## 2 Electrical Resistivity/Impedance Measurement: Is It Really that Simple?
### Corrosion Risk of Reinforcements
The same author in [74] highlighted that electrical resistivity reflects the concrete properties related to chloride penetration, corrosion initiation (i.e., corrosion probability), and propagation (i.e., corrosion rate). Since electrical resistivity of concrete reflects the transport of ions (including chloride), it is quite immediate to infer a possible correlation between resistivity and corrosion initiation. [PERSON] et al. [193] quantified the chloride concentration threshold leading to corrosion initiation by means of low-frequency impedance response (in the frequency range of 10 mHz-10 Hz). This threshold corresponds to the polarization resistance drop, which increases with low w/c ratio. The microstructure properties are reflected by polarization resistance, which consequently is able to characterize the activation of the corrosion process. However, this methodology can be used only as a comparative test because the external field used for the measurement accelerates chlorides transfer, thus distorting the steel behavior. Once the corrosion process has started, a low resistivity gives a high **corrosion rate**[191]; when corrosion begins, \(\rho\) can represent a \"controlling factor\" of its speed [194, 195]. After depassivation, an inverse relationship between concrete electrical resistivity and corrosion rate has been found [196, 28, 175, 197] but not with a general validity, since it depends on concrete composition [197], age, carbonation, and environmental conditions, especially with low chloride content [74]. [PERSON] and [PERSON] [109] adapted the four-point Wenner resistivity method to evaluate the corrosion rate of steel without the requirement of a direct electrical connection to the reinforcement rebars, as necessary for the Linear Polarization Resistance (LPR) method [198]. LPR consists in the introduction of a small perturbative DC signal to a corroding steel rebar and in the measurement of the corresponding electric potential change, to derive the polarization resistance; it requires the knowledge of the area of steel being perturbed. [PERSON]'s method alone cannot directly measure the corrosion rate; however, in this study, the short-circuit effect caused by steel reinforcement rebars was exploited to do measurements both in DC and AC (directly over a steel bar, parallel to the bar itself) to assess the resistive (i.e., the charge transfer resistance) and the capacitive (i.e., the double layer of charged ions on the surface of the steel rebar) components of the corrosion interface. This offers a quick method to quantify the corrosion rate on the surface of the considered rebar, since its instantaneous value is proportional to the charge transfer resistance itself [110]. [PERSON] [112] combined the resistivity measurement performed by four-point probe method and the galvanostatic resistivity measurement [110] with the use of a Multi-Layer Perceptron (MLP) **artificial neural network** (ANN) model. A dataset of 70% of the available experimental data was used for training, 15% for testing, and 15% for the MLP verification process. A correlation coefficient R\({}^{2}\approx 0.85\) with a MAPE (mean absolute percentage error) of 0.000266 was obtained for the first set of data (related to a specimen with a high corrosion rate), whereas R\({}^{2}\approx 0.98\) and MAPE error of 0.000027 for the second dataset (related to a specimen with a moderate corrosion rate), indicating very good performance of the neural network in the prediction of the corrosion current rate. In this way, also the influence of environmental conditions on electrical resistivity is considered. It is worth noting how ANNs have spread also in civil engineering applications [199, 200], giving important contributions to SHM. [PERSON] and [PERSON] [111] considered electrical resistivity (both in DC and AC) as input parameters for an artificial neural network base model for the estimation of corrosion current density.