## 2 Electrical Resistivity/Impedance Measurement: Is It Really that Simple?
### Stress and Strain  
Self-sensing construction materials have gained much interest for SHM purposes, enabling the perception of stress/strain by means of electrical resistivity measurements. Indeed, electrical resistivity enables concrete to behave as a smart material for the self-sensing of strain and stresses (piezoresistive effect), especially when conductive additions are used [68]. A good electrical conductivity is a fundamental prerequisite for piezoresistive behavior; it can be stated that cement-based material is the stress sensor, whereas the conductive addition makes the piezoresistive effect significative. Conductive fillers and/or fibers can be used at this aim, such as carbon-based materials (e.g., virgin/recycled carbon fibers, carbon nanotubes [207], carbon nanofibers [208], char, and carbon black [209]), graphene (e.g., graphene nanoplatelets [48]), steel fibers, graphite powder, nickel powder, titanium dioxide, and iron oxide. These functional fillers increase the concrete ability to sense not only stress and strain, but also internal damages (e.g., cracks). When a cement-based material contains a conductive addition, its electrical resistivity depends on its dispersion degree, the electrical conductivity of the addition, and of the interface between the addition and the cement matrix. Also, moisture plays an important role in the piezoresistive ability of concrete [48]. There are manifold applications of piezoresistivity property of concrete, such as SHM [121], traffic monitoring [210] (also including self-sensing pavement applications for vehicle detection [122]), and cement-based sensors [55]. Fractional Change of Resistivity (FCR)--or Fractional Change of Resistance--during loading/unloading phases is commonly considered and the sensitivity is evaluated by means of the Gauge Factor (GF), defined as the ratio of electrical resistivity variation (\(\Delta\rho/\rho\)) and strain (\(\varepsilon\)) [33]. Intrinsic self-sensing concrete is advantageous in terms of sensitivity, mechanical performance, durability, ease of installation, and maintenance [211]. **Carbon fibers** are often used to enhance the piezoresistive behavior; when short carbon fibers are added to the mortar mix, it can be noted that the electrical resistivity varies with the applied stress; in particular, \(\rho\) decreases with compression longitudinal loads (fiber push-in), whereas increases upon tension (fiber pull-out) [21]. [PERSON] and [PERSON] [212] observed that the DC electrical resistance increases upon tensile loading in specimens containing carbon fibers, due to the degradation of the fiber-matrix interface. This degradation is partly reversible, meaning that carbon fibers composites behave as strain sensors, in both transverse and longitudinal directions (even if FCR is higher in the case of longitudinal resistivity) [59]. The same authors [57] evaluated the electrical resistivity of cement pastes subjected to uniaxial compression; they considered paste specimens of two types, namely carbon fiber silica fume cement paste and carbon fiber latex cement paste. They evaluated electrical resistivity both in longitudinal and transverse directions, considering cubic (51 mm side) and rectangular specimens (\(150\times 12\times 11\) mm), observing a reversible decrease in both the resistivities, with the exception of some irreversible increase at the end of the first stress cycle due to minor damage. Carbon fibers were used also in combination with **graphite**[45]: the former form a conductive network, whereas the latter fill the spaces among fibers, increasing the smart agility of smart concrete. Electrical resistivity is negatively correlated with stress: it is possible to establish a quadratic polynomial relationship between the variance ratio of resistance (AR/R) and stress (or strain), with R\({}^{2}>0.95\) for different concrete compositions.