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Research Article
Li P, Li C, Li D, Chen R and Chen J (2024)
Modelling chloride diffusion in concrete with carbonated surface layer.
Magazine of Concrete Research 76(18): 1048–1058,
https://doi.org/10.1680/jmacr.23.00202
Paper 2300202
Received 23/08/2023;
Accepted 26/03/2024;
First published online 05/04/2024
Emerald Publishing Limited: All rights reserved
Magazine of Concrete Research
Modelling chloride diffusion in concrete with
carbonated surface layer
Ping Li
Runhao Chen
PhD student, Guangdong Provincial Key Laboratory of Durability for Marine
Civil Engineering, Shenzhen University, Shenzhen, PR China
Undergraduate student, Guangdong Provincial Key Laboratory of Durability
for Marine Civil Engineering, Shenzhen University, Shenzhen, PR China
Chuanfei Li
Jinghong Chen
Intermediate Engineer, Henan Country Garden Construction Engineering
Co. Ltd, Luoyang, PR China
Undergraduate student, Guangdong Provincial Key Laboratory of Durability
for Marine Civil Engineering, Shenzhen University, Shenzhen, PR China
Dawang Li
Professor, Guangdong Provincial Key Laboratory of Durability for Marine
Civil Engineering, Shenzhen University, Shenzhen, PR China
(corresponding author: [email protected])
Due to the demand for carbon neutrality, concrete carbonation has been reconsidered as an interesting topic because
of its potential for capturing carbon dioxide (CO2) from the atmosphere. Concrete carbonation can significantly
modify the chemical and microstructure properties of concrete and thus will have important effects on chloride
diffusion. This paper presents a chloride diffusion model in which the concrete cover is divided into three different
zones, each with their own defined porosity and chloride binding isotherm. The first is the fully carbonated concrete
near the surface, where the porosity and chloride binding isotherm can be obtained from the experimental data of
fully carbonated concrete. The second is the uncarbonated concrete near the reinforcement, where the porosity and
chloride binding isotherm can be obtained from the experimental data of normal concrete. The third is the transition
zone between the fully carbonated and uncarbonated concretes, where the porosity and chloride binding isotherm
can be assumed to vary continuously from the carbonated concrete to uncarbonated concrete. To validate the
present model, a comparison of the present model with published experimental results is provided, which
demonstrates the importance of considering different zones in the chloride diffusion model when the concrete has a
carbonated layer near the surface.
Keywords: cement/cementitious materials/concrete/durability-related properties/modelling
Notation
Dapp ¼
Cb
Cf
Cfw
Cs
Ct
D0
D1
D2
D3
Deff
MCl
σ
D0
ð1 þ αÞτ 2
apparent diffusion coefficient of
chlorides in concrete
bound chloride content in per-unit
volume of concrete
free chloride content in per-unit volume
of pore solution
free chloride content in concrete
(in wt.%)
chloride concentration in environment
to which the concrete is exposed
total chloride content in per-unit
volume of concrete
chloride diffusion coefficient in water
apparent diffusion coefficient of
chlorides in zone 1
apparent diffusion coefficient of
chlorides in zone 2
apparent diffusion coefficient of
chlorides in zone 3
effective diffusion coefficient of
chlorides in concrete
molar mass of chloride ions
(0.03545 kg/mol)
t
x
α
δCH
δCSH
ε
ρc
σ
τ
time
space coordinate
proportional constant used in linear
binding isotherm
calcium hydroxide carbonation depth
calcium silicate hydrate carbonation
depth
porosity of concrete
density of paste, mortar or concrete
(in kg/m3)
constrictivity of concrete pore surface
tortuosity of concrete
Introduction
Concrete carbonation and chloride attack are the two main
factors that cause the corrosion of reinforcing steel bars in concrete structures. Concrete carbonation is the reaction of carbon
dioxide dissolved in pore solution with calcium hydroxide and
calcium silicate hydrate in the cement paste. The reaction produces calcium carbonate and lowers the pH value to around
neutral level. The low pH destroys the protective oxide layer
surrounding the reinforcing steel and makes steel corrosion
possible (Stefanoni et al., 2017). Compared to carbonation,
Magazine of Concrete Research
Volume 76 Issue 18
Modelling chloride diffusion in concrete
with carbonated surface layer
Li, Li, Li, Chen and Chen
chloride attack is even more dangerous. Chloride ions diffused
into concrete from the environment surrounding concrete
structures can break down the passive layer of reinforcing steel
without the need to drop the pH levels. Corrosion takes place
as the chloride ions meet with the steel and the surrounding
passive material to produce a chemical process which forms
hydrochloric acid and macro corrosion cells on the bar
(Raupach and Schiessl, 1997). The hydrochloric acid turns
solid iron to liquid rust and results in large volume increase at
the steel–concrete interface and thus leads to concrete cracking, spalling and, eventually, failure (Shi et al., 2012).
double hydroxides (MgAl-NO2 LDHs) inhibitor on steel corrosion protection in concrete due to carbonation alone and the
coupled action of chloride penetration and carbonation. The
results revealed that MgAl-NO2 LDHs have a better inhibition
effect on steel corrosion by carbonation alone than the
coupled action of chloride penetration and carbonation.
Kumar et al. (2021) reported an experimental study on the
changes in the microstructure and performance of carbonated
reactive magnesium oxide (MgO) cement (RMC) samples
containing supplementary cementitious materials (SCMs) (fly
ash and ground granulated blast-furnace slag) under chloride
attack. It was shown that the inclusion of SCMs in RMC
samples increased their resistance to chloride attack. Pontes
et al. (2021) used the silver nitrate colorimetric method to
detect chloride penetration in carbonated concrete, in which
the tests were made in carbonated concrete samples and in carbonated concrete samples contaminated with chlorides. A
method of spraying sodium hydroxide solution before spraying
silver nitrate in concrete was used. The results showed that this
can eliminate carbonation interference in chloride ion penetration when measuring with the silver nitrate method. Tiwari
et al. (2021) investigated the corrosion inhibition effect of
generic compounds in simulated carbonated pore solution contaminated by chloride ions. The effectiveness of using generic
compounds in retarding corrosion rate in a combined chloride
and carbonated environment was demonstrated. Li et al.
(2022) presented a comprehensive predictive model of convection, diffusion and binding of chlorides in concrete during
wetting–drying cycles, in which both concrete carbonation and
chloride attack were considered. The simulation results demonstrated that carbonation has a significant effect on chloride
penetration. Tanaka (2022) presented chloride profiles in carbonated concrete, which showed that the complex chloride profiles should happen due to the high diffusivity in the
carbonated layer under the variable surface chloride content,
suggesting that the chloride ions run out from the carbonated
surface more easily. Recently, Martin and Bastidas (2023) conducted stress corrosion cracking failure analysis of AISI 1018
carbon steel reinforcing bars in carbonated and chloride contaminated environments. It was shown that the crack propagation rate was more pH-dependent than chloride-induced.
Nguyen and Castel (2023) examined the long-term durability
of underground reinforced concrete pipes in natural chloride
and carbonation environments. It was shown that concrete
cover of 25 mm and 20 mm seem adequate for 100 years of
service life in chloride and carbonation environments, respectively. Ramirez et al. (2023) conducted meta-analysis of the
results of corrosion current density obtained from steel
embedded in carbonated concrete by considering the characteristics of concrete and environment. The results showed higher
values of corrosion current (icorr) than expected and reported
in reference studies and standards at different exposure classes
of relative humidity. The high levels of icorr were found in lowand high-binder-content concretes, different paste volumes and
estimated porosities. Sun et al. (2023) examined the effect of
Since the mid-1980s there have been numerous research works
on the corrosion of reinforcing steel caused by concrete carbonation or chloride attack alone (Alexander and Beushausen,
2019) but not many on the interaction between carbonation
and chloride attack (Chen et al., 2022; Li et al., 2022; Shen
et al., 2019; Wang et al., 2017; Zhu et al., 2016). It was
reported that carbonation has both positive and negative
effects on chloride penetration (Stefanoni et al., 2017). The
former is that concrete carbonation reduces the porosity and
thus increases the resistance of concrete to chloride penetration
because of the volume increase resulting from the carbonation
reaction. The latter is because carbonated concrete has low
chloride binding capacity which accelerates the penetration
process of chloride ions in concrete. Research on the influence
of concrete carbonation on chloride penetration in concrete
started in the mid-1990s. For example, Dhir et al. (1993) experimentally investigated chloride ingress in the carbonated cover
of pulverised fuel ash concrete. It was found that the carbonation of concrete significantly reduced its resistance to chlorides.
Delnavaz and Ramezanianpour (2012) developed an artificial
neural network method to determine the relation between
chloride diffusion coefficients and concrete mix design in carbonated and non-carbonated concretes. Geng et al. (2016) presented an experimental study on the interaction between
concrete carbonation and chloride attack. The experiments
were carried out on chloride-contaminated cement pastes that
were then exposed to a carbon dioxide environment to see how
bound chlorides were affected by the carbonation. Liu et al.
(2017) reported the interacting mechanism between carbonation and chloride aerosol attack in ordinary Portland cement
concrete and demonstrated the effect of carbonation on chloride profiles. Poyet et al. (2017) examined the microstructure
and diffusivity of an old corrosion product layer and demonstrated its impact on steel rebar corrosion in carbonated
concrete. Zhang and Panesar (2018) assessed the influence of
both reactive magnesium oxide (r-MgO) replacement levels
and accelerated carbonation curing on the mechanical properties and rapid chloride permeability of concrete containing
reactive magnesium oxide. Li et al. (2019) and Xie et al. (2019)
investigated the influence of carbonation degree on chloride
diffusion and the corresponding chloride concentration distribution in carbonated concrete. Xu et al. (2020) examined the
effect of nitrite intercalated magnesium aluminum layered
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Modelling chloride diffusion in concrete
with carbonated surface layer
Li, Li, Li, Chen and Chen
carbonation curing on distribution and binding capacity of
chloride ions in cement pastes. It was shown that chloride ions
accumulated in the surface layer due to moisture evaporation
during the carbonation curing process. The transport of chloride ions in the paste under the mixed curing process was
affected by the coupling effects of carbonation and capillary
suction, resulting in inward migration of chloride ions. Tiwari
et al. (2023) also investigated the influence of corrosion inhibitors on two different concrete systems under a combined chloride and carbonated environment. It was demonstrated that the
chloride ions were responsible for initiating the corrosion, but
the carbonation aggravated the corrosion process.
resulting in a reduction of porosity and a decrease of pH value of
the concrete. The laboratory examination of concrete carbonation
using phenolphthalein solution often shows two distinct colours.
One is the original grey colour representing the fully carbonated
concrete and the other is a red colour representing the uncarbonated concrete. Between these two colours, however, there is a
transition zone where the colour changes gradually from the original grey colour to the red colour. Therefore, in general, the concrete can be divided into three zones according to the degree of
carbonation in concrete, namely, the fully carbonated concrete
zone, the partially carbonated concrete zone and the uncarbonated concrete zone (Chang and Chen, 2006; Ji et al., 2014; Liu
et al., 2018; Pan et al., 2018).
The literature survey described above shows that substantial
works have been carried out to improve our understanding of
the effect of carbonation on chloride penetration in concrete;
in particular, it was revealed that the porosity and the chloride
binding ability of carbonated concrete are significantly different from those of uncarbonated concrete. Note that concrete
carbonation often occurs only in a narrow layer near the
surface. This is partly because carbonation is a very slow
process, and partly because the inner concrete is almost fully
saturated, blocking the diffusion of gaseous carbon dioxide
(CO2). This means that even when concrete carbonation is
involved, only part of the concrete cover in a reinforced concrete structure is carbonated, whereas the rest is still uncarbonated. Hence, the chloride diffusion model needs to consider
both the carbonated and uncarbonated concrete. This paper
presents a chloride diffusion model in which partially carbonated ordinary Portland cement concrete cover is divided into
three different zones, each with their own defined porosity and
chloride binding isotherm. The first is the fully carbonated
concrete near the surface in which the porosity and chloride
binding isotherm are obtained from the experimental data of
fully carbonated concrete. The second is the uncarbonated concrete near the reinforcement in which the porosity and chloride
binding isotherm are obtained from the experimental data of
normal concrete. The third is the transition zone between the
fully carbonated and uncarbonated concretes in which the
porosity and chloride binding isotherm are assumed to vary
continuously from the carbonated concrete to the uncarbonated concrete. To validate the present model, a comparison of
the present model with published experimental results on
ordinary Portland cement concrete is provided, which demonstrates the importance of considering different zones in the
chloride diffusion model when concrete carbonation is
involved in the process.
Methodology related to carbonation and
chloride diffusion in concrete
Efforts have been made to develop simple methods to determine the positions of different zones by using the measured
pH values or the identified chemical elements in concrete
(Chang and Chen, 2006; Ji et al., 2014; Liu et al., 2018). It is
noted that the pH value is 8.5–9.0 in fully carbonated concrete
and 12.5–13.0 in uncarbonated concrete. In the partially carbonated concrete zone, the pH value can vary from 9.0 to 12.5.
If the different zones are distinguished by using the characteristic chemical elements, this can generally be determined by
using the reaction products of carbon dioxide with calcium
hydroxide and calcium silicate hydrate or the residuals of the
calcium hydroxide and calcium silicate hydrate remaining in
the concrete after the carbonation process. It has been
suggested that the depth where the calcium hydroxide or
calcium silicate hydrate retains 20% of its original content
after carbonation is referred to as the carbonation depth of the
calcium hydroxide or calcium silicate hydrate (Chen et al.,
2019). Based on this definition, two carbonation depths can be
identified. One is the calcium hydroxide carbonation depth
δCH and the other is the calcium silicate hydrate carbonation
depth δCSH. Since the reaction between carbon dioxide and
calcium hydroxide is much faster than that between carbon
dioxide and calcium silicate hydrate, it would be reasonable to
assume that in the zone of x = 0!δCSH both the calcium
hydroxide and calcium silicate hydrate have been carbonated,
whereas in the zone of x = δCSH!δCH only the calcium hydroxide has been carbonated. In the zone of x > δCH neither the
calcium hydroxide nor the calcium silicate hydrate is carbonated. Therefore, in the present study, three zones corresponding to x = 0!δCSH, x = δCSH!δCH and x > δCH are used to
define the fully carbonated concrete zone, partially carbonated
concrete zone and uncarbonated concrete zone, respectively.
Figure 1 graphically shows these two carbonation depths and
the corresponding three different zones in the concrete cover.
Concrete carbonation
Chloride diffusion model in partially carbonated
concrete
Concrete carbonation is a phenomenon in which carbon dioxide
dissolved in concrete pore solution reacts with the calcium
hydroxide and calcium silicate hydrate present in concrete,
It is well known that concrete carbonisation can affect the porosity and chloride binding capacity of concrete (Li et al., 2017).
Figure 2 graphically shows the variation of porosity with the
Magazine of Concrete Research
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Remaining mass proportion
1
Modelling chloride diffusion in concrete
with carbonated surface layer
Li, Li, Li, Chen and Chen
concrete, the following governing equation can be established
C-S-H fully
carbonated zone
C-S-H not fully carbonated zone
1:
CH fully carbonated zone
CH not fully carbonated zone
@Ct
¼ rðDeff rCf Þ
@t
where Ct is the total chloride content in per-unit volume of
concrete, t is time, Deff is the effective diffusion coefficient of
chlorides in concrete and Cf is the free chloride content in perunit volume of pore solution.
0.2
0
δCSH
CH
C-S-H
δCH
x
Phenolphthalein zone
The total chlorides can be expressed in terms of the free and
bound chlorides as follows
2:
Figure 1. Schematic diagram of calcium hydroxide (CH) and
calcium silicate hydrate (C-S-H or CSH) carbonation depths and
corresponding three different zones
where ε is the porosity of concrete and Cb is the bound chloride content in per-unit volume of concrete.
Note that the relationship between the free and bound chlorides can be expressed as follows
ε0
Concrete porosity
Carbonation content
3:
Noncarbonated
zone
Fully
Partially
carbonated carbonated
zone
zone
0
δCSH
δCH
Ct ¼ εCf þ Cb
x
Figure 2. Schematic diagram of variation of concrete carbonation
and porosity in partially carbonated concrete
degree of carbonation in the concrete cover. This means that
when considering the chloride diffusion in partially carbonated
concrete, the difference in porosity and in chloride binding
between fully carbonated, partially carbonated and uncarbonated
concretes must be taken into account. This difference however has
not been considered in most existing chloride diffusion models.
In order to consider the variation effects of porosity and
chloride binding on the diffusion of chlorides in concrete, the
assumption is made that the porosity and the chloride binding
isotherm in the fully carbonated concrete (zone 1) are different
from those in the uncarbonated concrete (zone 3), although
they are still assumed to be constants in either zone.
The porosity and the chloride binding isotherm in the
partially carbonated concrete (zone 2) are assumed to be the
continuous functions of coordinates that are differentiable at
the boundaries linked to other two zones. According to mass
conservation of the total chlorides in per-unit volume of
Cb ¼ α εCf
where α is the proportional constant if a linear binding isotherm is employed. Note that α has different values in different
zones because the fully carbonated and uncarbonated concretes have different chloride binding capacities.
In general, the effective diffusion coefficient of chloride ions in
concrete can be expressed as follows (van Brakel and Heertjes,
1974)
4:
Deff ¼
εσ
D0
τ2
where σ is the constrictivity of concrete pore surface, τ is the
tortuosity of concrete and D0 is the chloride diffusion coefficient in water.
Substituting Equations 2–4 into Equation 1 yields
5:
@ðεCf Þ
¼ r Dapp εrCf
@t
where Dapp = (σ/(1 + α)τ 2)D0 is the apparent diffusion coefficient of chlorides in concrete.Note that the porosity of concrete
can also affect the constrictivity and tortuosity. In general, the
lower the porosity, the smaller the constrictivity and the larger
tortuosity. Carbonated concrete has low porosity and low
chloride binding capacity. The former leads to a decrease but
the latter results in an increase of the apparent diffusion coefficient. Thus, the final increase or decrease depends on which
one is dominant. For concrete with low chloride binding
capacity, the porosity effect is likely more important than the
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Modelling chloride diffusion in concrete
with carbonated surface layer
Li, Li, Li, Chen and Chen
chloride binding effect, and in this case the apparent diffusion
coefficient in carbonated concrete would be lower than that in
corresponding uncarbonated concrete.
where Cfw in wt.% is the free chloride content in concrete,
MCl = 0.03545 kg/mol is the molar mass of chloride ions and
ρc in kg/m3 is the density of paste, mortar or concrete.
For a one-dimensional diffusion problem, applying Equation 5
to three different zones and noting that the porosities in zone 1
and zone 3 are constants gives the following formulae.
It should be noted herein that, because of the variation of porosity between different zones, the chloride profiles plotted
based on Cf and Cfw would be different.
For zone 1 where x ≤ δCSH:
@Cf
@
@Cf
D1
¼
6:
@x
@t
@x
Experimental results on chloride diffusion in partially carbonated concrete show that the chloride profile exhibits an initial
drop in the fully carbonated concrete zone, followed by a slight
upsurge in the partially carbonated concrete zone and then a
decrease in the uncarbonated concrete zone (Li et al., 2018,
2019; Sun et al., 2023), as shown in Figure 3. The drop in concentration in the fully carbonated concrete zone and in the
uncarbonated concrete zone can be explained simply by the
diffusion equations given by Equations 6 and 8, which follow
Fick’s second law, while the concentration upsurge in the partially carbonated concrete zone is believed to be due to the
convection term caused by the porosity variation in the zone
as described here by Equation 7. Typically, the second peak in
the chloride profile is located very close to the calcium hydroxide carbonation depth δCH determined by phenolphthalein
(Liu et al., 2016; Xie et al., 2019; Zhang and Shao, 2016).
For zone 2 where δCSH ≤ x ≤ δCH:
@Cf
@
@Cf
1 @Cf @ ðεD2 Þ
D2
¼
þ
7:
@x
@x
ε @x
@t
@x
For zone 3 where x ≥ δCH:
@Cf
@
@Cf
D3
¼
8:
@x
@t
@x
where D1, D2 and D3 are the apparent diffusion coefficients of
chlorides in zone 1, zone 2 and zone 3, respectively.
Equations 6–8 indicate that, apart from the difference in
apparent diffusion coefficient in the three different zones,
another difference is Equation 7 that has an additional convection term which is due to the existence of the interface zone
between the fully carbonated and uncarbonated concretes. The
initial condition and boundary conditions required for solving
Equations 6–8 can be expressed as follows
9:
Cf ð0; xÞ ¼ 0
10:
Cf ðt; 0Þ ¼ Cs
11:
Cf ðt; 1Þ ¼ 0
Cfw ¼ 100 Cf The chloride diffusion model proposed above is validated by
using four sets of experimental data reported in literature. The
first set was obtained from the work of Sun et al. (2023), in
which cement paste specimens with a water-to-cement ratio of
0.45 were carbonated first for 7 days in an accelerated carbonation chamber (20% carbon dioxide concentration, 60 + 5%
relative humidity, room temperature), followed by standard
curing for 21 days. The specimens were then immersed in 3.5%
sodium chloride (NaCl) solution for 7 and 14 days, at which
time the chloride concentrations were measured. The second
C (t, x)
Cs
where Cs is the chloride concentration in the environment to
which the concrete is exposed.In addition, continuity conditions for both the concentration and flux of free chlorides
are required at the interfaces x = δCSH and x = δCH. Note that
Cf expressed in mole/m3 is the free chloride concentration in
pore solution, whereas in most experimental tests the chloride
concentration is often represented by using the unit of wt.% of
paste, mortar or concrete. The conversion between the two
units can be obtained as follows
12:
Validation of chloride diffusion model in
partially carbonated concrete
εMCl
ρc
Fully
Partially
Noncarbonated carbonated carbonated
zone
zone
zone
0
δCSH
Phenolphthalein zone
δCH
Figure 3. Schematic diagram of chloride profile in partially
carbonated concrete
x
Magazine of Concrete Research
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Modelling chloride diffusion in concrete
with carbonated surface layer
Li, Li, Li, Chen and Chen
set was obtained from the work of Li et al. (2018, 2019), in
which ordinary Portland cement (OPC) concrete specimens
with a water-to-cement ratio of 0.6 first had a moisture curing
for 90 days, then were subjected to accelerated carbonation in
a carbonation chamber (20% carbon dioxide concentration,
65% relative humidity, room temperature) for 90 days; they
were then immersed in 165 g/l sodium chloride solution for 35
days after which time the chloride concentrations were
measured. The third and fourth sets were obtained from the
work of Ye et al. (2016) on two kinds of concretes with a
7 days R2 = 0.86
14 days R2 = 0.97
0.5
0.14
0.13
0.4
0.12
0.3
0.2
0.11
0.5
0.4
0.12
0.3
0.2
0.10
0
5
10
15
20
25
0.11
0.1
0.1
0
0.10
0
30
0
5
10
Depth: mm
(a)
0.13
0.12
0.11
0.10
0.2
Chloride content: wt.%
0.4
20
25
30
0.15
2.5
Porosity
Chloride content: wt.%
PC-II-6-free
PC-II-10-free
PC-II-6-simulation
PC-II-10-simulation
PC-II-6-porosity
PC-II-10-porosity
PC-II-6 R2 = 0.94
PC-II-10 R2 = 0.97
0.6
15
Depth: mm
(b)
1.0
0.8
0.13
0.14
FS-II-6-free
FS-II-10-free
FS-II-6-simulation
FS-II-10-simulation
FS-II-6-porosity
FS-II-10-porosity
FS-II-6 R2 = 0.98
FS-II-10 R2 = 0.98
2.0
1.5
1.0
0.13
0.12
0.11
0.10
Porosity
0.6
0.14
OPC60-free
OPC60-simulation
Porosity
R2 = 0.96
0.6
0.15
Chloride content: wt.%
0.7
Porosity
Chloride content: wt.%
0.7
0.16
7 days-free
14 days-free
7 days-simulation
14 days-simulation
Porosity
0.8
Porosity
0.9
0.09
0.5
0.08
0
0
5
10
15
20
Depth: mm
(c)
25
0
0.09
30
0
5
10
15
20
25
0.07
30
Depth: mm
(d)
Figure 4. Comparison of chloride profiles between model prediction and experimental results for (a) cement paste specimens; (b) OPC
concrete specimens; (c) OPC concrete specimens in drying–wetting cycle; (d) FS concrete specimens in drying–wetting cycle. A full-colour
version of this figure can be found on the ICE Virtual Library (www.icevirtuallibrary.com)
Table 1. Parametric values used in calculation
Cement paste
Parameter
δCSH
δCH
Cs
ε1
ε3
D1
D3
7 days
8.5
14
0.85
0.10
0.16
3.7 10−11
9.5 10−11
14 days
0.65
3 10−11
OPC concrete
OPC concrete
PC-II-6
7.5
16
0.63
0.10
0.14
3.50 10−11
1.45 10−11
3.0
5.0
0.79
0.098
0.128
1.05 10−11
5.40 10−11
PC-II-10
5.0
9.0
0.88
0.095
1.36 10−11
2.0 10−11
FS concrete
FS-II-6
3.1
9.0
1.81
0.078
0.144
3.4 10−11
1.8 10−11
FS-II-10
3.4
9.0
2.25
0.073
1.95 10−11
1.7 10−11
Unit
mm
mm
wt.%
—
—
m2/s
m2/s
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Modelling chloride diffusion in concrete
with carbonated surface layer
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water-to-cement ratio of 0.45, using a 15% sodium chloride
solution for two different drying–wetting cycles (6 cycles and
10 cycles), including pure OPC-based concrete and mixture FS
containing fly ash and slag. In Figure 4, II refers to soaking
for 4 days, drying for 2 days and then accelerating carbonation
for 2 days. The parametric values used in the present model
are given in Table 1, in which δCSH and δCH are calculated
from the experimentally obtained carbonation data. ε1, D1 and
ε3, D3 are assumed based on the porosities and apparent diffusion coefficients normally used for carbonated concrete and
uncarbonated concrete, respectively, whereas ε2 and D2 are
interpolated using spline functions based on the values of ε1, ε3
and D1, D3, respectively. Figure 4 shows the comparison of the
calculated and experimentally measured chloride profiles. It
can be seen from the figure that the chloride profiles calculated
from the present model are generally very close to the experimental data, particularly in the partially carbonated concrete
zone where the porosity has a significant change. The slight
difference between the model prediction and experimental data
is observed only in the fully carbonated concrete zone, which
is probably due to the linear binding isotherm used in the calculation model, which might be an oversimplification.
Table 2. Values used in parametric analysis
Parameter
Default
value
δCH: mm
δCSH: mm
15
0.7δCH
Cs: mol/m3
ε1
ε3
D1: m2/s
D3: m2/s
3600
0.105
0.15
0.1D3
1.0 10−12
Values used for parametric
analysis
5, 10, 15, 20, 25
0.5δCH, 0.6δCH, 0.7δCH, 0.8δCH,
0.9δCH
—
0.5ε3, 0.6ε3, 0.7ε3, 0.8ε3, 0.9ε3
—
0.1D3, 0.2D3, 0.3D3, 0.4D3, 0.5D3
—
Parametric analysis of the diffusion model
The calculation of chloride profiles using the present chloride
diffusion model requires seven parameters: two depths (δCSH,
δCH) related to carbonation; two porosities (ε1, ε3) and two diffusion coefficients (D1, D3) related to fully carbonated and
uncarbonated concretes; and the surface chloride concentration
(Cs). The values of these parameters should be determined
based on the concrete before and after carbonation. For
example, mercury porosimetry, helium pycnometry, image
analysis or water absorption can be used to measure the porosities of fully carbonated and uncarbonated concretes to obtain
ε1 and ε3, the chloride diffusion tests of fully carbonated and
uncarbonated concretes can be used to obtain D1 and D3,
while the two depths, δCSH and δCH, can be measured directly
during the carbonation tests of concrete. The porosity and diffusion coefficient (ε2, D2) in the partially carbonated concrete
zone can be interpolated directly by using spline functions
based on the continuous conditions of the function and its
derivate because the layer of the zone is rather thin. The
purpose of this section is to examine how the carbonation
depths, porosity and chloride diffusion coefficient in the fully
carbonated concrete affect the shape and distribution of the
calculated chloride profile in the partially carbonated concrete
cover. Table 2 shows the parametric values used in the parametric analysis, where four parameters, each with five specified
values, are analysed. When a parameter is under investigation
using a value shown in the third column in Table 2, all other
0.6
δCH = 5 mm
δCH = 10 mm
δCH = 10 mm
δCH = 15 mm
δCH = 20 mm
0.4
δCH = 25 mm
0.3
0.2
0.1
δCH = 15 mm
0.5
Chloride content: wt.%
0.5
Chloride content: wt.%
δCH = 5 mm
0.6
δCH = 20 mm
δCH = 25 mm
0.4
0.3
0.2
0.1
0
0
0
20
40
60
Depth: mm
(a)
80
100
0
10
20
30
40
Time: years
(b)
Figure 5. Effect of calcium hydroxide carbonation depth δCH: (a) chloride profiles at t = 50 years; (b) time history of chloride
concentration at x = δCH
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Magazine of Concrete Research
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Modelling chloride diffusion in concrete
with carbonated surface layer
Li, Li, Li, Chen and Chen
parameters use their default values shown in the second
column.
chlorides at the time of 50 years. It can be observed from the
figure that increasing the width of the carbonation zones from
5 mm to 25 mm results in a significant downward shift of the
chloride profile in both the partially carbonated and uncarbonated concrete zones, whereas it has little effect on the profile
in the fully carbonated concrete zone. This indicates that the
increase of the width of carbonated zones can effectively
reduce the chloride content inside the concrete. Figure 5(b)
plots the time-history of the free chloride concentration at the
Carbonation depths
Figure 5 shows the results obtained by using different δCH
values (5 mm to 25 mm) while the values of other parameters
are taken from the default values shown in the second column
in Table 2. Figure 5(a) presents the distribution profiles of free
0.4
0.6
δCSH = 0.5δCH
δCSH = 0.6δCH
δCSH = 0.6δCH
δCSH = 0.7δCH
δCSH = 0.8δCH
0.4
δCSH = 0.9δCH
0.3
0.2
Chloride content: wt.%
Chloride content: wt.%
0.5
δCSH = 0.5δCH
δCSH = 0.7δCH
0.3
δCSH = 0.8δCH
δCSH = 0.9δCH
0.2
0.1
0.1
δCH = 15 mm
0
0
0
20
40
60
80
0
100
10
20
30
Depth: mm
Time: years
(a)
(b)
40
50
Figure 6. Effect of calcium silicate hydrate carbonation depth δCSH: (a) chloride profiles at t = 50 years; (b) time history of chloride
concentration at x = δCH
0.8
0.6
ε1 = 0.8ε3
ε1 = 0.9ε3
0.5
ε1 = 0.6ε3
0.3
ε1 = 0.7ε3
Chloride content: wt.%
Chloride content: wt.%
ε1 = 0.5ε3
ε1 = 0.5ε3
ε1 = 0.6ε3
0.7
0.4
0.3
0.2
ε1 = 0.7ε3
ε1 = 0.8ε3
ε1 = 0.9ε3
0.2
0.1
0.1
0
0
0
20
40
60
Depth: mm
(a)
80
100
0
10
20
30
40
50
Time: years
(b)
Figure 7. Effect of porosity of fully carbonated concrete: (a) chloride profiles at t = 50 years; (b) time history of chloride concentration
at x = δCH
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Magazine of Concrete Research
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Modelling chloride diffusion in concrete
with carbonated surface layer
Li, Li, Li, Chen and Chen
place of x = δCH which is very close to the second peak point
in the chloride profile curve. It can be seen from the figure
that, for a given carbonation depth, the chloride concentration
at that point increases with time, but the rate of increase
reduces gradually with increased time. With the increase of
carbonation depth, the time-history curve shifts from up-left to
down-right, indicating that it results in not only decreased concentration but also longer diffusion time.
chloride concentration expressed by wt.% changes too,
although Cf itself does not change with porosity. It can be seen
from the figure that the increase of porosity in the fully carbonated concrete zone leads to an increase of chloride content in
that layer, but a decrease of chloride content in the uncarbonated concrete zone. The former can be explained by Equation
12 where Cfw is linearly proportional to the porosity. The latter
is due to the effect of the convection term in Equation 7,
which leads to an increase of the free chloride concentration at
the place of x = δCH, as demonstrated in Figure 7(b).
Figure 6 shows the results obtained by using different δCSH
values (7.5 mm to 13.5 mm) while the values of all other parameters remain unchanged. Note that since δCH does not
change, the increase in δCSH simply means that while the fully
carbonated concrete zone increases, the partially carbonated
concrete zone decreases. Hence, it would be expected that
when δCSH increases, the chloride concentration inside the concrete would be reduced, as is demonstrated in Figure 6(a). The
slight rise in chloride concentration in the fully carbonated
concrete zone when δCSH increases is because its accumulation
is caused by the slow inward ingress. Like the results shown in
Figure 5(b), the increase of the fully carbonated concrete zone
leads to the time-history curve of the free chloride concentration at the place of x = δCH shifting from up-left to downright, indicating that it results in not only decreased concentration but also longer diffusion time.
Porosity of fully carbonated concrete zone
Porosity change is an important factor caused by concrete carbonation. Figure 7 shows the results obtained by using different porosities in fully carbonated concrete (0.075 to 0.135)
while the values of all other parameters remain unchanged.
Note that when the surface layer porosity alters, the surface
Chloride diffusion coefficient in fully carbonated
concrete
Figure 8 shows the results obtained by using different chloride
diffusion coefficients in fully carbonated concrete (0.1D3 to
0.5D3) while the values of all other parameters remain
unchanged. It can be seen from the figure that, as the diffusion
coefficient increases in the fully carbonated concrete, the chloride profile, not only in the fully carbonated concrete zone but
also in the partially carbonated and uncarbonated concrete
zones, moves upwards, indicating that the chloride diffusion
coefficient in the fully carbonated concrete has a significant
influence on the transport of chloride ions in all three zones. It
can also be observed from Figure 8(a) that the smaller the diffusion coefficient, the steeper the chloride distribution profile
located in the fully carbonated concrete zone, whereas the
chloride distribution profiles located in the partially carbonated concrete zone are almost parallel to each other, and the
corresponding chloride concentration at the second peak point
increases remarkably with increased diffusion coefficient. Like
the results shown in Figure 6(b), the increase of the diffusion
coefficient in the fully carbonated concrete means that the
0.7
0.8
D1 = 0.1D3
D1 = 0.1D3
D1 = 0.2D3
0.6
D1 = 0.5D3
0.4
0.3
0.2
0.1
Chloride content: wt.%
Chloride content: wt.%
D1 = 0.4D3
0.5
D1 = 0.2D3
0.7
D1 = 0.3D3
D1 = 0.3D3
0.6
D1 = 0.4D3
D1 = 0.5D3
0.5
0.4
0.3
0.2
0.1
0
0
0
20
40
60
Depth: mm
(a)
80
100
0
10
20
30
40
Time: years
(b)
Figure 8. Effect of chloride diffusion coefficient in fully carbonated concrete: (a) chloride profiles at t = 50 years; (b) time history of
chloride concentration at x = δCH
50
Magazine of Concrete Research
Volume 76 Issue 18
time-history curve of the free chloride concentration at the
place of x = δCH shifts from down-right to up-left, indicating
that it results in not only increased concentration but also
shorter diffusion time.
Modelling chloride diffusion in concrete
with carbonated surface layer
Li, Li, Li, Chen and Chen
peak point and thus leads to a rise of chloride
concentration in the profile in all three zones. The increase
of porosity in the fully carbonated concrete zone leads to
an increase of chloride content in that layer, but a decrease
of chloride content in the uncarbonated concrete zone.
Conclusion
Acknowledgements
Concrete carbonation can change the chemical composition of
cementitious materials and the pore micro-structure of concrete
and thus will have an important impact on chloride penetration
in concrete. This study has developed a chloride diffusion model
which considers the effects of the change in both the porosity
and chloride binding capacity caused by concrete carbonation.
The proposed model has been validated using experimental data
published in literature. In addition, parametric analysis has been
carried out to illustrate the effects of various individual parameters on the penetration of chlorides in concrete cover containing fully carbonated concrete, partially carbonated concrete and
uncarbonated concrete. From the results obtained in the study,
the following conclusions can be drawn.
The authors would like to acknowledge the financial support
received from the National Natural Science Foundation of
China (Grant No. 51978406, 51520105012).
&
&
&
&
&
&
To model chloride diffusion in concrete when concrete
carbonation is involved, it is necessary to divide the
concrete cover into fully carbonated, partially carbonated
and uncarbonated concrete zones. Each zone should have
its own diffusivity, which can be represented by using the
porosity and apparent diffusion coefficient.
The porosity and apparent diffusion coefficient either in
the fully carbonated concrete or in the uncarbonated
concrete can be assumed to be constants, which can be
determined from the corresponding tests related to
carbonated concrete and non-carbonated concrete.
The porosity and apparent diffusion coefficient in the
partially carbonated concrete zone are the function of
coordinates which can be obtained by using the spline
interpolation function because the layer of the zone is very
narrow. The varying porosity in the partially carbonated
concrete zone leads to a diffusion equation that contains a
convection term.
The chloride profiles in both the fully carbonated concrete
zone and uncarbonated concrete zone follow the standard
diffusion curve described by Fick’s second law. However,
the chloride profile in the partially carbonated concrete
zone has an upsurge, which creates a second peak that is
observed in many experimentally obtained chloride
profiles.
Carbonation depth has an important influence on the
chloride diffusion in concrete. The increase of carbonation
depth not only can decrease the speed of the chloride
diffusion process in concrete but also reduce the chloride
concentration at the second peak point, leading to a
decrease of chloride concentration in the profile in all three
zones.
The increase in diffusion coefficient in fully carbonated
concrete increases the chloride concentration at the second
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