Van Quan Tran

Anthony Soive

Stéphanie Bonnet

Abdelhafid Khelidj

A numerical model including thermodynamic equilibrium, kinetic control and surface complexation in order to explain cation type effect on chloride binding capability of concrete

Keywords: Concrete, Chloride binding, Thermodynamic equilibrium, Kinetic control, Surface complexation, Cation type

The impact of cation type, sulphate and pH on chloride binding is studied using a numerical model combining thermodynamic equilibrium, kinetics and surface complexation. First, the model is validated by comparing numerical and experimental results obtained on a CEM II concrete material exposed to N aCl, KCl, M gCl 2 and CaCl 2 solutions. Then, the numerical results are discussed to improve our understanding of the differences in chloride binding capability generally observed in the literature. A strong coupling between cation, pH and sulfate affecting chloride binding is highlighted. After six months of exposure, chloride binding due to Kuzel's salt formation has little effect on chloride binding capability whatever the chloride salt solution.

The results also confirm the existence of a relationship between pH and chloride binding capability previously observed experimentally in the literature.

When some sulfate ions are present in the chloride solution, they reduce

Introduction

Chloride diffusion is one of the major cause of reinforcement corrosion in concrete exposed to seawater or de-icing salts. Many authors consider that corrosion initiation stage of steel reinforcement in concrete depends on the chloride threshold value which can be expressed in a number of different ways, such as: total chloride content in relation to the weight of cement (or concrete) [START_REF]Standard test method for acid-soluble chloride in mortar and concrete[END_REF], free chloride contents [START_REF] Alonso | Chloride threshold values to depassivate reinforcing bars embedded in a standardized {OPC} mortar[END_REF], [Cl -]/[OH -] (3; 4). To predict the chloride concentration threshold value in cementitious materials, the performance-based approach Fib model code [START_REF]fib, Materials[END_REF] requires the consideration of the empirical chloride binding isotherm. In this model, based on the analytical solution of the Fick's second law, the chloride binding isotherm is therefore one of the most significant input data of the Fib model code.

A survey of the literature reveals that a considerable amount of effort has been devoted in the last decade to the study of chloride binding in cementitious materials. Page et al. [START_REF] Page | Investigations of reinforcement corrosion. 1. the pore electrolyte phase in chloride-contaminated concrete[END_REF], for instance, show that the OH - concentration (or pH) arising from the external environment significantly affects chloride binding. Tritthart [START_REF] Tritthart | Chloride binding in cement ii. the influence of the hydroxide concentration in the pore solution of hardened cement paste on chloride binding[END_REF] and Sandberg et al. [START_REF]Symposium proceedings of Nordic miniseminar on chloride penetration into concrete structures[END_REF] both experimentally demonstrate that lower pH values give higher chloride ions binding, which may be accounted for by a competition among OH -and Cl -ions for the sorption sites of hydrated cement [START_REF] Tritthart | Chloride binding in cement ii. the influence of the hydroxide concentration in the pore solution of hardened cement paste on chloride binding[END_REF]. Moreover, Roberts [START_REF] Roberts | Effect of calcium chloride on the durability of pretensioned wire in prestressed concrete[END_REF] and Zhu et al. [START_REF] Zhu | Effect of chloride salt type on chloride binding behavior of concrete[END_REF] consider that an increase in pore solution pH enhances the solubility of chloroaluminate salt (Friedel's salt, Kuzel's salt) consequently reducing chloride binding due to chloroaluminate salt formation. Furthermore, Arya et al. [START_REF] Arya | Factors influencing chloride-binding in concrete[END_REF], Page et al. [START_REF] Page | Investigations of reinforcement corrosion. 1. the pore electrolyte phase in chloride-contaminated concrete[END_REF], Delagrave et al. [START_REF] Delagrave | Chloride binding capacity of various hydrated cement paste systems[END_REF], Zhu et al. [START_REF] Zhu | Effect of chloride salt type on chloride binding behavior of concrete[END_REF], DeWeerdt et al. [START_REF] Weerdt | The impact of sulphate and magnesium on chloride binding in portland cement paste[END_REF] and Song et al. [START_REF] Song | Influence of cation type on diffusion behavior of chloride ions in concrete[END_REF] experimentally observe that cations associated to chloride salts affect chloride binding capability.

These authors note that the maximum chloride binding capability is reached when the cementitious materials are exposed to a CaCl 2 solution. In a more detailed manner, Zhu et al. [START_REF] Zhu | Effect of chloride salt type on chloride binding behavior of concrete[END_REF] and Song et al. [START_REF] Song | Influence of cation type on diffusion behavior of chloride ions in concrete[END_REF] experimentally describe that the binding capability of chloride decreases in the order Ca 2+ > M g 2+ > N a + ≈ K + when the cementitious samples are exposed to CaCl 2 , M gCl 2 , N aCl and KCl solutions, respectively. Wowra et al. [START_REF] Wowra | Sorption of chlorides on hydrated cements and c3s pastes[END_REF] find that the Ca 2+ cations sorption onto C-S-H surfaces increases the positive charge and in turn the chloride binding in the double electrical layer. Moreover, according to Delagrave et al. [START_REF] Delagrave | Chloride binding capacity of various hydrated cement paste systems[END_REF], the nature of the associated cation significantly affects chloroaluminate solubility and accessibility of chloride ions to sorption sites.

On the basis of experimental results, Yuan et al. [START_REF] Yuan | Chloride binding of cement-based materials subjected to external chloride environment-a review[END_REF] suggest that, in the presence of N a + , cementitous materials have higher pH value than with Ca 2+ and M g 2+ . Zhu et al. [START_REF] Zhu | Effect of chloride salt type on chloride binding behavior of concrete[END_REF] demonstrate that N a + and K + may increase the pH value of pore solutions. These arguments imply that pore solution pH affects chloride binding capability. However, DeWeerdt et al. [START_REF] Weerdt | The impact of sulphate and magnesium on chloride binding in portland cement paste[END_REF] experimentally prove that the relationship between the decrease in pore solution pH and the increase in chloride binding for exposure solutions like M gCl 2 or CaCl 2 is not valid when the SO 2- A number of chloride transport models are found in the literature: some models based on Fick's second law or on the multispecies ionic transport equations ( 18), ( 19) and [START_REF] Nguyen | Study of electrical double layer effect on chloride transport in unsaturated concrete[END_REF], or physically and chemically coupled model [START_REF] Samson | Modeling the effect of temperature on ionic transport in cementitious materials[END_REF]. These models use global binding isotherms to determine the total chloride amounts as a function of the free chloride amounts. However, isotherms parameters must be calibrated on the basis of experimental data [START_REF] Baroghel-Bouny | Modelling of isothermal coupled moisture-ion transport in cementitious materials[END_REF]. are compared with some experimental data from the literature to validate the numerical model.

Reactive transport modeling and input data

In this section the reactive transport modeling is exposed on several aspects, such as reactive transport equations, thermodynamic and complexation formation constants and kinetics of dissolution/precipitation. However, the description of the model is intentionally reduced since it has been previously published and described in details for chloride transport in concrete [START_REF] Tran | Modelisation of chloride reactive transport in concrete including thermodynamic equilibrium, kinetic control and surface complexation[END_REF] and external sulphate attack [START_REF] Soive | External sulfate attack of cementitious materials: New insights gained through numerical modeling including dissolution/precipitation kinetics and surface complexation[END_REF].

Reactive transport equations

The coupling of chemistry and transport in porous media was used to describe the mineral phases evolution in time and space. Toughreact, which is based on integral finite differences method, has been developed for this purpose by solving chemically reactive nonisothermal flows of multiphase fuids in porous media [START_REF] Xu | TOUGHREACT User's Guide: A Simulation Program for Non-isothermal Multiphase Reactive Transport in Variably Saturated Geologic Media, version 2.0[END_REF]. A sequential iterative operator-splitting method is operated to solve the system.

In saturated condition without convection phenomena the main mechanism considered is diffusion which is coupled to chemistry according to the following equation:

∂φC j ∂t = D e ∇ (∇C j ) + q j (1)
where D e is the effective diffusion coefficient of species j (m 2 .s -1 ) which value is the same for all species, φ the porosity and C j the molar concentration of free species j in a pore solution (mol.m -3 of solution). q j is a source or sink term (mol.m -3 .s -1 ) that denotes the removing or releasing species j and that is evaluated by chemical calculations. In this study, q j combines sorption onto C-S-H surface (see paragraph 2.4), mineral dissolution/precipitation as explained in paragraphs 2.2 and 2.3 and aqueous complexation in solution.

Porosity can evolve with time by actualizing volume of each mineral species (25) that can precipitate or dissolve. Effective diffusion coefficient can also evolve, as follows:

D e n+1 = φ n+1 φ n D e n
where n labels the number of the time step.

Thermodynamic formation constants

The thermodynamic formation constants of species are taken from CEM-DATA07 and Nagra/PSI TDB thermodynamic databases [START_REF] Kulik | Gem-selektor geochemical modeling package: revised algorithm and gems3k numerical kernel for coupled simulation codes[END_REF]. The thermodynamic data are exposed in Table 1. C-S-H is supposed to be a mix of tobermorite (CaO/SiO 2 = 0.83) and jennite (CaO/SiO 2 = 1.67). The Helgeson-Kirham-Flowers (HKF) model ( 27) is used since it gives accurate activity coefficient with dominance of N aCl in the solution and when the true ionic strength of the solution is close to 1 [START_REF] Xu | TOUGHREACT User's Guide: A Simulation Program for Non-isothermal Multiphase Reactive Transport in Variably Saturated Geologic Media, version 2.0[END_REF], as in this study.

At equilibrium, the activity product, Q i , of the mineral species i must be equal to its equilibrium constant, K i . Q i writes as follows:

Q i = N j=1 (γ j C j ) ν j (2)
where γ, C, ν and N are the activity coefficient, the concentration, the stoichiometric coefficient and the number of the ionic species in the reaction, respectively.

Mineral dissolution and precipitation kinetics

Several studies have shown that a pure thermodynamic approach does not seem to be adapted for concrete exposed for several months (22; 23; 28; 29; 30). Moreover, for C-S-H the reactions can be very slow and even irreversible.

Table 1: Equilibrium constants of mineral dissolution/precipitation reactions at 25

• C Phase reaction log K T0 Jennite+2.33H + = 1.67Ca 2+ + HSiO - 3 + 2.76H 2 O -19.53 Tobermorite+0.66H + = 0.83Ca 2+ + HSiO - 3 + 1.16H 2 O -0.63 Portlandite+2H + = Ca 2+ + 2H 2 O -22.76 Monosulfoaluminate+12H + = 4Ca 2+ + 2Al 3+ + SO 2- 4 + 18H 2 O -72.44 Ettringite+12H + = 6Ca 2+ + 2Al 3+ + 3SO 2- 4 + 38H 2 O -56.67 Hydrotalcite+14H + = 4M g 2+ + 2Al 3+ + 17H 2 O -74.68 Kuzel's salts+12H + = 4Ca 2+ + 2Al 3+ + 0.5SO 2- 4 + Cl -+ 18H 2 O -73.24 Brucite+2H + = M g 2+ + 2H 2 O 17.11 Chrysotile+4H + = 3M g 2+ + 2HSiO - 3 + 3H 2 O -13.29 Sepiolite+2H + = 4M g 2+ + 6HSiO - 3 + 5H 2 O -29.01
In this study, the expression of the kinetic law given by Lasaga et al. is used (31):

r i = ±k i A ms,i 1 - Q i K i i = 1, .., N q (3)
where r indicates dissolution or precipitation (for positive and negative values, respectively), k is the rate constant (mol.m -2 .s -1 ). A ms is the specific reactive surface area (m 2 .g -1 ). More details can be found in Xu et al. and Steefel et al. (24;[START_REF] Steefel | Reactive transport codes for subsurface environmental simulation[END_REF].

Sepiolite Instantaneous

Surface complexation formation constants

In cementitious materials, physical and chemical reactions between aqueous species and specific surface sites of mineral species can occur. These reactions mostly take place onto C-S-H (37; 38; 39). When the cementitious materials are exposed to boundary solutions, anions and cations move through the material and reactions between the ions and the surface site of C-S-H (silanol ≡ SiOH) appears [START_REF] Elakneswaran | Ioncement hydrate interactions govern multi-ionic transport model for cementitious materials[END_REF]. A well-known model which is used in this study is the double diffuse layer model (see [START_REF] Dzombak | Surface complexation modelling : hydrous ferric oxide[END_REF] for a complete description).

Adsorption of X ions (Ca 2+ , N a + , K + , Cl -and SO 2- 4 in the present study) onto the C-S-H surface can be described by the following mass action law:

K eq = [≡ SiOHX] [≡ SiOH] {X} exp -F ψ 0 RT (4)
where K eq is the equilibrium constant. {X} is the activity of X ions. ψ 0 is the potential at the surface (V ). R is the molar constant (8.354

J.mol -1 .K -1 )
and T is the absolute temperature (K).

The sorption of Ca 2+ , N a + , K + , Cl -and SO 2- 4 ions on the C-S-H surface layer have been integrated in the database. They can be represented by sorption reactions (see Table 3). The equilibrium constants are taken from [START_REF] Elakneswaran | Ioncement hydrate interactions govern multi-ionic transport model for cementitious materials[END_REF] for N a + , K + , Cl -and Ca 2+ . That of SO 2- 4 is supposed to be equal to 8.5. The equilibrium constants for N a + and K + are supposed to depend on C/S ratio of C-S-H whereas those for Ca 2+ and Cl -are not. Furthermore, the value of the specific surface site of C-S-H is supposed to be equal to 500 m 2 .g -1 as suggested by Viallis et al. after calibration (37).

Concrete properties

The studied CEMII concrete is taken from the literature [START_REF] Song | Influence of cation type on diffusion behavior of chloride ions in concrete[END_REF]. The cement composition and the concrete mix-design are given in Tables 4 and5, respectively. After a 90-day curing period in saturated limewater at 20±1 • C,

or The concrete is supposed to be completely hydrated. Its mineral composition is calculated using the the GEMS-software and CEMDATA07 and Nagra/PSI TDB thermodynamic databases [START_REF] Kulik | Gem-selektor geochemical modeling package: revised algorithm and gems3k numerical kernel for coupled simulation codes[END_REF]. The mineralogical composition is given in Table 6. Assuming that alkalis N a and K are fully dissolved as suggested by

≡ SiOH + OH -↔≡ SiO -+ H 2 O ≡ SiOH + Ca 2+ ↔≡ SiOCa + + H + -9.4 (40)
≡ SiOH + Cl -↔≡ SiOHCl - -0.35 (40)
≡ SiOH + Ca 2+ + Cl -↔≡ SiOCaCl + H + -9.8 a,b ≡ SiOH + Ca 2+ + SO4
Trotignon et al. [START_REF] Trotignon | Predicting the long term durability of concrete engineered barriers in a geological repository for radioactive waste[END_REF], the initial chemical composition of the pore solution is calculated using the Toughreact software (24) (Table 7). Bound chloride (g/100g of concrete)

[cl ] (g/100g of concrete)

[cl ] (g/100g of concrete)

[cl ] (g/100g of concrete)

[cl ] (g/100g of concrete)

Discussion

As discussed above, the model proposed in this paper can compute chloride absorption on C-S-H, chloride binding due to Kuzel's salt formation and pH evolution. The following section provides some interpretive elements for a better understanding of the evolution of chloride binding capability as a function of boundary solution type. First, the chloride bound amount due to Kuzel's salts precipitation and to surface complexation on C-S-H is highlighted. Then, the influence of cations associated with chloride from surface complexation on C-S-H and its consequence in terms of pH is discussed. finally, additionally focus is made on magnesium and sulfate ions and their effect on chloride binding capability.

Kuzel's salt formation and surface complexation on C-S-H

Chloride ions can be adsorbed and absorbed on C-S-H. The solution. This latter case is discussed in Section 5.3.

Role of cation associated with chloride and pH

According to the chemical equations presented in Table 3, the reactions of the chloride ions bound on C-S-H to form ≡ SiOHCaCl or ≡ SiOHCl-are related directly or indirectly to pH. In the first case, the fixation of Cl -and Ca 2+ releases H + . In the second case, Cl -, Ca 2+ and OH -are competing in order to react with ≡ SiOH. The reactions with Ca 2+ and OH -release

H + .
Figures 3a,b,c,d show N a + , K + , Ca 2+ concentration and pH profiles as a function of the free chloride concentration after a 6-month exposure, respectively. As expected, N a + , K + and Ca 2+ have the highest concentrations within the concrete pore solutions exposed to N aCl, KCl and CaCl 2 , respectively. Regarding the other ions that are not present in the boundary solutions, the profiles are equivalent whatever the exposed solution, except Ca 2+ in the concrete specimens exposed to the M gCl 2 solution (cf. Figure 3c). The role of M gCl 2 is discussed in Section 5.3.

These results reveal that the boundary solution types causing a large amount of Ca 2+ in the concrete pore solutions (CaCl 2 and M gCl 2 ) also lead to a greater amount of bound chloride on C-S-H through the formation of ≡ SiOCaCl (cf. Figures 3c and2). According to Le Chatelier's principle, a higher Ca 2+ amount increases the number of ≡ SiOCa + and, consequently, leads to an increased positive and to a higher chloride ion amount bound on this surface charge. This is consistent with Wowra et al.'s proposal [START_REF] Wowra | Sorption of chlorides on hydrated cements and c3s pastes[END_REF].

Figure 3d shows that the pore solution pH of the concrete specimens exposed to CaCl 2 and M gCl 2 solutions is lower than in the N aCl and KCl solutions. This observation implies that the amount of chloride ion reating with C-S-H to form ≡ SiOHCl -is larger for CaCl 2 and M gCl 2 solutions than for N aCl and KCl solutions (cf. Figure 2). This proves that the pHchloride binding capability relationship experimentally observed in (7; 8) is verified by the model. Indeed, the higher the OH -concentration (higher pH) in pore solution is, the larger the number of ≡ SiOH transformed into ≡ SiO -according to Le Chatelier's principle. Then, the amount of ≡ SiOH decreases and chloride binding capability on C-S-H decreases. This confirms OH -and Cl -competing for sorption on C-S-H.

In conclusion, the pore solution pH value directly affects chloride binding capability. It depends on the solid/pore solution equilibrium like portlandite dissolution/precipitation and N a + and K + concentrations. In all the cases studied, the Portlandite dissolution is numerically observed (cf. Figure 4). This is less pronounced for concrete exposed to the CaCl 2 solution because of higher Ca 2+ concentrations. Nevertheless, the pH value is smaller. It may seem paradoxical considering the fact that the stronger the Portlandite dissolution, the higher the pH, but, because N a + and K + are stronger bases in the acid-base theory than Ca 2+ and M g 2+ , the pore solution pH of the concrete exposed to N aCl and KCl solutions is higher than with the CaCl 2 and M gCl 2 solutions.

Role of magnesium

Figure 1 shows that the chloride binding isotherm with the M gCl 2 solution behaves differently from the other solutions. With the M gCl 2 solution, a peak correspond with chloride binding capability appears for a chloride concentration slightly lower than the maximal value, i.e. within the concrete. In the meantime, the chloride binding capability is maximum on the concrete surface exposed to N aCl, KCl and CaCl 2 solutions.

The previous section demonstrates the relationship between chloride binding capability and Ca 2+ concentration and pH value, whereas Figure 2c shows that the Ca 2+ concentration in concrete decreases gradually from the exposed surface towards the interior after a 6-month exposure. Moreover, the pore solution pH on the surface with M gCl 2 exposure is the lowest of the four solutions (cf. Figure 2d). An increased M g 2+ concentration in the exposed solution indeed disturbs portlandite equilibrium and leads to the precipitation of brucite (cf. Figure 5). C-S-H (jennite and tobermorite) is also dissolved and release HSiO - 3 , which reacts with M g 2+ to precipitate chrysotile.

The numerical observation of brucite and M-S-H (chrysotile) formation is experimentally verified (47; 48; 49). C-S-H and portlandite dissolution also release a large amount of Ca 2+ into the pore solutions. The complete dissolution of Portlandite strongly affects the pH buffering system. Consequently, with such low pH close to the exposed surface, chloride binding capability increases. However, the C-S-H dissolution causes a decrease in the number of surface charges ≡ SiOHCl -, which reduces the ions binding capability of C-S-H on the exposed surfaces.

Furthermore, M g 2+ , which progresses within the concrete reacts with Al +3 coming from the monosulfoaluminate dissolution and precipitates hydrotalcite. As a result, the Al +3 concentration is no longer sufficient to precipitate Kuzel's salt despite the high chloride concentration or ettringite found just below the exposed surface. After a period of increase in the hydrotalcite amount, a small amount of ettringite and Kuzel's salt appears (cf. For concrete specimens exposed to a M gCl 2 solution, Ca 2+ leaching reduces the pH value and, in turn, chloride binding on ≡ SiOH increases. This can be considered the most significant impact of the M g 2+ cation on chloride binding capability. This can be explained by the fact that the higher the M gSO 4 amount, the lower the pH value (cf. Figure 7a). A comparison between the results obtained with concrete specimens exposed to M gCl 2 solutions without M gSO 4 and with 0.276 M of M gSO 4 shows this clearly. Another explanation is the number of chloride ions that can be adsorbed on C-S-H, which decreases as the amount of M gSO 4 increases, under all surface charge conditions: ≡ SiOHCl -or ≡ SiOCaCl (cf. Figures 7b andc). The same tendency is also observed as regards Kuzel's salt formation (cf. Figure 7d). However, Figure 8 shows that a large amount of sulfate is absorbed on the surface charge ≡ SiOH. Thus, a more negative surface charge ≡ SiOCaSO -

Role of sulfate

Conclusion

In this paper a physically and chemically based multiionic model considering thermodynamical reaction kinetics and surface complexation is proposed to investigate chloride binding capability of CEM II concrete exposed to different boundary chloride solutions. Some chloride binding isotherms from the literature are compared with the numerical results for concrete exposed to N aCl, KCl, CaCl 2 , M gCl 2 . The presence of sulfate ions in the M gCl 2 boundary solution with two different concentrations is also studied.

The results underline the influence of the cation type associated to the chloride boundary solution on the chloride binding capability. As observed in the literature, the chloride binding capability decreases in the order: Ca 2+ > M g 2+ > N a + ≈ K + . In addition, the numerical results show that the highest quantity of chloride that reacts is obtained by the sorption on ≡ SiOH, followed by the sorption on ≡ SiOCa + . The chloride ions quantity that reacts to form Kuzel's salts is the smallest one. This latter numerical observation is true whatever the chloride salt solution and the type of cation associated with chloride. As regards the chloride salt solution without sulfate, the competition between H + (or indirectly pH) and Cl -onto ≡ SiOH presents the most significant effect on chloride binding capability. Indeed, the higher the pH is, the lower the chloride quantity is adsorbed on C-S-H. These conclusions also confirm the relationship between pH and chloride binding capability observed experimentally in the literature.

This study also shows that the leaching of N a + and K + for the concrete exposed to a CaCl 2 solution and the leaching of N a + , K + and Ca 2+ for the concrete exposed to a M gCl 2 solution cause a local pH decrease and, thus, an increase in chloride binding capability. Regarding the M gCl 2 solution, the formation of hydrotalcite is enhanced and limits Kuzel's salt precipitation. The higher the Ca 2+ concentration is, the higher the chloride amount absorbed on ≡ SiOCa + .

Finally, the model is able to catch that when some sulfate ions are present in the chloride solution, they reduce chloride binding capability because of the sulfate absorption process on C-S-H. A more negatively charged surface ≡ SiOCaSO - 4 and competition between Cl -and SO 2- 4 replace ≡ SiOH in the presence of Ca 2+ in the solution. This reaction releases H + and decreases the pH.

These first results have to be confirmed with more experimental data on several concretes and for other ionic species than chlorides although data is missing in the literature. In addition, on the basis of the above study, it could be interesting to explore these findings and study chloride binding capability of concrete exposed to seawater, in which different cations and sulfate ions are present simultaneously.

4 3ions

 4 concentration is significant. Byfors[START_REF]Chloride binding in cement paste[END_REF] and Wowra et al.[START_REF] Wowra | Sorption of chlorides on hydrated cements and c3s pastes[END_REF] have previously shown that an increase in sulfate ion concentration causes a sharp decrease in chloride binding capability. DeWeerdt et al.[START_REF] Weerdt | The impact of sulphate and magnesium on chloride binding in portland cement paste[END_REF] suggest that one reason might be the chloride sorption process onto C-S-H and the chloride binding due to the chloroaluminate salt formation capacity. C-S-H indeed, when exposed to M gSO4 and M gCl 2 , fixes more SO 2- 4 ions than Cl -ions, leading to the decreased chloride sorption onto C-S-H. The SO 2- 4 ions react with the AFm phase to precipitate ettringite which is more stable than the chloroaluminate salts (Friedel's salt, Kuzel's salt) and as a result chloride binding due to chloroaluminate salt formation decreases.The experimental studies mentioned above emphasize the coupling effect of three different factors affecting chloride binding capability: cation of chloride salt, solution pH and sulfate concentration. It is, however, interesting to verify and confirm the arguments proposed through a numerical investigation. The numerical study presented in this paper is carried out through the development of a numerical model, its validation through the comparison with the experimental results found in the literature and the analysis of the chloride binding mechanism in a final section.

  Numerical models must describe simultaneously chloride sorption and binding due to the chloroaluminate salt formation. Chloride sorption can be described using a surface complexation model considering the surface charge and the double electrical layer. Chloride binding due to the chloroaluminate salt formation is described by chloroaluminate precipitation/dissolution using thermodynamic equilibrium and kinetic control. The aim of this paper is to investigate the factors affecting chloride binding in concretes exposed to chloride and other ions. A reactive transport model including thermodynamic equilibrium, kinetic control and surface complexation modelling that has been previously described for chloride ingress and external sulphate attack (22; 23) is used. First, the governing equations used to simulate the reactive transport model in saturated cementitious materials are presented: transport equations, surface complexation describing interaction on mineral surfaces, principle of thermodynamic equilibrium and kinetic laws. Then, the model input data of the model are discussed: parameters of solid species under kinetic constraints, surface complexation parameters, original mineralogical composition of hydrated cement, exposure conditions and numerical procedure, sorption reaction in thermodynamic database. Finally, the modelled results

4 . 1 . 1 M gCl 2

 4112 Figures1a,b,c and ddisplay the chloride binding isotherms of concrete after a 6-month exposure to 0.5 mol.L -1 of N aCl, 0.25 mol.L -1 of CaCl 2 , 0.5 mol.L -1 of KCl and 0.25 mol.L -1 of M gCl 2 solutions, respectively. The numerical chloride binding isotherms obtained are compared with the experimental data previously found in the literature[START_REF] Song | Influence of cation type on diffusion behavior of chloride ions in concrete[END_REF].The equilibrium computation gives a pH of 8.1 for all the chloride solutions. Further details on the pH calculation are given in[START_REF] Tran | The contribution toward understanding of mechanisms of depassivation of steel in concrete exposed to sea water: theory and thermochemical modeling[END_REF]. The fact that the experimental chloride binding isotherms for each exposed solution are successfully reproduced by the model confirms that the chloride binding

Figure 1 :

 1 Figure 1: Chloride binding isotherm of CEM II concrete after 3 months of exposure to a) 0.5 mol.L -1 N aCl solution, b) 0.25 mol.L -1 CaCl 2 solution, c) 0.5 mol.L -1 KCl solution and d) 0.5 mol.L -1 M gCl 2 solution at 20 • C (experimental data taken from the literature (14)).

Figure 2 :

 2 Figure 2: Chloride binding isotherm for CEM II concrete after a 6-month exposure to chloride sorption on C-S-H surface and chloride binding for a) 0.5 mol.L -1 N aCl, b) 0.25 mol.L -1 CaCl 2 , c) 0.5 mol.L -1 KCl and d) 0.5 mol.L -1 M gCl 2 solutions at 20 • C, respectively. Contribution of Kuzel's salt formation and chloride sorption on C-S-H sites (≡ SiOHCl -, ≡ SiOCaCl)

Figure 3 :CaCl 2 ,

 32 Figure 3: Concentration profile of CEM II concrete after six months of exposure to N aCl, CaCl 2 , KCl and M gCl 2 solution at 20 • C respectively: a) N a + , b) K + , c) Ca 2+ and d) pH.

  ] (g/100g of concrete) Portlandite quantity (mol/dm of mortar)

Figure 4 :

 4 Figure 4: Portlandite amount as a function of depth for concrete specimens exposed to N aCl, KCl, CaCl 2 and M gCl 2 solutions after a 6-month exposure, respectively.

Figure 5 :

 5 Figure 5: Mineral amount of CEM II concrete after six months of exposure in M gCl 2 solution at 20 • C.

Figure 5 )

 5 Figure5). Hydrotalcite, ettringite and Kuzel's salt precipitation may be in competition with each other with high magnesium concentration.

Figure 6

 6 Figure 6 displays the comparison between the chloride binding isotherms within concrete specimens exposed to 0.5 M of M gCl 2 solutions containing 0, 0.0276 M of M gSO 4 and 0.2760 M of M gSO 4 , respectively. The chloride binding capability is different depending on the concentration in the solution. In other words, the numerical results show that the higher SO -2 4 the

Figure 6 : 5 M

 65 Figure 6: Chloride binding capability after six months of exposure in 0.5 M M gCl 2 , 0.5 M M gCl 2 + 0.0276 M M gSO 4 and 0.5 M M gCl 2 + 0.2760 M M gSO 4 solution at 20 • C, respectively.

4 for the 0. 5 M 5 MFigure 7 :

 4557 Figure 7: a) Pore solution pH and chloride binding on b) ≡ SiOH, c) ≡ SiOCa + , d) Kuzel's salt formation after six months of exposure in 0.5 M M gCl 2 , 0.5 M M gCl 2 + 0.0276 M M gSO4 and 0.5 M M gCl 2 + 0.2760 M M gSO4 solutions at 20 • C, respectively.

Figure 9 :

 9 Figure 9: Mineral amount of CEM II concrete after six months of exposure in a 0.5 M M gCl 2 + 0.2760 M M gSO4 solution at 20 • C.

Table 2

 2

exposes the kinetic parameters for each mineral species. Data are taken from Baur et al. for Monosulfoaluminate, ettringite and C-S-H (32), from Gali et al. for portlandite (33), from Tambach et al. for hydrotalcite (34) and from Palandri and Kharaka for brucite, gibbsite and chrysolite (35).

Kuzel's salt is assumed to react instantaneously because of missing data. It is to note that the simulations are performed on concretes exposed to chlorides during several months that is to say for short exposition time compared to concrete service life. The kinetics approach is of interest to know which mineral species is susceptible to precipitate during this transient problem. The precipitation of Kuzel's salt is observed (by the model thanks to the kinetics approach) first and at low chloride concentration, while Friedel's salt is observed later and for greater concentration

[START_REF] Mesbah | Uptake of chloride and carbonate ions by calcium monosulfoaluminate hydrate[END_REF]

.

Table 2 :

 2 Parameters describing the kinetics of mineral reactions at 25

	dissolution
	Minerals	A ms	k	Ref
	Jennite	41.0	2.75 × 10 -12	(32)
	Tobermorite	41.0	2.75 × 10 -12	(32)
	Ettringite	9.8	7.08 × 10 -13	(32)
	Monosulfoaluminate 5.7	6.76 × 10 -12	(32)
	Portlandite	16.5	2.24 × 10 -8	(33)
	Hydrotalcite	9.8	1.00 × 10 -09	(34)

• C where k is the dissolution rate constant (mol.m -2 .s -1 ) and A ms the mineral specific reactive surface area (m 2 .g -1 ). Precipitation mechanism and associated constants are assumed to be similar to Kuzel's salt Instantaneous Gibbsite 9.8 × 10 -4 3.16 × 10 -12 (35) Brucite 9.8 × 10 -4 5.75 × 10 -9 (35) Chrysotile 9.8 × 10 -4 10.0 × 10 -12

Table 3 :

 3 Equilibrium constants of the surface complexation model.

	Equation

≡ SiOH ↔≡ SiO -+ H + -12.7

  T0 considered in the study some 100mm × 50mm specimens were drilled out. The side and bottom surfaces of the cylinder specimens were sealed with epoxy resin. An immersion test was conducted to determine the penetration depth of chloride and the chloride binding isotherms in saturated conditions at 20 • C under laboratory conditions. The concrete properties and experimental data are detailed in Song et al.[START_REF] Song | Influence of cation type on diffusion behavior of chloride ions in concrete[END_REF].

2-↔≡ SiOCaSO - 4 + H + -8.5 a,b ≡ SiOH jennite + N a + ↔≡ SiON a jennite + H + -13.745 (40) ≡ SiOH jennite + K + ↔≡ SiOK jennite + H + -13.745 (40) ≡ SiOH tobermorite + N a + ↔≡ SiON a tobermorite + H + -12.656 (40) ≡ SiOH tobermorite + K + ↔≡ SiOK tobermorite + H + -12.656 (40) Specific surface site of C-S-H A cs = 500 m 2 .g -1 (37) Sorption density of C-S-H Γ C-S-H = 8 × 10 -6 mol.m -2 (42), (43) a : Reaction on the C-S-H surface taken from (44) b : Value of log K

Table 4 :

 4 Chemical composition of cement, expressed as a percentage (%)[START_REF] Song | Influence of cation type on diffusion behavior of chloride ions in concrete[END_REF].Composition SiO 2 Al 2 O 3 F e 2 O 3 CaO M gO SO 3 N a 2 O K 2 O

	Content	21.70 5.09	4.32	64.64 0.92	1.08 0.21	0.53

Table 5 :

 5 Concrete mix-design (kg.m -3 ) (14).

	Cement Water Sand Gravel w/c
	312	156	746	1118	0.5

Table 6 :

 6 Mineralogical content (mol.dm -3 of concrete)

	Minerals	Content
	Jennite	0.9882
	Tobermorite	0.1384
	Ettringite	-
	Monosulfoaluminate 0.0421
	Portlandite	1.6011
	Hydrotalcite	0.0178

Table 7 :

 7 Initial composition of the pore solution in CEMII concrete (mol.kg -1 ) calculated using Toughreact at 20 • C.

		Concentration [mol/kg of pore solution]
	N a +	0.1366
	K +	0.2271
	Ca 2+	0.2979 × 10 -2
	M g 2+	0.4057 × 10 -10
	Al 3+	0.2348 × 10 -3

  Cl -and SO 2- 4 start competing for sorption with Ca 2+ on ≡ SiOH.

	0.20			2.5
	Because of the charge balance condition and the competition between chlo-ride and sulfate, the number of negative surface charges ≡ SiOHCl -must decrease. This can only happen if the chloride binding capability decreases when the solution contains a significant amount of SO 2-4 . 0.20 0.40 0.60 0.80 1.00 1.20 1.40 0.5 M MgCl2 + 0 M MgSO4 0.5 M MgCl2 + 0.0276 M MgSO4 0.5 M MgCl2 + 0.2760 M MgSO4 Bound sulfate on ΞSiOCaSO 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 [cl ] (g/100g of concrete) (g/100g of mortar) 0.0 0.5 1.0 1.5 2.0 0.00 0.05 0.10 0.15 Ettringite Jennite Tobermorite Portlandite Chrysotile Brucite Hydrotalcite Monosulfate Kuzel's salt Monosulfate, hydrotalcite, ettringite, tobermorite, Kuzel's salt and chrysolite quantity (mol/dm of mortar) Brucite, portlandite and jennite quantity (mol/dm of mortar)
	0.00
	0	0.03	0.06	0.09
		[cl ] (g/100g of concrete)
	Figure 8: Sulphate binding on ≡ SiOCaSO -4
	Chloride binding due to Kuzel's salt formation (cf. Figure 7d) is weakest
	when SO 2-4 concentration is highest. Ettringite formation then occurs at the
	expense of Kuzel's salt formation as shown in Figure 9. Results are differ-
	ent with the boundary solution without SO 2-4 . In contrast, the remaining
	mineral behaviors are similar. Consequently, for the 0.5 M M gCl 2 + 0.2760
	M M gSO4 solution, Ca 2+ leaching is not responsible for the low pH. The
	pH decrease is essentially due to the presence of SO 2-4 and to the adsorption
	reactions on C-S-H.

addition,

Acknowledgments

The present study work is a contribution to the French ANR MODEVIE project. The authors are grateful to the "Agence National de la Recherche" and the Ministries in charge of Sustainable Development, Town Planning and Transportation for their financial support to the project.