## 1 Introduction  
An effective maintenance strategy of concrete structures asks for a strong involvement of Structural Health Monitoring (SHM) because this makes it possible to minimize the required interventions and to optimize their cost-effectiveness. However, despite, in developed countries, the maintenance and repairing costs of concrete structures being estimated at around 3-4% of gross national product [1], at present, no regular monitoring techniques are widely applied. Inspections are preferred, even if their efficiency is more limited than the one provided by monitoring, which continuously provides data and information on the health status of the target structure. Furthermore, it is worth noting that the service life of a non-temporary concrete structure is quite long: for a common structure, it accounts to 50 years, for a strategic structure (e.g., a monument, a bridge, or other civil engineering structures), at least 100 years [2]. Since non-destructive techniques (NDTs) can provide data on the structure without the necessity of sampling the structure (therefore exposing the structure itself to higher risks of damage), they are preferred for SHM. Among NDTs, the measurement of electrical resistivity of concrete is gaining wider and wider consensus among the scientific and technical community. Indeed, the technique is easy to adopt, tests can be performed rapidly, and several factors related to concrete durability [3; 4; 5]can modify the resistivity of concrete, like water and chlorides penetration, carbonation, or presence of cracks. Electrical resistivity (\(\rho\) [\(\Omega\cdot\)m]) is the ability of a material to oppose the flow of electric current. The electrical resistivity of concrete varies from 10\({}^{1}\) to 10\({}^{5}\)\(\Omega\cdot\)m, mainly in relation to its moisture content and composition [6; 7; 8; 9; 10]. The composition includes cement type (fineness, composition, and soluble salts content), water to cement (w/c) ratio, type and size of aggregates, and presence of additions, either conductive or not. Indeed, as aggregates are concerned, they act as an obstacle in the electric current path, hence increasing the electrical resistivity of concrete [11]. Electrical resistivity depends on cement paste microstructure, characterized by the volume, the size, and the interconnection of pores, besides the pore solution, where different salts are dissolved, releasing ions (mainly K\({}^{+}\), Na\({}^{+}\), OH\({}^{-}\), and, in smaller extent, also Ca\({}^{2+}\) and SO\({}^{2-}\)) that enable conduction [12]. Porosity is governed by the w/c ratio: the higher the w/c ratio, the higher the total porosity [13] and, consequently, the lower the electrical resistivity [14; 15]. However, in highly saturated concrete, the effect of w/c ratio on electrical resistivity is less significant [6; 16] because moisture (thus water) plays a major role in defining concrete electrical properties. Supplementary cementitious materials (e.g., fly ash, silica fume, and ground granulated blast furnace slag (GGBFS), just to cite those mostly used) reduce both pores size and volume. A refinement of the pore structure increases \(\rho\). Indeed, these mineral additions (e.g., blast-furnace slag [17], fly ash [18], and silica fume [19]), are also generally added to release more durable concretes [20]. On the other hand, if conductive fillers or fibers are added to the mix-design, electrical resistivity decreases, and the material conduction partially moves from electrolytic to electric [21; 22; 23]. The electrolytic conductivity is related to mobile ionic species that form when water and binder are mixed together; concrete can be thought of as an electrolytic conductor, since the current mainly passes through the pore solution [24]. On the other hand, the electronic conductivity is related to the transportation of free electrons through the conductive phase (carbon or metal fillers/fibers). Contrarily, non-conductive polymeric fibers seem not to have a significant effect on the matrix electrical resistivity [22].