## 2 Materials and Methods
One of the factors affecting the output of the sensor is the frequency of the alternating voltage applied to the concrete specimen. With a high enough AC waveform frequency, the reactance can be minimized from the impedance readings, and the true resistance of the concrete samples is conveyed [57]. Based on the results obtained at different frequencies, as presented in Figure 5, it can be seen that the measured sensor output voltage under a constant input voltage with 8-volt magnitude (Vpp = 8 V), varies. The results showed that, at low and high frequencies, the voltage output of the sensor decreases, and at 2.5 kHz, this value increases to its maximum. Finding the proper frequency is critical as an increase in waveform frequency can result in higher power consumption and circuit complexity [57]. The electrical property changes are very sensitive to temperature, water, and humidity [58; 59], ingress of chemical elements that are commonly used in infrastructures service (such as deicing salts), and several other factors encountered in real-field applications. Previous studies demonstrated that temperature can affect the sensor output voltage in three ways: (a) thermal deformation of concrete; (b) thermally activated charge carriers (ions, holes, and electrons), when the MWCNTs concentration in concrete sensors is lower than percolation threshold; and (c) thermal-fluctuation-induced tunneling conduction [58; 60]. To mitigate the temperature effect on the results during a high-cycle fatigue test, which is generally accompanied by an increase in temperature, an air conditioning system was used in the present research, which ensured that a continuous air stream at 23 \({}^{\circ}\)C was directed to the concrete sensor specimens during the fatigue tests. [PERSON] et al. demonstrated that concrete resistivity changes as a function of the moisture content in smart concrete media. They observed that by decreasing the moisture level from 5.2% to 4.8%, the resistivity decrease due to the water layer between fibers was  
Figure 4: Polarization effect in normalized sensor resistivity response over time (minutes) under low-cycle load in a DC circuit. Figure 5: Measured alternating voltage (AV) versus frequency between the heads of the concrete sensor at constant input alternating voltage (AV). lost and therefore direct contact between fibers was achieved. The higher the decrease in moisture level, the higher the increase in resistivity because water acting as electrolyte was lost [58]. Based on these findings, in the present study, to eliminate moisture effects on the test results, the concrete sensors specimens were dried in an oven for 1 week at 80 \({}^{\circ}\)C and then rapidly covered by waterproofing epoxy resin. In this way, concrete was isolated from outside moisture effects. The presence of free ions in the micro-pores of concrete is another factor that may affect the sensor conductivity and increase test errors. To eliminate this effect, the specimens were cured for 28 days, stored for 90 days, and finally dried in an oven for 7 days (as mentioned above) to ensure that the most suitable and repeatable conditions for the hydration process were carried out. Probe detachment from the concrete medium in each loading cycle is another problem that may occur during the test and alter the results. To avoid probe disconnection in the fatigue setup, the probes were embedded within the concrete sensor specimen at a short distance from the specimen edges. In addition, the probes were fixed in properly. Moreover, the probes were located out of the mechanically stressed region of the concrete sensor specimen, as presented in Figure 6, to ensure that the probes remained always adherent to the concrete. To avoid the surface connection between concrete sensors and test apparatus, insulation sheets were used between the concrete specimen and any metal parts of the test apparatus.