## 2 Methods and Materials
### Electrical Resistivity Measurements  
The electrical resistivity characterizes the ability of the material to oppose the flow of electric current. A method for measuring the resistivity of a medium is the four-point electrodes method where the current \(I\) (A) is injected via two electrodes and the potential drop \(\Delta V\) (V) is measured between two other electrodes. The resistivity is connected to the electrical resistance (\(\Delta V/I\)) by a geometric factor \(G\) (m) that depends on the geometry of the structure as well as the configuration of the electrodes. The factor \(G\) is numerically determined by a finite element calculation using COMSOL Multiphysics(r) in a homogeneous medium. In the case of a medium with moisture gradients, an \"apparent\" resistivity \(\rho_{a}\) (\(\Omega\).m) is inferred for each of the electrode's configuration, using Equation (1):  
\[\rho_{a}=G\frac{\Delta V}{I}\,. \tag{1}\]In this study, we considered all the specimens in homogeneous moisture and temperature conditions; thus, the resistivity was assumed to be constant within the specimens and the measured apparent resistivities provided a good approximation of the resistivity (\(\rho_{a}=\rho\)).  
To make an electrical resistivity measurement, it is possible to carry out either a surface measurement [27; 28] or a measurement in depth using an embedded device [4; 29]. The use of embedded sensors offers the possibility of evaluating the concrete resistivity throughout a large thickness of the structure without the inherent loss of resolution with depth. In this study, electrical resistivity measurements were conducted using an embedded printed circuit board (PCB) sensor developed by [PERSON] et al. [26]. The PCB sensor has a ladder-like shape which improves the anchorage of the electrodes in the concrete. In this study, we used 19 electrodes, each with dimensions of 3 \(\times\) 1.5 mm\({}^{2}\), placed on either side of the sensor with an inter-electrode spacing of 2 cm on each side (Figure 1).  
Two measurement configuration modes are considered for this PCB sensor [26]. The first mode is the transmission configuration where \(I\) is injected on two stainless steel grids (\(\mathcal{O}\) = 10 cm) placed on either side of the sensor and \(\Delta V\) is measured between all pairs of consecutive electrodes located on the same side of the sensor (E1E3, E2E4, E3E5,..., E17E19) (Figure 1). The second mode is the Wenner configuration, where the quadrupole measurements C1P1P2C2 (where electrodes C1 and C2 are used for current injection, and electrodes P1 and P2 are used for potential drop measurements) are successively E1E3E5E7, E2E4E6E8, E3E5E7E9,..., E13E15E17E19 (Figure 1).  
For both configurations, [PERSON] et al. [26] showed that the apparent resistivity is a good estimation of the true resistivity at the middle of the electrodes where the potential is measured. Therefore, the measurements obtained along the sensor length can be seen as a resistivity profile with depth in concrete. Since all specimens are in homogeneous moisture and temperature conditions in this study, we expected measured resistivity profiles to exhibit flat trends over depth with comparable values between the two measurement configurations, assuming that there is no structural variability in each specimen.