127
Journal of Advanced Concrete Technology Vol. 1, No. 2, 127-138, July 2003 / Copyright © 2003 Japan Concrete Institute
Simultaneous Transport of Chloride and Calcium Ions in Hydrated
Cement Systems
Takafumi Sugiyama1, Worapatt Ritthichauy2 and Yukikazu Tsuji3
Received 6 January 2003, accepted 16 June 2003
Abstract
This paper presents a new method for numerically calculating the concentration profiles of both solid calcium and total
chloride ions (Cl-) in concrete in contact with 3% (0.5 mol/l) sodium chloride (NaCl) solution. Since the diffusion of ions
present in the pore solution is a primary controlling factor, the application of mutual diffusion coefficients of corresponding ions that are influenced by the concentration of other coexisting ions is proposed. The method of calculation is
based on the generalized form of Fick’s First Law suggested by Onsager, which is composed of the Onsager phenomenological coefficient and the thermodynamic force between ions, which occurs according to the gradient of electrochemical potential in a multicomponent concentrated solution for the pore solution. In addition, the chemical equilibrium
for Ca(OH)2 dissolution and C-S-H decalcification are also modeled and coupled with diffusion. Increased porosity due to
dissolved Ca2+ and a chloride binding isotherm are taken into consideration. The concentration profiles of solid calcium
and the presence of Friedel’s salt in mortar specimens are experimentally identified by the X-ray diffraction method
(XRD) and the thermal analysis (TG/DTA) as well as the total chloride profile using an acid extraction method after three
years of exposure to 0.5 mol/l NaCl solution. This experimental result verifies the calculation result.
1. Introduction
The transport of ions through concrete is closely related
to concrete degradation and is believed to be a diffusion-controlling phenomenon. This is especially true for
a saturated concrete that is always in contact with sea
water or ground water. The diffusion of ions is not molecular and is influenced by both chemical potential and
electrical potential. Since the pore solution of concrete
contains several different types of ions such as OH-,
SO42-, Ca2+, Na+ and K+ at high concentrations, the concentrations of the coexisting ions have a significant influence on the mobility of each ion (Otsuki et al. 1999;
Ritthichauy et al. 2002). In addition, the transport of ions
also involves a chemical reaction between solid cement
hydrates and the liquid causing dissolution and precipitation in the pore space (Fig. 1). Therefore, the thermodynamic law for diffusion and subsequent chemical
equilibrium must be taken into account to clarify the
mechanism of ion transport through a cement-based
material.
A number of research projects have been conducted on
the detrimental mechanism of the dissolution of Ca(OH)2
and the decalcification of calcium silicate hydrates
(C-S-H) on a cement-based material exposed to pure
1
Associate Professor, Department of Civil Engineering,
Gunma University, Japan.
E-mail: [email protected]
2
Ph.D. Student, Department of Civil Engineering,
Gunma University, Japan.
3
Professor, Department of Civil Engineering, Gunma
University, Japan.
water and/or aggressive solution (Carde et al. 1997;
Furusawa 1997; Saito et al. 1997). The degradation of
concrete due to the leaching of calcium ions is likely to
adversely affect the long term performance of concrete
structures such as radioactive waste facilities. However,
a series of dissolution/precipitation reactions can occur in
common resulting from the diffusion of ions through
concrete during its service life as long as external ions
diffuse in or internal ions diffuse out and disturb the
chemical equilibrium in the pore solution (Samson et al.
2000).
Chloride penetration through saturated concrete has
been normally understood by coupling the rate-controlling diffusion and chloride binding. However, Ono reported that the leaching of calcium ions from the concrete has the effect of increasing the chloride ingress
(Ono et al. 1978). Recently, Saito also reported that the
amount of calcium leaching was higher for mortar in
Decalcification
Dissolution
Na+
C-S-H
Ca(OH)2
OH-
Ca2++ 2OH-
Ca(OH)2
Dissolution
Ca2+
Ca2+
Cl-
SO42-
K+
Ca2+
C-S-H
Cl-
Cl Binding
Decalcification
Fig. 1 Schematic diagram of ion transport in cement－
based material.
T. Sugiyama, W. Ritthichauy and Y. Tsuji / Journal of Advanced Concrete Technology Vol. 1, No. 2, 127-138, 2003
Mutual transport
Caused by
• Gradient of electrochemical potential
• Electro-neutrality constraint
N
JK+
OH-
JNa+
ct
io
n
∑
Na+
At
tra
JCl- =
Repulsion
K+
n
tio
∂C Cl∂X
∂C D Cl-,OH- × OH
∂X
∂C K+
D Cl-, K+ ×
∂X
∂C Na+
D Cl-, Na+ ×
∂X
D Cl-, Cl- ×
Repulsion
∂x
n
io
ct
j=1
JCl-
Cl-
tra
J i = − ∑ D ij
∂C j
At
ns
Na+
Slower Na+
ct
io
n
Binary solution of
Na+ and Cl-
c
tra
2.1 General background of ion diffusion
In an electrolyte diffusion process, it is well known that
the movement of an aqueous species will occur as a
result of the driving forces resulting from the concentration gradient of that species itself and by those of the
other species. Moreover, another driving force is the
gradient of an electrical potential created by the difference in mobility of cations and anions. The way in which
the electrical potential or the electrostatic force has an
influence on the electrolyte diffusion is schematically
illustrated in Fig. 2. It is shown that in a binary electro-
Cl-
At
2. Modelling of ion diffusion and chemical
equilibrium
Faster Clin
y
ar ha
in c
ag tic
Im osta
tr
ec
el
contact with chloride solution compared to pure water in
his electrical acceleration test (Saito et al. 1997). The
reason is thought to be due to the increased porosity
resulting from the dissolution and the decalcification of
the cement hydrates in contact with chloride solution,
which is greater than in the case of contact with water
(Ono et al. 1978; Saito et al. 1997; Carde and Francois
1999). Thus chloride penetration through saturated concrete involves calcium leaching in addition to diffusion
and binding.
No research has been directed toward clarifying the
mechanism of chloride penetration into concrete taking
into consideration dissolved calcium ions as well as the
nature of the pore solution. The purpose of this research
is to propose a new calculation for chloride penetration
into a cement-based material on the basis of the thermodynamic theories applied to the diffusion of ions and
corresponding chemical reactions. The diffusion of ions
is considered in a multicomponent concentrated solution
and the matrix of mutual diffusion coefficient of every
ion existing in the pore solution in a cement-based material is calculated. The mutual diffusion coefficient that
is defined here is designated as Dij, the diffusion coefficient of ith species influenced by the interaction from jth
species (Cussler 1976; Felmy and Weare 1991; Oelkers
1996). Consequently, this Dij is coupled with a chemical
equilibrium concerning the dissolution and decalcification from the solid phase of concrete. For the chloride
penetration involved here, a chloride binding isotherm
must be coupled as well. Moreover, the pore structure
change due to the dissolved calcium ions in the concrete
is also considered. Therefore, the concentration profiles
of solid calcium and total chloride ions that penetrate into
the concrete can be calculated.
The calculated concentration profiles of solid calcium
and total chloride ions are verified through a comparison
with experimental results in which the mortar specimens
have been continuously exposed to 0.5 mol/l NaCl solution for 3 years. The X-ray diffraction method (XRD)
and the thermal analysis (TG/DTA) are applied to exhibit
the concentration profile and the presence of Friedel’s
salt. The total chloride ions profile is also obtained by the
acid extraction method.
At
tra
128
JOH-
Multicomponent concentrated solution
of Na+, K+, Cl- and OH-
Fig. 2 Schematic diagram of ion transport in multicomponent concentrated solution.
lyte solution of NaCl, the faster Cl- and the slower Na+
are constrained by the electrostatic force, to move at the
same rate. In addition to this, by the electro-neutrality
constraint these two ions must maintain the same diffusive flux throughout the transport in the solution.
Because of these electrostatic requirements, the flux of
NaCl is characterized by a single diffusion coefficient, i.e.
a mutual diffusion coefficient, which is an average of the
diffusion coefficients of Na+ and Cl-. This mutual diffusion coefficient can be imaginatively considered as a
chain tying Na+ and Cl- together. The faster Cl- accelerates the slower Na+, while at the same time, the slower
Na+ decelerates the faster Cl-, which keeps it from running away. All of these accelerating and decelerating
effects produce a mutual diffusion coefficient.
In a similar manner for a multicomponent concentrated solution system, instead of a single electrostatic
chain tying one cation and one anion, imagine that there
are a lot of chains connected together by all charged
species existing in the solution system, as in the example
shown in Fig. 2. There are attractive chains connecting
oppositely charged ions and repulsive chains connecting
similarly charged ions. One ion, e.g. OH-, which is much
more mobile than the others, can accelerate the movement of ions with an opposite charge, i.e. Na+ and K+, or
decelerate the movement of ions with a similar charge, i.e.
Cl-. Moreover, in some cases it can even cause the other
ions to move against their concentration gradient.
2.2 Development of calculation model for mutual diffusion coefficient
The diffusion coefficient of a species in a multicomponent solution can be calculated by considering the driving diffusive flux in the solution. Felmy and Weare
(1991) have developed a calculation model for multicomponent concentrated solution as the sea water com-
T. Sugiyama, W. Ritthichauy and Y. Tsuji / Journal of Advanced Concrete Technology Vol. 1, No. 2, 127-138, 2003
position. Therefore, by a similar definition of the driving
diffusive flux, this proposed model is also capable to
accommodate the multicomponent concentrated solution
as the pore solution in a cement-based material.
The forces driving the diffusion of an aqueous species
are basically originated from the thermodynamic force
that can be considered as the gradient of electrochemical
potential (∂µ/∂x). The electrochemical potential of ion j
(µj), which is composed of the chemical potential part of
ion j (µj,chem) and the electrical potential part (φ), can be
expressed by the following expression:
µj = µj,chem + zjFφ
(1)
where F = Faraday’s constant equals to 96485 C/equiv,
and zj = valence number of ion j.
As mentioned before, the thermodynamic force incurred by ion j (Xj) is the gradient of the electrochemical
potential given by Eq. (2).
Xj =
∂µ j
∂x
=
∂µ j, chem
+ z jF
∂x
∂φ
∂x
(2)
At this point a linear relation, which relates the flux of
ion i to the force incurred by ion j, is assumed and expressed in Eq. (3) (Felmy and Weare 1991).
ｎｓ
J i = − ∑ ｌij X j =
ｊ＝１
ｎｓ
∑ｌ
ij
(−
∂µ j,chem
ｊ＝１
− z jF
∂x
∂φ
)
∂x
(3)
where Ji = flux of ion i (mol/m2·s), and lij = the Onsager
phenomenological transport coefficient (hereafter Onsager coefficient).
The significance of this coefficient (lij) on transport in
a multicomponent concentrated solution will be discussed later.
The electrical potential gradient (∂φ/∂x) can be
eliminated from Eq. (3) by the electro-neutrality conn
straint in the solution ( z J = 0 ).
s
∑
i =1
i i
From this step, µj will be used as an abbreviation of
µj,chem. By substituting the flux equation in Eq. (3) into
the electro-neutrality constraint, one can derive Eq. (4).
ns
∂φ
=−
∂x
ns
∑∑ z k l kl
k =1 l =1
ns ns
(4)
F∑∑ z k z l l kl
k =1 l =1
By substituting Eq. (4) into the flux equation of Eq. (3),
the flux equation of ion i becomes the following equation.

 ∂µ
ns

j
+ zj
J i = ∑ l ij −
j=1
 ∂x

At this stage of the calculation, determining the Onsager coefficient (lij), which is the function of ion concentrations in the solution, particularly in relatively diluted solutions, is necessary. However, in a system of
porous media, the off-diagonal terms of this Onsager
coefficient (lij, i ≠ j) can be approximated to 0. In the
other words, it can be negligible compared to the
on-diagonal term of the Onsager coefficient (lij, i = j)
without significant error.
Therefore, the on-diagonal term of the Onsager
coefficient was simplified for some levels of
concentration of solution (less then 1.0 mol/l) as shown
by Oelkers (1996). This modification enables the
application of the levels of concentration provided in the
pore solution of a cement-based material with reasonable
accuracy. The concentration of ions in the pore solution
is taken into account for this Onsager coefficient and it
can be computed from the following equation (Oelkers
1996):
0
l ii =
Di Ci
RT
(6)
where D0i = tracer diffusion coefficient in dilute solution
of ion i (m2/s), Ci = concentration of ion i in the solution
(mol/l-solution), R = gas constant, equal to 8.3145
(J/mol·K), and T = absolute temperature (K).
Consequently, the gradient of electrochemical potential is converted to the gradient of concentration by the
following equation:
∂µ j
∂x
=
∂µ j
∂C j
×
∂C j
∂µ l 

∂x 
k =1 l =1

ns ns
∑
∑ z k z l l kl 
k =1 l =1
ns
ns
∑∑z
l
k kl
(5)
(7)
∂x
The definition of chemical potential (µj) can be extended to the following expression:
µ j = µ 0j + RT ln C j + RT ln γ j
(8)
where γj = mean activity coefficient of ion j, and µ0j =
chemical potential in the standard state of the solution,
which is a constant number.
Therefore, the following equation can be derived:
 1
∂ ln γ j
= RT 
+

∂C j
 C j C j ∂ ln C j
∂µ j
∂µ l
∂x
129




(9)
Consequently, the generalized form of the Fick’s First
Law suggested by Onsager is as shown in the following
expression (Felmy and Weare 1991; Oelkers 1996):
ns
J i = −∑ D ij
j=1
∂C j
∂x
(10)
where Dij = the mutual diffusion coefficient (m2/s) of ion
i in free liquid phase influenced by the concentration
gradient of ion j (∂Cj/∂x).
By substitution of all the expressions from Eq. (6) to
Eq. (9) into Eq. (5), and comparison with the similar flux
130
T. Sugiyama, W. Ritthichauy and Y. Tsuji / Journal of Advanced Concrete Technology Vol. 1, No. 2, 127-138, 2003
term in Eq. (10), the expression of mutual diffusion coefficient can be derived as shown in Eq. (11):


 z D0C
∂ ln γ j  (11)
∂ ln γ i
 i i i
0
z j D j (1 +
D ij = δ ij D (1 +
)− n
)
s
∂ ln C i
∂ ln C j 
 z 2 D0 C
∑ k k k

 k =1
0
i
where δ = Kronecker delta which is equal to 1 if i = j, but
equal to 0 if i ≠ j, and γi = mean activity coefficient of ion
i.
The derivative of γi relative to the concentration can be
calculated by the Debye-Hückel theory as shown in the
following equation (Tang 1999):
0.509 × Z i2
∂ ln γ i
= −2.302 × C i ×
∂ ln C i
2 I (1 + 3.286α i I ) 2
(12)
where αi = ion size parameter of ion i (nm), and I = ionic
strength of the solution (mol/l).
As stated before, the definition of Dij is based on the
assumption that the mutual movement of separated ions
is caused not only by the electro-neutrality constraint, but
also by the electrochemical potential gradient created by
the difference in mobility of each ion. Therefore, the
movement of ions can be considered similar to that of
uncharged species.
In general, the matrix of mutual diffusion coefficients
is not symmetric, i.e. Dij ≠ Dji. The on-diagonal terms
(Dii) are generally larger than the off-diagonal terms (Dij,
i ≠ j). Using the initial values quoted in Table 1 as the
input parameters, the matrix of Dij expressed in m2/s at
these particular concentrations in a multicomponent
concentrated solution composed of 6 ions is as shown in
Table 2. The positive values in this table denote attraction between ions, while the negative values denote repulsion between ions. In addition, it can be noticed that
the values in on-diagonal terms are higher than those in
off-diagonal terms for almost all ions.
The difference between the values of the diffusion
coefficient in the on-diagonal term and those in the
off-diagonal term of an ion can be either a significant or
insignificant value. The significance depends on the
concentrations of a pair of two ions. For example,
DK+,Ca2+ is only 16% compared to DK+,K+, however,
DK+,OH- is 53% compared to DK+,K+. The fact that the
concentration of OH- is much higher than that of Ca2+ can
be considered to be a major factor contributing to this
difference.
2.3 Application of mutual diffusion coefficient
for cement-based material
The matrix of mutual diffusion coefficients (Dij) is calculated by considering the initial concentration of ions
present in the pore solution of a cement-based material
with a set of chemical components in an external solution.
To simulate ion diffusion through the pore solution at
each particular time and position of ions by applying the
mutual diffusion coefficients and the equation of continuity, the generalized form of Fick’s Second Law can be
written as the following equation.
Table 1 Parameters for calculation of [D]i,j matrix and
initial concentration of ions presented in pore solution.
Ions
Ci
(mol/l)
αi
(nm)
D0i
(m2/s)
Ca2+
Na+
K+
SO42ClOH-
0.02*
0.20§
0.30§
0.03§
0.00§
0.48£
0.60
0.40
0.30
0.40
0.30
0.35
7.92×10-10
1.33×10-9
1.96×10-9
1.07×10-9
2.03×10-9
5.26×10-9
∂ 2C j
∂C i n s
= ∑ D ij,I
∂t
∂x 2
i =1
(13)
where Dij,I = intrinsic mutual diffusion coefficient.
The numerical method applied to Eq. (13) is the finite
difference method (Crank 1995).
For a general porous media, the intrinsic mutual diffusion coefficient is defined by accounting for the characteristic of the pore structure of the media. In this research, the intrinsic mutual diffusion coefficient is defined as the following equation.
*
Given number for initial Ca2+ in pore solution
Referred from Suzuki et al. (1993)
£
Based on electro-neutrality constraint
D ij,I = D ij K xt
§
(14)
Table 2 Example of calculated matrix of mutual diffusion coefficients at initial concentration ([D]i,j x 10-9 m2/s).
j
Ca2+
Na+
K+
SO42-
Cl-
OH-
Ca2+
0.778
-0.012
-0.017
0.019
0.018
0.047
+
-0.118
1.231
-0.146
0.159
0.151
0.392
i
Na
[D]i,j =
+
K
-0.261
-0.219
1.637
0.352
0.334
0.866
SO42-
0.028
0.024
0.035
1.032
-0.037
-0.095
Cl-
0.0
0.0
0.0
0.0
2.030
0.0
1.120
0.941
1.386
-1.513
-1.435
1.541
OH
-
T. Sugiyama, W. Ritthichauy and Y. Tsuji / Journal of Advanced Concrete Technology Vol. 1, No. 2, 127-138, 2003
where Kxt = characteristic parameter that represents the
pore structure of material in a function of position and
time.
For example, this is expressed using the porosity (εxt)
and the tortuosity (τ(εxt)) of a cement-based material as
shown in Eq. (15).
K xt =
ε xt
τ (ε xt )
(15)
2
τ=
εδD f
Di
(16)
where δ = constrictivity of pore structure, Df = diffusion
coefficient in pure solution (m2/s), and Di = measured
diffusion coefficient of a cement-based material (m2/s).
In this research, the tortuosity of a mortar specimen
was determined by a steady state chloride migration test
for Di in Eq. (16) (Sugiyama et al. 1993, 2001). In addition, the constrictivity of the pore structure was assumed
to be 1.0 and the diffusion coefficient of chloride ion in a
pure solution was used for Df to calculate the tortuosity.
The calculated tortuosity was used to be a constant despite the change in porosity. The change in porosity is
explained later in Eq. (20) in this paper.
2.4 Chemical equilibrium for Ca(OH)2 dissolution and C-S-H decalcification
It is normally understood that the dissolution of Ca(OH)2
and the decalcification of the C-S-H phase occur so as to
maintain the chemical equilibrium of Ca2+ between the
solid hydrates and the pore solution. Once the concen-
Cs
Concentration of Ca2+ in solid phase
tration of Ca2+ in the pore solution of a cement-based
material is decreased by diffusion, the dissolution of
Ca(OH)2 starts, following the depletion of Ca(OH)2, and
the decalcification of the C-S-H phase then occurs
(Saito et al. 2000).
The dissolution of Ca(OH)2 and the partial decalcification of C-S-H are followed by the following chemical
equilibrium equations (Saito et al. 2000):
Ca(OH)2
The formula for the relation between tortuosity and
porosity is shown in the following equation (Atkinson
and Nickerson 1984):
Ca2+ from
Ca(OH)2
Æ Ca2+ + 2OH-
0.0015
0.020
Cl
Concentration of Ca2+ in pore solution
(mol/l-solution)
Fig. 3 Relation between Ca2+ in solid phase (Cs) and in
pore solution (Cl) [Based on Buil et al. (1992)].
(17)
xCaO·SiO2·zH2O Æ
(x-S1)CaO· (1-S2)SiO2· (z-S1)H2O+S1Ca(OH)2+ S2SiO2
(18)
Chemical equilibrium of the solid cement hydrates and
the pore solution with regard to Ca2+ is applied according
to the model shown in Fig. 3 (Buil et al. 1992). The
initial concentration of Ca2+ in the pore solution is 0.02
mol/l-solution and must be maintained as long as the
Ca(OH)2 remains in the solid. Subsequently, after all the
Ca(OH)2 is dissolved, the decalcification of C-S-H will
ensue depending on the concentration of Ca2+ with the
chemical equilibrium provided in the curve portion of the
model.
The governing equation of the transport of Ca2+ is
normally given with a diffusion term as well as a reaction
term (Delegrave et al. 1997; Furusawa 1997), and is
expressed as follows.
∂ 2 C j ∂Si
∂C i
−
= ∑ D ij
∂t
∂t
∂x 2
j
(19)
where Ci = Ca2+ concentration (mol/m3), Dij = diffusion
coefficient of Ca2+ which is influenced by the other ions
(m2/s), and ∂Si/∂t = rate of the dissolution of Ca(OH)2 or
decalcification of C-S-H (mol/m3⋅s).
The local equilibrium assumption implies that the
diffusion rate is very slow compared to the dissolution
rate. Therefore, the rate of the system should be controlled by diffusion.
Depending on the amount of dissolved Ca2+ from the
solid phase of cement hydrates, the pore structure can be
changed and included in this present model. The expression for the change in porosity is shown in Eq. (20)
(Buil et al. 1992):
ε xt = ε ini + ρ c ⋅
Ca2+ from
C-S-H
131
M CH
⋅ (SC ini − SC xt )
d CH
(20)
where εini = initial porosity, ρc = the volume density of
the cement paste, MCH = molecular weight of Ca(OH)2
(g/mol), dCH = density of Ca(OH)2 (g/l), SCini = initial
solid calcium concentration (mol/l-paste), and SCxt =
solid calcium concentration at a particular position and
time (mol/l-paste).
According to Eq. (20), it is assumed that the dissolution of Ca(OH)2 has the same consequence on the
transport properties of the cement-based material as the
decalcification of C-S-H. The increased porosity can
T. Sugiyama, W. Ritthichauy and Y. Tsuji / Journal of Advanced Concrete Technology Vol. 1, No. 2, 127-138, 2003
increase the diffusion coefficient of ions according to Eq.
(15).
2.5 Chemical equilibrium for chloride binding
isotherm
The present transport model is coupled with a chloride
binding isotherm. In the presence of penetrating Cl-, the
chemical equilibrium that governs the reaction inside the
pore solution of a cement-based material is as shown in
the following equations.
2Cl- aq + Ca(OH)2 s Æ CaCl2 s + 2OH- aq
(21)
The C3A that remains in unhydrated cement particles
will chemically react, producing calcium chloroaluminate or Friedel’s Salt (3CaO·Al2O3·CaCl2·10H2O), as
shown in the following simplified chemical reaction
equation (Neville 1999):
CaCl2 + C3A Æ 3CaO·Al2O3·CaCl2·10H2O
(22)
In the calculation of a concentration profile for chloride ions that penetrate into a cement-based material, the
total amount of chloride ions can be calculated by the
summation of the amount of free chloride and the amount
of bound chloride as shown in the following expression:
CT = εxt·Cff + Cb
(23)
where CT = amount of total chloride (kg/m3-material), Cff
= amount of free chloride in pore solution
(kg/m3-solution), and Cb = amount of bound chloride
(kg/m3-material).
Chloride ions present in the pore solution of a cement-based material may be immobilized by ion exchange and by sorption onto the monosulphate or C-S-H
phases. To account for these binding phenomena as well
as the chemical binding given in Eq. (21) and Eq. (22),
the Freundlich equation is adapted for the chemical
equilibrium. Then the amount of the bound chloride is
calculated in a function of the concentration of free
chloride ions as shown in Eq. (24) (Tang and Nilsson
1996):
Cb = e

[ OH ]
α OH  1−
 [ OH ]ini



⋅e
Eb  1 1
 −
R  T T0




⋅ Wgel ⋅
fa
C βff
1000
addition, it also produces 2 moles of OH-.
However, it is understood that the behavior of the
dissolution and decalcification of cement hydrates becomes more complex in the presence of chloride ions.
This may not be simply expressed by Eq. (21) but requires careful considerations though little information on
this matter has been reported. Then, a relative comparison between an NaCl solution and distilled water as a
leachant must be made.
In order to explain the different behavior with regard
to the dissolution of Ca(OH)2 and decalcification of
C-S-H in the presence of chloride ions, a preliminary test
was carried out. It is assumed that the rate of the dissolution of Ca(OH)2 is different from the rate of the decalcification of C-S-H, which are both given linearly and
expressed schematically in Fig. 4.
Cylindrical shapes of 100 mm diameter and 10 mm
thickness were prepared using cement paste. After 4
weeks of curing in a saturated lime solution, they were
coated with an epoxy adhesive on their circumferential
surface and one end surface to ensure subjection of the
specimens to leaching in only one direction. Then a
leaching test of these specimens in contact with either
distilled water or 0.5 mol/l NaCl solution was conducted.
During this test, each solution was agitated and renewed
periodically. The exposed area for each specimen was
one of its end surfaces, with a cross section area of
7.85×10-3 m2. Figure 5 shows a cumulative leached
amount of Ca2+ over elapsed time that is higher for the
NaCl solution than for distilled water.
The slope of the trend lines shown in this figure corresponds to the rate of the dissolution of Ca(OH)2 in
mol/m3⋅s units. From the experimental result, it is found
that the dissolution rate of Ca(OH)2 with a NaCl solution
is approximately 2.5 times that with distilled water.
Therefore, in this model, this effect was considered for
the presence of Cl- in the pore solution at the section
where the dissolution of Ca(OH)2 occurred due to the
concentration gradient of Ca2+.
The rate of C-S-H decalcification is assumed to be 5%
of that of the Ca(OH)2 dissolution because its behavior of
partial decalcification is relatively slow (Delagrave et al.
(24)
where αOH = constant for hydroxide-dependent, [OH] =
concentration of OH- (mol/l), [OH]ini = initial concentration of OH- (mol/l), Eb = activation energy for chloride
binding (40000 J/mol), R = gas constant (8.3145
J/mol·K), T = absolute temperature (K), T0 = absolute
temperature at which the binding isotherm is obtained
(293 K), fa, β = adsorption constants for chloride binding,
and Wgel = the quantity of hydrate gel (kggel/m3-material).
2.6 Behavior of dissolution and decalcification
in presence of chloride ions
According to Eq. (21) the consumption of 1 mole of
Ca2+ from Ca(OH)2 in the solid phase is accompanied
by 2 moles of Cl- that penetrates into the concrete. In
Cumulative leached amount
132
R4
R3
R1
R2
R1 Dissolution rate of Ca(OH)2 in distilled water
R2 Dissolution rate of C-S-H in distilled water
R3 Dissolution rate of Ca(OH)2 in 0.5 M NaCl
R4 Dissolution rate of C-S-H in 0.5 M NaCl
Exposure period
Fig. 4 Model accounted for dissolution rate of Ca(OH)2
and C-S-H in different leachant.
133
Cumulative leached amount of Ca2+ (mg)
T. Sugiyama, W. Ritthichauy and Y. Tsuji / Journal of Advanced Concrete Technology Vol. 1, No. 2, 127-138, 2003
1200
Table 4 Physical properties of fine aggregate.
Saturated surface-dry density (g/cm3)
1000
3
800
600
400
In distilled water
In 0.5 mol/l NaCl
200
0
0
20
40
60
80
100
Exposure period (days)
Fig. 5 Experimental results for determining dissolution
rate of Ca(OH)2 from leaching test of cement paste.
1997; Saito et al. 2000). This value was evaluated from
the inverse analysis that showed that 5% of the dissolution rate of Ca(OH)2 for the decalcification rate of C-S-H
can be fitted to the experimental results of the leaching
amount of Ca2+ over elapsed time.
3. Verification of proposed calculation
model
3.1 Materials and experimental details
In this research, for verification purpose the calculation
model is applied to simulate the concentration profiles of
solid calcium and total chloride ions and compared with
the experiments. Two series of mortar specimens of the
water to cement ratios of 0.45 and 0.65 were prepared
with ordinary portland cement and local sand. The
chemical composition of the cement and the physical
properties of sand are given in Table 3 and Table 4,
respectively. The mix proportions of mortar specimens
are shown in Table 5.
A cylindrical shape 50 mm in diameter and 100 mm in
length was cast and sliced at both ends before the exposure test so that the total length of each specimen was 50
mm. To ensure unidirectional direction of chloride ions
Oven-dry density (g/cm )
2.57
Water absorption (%)
2.35
Fineness modulus
2.77
Percentage of solid volume (%)
64.6
penetration, the circumferential surface and one end
surface of the mortar were coated with an epoxy adhesive.
After a curing period of 4 weeks, the mortar specimens
were immersed in an NaCl solution with a constant
concentration of 0.5 mol/l under a controlled room
temperature of 25°C. The mortar specimens were not
dried before the leaching test. As the concentration of
some ions in the external NaCl solution would naturally
change because of leaching or penetration over the
course of the exposure period, the external NaCl solution
was renewed periodically to maintain the concentration
of NaCl solution at 0.5 mol/l.
Each mortar specimen was separately placed in its
container and immersed completely with NaCl solution.
The volume of each container was approximately 2,000
cm3. A sufficient volume of the container compared to
the leaching surface area of the specimen was provided,
so that the increased concentration of Ca2+ due to the
dissolution of the solid calcium would not disturb the
boundary condition of the initial concentration of Ca2+ in
the NaCl solution. Furthermore, periodical agitation of
the NaCl solution was provided to reduce the possibility
of precipitation of CaCl2 at the surface of the specimens.
After three years of exposure, the specimen was sliced
into 10-mm thick disks and the amount of Ca(OH)2 in the
disks were examined quantitatively by TG/DTA and
XRD. In addition, the total amount of chloride ions in
each disk was also examined according to JCI-SC4.
3.2 Experimental results
The existence of Ca(OH)2 in the second slice (10 to 20
mm from the exposure surface) and the fourth slice (40 to
50 mm from the exposure surface) of the mortar specimen with a water to cement ratio of 0.65 is clearly con-
Table 3 Chemical composition of ordinary portland cement.
Chemical
compound
Weight (%)
Insoluble
residue
0.1
MgO
SO3
SiO2
Al2O3
Fe2O3
CaO
Cl-
1.4
2.0
21.2
5.1
2.8
64.5
0.005
Table 5 Mix proportion of mortar specimens.
Specimen
Mortar
Unit weight of material (kg/m3)
W
C
S
Flow
(mm)
Compressive strength
(N/mm2)
45
262
583
1454
154
53.5
65
339
523
1304
218
34.5
W/C
2.63
134
T. Sugiyama, W. Ritthichauy and Y. Tsuji / Journal of Advanced Concrete Technology Vol. 1, No. 2, 127-138, 2003
in the first slice but was found in the second and the
fourth slices.
The amount of Ca(OH)2 in each slice of this mortar
specimen is calculated using a method proposed by Suzuki et al. (1990). The calculated amounts of Ca(OH)2
are 0%, 2.10%, 3.38%, and 4.30% (% of weight of the
powder sample) according to the distance from exposure
surface, 0 to 10 mm, 10 to 20 mm, 20 to 30 mm, and 40 to
50 mm, respectively. Similarly the amount of Ca(OH)2
was determined at the same distance from the exposure
surface for the mortar specimen with a water to cement
ratio of 0.45.
Ca(OH)2
Friedel’s salt
0-10 mm
10-20 mm
40-50 mm
0
5
10
15
20
25
30
35
40
45
50
55
2θ
Fig. 6 Experimental results from XRD analysis.
20
Friedel’s
salt
0
0-10 mm
DTA (µV)
Ca(OH)2 10-20 mm
-20
40-50 mm
-40
Ca(OH)2
-60
-80
0
100
200
300
400
500
600
700
Temperature (℃)
Fig. 7 Experimental results from TG/DTA analysis.
firmed by the XRD results, as shown in Fig. 6. On the
other hand, no peak at the same 2θ for Ca(OH)2 is recognized for the first slice of 0 to 10 mm from the exposure surface. XRD also exhibits the existence of Friedel’s
salt in every slice of this mortar specimen. The degree of
dissolution for the Friedel’s salt is approximately
0.01g/100g-water (Abate and Scheetz 1995), which is
about one tenth of that of Ca(OH)2. Therefore, the
Friedel’s salt appeared to remain in a non-dissolved state
even in the first slice in this experiment.
The DTA curves are shown in Fig. 7 for each slice of
the same specimen. Again, no Ca(OH)2 was recognized
3.3 Verification of calculation results with experimental results
Regarding the input values of the calculation model, the
initial concentrations of Ca(OH)2 and C-S-H, initial
porosity, tortuosity, and the constants in the chloride
binding isotherm for mortar specimens with water to
cement ratios of 0.45 and 0.65 are shown in Table 6.
The initial concentration of Ca(OH)2 of the mortar
specimens was experimentally determined by TG/DTA
using a companion specimen. In addition, the initial
concentration of C-S-H was estimated by the experimental results given by Saito et al. (2000), where similar
mix proportions and materials were used. The initial
porosity was measured by the weight loss method after
the specimen was oven-dried at 105°C for 24 hours.
The comparisons of the solid calcium profile from the
calculation and that from the leaching test for mortar
specimens with water to cement ratios of 0.45 and 0.65
are shown in Fig. 8(a) and Fig. 8(b), respectively. The
solid calcium concentration obtained from the experiment for each slice is considered as a representative
value at each average depth, i.e. 5 mm, 15 mm, 25 mm,
and 45 mm, respectively. The amount of solid calcium
shown on the Y-axis of the graph is expressed as the total
concentration of solid calcium.
It can be seen that the calculated amounts of solid
calcium at 5, 15, 25, and 45 mm from the exposure surface exhibit good agreement with the experimental results for both specimens with different water to cement
ratios. If it is assumed that the amount of Ca(OH)2 becomes zero (as shown by the lower dotted line in the
figure) at the degradation front, then this degradation
front is at a distance of 4 mm from the exposure surface
for the mortar specimen with the water to cement ratio of
0.45 and at a distance of 10 mm from the exposure surface for the mortar specimen with the water to cement
Table 6 Input values for calculation.
W/C
45
Ca(OH)2
(mol/l-mortar)
2.50
C-S-H
(mol/l-mortar)
3.92
65
1.66
2.60
From Tang and Nilsson (1996)
§
Based on mix proportion of mortar
*
Initial
porosity
0.15
0.20
Tortuosity
5.0
3.0
Constant for chloride binding
Wgel (kggel/m3-mortar) §
β*
552
3.57
0.38
516
fa*
135
Mortar specimen (50 mm diameter)
exposed to 0.5 mol/l NaCl solution
8
7
6
Ca(OH)2
5
4
3
2
C-S-H
Calculation
Experiment
1
0
0
10
20
30
40
Distance from exposure surface (mm)
50
Concentration of solid calcium (mol/l-mortar)
Concentration of solid calcium (mol/l-mortar)
T. Sugiyama, W. Ritthichauy and Y. Tsuji / Journal of Advanced Concrete Technology Vol. 1, No. 2, 127-138, 2003
Mortar specimen (50 mm diameter)
exposed to 0.5 mol/l NaCl solution
8
7
6
5
4
Ca(OH)2
3
2
Calculation
Experiment
1
0
0
10
20
30
40
Distance from exposure surface (mm)
(a) W/C = 0.45
C-S-H
50
(b) W/C = 0.65
Fig.8 Calculated and experimental results of solid calcium profile after 3 years of exposure.
3.4 Profile of total chloride concentration
The mortar specimen with the water to cement ratio of
0.65 exposed to a 0.5 mol/l NaCl solution for 3 years was
also investigated for the amount of total concentration of
chloride ions using the JCI-SC4 method. The comparison
of the calculated results and the experimental results is
shown in Fig. 9. The calculated profile by the proposed
model (Cal-1) of the total concentration of chloride ions
exhibited good agreement with the experimental results.
It should be noted that the porosity of the surface was
assumed to be 1.0 for the calculation. This means that the
physical characteristics of the surface layer were deemed
to play no role against ionic diffusion.
In the same figure, the result calculated using the
proposed model shows better result than the result obtained assuming that only chloride ions (Cal-2) exist in
the pore solution of the corresponding mortar specimen.
Even for Cal-2, the effect of increased porosity was taken
into account. The total chloride profile obtained from the
experiment was further compared with the calculation
result by a well-known error function method shown by
Cal-3. The apparent diffusion coefficient of chloride ions
for the mortar specimen was assumed to be 5.0×10-12
m2/s, based on the research of Maruya et al. (1992),
although the water to cement ratio of his mortar specimen was 50%. By comparing the calculated chloride
profiles with Cal-1, Cal-2, and Cal-3, it can be inferred
that consideration of coexisting ions in a multicomponent concentrated solution is necessary for an accurate
understanding of ion transport in concrete.
The total concentration of chloride ions is as high as
approximately 4 kg/m3-mortar after 3 years of exposure
at a distance of 45 mm from the exposure surface. This is
attributed to the high water to cement ratio of this
specimen. Therefore, it is proved that the presence of
chloride ions can partially reduce the concentration of
Ca(OH)2 as previously explained in section 3.3.
20
Total chloride content (kg/m3-mortar)
ratio of 0.65. It is apparent that the impervious mortar
specimen with the water to cement ratio of 0.45 exhibited
less degradation than the mortar specimen with the water
to cement ratio of 0.65.
The calculated remaining solid calcium concentration
is slightly lower than the initial solid calcium concentration (as shown by the upper dotted line indicating the
sum of the Ca(OH)2 and C-S-H) at deeper sections. The
Ca(OH)2 concentration is reduced by the chloride diffusion and subsequent binding. In this way, the diffusion of
chloride ions partially controls the reduction of Ca(OH)2
although the dissolution of Ca(OH)2 never occurs due to
the concentration gradient of Ca2+.
In addition, experimental results show that hydroxide
ions counter diffuse against the diffusion of chloride ion
(Sergi et al. 1992). This may be partially attributed to the
reduction of Ca(OH)2 in the presence of chloride ions.
The closure of the pore system in mortar due to the
precipitation is not considered in this calculation because
of the little amount of knowledge in this area.
Cal-1
Cal-2
Cal-3
Exp
16
12
8
4
0
0
10
20
30
40
50
Distance from exposure surface (mm)
Fig. 9 Calculated and experimental results of total chloride
content for mortar specimen with water to cement ratio
0.65.
Free chloride concentration (mol/l-solution)
136
T. Sugiyama, W. Ritthichauy and Y. Tsuji / Journal of Advanced Concrete Technology Vol. 1, No. 2, 127-138, 2003
no result is given for the cumulative amount of Na+ for
this solution. It is clearly shown that the cumulative
leached amounts of Ca2+ are much higher than the cumulative leached amounts of K+ for both specimens.
Although the diffusion coefficient and concentration in
the pore solution of K+ are much higher than for Ca2+, as
a result of dissolution from a solid structure, the cumulative leached amount of Ca2+ was higher than the cumulative leached amount of K+. Higher amounts of Ca2+
leached out over time have been recorded in past experiments by Saito et al. (1993).
The cumulative leached amount of Ca2+ from mortar
specimen with the water to cement ratio of 0.45 in Fig.
11(a) shows a slight upward trend. This is due in part to
the influence of coexisting ions, which slightly increase
the diffusion coefficient of Ca2+. Although not shown in
this result, as time elapses, the calculated result, for
example after 10 years, will also exhibit a downward
curve like the mortar specimen with the water to cement
ratio of 0.65 shown in Fig. 11(b).
0.6
3 year of
exposure
0.5
0.4
0.3
0.2
1 year of
exposure
0.1
0
0
10
20
30
40
50
Distance from exposure surface (mm)
Fig. 10 Calculation of free chloride concentration profiles
for mortar specimen with water to cement ratio 0.65.
The calculated result of the free Cl- concentration
profile for the mortar specimen with the water to cement
ratio of 0.65 is also shown in Fig. 10. The concentration
of Cl- became as high as 0.3 mol/l of solution at 45 mm
from the surface after 3 years of exposure.
5. Conclusions
A new calculation model for ions transport in a cement-based material to study the simultaneous transport
of calcium ions and chloride ions is proposed. A limited
number of experimental results show a good agreement
with the calculations.
Based on this research, the following conclusions are
drawn:
(1) The concentration profiles calculated by this
method show that no Ca(OH)2 is present within 4 mm
and 10 mm from the surface exposed for three years to a
0.5 mol/l NaCl solution in the case of mortar specimens
with water to cement ratios of 0.45 and 0.65, respectively.
These calculated profiles were confirmed by the exposure tests.
(2) A pore solution in a cement-based material
containing several types of ions at high concentrations
4. Calculation of leached amount of calcium
ions
The proposed calculation model can be used to predict
the cumulative leached amount of some ions, for example, Ca2+ and K+.
The calculated results of the cumulative leached
amount of ions from 50-mm-diameter mortar specimens
with water to cement ratios of 0.45 and 0.65 exposed to
0.5 mol/l NaCl solution for an exposure time of up to 3
years are shown in Fig. 11(a) and Fig. 11(b), respectively,
although no experimental data is provided. Since Na+
ions are initially present in the leachant of NaCl solution,
Mortar specimen (50 mm diameter)
exposed to 0.5 mol/l NaCl solution
1200
1000
Ca2+
K+
800
Mortar specimen (50 mm diameter)
exposed to 0.5 mol/l NaCl solution
1400
Cumulative leached amount (mg)
Cumulative leached amount (mg)
1400
600
400
200
0
1200
1000
Ca2+
K+
800
600
400
200
0
0
200
400
600
800
Exposure period (days)
(a) W/C = 0.45
1000
1200
0
200
Fig. 11 Calculated results for cumulative leached amount of Ca
400
600
800
Exposure period (days)
1000
(b) W/C = 0.65
2+
and K+ (3 years exposure).
1200
T. Sugiyama, W. Ritthichauy and Y. Tsuji / Journal of Advanced Concrete Technology Vol. 1, No. 2, 127-138, 2003
taining several types of ions at high concentrations must
be treated as a multicomponent concentrated solution.
The application of a mutual diffusion coefficient is proposed to clarify the diffusion mechanism of each type of
ion present in the pore solution.
(3) The transport of ions in a cement-based material
must be coupled with diffusion and corresponding
chemical reactions. The presence of chloride ions in the
pore solution accelerates the cumulative amount of Ca2+
that is leached out to the external solution. In addition,
the concentration of Ca(OH)2 in the solid phase is partially reduced by the binding of chloride ions.
(4) More refined determination of the rate of dissolution of Ca(OH)2 and the rate of decalcification of C-S-H
should be worked on in the future for the development of
more reliable ion transport through cement-based materials. In addition, more precise determination of pore
structure characteristics must also be considered.
Acknowledgments
Part of this present research work is funded by the Japan
Society for the Promotion of Science (Research No.:
13750438). The authors also would like to thank Dr.
Saito from Obayashi Corp. for his valuable suggestions
regarding this research.
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