Comparison of existing chloride ingress models within concretes exposed to seawater

Abstract

Numerous models to predict chloride ingress within concretes for different environmental conditions (immersed in seawater, located in the tidal zone or exposed to sea spray) have already been developed. Thanks to a benchmark, the objective of this paper is to contribute to the choice of a reliable engineering model for predicting chloride ingress in the case of saturated conditions. This study focus on a comparison between various physico-chemical models which rely on different approaches to account for transport phenomena and binding of chloride ions onto the cementitious matrix. The authors draw special attention to models using a limited number of input data (3 or 4): accessible-to-water porosity ($\phi _{\text{w}}$), effective chloride diffusion coefficient ($D_{\text{Cl}^-}$) and one or two parameter(s) characterizing the physical binding of ions Cl⁻. They are determined through the analysis of two simple and repeatable experimental tests: $\phi _{\text{w}}$ is measured directly by hydrostatic weighing and the other parameters are fitted by inverse analysis performed of a total chloride content (tcc) profile at a given exposure time. An application of the method and a comprehensive comparison between predicted chloride profiles and experimental data (tcc profiles at other ages than the one used for the fitting and free chloride concentration profiles) have been carried out for two mortars and seven concretes exposed to laboratory or in-situ conditions. The performance of the studied models is assessed thanks to statistical tools and recommendations are pointed out for the development of new numerical models.

Description of ion adsorption onto C-S-H [16]

Table 7 resumes the considered equations describing the competitive adsorption onto solid matrix. The authors add the hypothesis that the capacity of solid matrix to adsorb is constant for all ions. Constants of adsorption reaction are assumed to be equal to those of adsorption reactions onto C-S-H. Such hypothesis is equally used by some authors of the literature [47, 16]. Thus, analytical relationships (see Eq. 13) between the content of bound ions and the free concentration of ions can be written. First, let us note the denominator D and the vector $\mathbf {C}$ as:

$$\begin{aligned} D = &1+K_{\text{OH}}c_{{\text{OH}}^-} + (K_{\text{Ca}}+K_{{\text{CaSO}}_4}c_{{\text{SO}}_4^{2-}} + K_{\text{CaCl}}c_{{\text{Cl}}^-}) \frac{c_{{\text{Ca}}^{2+}}}{c_{{\text{H}}^{+}}} \nonumber \\&\qquad + \frac{{\text{K}}_{\text{Na}}c_{{\text{Na}}^+}+{\text{K}}_{\text{K}}c_{{\text{K}}^+}}{c_{{\text{H}}^{+}}}+{\text{K}}_{\text{Cl}}c_{{\text{Cl}}^-} \end{aligned}$$

(11)

$$\begin{aligned} \mathbf {C} = \left( c_{{\text{Cl}}^-}~c_{{\text{OH}}^-}~c_{{\text{SO}}_4^{2-}}~c_{{\text{Na}}^+}~c_{{\text{K}}^+}~c_{{\text{Ca}}^{2+}} \right) \end{aligned}$$

(12)

Analytical relationships are then:

$$\begin{aligned} {\left\{ \begin{array}{ll} s_{\text{OH}} = f^{\text{OH}}_{\text{Kari}}(\mathbf {C}) = C_{\text{ads}} \frac{{\text{K}}_{\text{OH}}c_{{\text{OH}}^-}}{D} \\ s_{\text{Cl}} = f^{\text{Cl}}_{\text{Kari}}(\mathbf {C}) = C_{\text{ads}} \frac{({\text{K}}_{\text{CaCl}}\frac{c_{{\text{Ca}}^{2+}}}{c_{{\text{H}}^{+}}} + {\text{K}}_{\text{Cl}})c_{{\text{Cl}}^-}}{D}\\ s_{\text{Ca}} = f^{\text{Ca}}_{\text{Kari}}(\mathbf {C}) = C_{\text{ads}} \frac{({\text{K}}_{\text{Ca}}+{\text{K}}_{{\text{CaSO}}_4}c_{{\text{SO}}_4^{2-}} + {\text{K}}_{\text{CaCl}}c_{{\text{Cl}}^-})c_{{\text{Ca}}^{2+}}}{D~c_{{\text{H}}^{+}}} \\ s_{{\text{SO}}_4 } = f^{{\text{SO}}_4}_{\text{Kari}}(\mathbf {C}) = C_{\text{ads}} \frac{{\text{K}}_{{\text{CaSO}}_4}c_{{\text{SO}}_4^{2-}} c_{{\text{Ca}}^{2+}}}{D~c_{{\text{H}}^{+}}} \\ s_{\text{Na}} = f^{\text{Na}}_{\text{Kari}}(\mathbf {C}) = C_{\text{ads}} \frac{{\text{K}}_{\text{Na}}c_{{\text{Na}}^+}}{D~c_{{\text{H}}^{+}}} \\ s_{\text{K}} = f^{\text{K}}_{\text{Kari}}(\mathbf {C}) = C_{\text{ads}} \frac{{\text{K}}_{\text{K}}c_{{\text{K}}^+}}{D~c_{{\text{H}}^{+}}} \\ \end{array}\right. } \end{aligned}$$

(13)

where the parameter $C_{\text{ads}}$ has to be calibrated.

Table 7 The equilibrium constants K for physical adsorption onto C-S-H [16]