## 2 Electrical Resistivity/Impedance Measurement: Is It Really that Simple?
### Compressive Strength and Elastic Modulus  
The prediction of concrete strength in a simple and effective way is fundamental in order to optimize the construction times. There are some applications of electrical resistivity measurement related to the prediction of **compressive strength** (commonly controlled at 28 days) and **elastic modulus**. The increase of hydration products goes together with the microstructure formation; when hydration products start blocking the pores conduction path and tortuosity increases, electrical resistivity sharply increases, as well as a compressive strength gain [35]. Therefore, the electrical resistivity can be considered as a predictor of the compressive strength of cementitious materials; since compressive strength value is used for quality control, also electrical resistivity measurement can be employed with that aim. Many authors identified **linear relationships between compressive strength and electrical resistivity** of concrete [31; 168], since both \(\rho\) and compressive strength depends on the matrix porosity and structure compactness. [PERSON] and [PERSON] [34] stated that electrical resistivity of concrete increases with increasing age--the more the lower w/c ratio is-- cement, and aggregates used [137]. [PERSON] et al. [135] evidenced a linear relationship (y = 8.7648x + 20.406, with R\({}^{2}\) = 0.9634) considering compressive strength at 28 days and electrical resistivity at 24 h. [PERSON] and [PERSON] [16] found relationships between 28-day compressive strength and 7-day electrical resistivity values. They report errors \(<\) 10% in the compressive strength estimation when a model based on a theoretical equation related to concrete hydration process is used, considering also a correction factor for the surface temperature of concrete. [PERSON] et al. [137] observed a linear relationship between electrical resistivity and concrete strength, reporting a strong correlation (R\({}^{2}\) = 0.97). This was justified by the presence of dissolved ions. Similarly, [PERSON] et al. [136], after temperature correction, established a linear relationship between compressive strength and concrete electrical resistivity, independent of curing temperature and w/c ratio (y = 4.51x - 3.80, with R\({}^{2}\) = 0.98). [PERSON] et al. [14] established a linear relationship between 1-day compressive strength and 24-h electrical resistivity of cement paste (y = 0.1725x + 36.106, with R\({}^{2}\) = 0.9371). [PERSON] et al. [31] found a linear relationships between electrical resistivity and compressive strength at 28 and 91 days of curing also in the presence of GGBFS. [PERSON] et al. [134] established a power relationship between 1-day electrical resistivity and w/c ratio similar to that between compressive strength and w/c ratio [169]. On the other hand, they established a linear relationship between 2-day compressive strength and 1-day resistivity (y = 1.609 + 3.8497x, with R\({}^{2}\) = 0.993) and a logarithmic relationship between 7-day (or 28-day) compressive strength and 1-day resistivity (y = 5.4302 + 19.179 lnx with R\({}^{2}\) = 0.987 and y = 15.427 + 21.835 lnx with R\({}^{2}\) = 0.976 for 7-day and 28-day compressive strength, respectively). Finally, [PERSON] and [PERSON] [133] established a logarithmic relationship between 7-day or 28-day elastic modulus and 1-day electrical resistivity (R\({}^{2}\) > 0.90). Moreover, knowing the aggregate content, the 7-day (or 28-day) compressive strength can be derived from the 1-day electrical resistivity, according to a linear relationship (R\({}^{2}\) > 0.95). Aggregates largely increase the concrete bulk electrical resistivity with an exponential correlation [120]. On the other hand, [PERSON] et al. [100] do not recommend to use \(\rho\) as a compressive strength indicator since the pore solution greatly affects electrical resistivity, but has no influence on compressive strength. Also the **elastic modulus can be related to electrical resistivity**; [PERSON] et al.