simultaneous transport of chloride and calcium … transport of chloride and calcium ions in...

Journal of Advanced Concrete Technology Vol. 1, No. 2, 127-138, July 2003 / Copyright © 2003 Japan Concrete Institute 127

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 corre-sponding 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 phenome-nological coefficient and the thermodynamic force between ions, which occurs according to the gradient of electro-chemical 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 diffu-sion-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 mo-lecular 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-, SO4

2-, Ca2+, Na+ and K+ at high concentrations, the con-centrations of the coexisting ions have a significant in-fluence 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 precipi-tation in the pore space (Fig. 1). Therefore, the thermo-dynamic 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

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-control-ling diffusion and chloride binding. However, Ono re-ported that the leaching of calcium ions from the con-crete 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

1Associate Professor, Department of Civil Engineering, Gunma University, Japan. E-mail: [email protected] 2Ph.D. Student, Department of Civil Engineering, Gunma University, Japan. 3Professor, Department of Civil Engineering, Gunma University, Japan.

DissolutionC-S-H

Decalcification

Dissolution

Ca(OH)2

Cl Binding

OH- Ca2+

Na+

Cl- SO42-

C-S-H

Decalcification

Ca(OH)2

Ca2++ 2OH-

Cl-

Ca2+

Ca2+

K+

DissolutionC-S-H

Decalcification

Dissolution

Ca(OH)2

Cl Binding

OH- Ca2+

Na+

Cl- SO42-

C-S-H

Decalcification

Ca(OH)2

Ca2++ 2OH-

Cl-

Ca2+

Ca2+

K+

Fig. 1 Schematic diagram of ion transport in cement－based material.

128 T. Sugiyama, W. Ritthichauy and Y. Tsuji / Journal of Advanced Concrete Technology Vol. 1, No. 2, 127-138, 2003

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 con-crete 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 ther-modynamic 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 ma-terial is calculated. The mutual diffusion coefficient that is defined here is designated as Dij, the diffusion coeffi-cient 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 decalcifica-tion 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 solu-tion 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.

2. Modelling of ion diffusion and chemical equilibrium

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 concentra-tion 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 differ-ence 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-

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 diffu-sive 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 diffu-sion coefficient can be imaginatively considered as a chain tying Na+ and Cl- together. The faster Cl- acceler-ates the slower Na+, while at the same time, the slower Na+ decelerates the faster Cl-, which keeps it from run-ning away. All of these accelerating and decelerating effects produce a mutual diffusion coefficient.

In a similar manner for a multicomponent concen-trated 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 move-ment 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 mu-tual diffusion coefficient The diffusion coefficient of a species in a multicompo-nent solution can be calculated by considering the driv-ing diffusive flux in the solution. Felmy and Weare (1991) have developed a calculation model for multi-component concentrated solution as the sea water com-

x

CDJ j

n

1jiji

s

∂

∂−= ∑

=

∑N

=JCl- XC

D , ∂∂

×

XC

D , ∂∂

×

XC

D , ∂∂

×

XC

D , ∂∂

× Cl- Cl-

Cl- OH-

Cl- K+

Cl- Na+

Cl-

OH-

K+

Na+

Cl-

Na+K+

OH-

AttractionAttracti

on

Attraction Attracti

on

Repulsion

Rep

ulsi

on

Mutual transport

Imaginary

electrostatic chain

Cl-Faster Cl-

Na+

Slower Na+

Caused by

• Gradient of electrochemical potential

• Electro-neutrality constraintBinary solution of

Na+ and Cl-

Multicomponent concentrated solution of Na+, K+, Cl- and OH-

JCl-

JNa+JK+

JOH-

x

CDJ j

n

1jiji

s

∂

∂−= ∑

=

∑N

=JCl- XC

D , ∂∂

×

XC

D , ∂∂

×

XC

D , ∂∂

×

XC

D , ∂∂

× Cl- Cl-

Cl- OH-

Cl- K+

Cl- Na+

Cl-

OH-

K+

Na+

∑N

=JCl- XC

D , ∂∂

×

XC

D , ∂∂

×

XC

D , ∂∂

×

XC

D , ∂∂

× Cl- Cl-

Cl- OH-

Cl- K+

Cl- Na+

Cl-

OH-

K+

Na+

XC

D , ∂∂

×

XC

D , ∂∂

×

XC

D , ∂∂

×

XC

D , ∂∂

× Cl- Cl-

Cl- OH-

Cl- K+

Cl- Na+

Cl-

OH-

K+

Na+

Cl-

Na+K+

OH-

AttractionAttracti

on

Attraction Attracti

on

Repulsion

Rep

ulsi

on

Mutual transport

Imaginary

electrostatic chain

Cl-Faster Cl-

Na+

Slower Na+

Caused by

• Gradient of electrochemical potential

• Electro-neutrality constraintBinary solution of

Na+ and Cl-

Multicomponent concentrated solution of Na+, K+, Cl- and OH-

JCl-

JNa+JK+

JOH-

Fig. 2 Schematic diagram of ion transport in multicom-ponent concentrated solution.

T. Sugiyama, W. Ritthichauy and Y. Tsuji / Journal of Advanced Concrete Technology Vol. 1, No. 2, 127-138, 2003 129

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 in-curred by ion j (Xj) is the gradient of the electrochemical potential given by Eq. (2).

xFz

xxX j

chem,jjj ∂

φ∂+

∂µ∂

=∂µ∂

= (2)

At this point a linear relation, which relates the flux of ion i to the force incurred by ion j, is assumed and ex-pressed in Eq. (3) (Felmy and Weare 1991).

)x

Fzx

(ｌXｌJ jchem,j

ｎ

ｊ＝１ijj

ｎ

ｊ＝１iji

ｓｓ

∂φ∂

−∂

µ∂−=−= ∑∑ (3)

where Ji = flux of ion i (mol/m2·s), and lij = the Onsager phenomenological transport coefficient (hereafter On-sager coefficient).

The significance of this coefficient (lij) on transport in a multicomponent concentrated solution will be dis-cussed later.

The electrical potential gradient (∂φ/∂x) can be eliminated from Eq. (3) by the electro-neutrality con-straint in the solution (∑

=

=sn

1iii 0Jz ).

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).

∑∑

∑∑

= =

= = ∂µ∂

−=∂φ∂

s s

s s

n

1k

n

1lkllk

n

1k

n

1l

lklk

lzzF

xlz

x (4)

By substituting Eq. (4) into the flux equation of Eq. (3), the flux equation of ion i becomes the following equa-tion.

∑∑∑

∑∑=

= =

= =

∂µ∂

+∂

µ∂−=

s

s s

s s

n

1jn

1k

n

1lkllk

n

1k

n

1l

lklk

jj

iji

lzz

xlz

zx

lJ (5)

At this stage of the calculation, determining the On-sager coefficient (lij), which is the function of ion con-centrations in the solution, particularly in relatively di-luted 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):

RTCD

l i0i

ii = (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 poten-tial is converted to the gradient of concentration by the following equation:

xC

Cxj

j

jj

∂

∂×

∂

µ∂=

∂

µ∂ (7)

The definition of chemical potential (µj) can be ex-tended to the following expression:

jj0jj lnRTClnRT γ++µ=µ (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:

∂

γ∂+=

∂

µ∂

jj

j

jj

j

ClnCln

C1RT

C (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):

xC

DJ jn

1jiji

s

∂

∂−= ∑

=

(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


term in Eq. (10), the expression of mutual diffusion co-efficient can be derived as shown in Eq. (11):

∂

γ∂+−

∂γ∂

+δ=

∑=

)Cln

ln1(Dz

CDz

CDz)

Clnln

1(DDj

j0jjn

1kk

0k

2k

i0ii

i

i0iijij s

(11)

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):

2i

2i

ii

i

)I286.31(I2Z509.0

C302.2Cln

lnα+

×××−=

∂γ∂ (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 attrac-tion between ions, while the negative values denote re-pulsion 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 cal-culated 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 conti-nuity, the generalized form of Fick’s Second Law can be written as the following equation.

∑= ∂

∂=

∂∂ sn

1i2

j2

I,iji

xC

Dt

C (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 dif-

fusion coefficient is defined by accounting for the char-acteristic of the pore structure of the media. In this re-search, the intrinsic mutual diffusion coefficient is de-fined as the following equation.

xtijI,ij KDD = (14)

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+ 0.02* 0.60 7.92×10-10 Na+ 0.20§ 0.40 1.33×10-9 K+ 0.30§ 0.30 1.96×10-9

SO42- 0.03§ 0.40 1.07×10-9

Cl- 0.00§ 0.30 2.03×10-9 OH- 0.48£ 0.35 5.26×10-9

* Given number for initial Ca2+ in pore solution § Referred from Suzuki et al. (1993) £ Based on electro-neutrality constraint

Table 2 Example of calculated matrix of mutual diffusion coefficients at initial concentration ([D]i,j x 10-9 m2/s).

i j Ca2+ Na+ K+ SO42- Cl- OH-

Ca2+ 0.778 -0.012 -0.017 0.019 0.018 0.047 Na+ -0.118 1.231 -0.146 0.159 0.151 0.392 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

[D]i,j =

OH- 1.120 0.941 1.386 -1.513 -1.435 1.541


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

xt2

xtxt ετ

ε= (15)

The formula for the relation between tortuosity and porosity is shown in the following equation (Atkinson and Nickerson 1984):

i

f

DDεδ

=τ (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 addi-tion, 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 de-spite 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 dissolu-tion 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-

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 decalcifi-cation of C-S-H are followed by the following chemical equilibrium equations (Saito et al. 2000):

Ca(OH)2 Ca2+ + 2OH- (17)

xCaO·SiO2·zH2O

(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.

∑ ∂∂

−∂

∂=

∂∂

j

i2

j2

iji

tS

xC

Dt

C (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 con-trolled 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 ex-pression for the change in porosity is shown in Eq. (20) (Buil et al. 1992):

)SCSC(dM

xtiniCH

CHcinixt −⋅⋅ρ+ε=ε (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 dissolu-tion 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

0.0015 0.020

Ca2+ from C-S-H

Cs

Cl

Con

cent

ratio

n of

Ca2

+in

sol

id p

hase

Concentration of Ca2+ in pore solution (mol/l-solution)

Ca2+ from Ca(OH)2

0.0015 0.020

Ca2+ from C-S-H

Cs

Cl

Con

cent

ratio

n of

Ca2

+in

sol

id p

hase

Concentration of Ca2+ in pore solution (mol/l-solution)

Ca2+ from Ca(OH)2

Fig. 3 Relation between Ca2+ in solid phase (Cs) and in pore solution (Cl) [Based on Buil et al. (1992)].


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 CaCl2 s + 2OH- aq (21)

The C3A that remains in unhydrated cement particles will chemically react, producing calcium chloroalumi-nate or Friedel’s Salt (3CaO·Al2O3·CaCl2·10H2O), as shown in the following simplified chemical reaction equation (Neville 1999):

CaCl2 + C3A 3CaO·Al2O3·CaCl2·10H2O (22)

In the calculation of a concentration profile for chlo-ride 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 ce-ment-based material may be immobilized by ion ex-change 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):

β

−

−α

⋅⋅⋅= ffa

gelT1

T1

RE

]OH[]OH[1

b C1000

fWeeC 0

b

iniOH

(24)

where αOH = constant for hydroxide-dependent, [OH] = concentration of OH- (mol/l), [OH]ini = initial concen-tration 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

addition, it also produces 2 moles of OH-. However, it is understood that the behavior of the

dissolution and decalcification of cement hydrates be-comes more complex in the presence of chloride ions. This may not be simply expressed by Eq. (21) but re-quires careful considerations though little information on this matter has been reported. Then, a relative compari-son 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 disso-lution of Ca(OH)2 is different from the rate of the decal-cification 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 cor-responds 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.

R1

R2

R3

R4

Cum

ulat

ive

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hed

amou

nt

Exposure period

R1 Dissolution rate of Ca(OH)2 in distilled waterR2 Dissolution rate of C-S-H in distilled waterR3 Dissolution rate of Ca(OH)2 in 0.5 M NaClR4 Dissolution rate of C-S-H in 0.5 M NaCl

R1

R2

R3

R4

Cum

ulat

ive

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hed

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nt

Exposure period



Fig. 4 Model accounted for dissolution rate of Ca(OH)2 and C-S-H in different leachant.


1997; Saito et al. 2000). This value was evaluated from the inverse analysis that showed that 5% of the dissolu-tion 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 expo-sure test so that the total length of each specimen was 50 mm. To ensure unidirectional direction of chloride ions

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 speci-men with a water to cement ratio of 0.65 is clearly con-

0

200

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600

800

1000

1200

0 20 40 60 80 100Exposure period (days)

Cum

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nt o

f Ca2+

(mg)

In distilled waterIn 0.5 mol/l NaCl

0

200

400

600

800

1000

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0 20 40 60 80 100Exposure period (days)

Cum

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nt o

f Ca2+

(mg)

In distilled waterIn 0.5 mol/l NaClIn distilled waterIn distilled waterIn 0.5 mol/l NaClIn 0.5 mol/l NaCl

Fig. 5 Experimental results for determining dissolution rate of Ca(OH)2 from leaching test of cement paste.

Table 3 Chemical composition of ordinary portland cement.

Chemical compound

Insoluble residue MgO SO3 SiO2 Al2O3 Fe2O3 CaO Cl-

Weight (%) 0.1 1.4 2.0 21.2 5.1 2.8 64.5 0.005

Table 5 Mix proportion of mortar specimens.

Unit weight of material (kg/m3)Specimen W/C

W C S Flow (mm)

Compressive strength (N/mm2)

45 262 583 1454 154 53.5 Mortar

65 339 523 1304 218 34.5

Table 4 Physical properties of fine aggregate.

Saturated surface-dry density (g/cm3) 2.63

Oven-dry density (g/cm3) 2.57

Water absorption (%) 2.35

Fineness modulus 2.77

Percentage of solid volume (%) 64.6


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 rec-ognized for the first slice of 0 to 10 mm from the expo-sure 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

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 Su-zuki 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.

3.3 Verification of calculation results with ex-perimental 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 experi-mental 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 experi-ment 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 sur-face exhibit good agreement with the experimental re-sults for both specimens with different water to cement ratios. If it is assumed that the amount of Ca(OH)2 be-comes 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 sur-face for the mortar specimen with the water to cement

0 5 10 15 20 25 30 35 40 45 50 552θ

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 552θ

Ca(OH)2

Friedel’s salt

0-10 mm

10-20 mm

40-50 mm

Fig. 6 Experimental results from XRD analysis.

-80

-60

-40

-20

0

20

0 100 200 300 400 500 600 700Temperature (℃)

0-10 mm

10-20 mm

40-50 mm

Ca(OH)2

Ca(OH)2

Friedel’s salt

DTA

(µV

)

-80

-60

-40

-20

0

20

0 100 200 300 400 500 600 700Temperature (℃)

0-10 mm

10-20 mm

40-50 mm

Ca(OH)2

Ca(OH)2

Friedel’s salt

DTA

(µV

)

Fig. 7 Experimental results from TG/DTA analysis.

Table 6 Input values for calculation.

Constant for chloride binding W/C Ca(OH)2 (mol/l-mortar)

C-S-H (mol/l-mortar)

Initial porosity Tortuosity fa

* β* Wgel (kggel/m3-mortar) § 45 2.50 3.92 0.15 5.0 552 65 1.66 2.60 0.20 3.0

3.57 0.38 516

*From Tang and Nilsson (1996) §Based on mix proportion of 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 concentra-tion (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 diffu-sion 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.

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 ob-tained 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 speci-men 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 multicompo-nent 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.

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(a) W/C = 0.45

Mortar specimen (50 mm diameter) exposed to 0.5 mol/l NaCl solution

CalculationExperiment

Ca(OH)2

C-S-H

Con

cent

ratio

n of

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alci

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Distance from exposure surface (mm)

(b) W/C = 0.65

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Ca(OH)2

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tar)

0 10 20 30 40 500 10 20 30 40 50Distance from exposure surface (mm)

(a) W/C = 0.45

Mortar specimen (50 mm diameter) exposed to 0.5 mol/l NaCl solutionMortar specimen (50 mm diameter) exposed to 0.5 mol/l NaCl solution

CalculationExperimentCalculationExperiment

Ca(OH)2

C-S-H

Con

cent

ratio

n of

sol

id c

alci

um (m

ol/l-

mor

tar)


(b) W/C = 0.65

0 10 20 30 40 500 10 20 30 40 50


Ca(OH)2

C-S-HCalculationExperiment

Fig.8 Calculated and experimental results of solid calcium profile after 3 years of exposure.

0 10 20 30 40 50Distance from exposure surface (mm)

0

4

8

12

16

20

Cal-1 Cal-2 Cal-3 Exp

Tota

l chl

orid

e co

nten

t (kg

/m3 -

mor

tar)

0 10 20 30 40 500 10 20 30 40 50Distance from exposure surface (mm)

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l chl

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nten

t (kg

/m3 -

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tar)

0

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Tota

l chl

orid

e co

nten

t (kg

/m3 -

mor

tar)

Fig. 9 Calculated and experimental results of total chloridecontent 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.

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 exam-ple, 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,

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 cu-mulative 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 cumu-lative leached amount of Ca2+ was higher than the cu-mulative leached amount of K+. Higher amounts of Ca2+ leached out over time have been recorded in past ex-periments 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).

5. Conclusions

A new calculation model for ions transport in a ce-ment-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 expo-sure tests.

(2) A pore solution in a cement-based material containing several types of ions at high concentrations

0

0.1

0.2

0.3

0.4

0.5

0.6

1 year of exposure


3 year of exposure

Free

chl

orid

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tratio

n (m

ol/l-

solu

tion)

0 10 20 30 40 500

0.1

0.2

0.3

0.4

0.5

0.6

1 year of exposure


3 year of exposure

Free

chl

orid

e co

ncen

tratio

n (m

ol/l-

solu

tion)

0 10 20 30 40 500 10 20 30 40 50

Fig. 10 Calculation of free chloride concentration profiles for mortar specimen with water to cement ratio 0.65.

0

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800

1000

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1400

0 200 400 600 800 1000 1200Exposure period (days)

Cum

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(a) W/C = 0.45

Ca2+

K+


0

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1400


Cum

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Ca2+

K+

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1400


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Ca2+

K+


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Cum

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Ca2+

K+Ca2+

K+


0

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1400


Cum

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Ca2+

K+

0

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1400


Cum

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leac

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amou

nt (m

g)

(b) W/C = 0.65


Ca2+

K+Ca2+

K+

Fig. 11 Calculated results for cumulative leached amount of Ca2+ and K+ (3 years exposure).


taining several types of ions at high concentrations must be treated as a multicomponent concentrated solution. The application of a mutual diffusion coefficient is pro-posed 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 par-tially reduced by the binding of chloride ions.

(4) More refined determination of the rate of dissolu-tion 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 mate-rials. 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. References Abate, C. and Scheetz, B. (1995). “Aqueous phase

equilibria in the system CaO-AL2O3-CaCl2-H2O : The significance and stability of Friedel’s salt.” Journal of American Ceramic Society, 78(4), 939-944.

Atkinson, A. and Nickerson, A.K. (1984). “The diffusion of Ions through water-saturated cement.” Journal of Materials Science, 19, 3068-3078.

Buil, M., Revertegat, E. and Oliver, J. (1992). “A model of the attack of pure water or undersaturated lime solutions on cement.” In: Gilliam T.M. and Wiles C.C. Eds. Stabilization and Solidification of Hazardous, Radioactive, and Mixed Wastes, 2nd Volume, STP, 1123. Philadelphia: ASTM, 227-241.

Carde, C., Escadeillas, G. and Francois, R. (1997). “Use of ammonium nitrate solution to simulate and accelerate the leaching of cement pastes due to deionized water.” Magazine of Concrete Research, 49(181), 295-301.

Carde, C. and Francois, R. (1999). “Modeling the loss of strength and porosity iIncrease due to the leaching of cement pastes.” Cement and Concrete Composites, 21, 181-188.

Crank, J. (1995). “The Mathematics of Diffusion.” 2nd ed. New York: Oxford University Press.

Cussler, E.L. (1976). “Multicomponent Diffusion.” Amsterdam: Elsevier Scientific Publishing Company.

Delegrave, A., Gérard, B. and Marchand, J. (1997). “Modeling the calcium leaching mechanism in hydrated cement pastes.” In: Scrivener, K.L. and Young J.F. Eds. Mechanisms of Chemical Degradation

of Cement-Based Systems. Boston: E&FN SPON, 38-49.

Felmy, A.R. and Weare, J.H. (1991). “Calculation of multicomponent ionic diffusion from zero to high concentration: I. The system Na-K-Ca-Mg-Cl-SO4-H2O at 25°C.” Geochimica et Cosmochimica Acta, 55, 113-131.

Furusawa, Y. (1997). “Recent developments in studies on calcium leaching and concrete degradation.” Concrete Journal, 35(12), 66-69 (in Japanese).

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Neville, A.M. (1999). “Properties of Concrete.” 4th ed. England: John Wiled & Sons, Inc.

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Ono, M., Nagashima, M., Otsuka, K. and Ito, T. (1978). “Mechanism of the chemical attack of seawater in cement hydration.” Cement Gijyutu Nenpo, 32, 100-103 (in Japanese).

Otsuki, N., Miyazato, S., Minagawa, H. and Hirayama, S. (1999). “Theoretical simulation of ion migration in concrete.” Concrete Research and Technology, 10(2), 43-49 (in Japanese).

Ritthichauy, W., Sugiyama, T. and Tsuji, Y. (2002). “Calculation of diffusion coefficient of ion in multicomponent solution for ion movement in concrete.” Proceedings of Japan Concrete Institute, Tsukuba 19-21 June 2002. Tokyo: Japan Concrete Institute, 669-674.

Saito, H., Nakane, S. and Fujiwara, A. (1993). “Effects of electrical potential gradients on dissolution and deterioration of cement hydrate by electrical acceleration test method.” Concrete Research and Technology, 4(2), 69-78 (in Japanese).

Saito, H., Nakane, S., Tsuji, Y. and Fujiwara, A. (1997). “Application of accelerated electrical test method to deterioration of cement hydration products by chemical attack.” Journal of Materials, Concrete Structures and Pavements, 564(V-35), 189-197 (in Japanese).

Saito, H., Tsuji, Y. and Kataoka, H. (2000). “A model for predicting degradation due to dissolution of cement hydrate.” Transaction of the Japan Concrete Institute, 22, 119-130.

Samson, E., Marchand, J. and Beaudoin, J.J. (2000). “Modeling the influence of chemical reaction on the mechanisms of ionic transport in porous materials.” Cement and Concrete Research, 30, 1895-1902.

Sergi, G., Yu, S.W. and Page, C.L. (1992). “Diffusion of chloride and hydroxyl ions in cementitious materials


exposed to a saline environment.” Magazine of Concrete Research, 44(158), 63-69.

Sugiyama, T., Bremner, T.W. and Holm, T.A. (1993). “Effect of stress on chloride permeability in concrete.” Proceedings on Durability of Building Materials and Components, 6, 239-248.

Sugiyama, T., Tsuji, Y. and Bremner, T.W. (2001). “Relationship between coulomb and migration coefficient of chloride ions for concrete in a steady-state chloride migration test.” Magazine of Concrete Research, 53(1), 13-24.

Suzuki, K., Nishikawa, N., Yamaide, Y. and Taniguchi, I. (1990). “Study on an analytical method for cement hydration system to evaluate durability of concrete.”

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Tang, L. and Nilsson, L.O. (1996). “Service life prediction for concrete structures under seawater by a numerical approach.” Durability of Building Materials and Components 7, 1, 97-106.

Tang, L. (1999). “Concentration dependence of diffusion and migration of chloride ions - Part 2: Experimental evaluations.” Cement and Concrete Research, 29, 1469-1474.

simultaneous transport of chloride and calcium … transport of chloride and calcium ions in...

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