## 3 Results and Discussion
### G-Value Concept and Its Relationship with Damage  
The decrease in the electrical resistance as a function of the number of cycles described in Section 3.2 was observed in all of the 18 specimens that were tested under cyclic load patterns. To find a possible correlation between the average electrical responses of the sensor over time in each cycle with the different levels of stress (S) in the fatigue test, the best linear regression model fitted to each sensor response at any stress levels is presented in Figure 10 and the slope of the model is called the G-value. The greater the stress level, the greater the damage; therefore, the absolute value of the G-value represents the damage rate per cycle in fatigue loading.  
This study results can be validated by [PERSON]'s [53] results, who found similar relationships between stress level and the fractional change in the resistance response Delta R/R\({}_{0}\) of self-sensing concrete. According to [PERSON], the irreversible part of Delta R/R\({}_{0}\) increased with the increase in stress level and fatigue cycle number [53]. By taking a closer look at [PERSON]'s results, it can be seen that the slopes of the baseline of the Delta R/R\({}_{0}\) response at different stress levels are approximately the same among different fatigue cycles, but the baseline slopes between two constant stress levels increase by increasing the number of fatigue cycles. This means that the irreversible Delta R/R\({}_{0}\) increases in each cycle in the constant stress level, so the slope increases.  
As [PERSON] mentioned [20], this variation in the slope of the baseline of the fractional change in the resistance (G-value) can be attributed to the damage propagation rate in the cement matrix. Based on literature findings, the G-value can be positive or negative related to two opposite mechanisms. One is the reduction of the gap between adjacent MWCNTs or the enhancement of the chance of touching one another, which contributes to a decrease in the resistivity of the self-sensing concrete. Such a mechanism is strongly related to the loading pattern (i.e., static or dynamic), the number of conductive fibers and their properties (i.e., length, diameter, and surface activity), dispersion quality, etc. The other is damage in the cement matrix, in the form of flaws and cracks, which can cut the MWCNTs and increase the resistivity of the self-sensing concrete. [PERSON] and [PERSON] verified the presence of these two opposite mechanisms by acoustic emission technique [10]. Based on their findings in comparison with this research results, it can be concluded that when an external load is applied to the concrete, the interaction of these two opposite mechanisms will result in different amounts of G-value. As illustrated in Figure 10, for higher stress levels (i.e., 90% and 80%), the G-value is negative. By increasing the stress level in the three-point bending fatigue test, the intensity of stress in the compression and tension area will increase. The experimental evidence that the G-value is negative in these cases seems to indicate that for the specific concrete sensor composition and settings adopted, the compression behavior  
Figure 10: Average electrical responses of self-sensing concrete specimens during the fatigue test under different stress levels.  
is the dominant effect at 90% and 80% stress levels, so the response variation is mainly due to the variation in connectivity between MWCNTs in the compression region. For lower stress levels (i.e., 70%), the G-value is positive. For this stress level, it can be assumed that the compression is not high enough to decrease the distance between MWCNTs and increase the conductivity for the specific concrete characteristics of the sensor studied. Therefore, the effect observed for S = 90% and 80% cannot be sufficiently manifested, and micro-cracking and cutting MWCNTs connections are the dominant effects that cause the decrease in conductivity and positive G-value.