## 2 Materials and Methods  
In this study, prismatic concrete sensors suitable to be embedded in self-sensing concrete elements were produced. To this purpose, multi-walled carbon nanotubes (MWCNTs) obtained from the Iranian Research Institute of Petroleum Industry (RIPI) were used and added to the concrete mix in a 0.15% proportion by weight of cement content, in analogy with previous studies [42; 43]. Using MWCNTs instead of carbon fibers (CFs) helps to increase the sensor's ability to detect crack initiation and propagation under fatigue conditions. This allows the use of a lower amount of MWCNTs than CFs so that lesser reinforcement is introduced and the mechanical properties of the sensors are more similar to those of the plain concrete they should be embedded into, with respect to the sensors using CFs. The main properties of the MWCNTs used are given in Table 1 and their microstructure is shown in Figure 1. Figure 2 summarizes the aggregate grading specifications for the concrete. The concrete mix design adopted is shown in Table 2. The aggregates were mixed to minimize the voids and hence maximize the density based on the Fuller curve. Type II Portland cement from Abyek Cement Company was used. Besides, 0.02 wt% tributyl phosphate produced by Sigma-Aldrich Co. was used as a defoamer. A dark brown solution of polycarbonate-based superplasticizer (Sarapus construction chemical manufacture) with 36%  
MWCNTs and surfactants were weighted and mixed in water and the solution was stirred for 10 min with a magnetic stirrer (WIFESTEER MSH-20B); then it was sonicated in an ultrasonic bath for 2 h and afterward with an ultrasonic probe for a further 90 min. The temperature was controlled during sonication to prevent damage to the MWCNTs structure [42]. The cement was added to the mixture in a high-speed mixer (3600 rpm--Pars-Khazar Co.). To eliminate the air bubble formation in the mix, tributyl phosphate was used as a defoamer. The aggregate fraction was added during the mixing process and the concrete was cast in molds (10 \(\times\) 10 \(\times\) 40 cm\({}^{3}\)) by applying a proper vibration. The concrete specimens were removed from the molds after 24 h and subsequently, they were cured in water at 25 \({}^{\circ}\)C for 28 days according to ASTM C192 [45]. In Figure 3 [46] these steps are presented. Two types of circuits have been used to measure the response of concrete sensors in previous studies, either with direct current (DC) or alternating current (AC) [21; 47; 48; 49], combined with two types of electrode schemes consisting of two-probe [16; 50; 51; 52; 53] and four-probe setups [23; 50; 54]. The use of direct current circuits is responsible for a resistance variation over time due to a polarization effect, as exemplified in Figure 4, where the evolution of the electrical resistance and deflection of the sensor in a three-point-bending fatigue test is presented (normalized values). The polarization effect changes the sensor resistivity response over time under constant low-cycle load in the DC circuit. The polarization effect occurs when the concrete sensor works as a capacitor. In the polarization effect, the reverse current generated in the concrete sensor due to sensor charging causes the reduction of the electrical current over time [55]. In this study, an alternating current generator was used with a four-probe set-up in the concrete sensor circuit that is an effective solution to eliminate the polarization effect, suggested by some works [52; 56]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Cement** & **MWCNTs** & **Fine Sand** & **Coarse Sand** & **Fine Gravel** & **Coarse Gravel** & **Water** \\ \hline kg/m\({}^{3}\) & 380 & 0.57 & 980.397 & 172.4 & 574.416 & 191.224 & 178.592 \\ Percentage & 15.34 & 0.023 & 39.58 & 6.96 & 23.19 & 7.72 & 7.21 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mix design. Figure 3: Cement-based concrete sensor preparation steps. Figure 2: Different aggregate grading test results according to Standard ASTM C136/C136M-14 [44].