## 2 Electrical Resistivity/Impedance Measurement: Is It Really that Simple?
### Defects and Damages Detection  
Cracks (provoked by internal stresses [217] or external loadings [218], such as mechanical loads [219], drying shrinkage [220], and freezing action [221]) weaken the matrix resistance, besides constituting a preferential ingress path for contaminants [222], fluids and ion flows, which ease corrosion processes; therefore, durability of concrete is significantly affected by cracks and other damages formation. When cracks form, conductive pathways are partially destroyed. As a consequence, electrical resistivity increases. In this case, and consequently, the electrical resistance can be used as a **damage sensor** besides strain sensor. [PERSON] and [PERSON] [51] observed that electrical resistance has abrupt changes when crack initiates and propagates in steel fiber reinforced cement matrix composites. Real-time monitoring makes it possible to promptly detect damages when they occur, easing the detection of the causes of these damages and enabling a timely repairing action, hence prolonging structural service life. Electrical resistivity of concrete is sensitive to concrete stress-strain and cracking behavior, with a response mainly depending on the load level and the water saturation degree [76]. In fact, crack formation and propagation cause changes in the path of electric current, hence \(\rho\) will change, following their evolution in time. It is worth underling that the effect will be dependent on the cracks conditions, as demonstrated by [PERSON] et al. [119] with a 4-probe resistivity meter. If cracks are insulating (i.e., dry concrete, where cracks are filled with air or sometimes dust, showing a high electrical resistivity), \(\rho\) will increase; if they are water-saturated (i.e., wet concrete), \(\rho\) will decrease (since water has a good electrical resistivity) [119]; in fact, possible impurities present in the mixture can alter electrical resistance, increasing or decreasing it depending on their nature (e.g., metallic or dust particles). The same meter was used by [PERSON] et al. [118] for the comparison of electrical resistivity measurements and transmission of ultrasonic (US) surface waves in crack detection; both the techniques are suitable to localize the main cracks, but not to measure the crack depths. The information provided by electrical resistivity can be useful to complement US results, distinguishing between wet and dry cracks. However, secondary cracks represent a disturbing factor for electrical resistivity measurements. [PERSON] and [PERSON] [98] used the resistivity meter SYSCAL R1 plus, with 24 electrode connected to a multicore cable system, for the evaluation of both artificial cracks (made of plastic sheets) and loading cracks. The wider the crack width, the higher the electrical resistivity. Electric imaging can provide 2D representation useful for crack detection. [PERSON] et al. [75] noticed a dramatic change in impedance values when a sudden growth in crack occurred; the real part of the electrical impedance increases through the fracture process, following the crack opening. [PERSON] et al. [41] monitored the cracks initiation and propagation by means of electrical resistivity measurements; in fact, FCR is dominated by the cracks opening, showing the same trend of opening with load. Also, cementitious materials with conductive additions were evaluated for damage detection. It is worth noting that conductive fibers/fillers can be used as a reinforcement, providing the so-called \"crack-bridging effect\". [PERSON] et al. [46] analyzed cement composites containing CNTs, confirming the possibility to detect crack (and to evaluate their width) by means of electrical resistivity measurements, provided that the specimen under test is moist. Otherwise, under dry conditions, the crack breaks the conductive network of CNTs and the electrical conductivity is not influenced by the crack width anymore. Also, [PERSON] et al.