*2.2. Case Study*

The multispecies approach proposed is used to simulate all the ion movements in the migration cell during the standard migration test on ordinary concrete for 15 days. The composition of the concrete used is given in Table 1. The chemical composition of the pore solution of the concrete used is taken from Refs. [8,34] (see Table 2). The standard migration test simulated is composed of two compartments: the upstream and downstream compartments containing a basic solution of 25 mM NaOH and 83 KOH. In addition, 500 mM of NaCl is added to the upstream. An electrical field of 300 V·m−<sup>1</sup> is applied at the sample boundaries. Concrete samples of 1 cm thickness are used (1D modelling). In this study, the numerical results show the ion profiles in the material tested that are useful for the calculation of the diffusion coefficient at the non-steady state [4,35].

**Table 1.** The composition of the concrete used.


**Table 2.** Initial and boundary conditions used.


#### **3. Results and Discussion**

Figures 1 and 2 show the simulated profiles of Cl−, Na+, K+, OH<sup>−</sup>, H+, Ca2+ and SO4 2− in the sample at the end of the migration test (after 15 days) with and without considering the electrode processes, respectively. The free chloride concentration in the pore solution is maximum along the sample depth (~459 mol·m−3) because of their migration from the upstream to the sample. The max concentration is relatively different compared to the literature's data without considering the thermodynamic equilibrium (the participation of chloride with the other ions in the pore solution to form salts). For these models in the literature, the max concentration is equal to the boundary condition on the side of the upstream (500 mol·m<sup>−</sup>3) [2]. Bulleted lists look like this:

**Figure 1.** Profiles of Cl−, Na+, K+, OH−, H+, Ca2+ and SO4 <sup>2</sup><sup>−</sup> in the sample at the end of the migration test (15 days) considering electrode processes.

**Figure 2.** Profiles of Cl−, Na+, K+, OH−, H+, Ca2+ and SO4 <sup>2</sup><sup>−</sup> in the sample at the end of the migration test (15 days) without considering electrode processes.

Moreover, we noted an increase in the concentrations of Na+ and K+ in the pore solution due to their migration from the downstream to the sample tested. The increase in Ca2+ and SO4 <sup>2</sup><sup>−</sup> concentrations are due to the dissolution of the portlandite, monosulfoaluminates, and trisulfoaluminates under the electrical field [36,37].

Finally, a difference between the concentration of H+ and OH<sup>−</sup> with and without considering the electrode processes is noticed. This is reflected by the electroneutrality ensured in the case of the migration modelling with electrode processes and not ensured in the case of the modelling without electrode processes (see Figure 3). This impacts also the concentration of the other ions in the pore solution. The electroneutrality was calculated using Equation (5). The results obtained confirm the need of considering the electrode processes in the chloride migration modelling.

$$
\sum \mathbf{C}\_i \mathbf{z}\_i = \mathbf{0} \tag{5}
$$

**Figure 3.** Electrochemical imbalance in the pore solution of the sample, deduced from ion concentrations in the steady state with and without considering electrode processes.
