Numerical Simulation of Convection–Diffusion Coupling Transport of Water and Chloride in Coated Concrete

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Numerical Simulation of Convection–Diffusion Coupling
Transport of Water and Chloride in Coated Concrete
Yuncheng Wang1; Lanxin Wang2; Yanchun Miao3; Fengjuan Wang4; Liguo Wang5;
Song Mu6; Sen Gao7; Zhiyong Liu8; and Jinyang Jiang9
Abstract: Chloride transport is one of the most serious problems facing reinforced concrete structures, and coatings can effectively block the
intrusion of chloride ions. In order to evaluate the resistance of coatings to chloride ion erosion more quickly and accurately, based on the
transport mechanism of chloride and water in coated concrete, a two-dimensional mesoscale model of concrete containing coating, aggregate,
and matrix was established in this paper. In response to the transport mechanism of chloride ions in coated concrete, a coupled convection–
diffusion numerical model considering the binding effect of chloride, temperature effect, and hydration effect is established. The idealized
service life conditions of the coating are introduced, and the influence of coating type, coating thickness, and coating service life on the
distribution of erosive agents inside the coated concrete is analyzed. After analysis and research, it is recommended that coating concrete
exposed to 3.5% NaCl erosion use a film-forming coating with an expected life of more than 10 years and a coating thickness of at least
1.5 mm, preferably chlorinated polyvinyl chloride (CPVC) and chlorinated polyethylene (CPE) coatings. DOI: 10.1061/JMCEE7.MTENG-
17784.© 2024 American Society of Civil Engineers.
Author keywords: Concrete; Coating; Chloride; Numerical; Simulation.
Introduction
Reinforced concrete is one of the most widely used building ma-
terials in the world (Mehta 1991). With the progress of the human
age, more and more reinforced concrete structures have been built
in severe environments to provide the material basis for human
mobility and habitation (Wang et al. 2024a). In severe environ-
ments, chloride erosion has a negative effect on the durability of
reinforced concrete, and poor durability is the main reason for the
failure of concrete structures (Jin and Zhao 2014; Liu et al. 2023;
Qian et al. 2023,r38 2024; Yu et al. 2003).
Currently, extensive investigations have exhibited that additive
technology such as anticorrosion admixtures (Ming et al. 2023;
Plank et al. 2015;Song et al. 2020), coatings (Sui et al. 2022;Wang
et al. 2023;Xiao et al. 2020), and high-performance concrete (Yin
et al. 2022) preparation could enhance the durability of concrete
structure. However, admixtures and high-performance concrete will
cost a lot in terms of raw materials and construction (Gandage
2023;Hameed et al. 2022;Malagavelli and Rao 2010;Souza et al.
2020), and the difficulty of construction will increase (Mansor et al.
2018;Saidani et al. 2016). Compared with the aforementioned
methods, coating protection technology has advantages of easy con-
struction, low cost, significant effects, and convenient maintenance.
Coatings can effectively prevent the transport of chloride and chemi-
cal erosion while also improving the aesthetics and easy cleanliness
of concrete surfaces (Jiang et al. 2023). Therefore, coating protection
has been widely used, and many studies have been conducted.
It has been proven through experiments that applying protective
coatings on the surface of concrete can effectively block corrosive
substances due to the physical barrier effect of coatings, which can
prevent water transport in the concrete, thereby preventing chloride
ions from penetrating into the interior with water. Moreover, the
diffusion coefficient of corrosive ions in the coating is extremely
small, so the protective coating has a good blocking effect on the
diffusion of various ions, thus reducing the adverse impact on the
life span of concrete structures caused by ion erosion (Almusallam
et al. 2003;Ibrahim et al. 1997;Pan et al. 2017). However, the pro-
cess of chloride ion erosion of concrete is slow and long-lasting,
which was mainly studied and verified through experiments (Wang
et al. 2024b). The experimental approach could accurately simulate
the service environment in which concrete corrodes, but it also
exhibits the disadvantages of low efficiency, long test period, and
susceptibility to external factors. Therefore, establishing a reliable
numerical model of erosion medium transport in coated concrete
1Ph.D. Candidate, Jiangsu Key Laboratory for Construction Materials,
Southeast Univ., Nanjing 211189, China. Email: wangyc950902@foxmail
.com
2Ph.D. Candidate, Jiangsu Key Laboratory for Construction Materials,
Southeast Univ., Nanjing 211189, China. Email: wanglx@seu.edu.cn
3Ph.D. Candidate, Jiangsu Key Laboratory for Construction Materials,
Southeast Univ., Nanjing 211189, China. Email: 230238704@seu.edu.cn
4Professor, Jiangsu Key Laboratory for Construction Materials,
Southeast Univ., Nanjing 211189, China. Email: fjwang1118@163.com
5Assistant Researcher, Jiangsu Key Laboratory for Construction Mate-
rials, Southeast Univ., Nanjing 211189, China. Email: wlg_seu@sina.com
6Senior Engineer, State Key Laboratory of High Performance Civil
Engineering Materials, Sobote New Materials Co., Ltd., No.118, Liquan
Rd., Jiangning District, Nanjing, Jiangsu 211189, China. Email: musong@
cnjsjk.cn
7Assistant Engineer, Jiangsu Huamei Construction Investment Group
Co., Ltd., No. 7 Qiantang Rd., Yunlong District, Xuzhou 221111, China.
Email: 827840594@qq.com
8Professor, Jiangsu Key Laboratory for Construction Materials, South-
east Univ., Nanjing 211189, China. Email: liuzhiyong0728@163.com
9Professor, Jiangsu Key Laboratory for Construction Materials,
Southeast Univ., Nanjing 211189, China (corresponding author). Email:
jiangjinyang16@163.com
Note. This manuscript was submitted on September 24, 2023; approved
on May 7, 2024; published online on September 30, 2024. Discussion per-
iod open until February 28, 2025; separate discussions must be submitted
for individual papers. This paper is part of the Journal of Materials in Civil
Engineering, © ASCE, ISSN 0899-1561.
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can greatly save material costs required for experiments and im-
prove research efficiency.
There is little research on the numerical simulation of the dura-
bility of coated concrete. Yoon (2017) used finite-element and finite-
difference methods to simulate the electrotransport behavior of
chloride ions in coated concrete under one-dimensional conditions.
However, this research mainly focused on the differences in accu-
racy between finite element and finite difference methods. Dong
and Ye (2019) conducted a more systematic study. Based on Fick’s
second law, they established a two-dimensional homogeneous plane
coating concrete transport model, and further analyzed the impact of
coating on chloride concentration and concrete life.
There are also some investigations that focused on the predic-
tion of the service life of coated concrete (Ecchuya et al. 2018;
Etchuya et al. 2020;Li et al. 2015), most of which are based on the
analytical solution of Fick’s second law, using the measured surface
chloride concentration of coated concrete to calculate the service
life, which is different from the cause of steel corrosion caused by
chloride. In essence, chloride ions penetrate the concrete coating,
passing through the dense coating before entering the concrete it-
self. Moreover, the invasion of chloride ions often occurs simulta-
neously with water, and the transport of water and ions in concrete
is a very complex behavior. Its transport behavior can be divided
into the following three ways: convection (Jiang et al. 2021), dif-
fusion (Yang et al. 2022), which are driven by water saturation, and
ion concentration, respectively.
As Dong and Ye (2019) mentioned, the pore structure of con-
crete changes during the transport of erosion agents, and factors
such as the binding effect of chloride should be considered. Pre-
vious studies only focused on the apparent phenomenon of chlo-
ride transport (Guimarães et al. 2011;Mangat and Molloy 1994;
Shazali et al. 2012), without delving into the nature of its transport
or considering the influence of single factors on the transmission
properties of chloride. With the in-depth research, more and more
scholars have found that water migration can drive harmful corro-
sive agents such as chloride to penetrate into cement-based mate-
rials. Therefore, the focus of many research efforts has shifted from
considering the impact of single factors to the transport under the
condition of multifactor coupling (Nayak et al. 2019). These re-
search efforts have promoted the transition from single factor to
multifactor coupling in the evaluation of durability of major con-
crete projects (Kuhl et al. 2004;Ulm et al. 2000).
Due to the presence of convection and chloride binding, the
transport behavior of chloride is different from that of water. In re-
cent years, a numerical model for the coupled diffusion–convection
transport of water and chloride in concrete has attracted attention
(Ababneh et al. 2003;Li et al. 2008,2009;Zhang 2008). Compared
with previous models, this model is more closely aligned with the
nature of chloride transport in concrete and has been proven to be
an accurate method for predicting the distribution of erosion agents
(Jin and Zhao 2014;Liu et al. 2021).
However, research on chloride transport in concrete under coat-
ing protection put emphasis on experimental aspects, resulting a
lack of research on predicting the service life of concrete structures
with protective coatings. For coated concrete, more attention should
be paid to the differences in the transport behavior of water and
chloride ions in the coating, aggregate, and matrix. In addition, the
resistance to chloride transport varies greatly among different coat-
ings, resulting the various degree of chloride ion diffusion in con-
crete. Therefore, it is needed to study a new numerical simulation
research method to accurately evaluate the work performance of
and the service life of concrete with protective coatings in chloride
environments in order to provide theoretical basis for the applica-
tion of coatings in civil engineering.
A two-dimensional mesoscale model of concrete containing coat-
ing, aggregate, and matrix was established in this paper. In response
to the transport mechanism of chloride ions in coated concrete,
a coupled convection–diffusion numerical model considering the
binding effect of chloride, temperature effect, and hydration effect
is established. The idealized service life conditions of the coating
are introduced, and the influence of type, thickness, and service
life of the coating on the distribution of erosive agents inside the
coated concrete is analyzed.
Modeling
Geometric Model
At the mesoscopic scale, coated concrete is regarded as an organic
combination of the coating, aggregate, interface transition zone
(ITZ), and paste. It has been demonstrated in relevant studies that
the shape of the aggregate has a relatively small impact on concrete
performance (Miao et al. 2023;Rocco and Elices 2009). Therefore,
to simplify the numerical model, the aggregate is assumed to be
circular. Using the Monte Carlo method, a numerical model of con-
crete shown in Fig. 1(b) was generated based on the interference
judgment condition depicted in Fig. 1(a). The concrete size is
100 ×100 mm, with a volume fraction of aggregate set to 0.6 and
a particle size range of 1–10 mm. The particles are randomly gen-
erated and placed, and the entire geometric model is meshed using
free triangular grids with a minimum mesh size of 0.01 mm. To
enhance the accuracy of solving the equation in the coated concrete,
four layers of boundary layer grids are set on the coating’s surface,
as shown in Fig. 1(c).
Governing Equation of Concrete
In practical engineering, concrete is often in a nonsaturated state for
an extended period, and the penetration of chloride in nonsaturated
concrete is influenced not only by the diffusion caused by the chlo-
ride concentration gradient but also by water convection (Homan
et al. 2016). The chloride flux across the cross section of the con-
crete can be determined by considering the diffusion flux of chlo-
ride in water and the transmission flux of water
J¼JdþJcð1Þ
where Jd= diffusion flux of chloride in water; and Jc= convection
flux of chloride caused by water convection.
In Eq. (2), the chloride diffusion flux Jdcan be calculated using
Fick’s law (Wang et al. 2024c)
Jd¼−Dc∇cð2Þ
where Dc= chloride diffusion coefficient (m2=s); and c= concen-
tration of chloride in the pore solution.
The chloride diffusion coefficient is observed to decrease with
increasing age, and its value can be influenced by both water sat-
uration and the binding effect of cement-based materials on chloride.
Hence, in the model, the reference value for the chloride diffusion
coefficient in cement-based materials under a specific condition
(time and saturation) is considered. Three correlation functions,
denoted as kct,kcT ,andkcb, are introduced to represent the modi-
fying relationships of age, temperature, and chloride binding on
the diffusion coefficient, respectively. Therefore, the expression
for the chloride diffusion coefficient can be given as follows:
Dc¼D0
ckctkcT kcb ð3Þ
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where D0
c= chloride diffusion coefficient under certain age, tem-
perature, and without considering the binding effect of chloride;
and kct,kcT ,andkcb = modifying coefficients of age, temperature,
and chloride binding on the diffusion coefficient, respectively. An
exponential function (Mangat and Molloy 1994) can express the
relationship between the chloride diffusion coefficient and time as
follows:
kct ¼t0
tþt0m
ð4Þ
where tand t0= erosion time of chloride and the curing age at the
time of testing; m= time-dependency coefficient (Thomas et al.
2009). Feng (2017) tested more than 2,000 sets of outdoor samples
and engineering data, and found that the time-dependent coeffi-
cient of chloride diffusion coefficient had little correlation with the
water-binder ratio, environment, and curing age. Taking mas a
constant value of 0.6304 was more accurate.
The effect of temperature on the diffusion process of chloride
can be described as Arrhenius’law
kcT ¼exp U
Rg1
Tref
−1
T ð5Þ
where U= activation energy of the chloride diffusion process
(kJ=mol), and a value of 30 kJ=mol is recommended; Rg= relative
gas constant, 8.314 ×10−3kJ=K · mol; and Tand Tref = temper-
ature and reference temperature (K).
Considering the binding effect of cement-based materials on
chloride, which reduces the diffusion coefficient of chloride, a lin-
ear model is adopted
kcb ¼1
1þRb
ð6Þ
where Rb= chloride binding coefficient, which is an empirical
parameter.
Eqs. (5)–(7) integrate the effects of concrete age, saturation, and
chloride binding, and can be used to obtain the chloride diffusion
coefficient as follows:
Dc¼D0
ct0
tþt0m
exp U
Rg1
Tref
−1
T 1
1þRb
ð7Þ
For the chloride convection flux Jcmentioned in Eq. (1), it can
be considered as the product of the chloride concentration in the
pore fluid and the flow velocity
Jc¼cv ð8Þ
where v= flow velocity of water (m=s). The flow velocity vof
water in cement-based materials can be calculated by Darcy’s law
v¼−DwðsÞ∇sð9Þ
where s= water saturation; and DwðsÞ= water transport coefficient
in cement-based materials. Similarly, the water transport coefficient
is also affected by the material age and saturation, and the water
transport coefficient is corrected as follows:
DwðsÞ¼D0
wkwtkws ð10Þ
where D0
w= water transport coefficient at a certain age and satu-
ration; and kwt and kws = correction factors for age and saturation
on the moisture transport coefficient.
Hall and Hoff (2002) and Janssen et al. (2007) have rigorously
derived that the relationship between the saturation degree of build-
ing materials and the water transport coefficient, which can be rep-
resented by an exponential function
Fig. 1. Establishment of geometric model and grid division of coated concrete: (a) conditions for judging the interference; (b) geometric model; and
(c) grid division.
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kws ¼expðnsÞð11Þ
where n= constant, usually taken as 6.
The moisture transport coefficient of cement-based materials is
affected by the age of the concrete (Bažant and Najjar 1972), and
the older the age, the lower the water transport coefficient
kwt ¼0.13 þffiffiffiffiffi
13
t
rð12Þ
Then, considering the effects of age and saturation, the modified
water transport coefficient can be expressed
DwðsÞ¼D0
wexpðnsÞ 0.13 þffiffiffiffiffi
13
t
r!ð13Þ
The ITZ surrounding the concrete aggregate expedites the trans-
port of chloride and water. The diffusion coefficient of ITZ can be
expressed as follows:
Dc;ITZ ¼keq
ITZDcð14Þ
Dw;ITZ ¼keq
ITZDwð15Þ
where Dc;ITZ and Dw;ITZ = chloride diffusion coefficient and water
transport coefficient within the ITZ, respectively; and keq
ITZ = ratio of
the diffusion coefficient of ITZ to the inherent diffusion coefficient
of mortar. Extensive research has established that the value of keq
ITZ
typically ranges between 5 and 15.
By combining Eqs. (1), (2), (7)–(9), and (13), the chloride flux J
can be solved as follows:
J¼−Dc∇c−cDwðsÞ∇sð16Þ
According to the law of conservation of mass, the governing
equation for chloride transport can be obtained as follows:
∂c
∂t¼−∂J
∂xð17Þ
∂c
∂t¼∇½Dc∇cþcDwðsÞ∇sð18Þ
According to the law of conservation of mass of water in cement-
based materials, the water transport control equation (Jin et al. 2009)
is as follows:
∂s
∂t¼∇½DwðsÞ∇sð19Þ
Eqs. (18) and (19) are the governing equations of the complete
convection–diffusion coupled numerical model of concrete.
Governing Equation of Coating
Due to the continuous random motion of molecules, chloride and
moisture will gradually penetrate the coating with the random mo-
tion of molecules. Assuming that the internal components of the
film-forming coating are evenly distributed and do not react with
water and chloride, and that there is no adsorption, binding, or exo-
thermic phenomenon during the migration of water and ions in the
film-forming coating, the migration behavior of water molecules
and chloride ions in the aforementioned process obeys Fick’s second
law and can be calculated according to the following equations:
∂sc
∂t¼∇½Dc
s∇scð20Þ
∂cc
∂t¼∇½Dc
c∇ccð21Þ
where Dc
sand Dc
c= moisture transport coefficient and the chloride
diffusion coefficient of coating (m2=s); and scand cc= water sat-
uration and chloride concentration of coatings.
Initial and Boundary Conditions
Initial Conditions
When there is no external chloride in the sample, the initial con-
centration of chloride in the cement-based material at each location
is zero, and the initial water saturation is ss
sðx>dc;t¼0Þ¼ssð22Þ
cðx>dc;t¼0Þ¼0ð23Þ
where ss= initial water saturation of concrete; sscan be a fixed
value or a function that varies with time and location. For film-
forming coatings, both the initial water saturation and chloride con-
tent are zero, so then
scð0<x≤dc;t¼0Þ¼0ð24Þ
ccð0<x≤dc;t¼0Þ¼0ð25Þ
External Boundary Condition
The model is established with only one side of the coating consid-
ered. When the coating is immersed in a chloride solution, the ex-
ternal boundary conditions are imposed on the surface of the coating
that is in contact with the solution
scðx¼0;t>0Þ¼1ð26Þ
ccðx¼0;t>0Þ¼csð27Þ
where cs= chloride concentration of chloride solution (mol=m3).
The remaining external surfaces are all flux-free boundary
conditions.
Internal Boundary Condition
At the internal boundary between the concrete and the coating,
the continuity of fluxes for water and chloride ions is maintained,
and the consistency of concentrations for water and chloride is
preserved
scðx¼dcÞ¼sðx¼dcÞð28Þ
ccðx¼dcÞ¼cðx¼dcÞð29Þ
The solution of the governing equations for the physical fields
of the aforementioned concrete and coatings has been compre-
hensively conducted within COMSOL Multiphysics 6.1, ensuring
accurate and reliable results. The problem is solved using the Multi-
frontal Massively Parallel sparse direct Solver, with the Jacobian
matrix being updated at each time step.
Validation
Thomas and Bamforth (1999) conducted an experiment on ordinary
portland cement concrete (OPC), fly ash concrete (FAC), and slag
concrete (SGC) that were exposed to the marine environment for
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8 years. Prior to exposure, the samples were naturally cured out-
doors for 28 days, during which the nonuniform distribution of ini-
tial humidity inside the concrete caused by hydration and surface
drying was predicted using the model of Selih et al. (1996). The
boundary conditions used by Selih et al. (1996) for the initial dis-
tribution of unsaturated moisture were incorporated based on the
convection–diffusion model, and the model parameters were set ac-
cordingly. Table 1presents the parameters used for validation with
the work of Thomas and Bamforth (1999).
The distribution of chloride concentration in the prepared con-
crete by Thomas and Bamforth (1999) was then calculated and
compared, as shown in Fig. 2.
The present model accurately predicted the chloride intrusion at
depths greater than 5 mm. However, there was a slight deviation
from the test values of Thomas and Bamforth (1999)inthe0–5-mm
range, possibly due to the exposure of actual concrete to the marine
environment. The alternation of dryness and wetness in this envi-
ronment accelerates chloride ion intrusion. Additionally, a higher
peak intensity of chloride ion was observed in the convective zone
within the 0–10-mm range.
Parameters for Coating Concrete
The impact of the type, life span, and thickness of coatings on the
transport resistance of concrete is analyzed by taking the chloride-
eroded environment in 3.5% NaCl solution as an example. The
parameters of the environment and concrete used in this model are
given in Table 2.
Four distinct film-forming coatings are currently offered in the
market, namely, chlorinated polyvinyl chloride coating (CPVC),
chlorinated polyethylene coating (CPE), polychloroprene lotion
coating (CR), and chlorinated lotion coating (PVDC), and their
respective intrinsic chloride diffusion coefficients are provided in
Tab le 3. However, because there is limited research on the intrinsic
water transport coefficients of these coatings, it is assumed that
their intrinsic water transport coefficients and intrinsic chloride
diffusion coefficients remain constant.
The aging process of a coating is complex and can result in an
increase in its intrinsic diffusion coefficient. Cracks that arise due
to aging can compromise the protective ability of cement-based
materials in a short period of time. To simplify this phenomenon,
Table 1. Parameters for validation with the work of Thomas and Bamforth (1999)
Parameter OPC FAC SGC Unit References
cs0.3 0.5 0.5 % Thomas and Bamforth (1999)
m0.1 0.7 1.2 —Thomas and Bamforth (1999)
t028 28 28 Days Thomas and Bamforth (1999)
D0
c(mortar) 8×10−12 6×10−12 2.5×10−11 m2=s Thomas and Bamforth (1999)
D0
w(mortar) 1.44 ×10−12 1.44 ×10−12 1.44 ×10−12 m2=s Yang (2017)
Thickness of ITZ 50 50 50 μm Grondin and Matallah (2014),
Li et al. (1999), and Zhou et al. (2022)
keq
ITZ 10 10 10 —Chen et al. (2020) and Yu and Lin (2020)
Fig. 2. Comparison of modeled and measured chloride concentrations: (a) OPC; (b) FAC; and (c) SGC. (Data from Thomas and Bamforth 1999.)
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the model assumes that once the coating reaches the end of its pro-
tective lifetime, its intrinsic diffusion coefficient will rise to that
of ions in water. The coating’s diffusion coefficient can then be
calculated by Eq. (30)
Dc
s¼Dc
c¼Dc
ct≤lifec
Dw0t>lifec
ð30Þ
where lifec= life span of the coating; and Dw0= ion diffusion co-
efficient in solution. The diffusion coefficient of ions in the pore
solution of concrete was determined through experiments by Zuo
et al. (2010), and the value can be taken as 1.04 ×10−10 m2=s.
Discussion
Distribution of Chloride and Water in Coated Concrete
The saturation and chloride distribution in the coating and concrete
of the CPVC-coated concrete at 1, 2, 5, 10, 15, 30, 50, and 100 years
are illustrated in Figs. 3and 4. It is noted that the concrete surface is
coated with a thickness of 2 mm CPVC layer, and the coating has a
life span of 10 years. Furthermore, the boundary condition for the
analysis is set at 443 mol=m3(corresponds to 3.5% NaCl).
Figs. 3and 4demonstrate that during the 10-year period when
the coating was effective, only the uneven moisture within the con-
crete was being balanced toward homogenization, and only negli-
gible amounts of outside water and chloride ions were allowed to
intrude into the concrete. This suggests that the impact of water and
chloride ions was effectively prevented by the coating, and the ero-
sion resistance of the concrete was enhanced. Once the coating be-
came ineffective, a significant increase in the diffusion coefficient
of water and choloride ions within the coating was observed, re-
sulting in a considerable increase in the moisture and chloride con-
centration inside the concrete. Because chloride transport mainly
occurs via water and is subject to adsorption and binding within
the concrete, the moisture transport rate is much faster than that of
concrete. By 30 years, the concrete is almost fully saturated, and
the chloride ions within the concrete have yet to reach a steady
state, even after 100 years, and the concentration of chloride ions
in the concrete continues to progressively increase over the 30- to
100-year period.
Influence of the Volume Fraction of Aggregate
The influence of volume fraction of aggregate on the spatiotempo-
ral distribution of chloride concentration in concrete is illustrated in
Fig. 5. As evidenced from the figure, distinct variations were ob-
served in the transport behaviour of coated concrete when varying
the aggregate volume fractions. Intriguingly, numerous prior inves-
tigations have postulated that an increase in aggregate volume frac-
tion correlates with a deterioration in the permeability of concrete.
Nevertheless, our study revealed a noteworthy finding: the per-
meability of coated concrete exhibited comparable characteristics
at 50% and 60% aggregate volume fractions. However, a noteworthy
exception was observed: the chloride ion content in coated concrete
with a 40% aggregate volume fraction was significantly lower, par-
ticularly at deeper depths, attributed to the existence of the interfacial
transition zone. This observation aligns with the patterns reported by
Liu et al. (2021).
Influence of the Life Span of Coatings
The influence of coating life span on the spatiotemporal distribu-
tion of chloride concentration in concrete is illustrated in Fig. 6.It
can be observed that with time, the concentration of chloride ions in
concrete increased, showing an initially sharp but gradually slow-
ing trend. The onset of chloride in concrete was delayed by coating
application and the diffusion rate of chloride was retarded. Impor-
tantly, the chloride concentration in concrete is closely related to
the life span of the coating. Increasing the life span of the coating
delays the initiation of chloride ion penetration into concrete and
linearly reduces the chloride concentration in concrete. Therefore,
the enhancement of coating life span can effectively mitigate chlo-
ride erosion, reduce the chloride concentration in concrete through-
out its service life, and prolong the service life of concrete.
Influence of the Thickness of Coatings
The influence of coating thickness on the spatiotemporal distribu-
tion of chloride concentration in concrete is demonstrated in Fig. 7.
It can be observed that an increase in coating thickness can effec-
tively reduce the final chloride concentration both on the surface
and inside the concrete, with the reduction inside the concrete being
more significant. When the coating thickness was less than or equal
Table 2. Parameters of environment and concrete
Parameter Value Unit References
cs443 (corresponds to 3.5% NaCl) mol=m3—
T293.15 K —
m0.6304 —Feng (2017)
n6—Liu et al. (2021)
t028 Days —
Rb1—Liu et al. (2021)
D0
c4.0×10−12 m2=s Yang (2017)
D0
w1.44 ×10−12 m2=s Yang (2017)
Volume fraction of aggregate 40/50/60 % —
Thickness of ITZ 50 —Grondin and Matallah (2014), Li et al. (1999),
and Zhou et al. (2022)
keq
ITZ 10 —Chen et al. (2020) and Yu and Lin (2020)
Table 3. Types of coatings and their intrinsic chloride diffusion coefficients
Type
Intrinsic chloride diffusion
coefficients (m2=s)
CPE 1.2×10−16
CR 2.8×10−14
PVDC 4.3×10−15
CPVC 1.4×10−15
Source: Data from Liu (2021).
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to 1.5 mm, there was no delay in the appearance of chloride ions on
the concrete surface. However, when the coating thickness exceeded
1.5 mm, the chloride concentrationration on the concrete surface
gradually increased. This indicates that the coating thickness should
be at least 1 mm to effectively prevent media penetration into the
concrete during the expected life span of the coating. Nevertheless,
even if the coating thickness gradually increased to 3 mm, chloride
penetration into the concrete surface still occurred.
Fig. 3. Distribution of water saturation in concrete with coating: (a) 1 year; (b) 2 years; (c) 5 years; (d) 10 years; (e) 15 years; and (f) 30 years.
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Fig. 4. Distribution of chloride concentration in concrete with coating: (a) 1 year; (b) 2 years; (c) 5 years; (d) 10 years; (e) 15 years; (f) 30 years;
(g) 50 years; and (h) 100 years.
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Influence of the Type of Coating
Fig. 8compares the influence of different coating types on the spa-
tial and temporal distribution of chloride concentration in concrete.
After the application of protective coatings, the chloride ion content
within the concrete can be significantly reduced within a short
period of time. The coatings effectively delay the intrusion of chlo-
ride ions into the concrete, thereby reducing the concentration of
chloride ions within the concrete and enhancing its service life.
Given the assumption of identical thicknesses and lifetimes for all
protective coatings, the difference in performance among different
Fig. 5. Distribution of chloride with different volume fractions of aggregate: (a) surface chloride concentration; and (b) 30-mm chloride concentration.
Fig. 6. Distribution of chloride with different coating life spans: (a) surface chloride concentration; and (b) 30-mm chloride concentration.
Fig. 7. Distribution of chloride with different coating thicknesses: (a) surface chloride concentration; and (b) 30-mm chloride concentration.
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types of coatings is minimal over the same duration. Among
them, CPE and CPVC exhibited the best barrier effect, followed
by PVDC, whereas CR demonstrated the poorest protective
performance.
Conclusion
This work established a two-dimensional convection–diffusion
mesoscale numerical model of water and chloride transport in
coated concrete, and the effects of coating type, coating thickness,
and coating service life on the internal water saturation and chloride
content of concrete were discussed. The following conclusions
are drawn:
•In the environment provided in this paper, within the 10-year life
span of the coating, there was no significant amount of water or
chloride ions inside the concrete. Increasing the service life of
coatings can effectively reduce the chloride concentration in
concrete during its entire service life.
•In the environment provided in this paper, the coating thickness
should be at least 1 mm to effectively prevent chloride penetra-
tion into the concrete during the expected life of the coating.
However, even if the coating thickness gradually increases to
3 mm, chloride will still penetrate into the concrete surface over
time.
•Among these four kinds of film-forming coating listed in this
paper, CPE and CPVC coatings had the best barrier effect, fol-
lowed by PVDC, whereas CR had the worst protective effect.
Therefore, it is recommended to use CPE and CPVC coatings in
engineering.
Data Availability Statement
The data are available from the first author or corresponding author
upon request.
Acknowledgments
The authors greatly acknowledge the National Key R&D Program
of China (2021YFF0500803), the National Outstanding Youth
Science Fund Project of National Natural Science Foundation
of China (51925903), the National Natural Science Foundation
of China Joint Fund for regional innovation and development
(U21A20150), the Science Foundation for Distinguished Young
Scholars of Jiangsu Province (BK20220071), the Fundamental
Research Funds for the Central Universities (RF1028623199),
and the State Key Laboratory of High Performance Civil Engineer-
ing Materials (2020CEM001).
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