of possible outcomes. These describe
economic (A1, A2) and environmental (B1, B2) focused future developments with local (A2, B2)
or global (A1, B1) orientations. The three groups within the A1 family are characterizing
alternative developments of energy technologies: A1FI (fossil fuel intensive), A1B (balanced),
and A1T (predominantly non-fossil fuel). Additionally, a reference concentration level
(reference 2000) is chosen which represent the CO
2
level in 2000 on which the current
experiences and standards are roughly based. The predicted global atmospheric CO
2
concentrations corresponding to the selected scenarios are depicted in Figure 2. The shaded
areas show the ±σ range considering lower, medium and higher carbon cycle feedbacks.
Figure 2: CO
2
concentration for various SRES climate change scenarios [IPCC, 2007].
Due to the limited available data on the actual density functions of CO
2
concentration normal
distribution is fitted to the mean and +σ upper quantile value. Other environmental variables
are approximated from earlier measured data of Hungarian meteorological stations. This is
justified by the fact that the expected change to 2100 in the average value of relative
humidity and precipitation is not significant [Bartholy et al., 2011].
3. RELIABILITY ANALYSIS
The uncertainties of the model variables are considered through Level III probabilistic analysis,
where all variables are taken into account by their exact probability density functions and the
exact probability of failure is determined [JCSS, 2000]. Here the exact means that the exact
Time [year]
1900 1920 1940 1960 1980
historical data A1FI + σ
A1FI μ
A1FI - σ
2000 2020 2040 2060 2 080 2100
Time [year]
2000 2020 2040 2060 20 80 2100
400
600
800
1000
B2 + σ
B2 μ
B2 - σ
A2 + σ
A2 μ
A2 - σ
B1 + σ
B1 μ
B1 - σ
A1T + σ
A1T μ
A1T - σ
A1B + σ
A1B μ
A1B - σ
CO
2
concentration [ppmv]
400
600
800
1000
CO
2
concentration [ppmv]
400
600
800
1000
CO
2
concentration [ppmv]
Time [year]
2000 2020 2040 2060 2 080 2100
400
600
800
1000
CO
2
concentration [ppmv]
Time [year]
2000 2020 2040 2060 2080 2100
400
600
800
1000
CO
2
concentration [ppmv]
Time [year]
Time [year]
2000 2020 2040 2060 2 080 2100
2000 2 020 2040 2060 2080 2100
400
600
800
1000
CO
2
concentration [ppmv]
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solution of the mathematically formulated problem is approached by numerical techniques.
The limit state function (g) for the depassivation of reinforcement is expressed in Eq. (11).
()
5()
c
g
ammxt=− −
(11)
Where a is the minimum concrete cover which can be calculated by reducing the nominal
cover (a
nom
) with a safety margin (Δa), Eq. (12).
nom
aa a=−Δ
(12)
The safety margin for typical structures is 10mm [EN-2, 2004; CEB-fib, 2006], this value is
adopted in this study. The additional 5mm reduction reflects the experimental fact that the
depassivation of reinforcement happens when the carbonation front reaches 5mm vicinity of
the rebar [Yoon et al., 2007].
The introduced method for determination of carbonation depth only requires matrix
operations, thus the evaluation of the limit state function is not computationally intensive.
Moreover, the chosen probability of failure corresponding to depassivation is around 0.1.
Therefore, significantly fewer evaluations are required to obtain low-variance solution than
in case of ultimate limit states. Based on the above considerations crude Monte Carlo
method is chosen to carry out the Level III reliability analysis. Table 1 summarizes the
variables with their probabilistic properties.
Table 1: Stochastic properties of model variables.
Distribu-
tion Mean COV Reference
Relative humidity of carbonated layer (RH
real
), [-] Beta 0.70 0.125 [CEB-fib, 2006]
Reference relative humidity (RH
ref
), [-] Constant 0.65 0 [CEB-fib, 2006]
Exponent (g
e
), [-] Constant 2.50 0 [CEB-fib, 2006]
Exponent (f
e
), [-] Constant 5.00 0 [CEB-fib, 2006]
Regression exponent (b
c
), [-] Normal -0.567 0.042 [CEB-fib, 2006]
Period of curing (t
c
), [day] Constant 2.00 0
Inverse carbonation resistance (R
NAC
-1
),
[mm
2
/yr/(kg/m
3
)] Normal varying varying [CEB-fib, 2006]
Regression parameter (k
t
), [-] Normal 1.25 0.28 [CEB-fib, 2006]
Error term (
ε
tm
), [mm
2
/yr/(kg/m
3
)] Normal 315.50 0.152 [CEB-fib, 2006]
Equivalent water cement ratio, [-] Constant 0.60 0 [CEN, 2002]
CO
2
concentration of atmosphere (C
Satm
), [ppmv] Normal varying varying [IPCC, 2007]
CO
2
concentration due to emission (C
Semi
), [ppmv] Normal 0.15*C
S,atm
0.15 [Stewart et al.,
2011]
Probability of driving rain (p
SR
), [-] Constant 0.10 0
Exponent of regression (b
w
), [-] Normal 0.446 0.365 [[CEB-fib, 2006]
Time of reference (t
0
), [yr] Constant 0.0767 0 [CEB-fib, 2006]
Time of wetness (ToW), [-] Constant 0.20 0
Nominal concrete cover (a), [mm] Weibull varying 8/
μ
a
[CEB-fib, 2006]
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The correctness of Monte Carlo simulation is confirmed by the examples available in CEB-fib
MC SLD. The calculations are completed using data predicted for Hungary, but the presented
method can be used irrespectively of geographic location.
4. ANALYSIS RESULTS
4.1. Assessment the error of constant CO
2
approximation
The above presented carbonation model coupled with climate change predictions is used to
estimate the error of – in previous studies applied – constant CO
2
level. Hereinafter in all
calculations the beginning of carbonation is year 2000. Two different constant
approximations are examined. One with a single average CO
2
level over the whole considered
time domain (I) and one with time-varying average CO
2
level (II). The latter implies that the
average concentration is calculated for every time instant by taking the average of preceding
concentrations; this approach was applied by Stewart et al. (2011). Comparison the mean
values of approximation (I) to exact time-varying solution for CEM I 42.5R cement is shown in
Figure 3.
Figure 3: Mean value of carbonation depth in time for time-varying, averaged and reference CO
2
concentration.
For various climate change scenarios the comparison of reference, varying average
(approximation II) and exact time-varying solutions are illustrated in Figure 4.
A1B mean values
Time [yr]
Carbonation depth [mm]
0 102030405060708090100
00
5
10
15
20
25
Time [yr]
Carbonation depth [mm]
0 102030405060708090100
0
5
10
15
20
25
Time [yr]
Carbonation depth [mm]
0 102030405060708090100
0
5
10
15
20
25
Time [yr]
Carbonation depth [mm]
0 102030405060708090100
0
5
10
15
20
25
Time [yr]
Carbonation depth [mm]
0010 20 30 40 50 60 70 80 90 100
5
10
15
20
25
0
Time [yr]
Carbonation depth [mm]
10 20 30 40 50 60 70 80 90 100
5
10
15
20
25
variable CO
2
average CO
2
reference 2000
variable CO
2
average CO
2
reference 2000
variable CO
2
average CO
2
reference 2000
variable CO
2
average CO
2
reference 2000
variable CO
2
average CO
2
reference 2000
variable CO
2
average CO
2
reference 2000
A1FI mean values A1T mean values
A2 mean values B1 mean values B2 mean values
CEM I 42,5R CEM I 42,5R CEM I 42,5R
CEM I 42,5RCEM I 42,5RCEM I 42,5R
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Figure 4: Mean value of carbonation depth in time for time-varying, varying average and reference CO
2
concentration.
The calculations are completed with CEM I 42.5R +FA and CEM III\B 42.5 cement types as
well, the results follow very similar trend as shown in Figure 4. The upper row of Figure 5
shows the error of varying average approximation for the three cement types. Both varying
average and exact time-varying solutions contain the effect of initial CO
2
level which distorts
the comparison and lessen the difference between the two approaches. Thus, the difference
of the two approaches is calculated in respect of increase over the reference curve; these
data are visualized in the lower row of Figure 5.
variable CO
2
varying average CO
2
reference 2000
variable CO
2
varying average CO
2
reference 2000
variable CO
2
varying average CO
2
reference 2000
variable CO
2
varying average CO
2
reference 2000
variable CO
2
varying average CO
2
reference 2000
variable CO
2
varying average CO
2
reference 2000
CEM I 42,5R CEM I 42,5R CEM I 42,5R
CEM I 42,5R
CEM I 42,5R CEM I 42,5R
Carbonation depth [mm]
Carbonation depth [mm] Carbonation depth [mm]
Carbonation depth [mm]
Carbonation depth [mm]Carbonation depth [mm]
A1FI mean values
Time [yr]
A1T mean value
s
Time [yr]
A2 mean values
Time [yr]
0 102030405060708090100
0
5
10
15
20
25
0 102030405060708090100
0
5
10
15
20
25
10 20 30 40 50 60 70 80 90 100
0
5
10
15
20
25
10 20 30 40 50 60 70 80 90 100
0
5
10
15
20
25
10 20 30 40 50 60 70 80 90 100
0
5
10
15
20
25
10 20 30 40 50 60 70 80 90 100
0
5
10
15
20
25
B1 mean val ues
Time [yr]
B2 mean values
Time [yr ]
A1B mean values
Time [yr]
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Creative Construction Conference 2013
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Figure 5: Error of varying average approximation in absolute and increment terms.
4.2. Examination of Eurocode’s durability specifications
Since the current specifications are not taking into account the effect of climate change
and the recommendations “are not based on physically and chemically correct models but
more on practical (sometimes bad) experience. In the future currently applied rules
urgently have to be calibrated against the full probabilistic approach [CEB-fib, 2006].”
Following this recommendation the reliability of durability specifications of Eurocode in the
light of climate change is examined. As an illustrative example a reinforced concrete
structure with 100 year service life (built in 2000) is analyzed with the above presented
approach. It assumed to belong to structural class S6 and exposure class XC2, the
corresponding recommended minimum concrete cover is 35mm. Three different cement
types are studied (CEM I 42.5R, CEM I 42.5R+FA, CEM III\B 42.5); other parameters are
listed in Table 1. The probability of depassivation and the increase in probability of
depassivation is illustrated in Figure 6 for various climate change scenarios. In the lower
row figures (Figure 6) the initial 30 years period is not illustrated because the results show
large scatter. Higher simulation number would be required to get reliable results in that
region with low probability of failure. It should be noted that in the first 30 years the effect
of climate change is low thus not particularly interesting for the current study. In this
illustrative example, the time-varying average approach for CEM I 42.5R, CEM I 42.5R+FA
and CEM III\B 42.5 overestimates the probability of depassivation - compared to the
mathematically sound solution presented in Section 2.1 - by maximum 13%, 18% and 3,1%
respectively. The maximum is in every case corresponding to A1FI scenario, for the other
predictions the error is slightly lower.
CEM I 42.5
R
Time [yr]
Error of varying average
approximation [%]
Error in increment of varying
average approximation [%]
0 102030405060708090100
-1
0
1
2
3
4
5
6
CEM I 42.5 R+FA
Time [yr]
Error of varying average
approximation [%]
0 102030405060708090100
-1
0
1
2
3
4
5
6
Time [ yr]
Error of varying average
approximation [%]
0 102030405060708090100
-1
0
1
2
3
4
5
6
CEM III\B 42.5
CEM III\B 42.5
A1FI A1FI
A1FI
A1FI
A1FI
A1FI
A1B A1B
A1B
A1B
A1B
A1B
A1T
A1T A1T
A1T
A1T
A1T
A2
A2 A2
A2
A2
A2
B1
B1
B1
B1
B1
B1
B2
B2
B2
B2
B2
B2
CEM I 42.5 R
Time [yr]
40 50 60 70 80 90 100
0
10
20
30
40
50
60
70
Error in increment of vary ing
average approximation [%]
Time [yr]
40 50 60 70 80 90 100
0
10
20
30
40
50
60
70
Error in increment of varying
average approximation [%]
Time [yr]
40 50 60 70 80 90 100
0
10
20
30
40
50
60
70
CEM I 42.5 R+FA
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Figure 6: Probability of depassivation and increase in risk due to climate change.
The significant difference between the results of CEM I and CEM III is explained by the about
eight times higher carbonation resistance of CEM I. It should be noted that CEM I and II type
cements are the most widely used cement types and the high early strength CEM III type is
rarely used. The European concrete specification (EN-206-1) does not differentiate between
cement types regarding exposure classes and covers [CEN, 2000]. Although the
experimentally determined diffusion coefficients and the numerical results show significant
difference based on cement type (Figure 6.). It may be worthwhile to prescribe the applicable
cement types as well in the durability requirements to avoid low carbonation resistant
cements such as CEM III\B.
5. DISCUSSION OF RESULTS AND CONCLUSIONS
The obtained results and trends are in good agreement with the data available in the
literature, the calculations confirmed many findings of previous studies, e.g. for structures
built in 2000 the effect of climate change in the first 25-35 years is low [Talukdar and Banthia,
2013].
Based on the full probabilistic reliability analysis of concrete carbonation, using multiple
climate change scenarios, the following conclusions can be made for the Carpathian basin
region: (i) Firstly, climate change has clearly significant effect on the carbonation of concrete,
this could be manifested in even a 21 % increase in carbonation depth to the end of the
century compared to 2000 year reference. To 2050 and 2100 the average carbonation depth
is expected to increase by approximately 7% and 15% respectively. (ii) A numerical procedure
is proposed to directly take into account the variability of CO
2
concentration in time. The
CEM I 42.5 R+FA
CEM I 42.5 R
t
SL
= 100 years
XC2
t
SL
= 100 years
XC2
t
SL
= 100 years
XC2
t
SL
= 100 years
XC2
t
SL
= 100 years
XC2
Time [yr]
Increase in prob ability of depassivation [%]
00
10 20 30 40 50 60 70 80 90 100
Time [yr]
0
10
20
30
40
50
60
70
80
90
Increase in probability of depassivation [%]
10 20 30 40 50 60 70 80 90 100 0
Increase in probability of depassivation [%]
10 20 30 40 50 60 70 80 90 100
10
20
30
40
50
60
70
80
90
A1FI
A1FI
reference 2000
A1B
A1B
A1B
A1T
A1T
A1T A1T
A2
A2
A2 A2
B2
B2
B2
B2
B1
B1
B1
B1
CEM III\B 42.5
CEM III\B 42.5
t
SL
= 100 years
XC2
Time [yr ]
0
A1FI
A1FI
CEM I 42.5 R
Time [yr]
Probability of depassivation [%]
0 102030405060708090100
0
0.05
0.1
0.15
0.2
0.25
0.3
Probability of depassivation [%]
0 102030405060708090100
Probability of depassivation [%]
0 102030405060708090100
0.05
0.1
0.15
0.2
0.25
0.3
CEM I 42.5 R+FA
Time [yr]
A1B
A1FI
A1FI
A1B
A1B
A2
A2
A1T
A1T
B1
B1
reference 2000
reference 2000
B2
B2
Time [yr]
5
10
15
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
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analyses showed that in the previous studies applied varying average CO
2
level yields to
maximum 6% error in respect of carbonation depth and maximum 18% in probability of
depassivation. The single value average approximation gives even worse prediction. It should
be emphasized that these approximations are always overestimate the carbonation depth.
(iii) Climate change scenarios have considerable effect on the degree of change but their
predicted trend is unanimously increasing in respect of carbonation depth and the risk of
depassivation. (iv) New structures built in 2000 and designed according to Eurocode are
expected to be affected slightly by climate change in the first 25-35 years. Nonetheless, to
the end of the century the increase in the risk of depassivation due to climate change for
CEM I 42.5R and CEM I 42.5 R+FA could increase by 35-65% and 50-90% respectively. Based
on the findings and literature data the revision of current standardized specifications
regarding concrete durability in the light of climate change is needed.
ACKNOWLEDGEMENT
The results discussed above are supported by the grant TÁMOP-4.2.2.B-10/1--2010-0009.
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Creative Construction Conference 2013
July 6 – 9, 2013, Budapest, Hungary
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Creative Construction Conference 2013
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Editors-in-chief:
Miklós Hajdu
Mirosław J. Skibniewski
All rights are reserved for the Ybl Miklós Faculty of Architecture and Civil Engineering
at Szent István University, Budapest, Hungary,
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