## 3 Results and Discussion
### Electrical Conductivity of the Development CFRCM and SFRCM  
Electrical conductivity of cement mortar occurs in electronic conduction as well as in ionic conduction. Electronic conduction signifies the flow of electric current due to the movement of free electrons in fibers, and ionic conduction refers to electrical conductivity due to the movement of ions in the water of pores [57]. In a cement mortar, when the volume fraction of fibers starts from \"0\", increases gradually, and the proportion exceeds a certain percentage, the distance between the fibers is narrowed and electrons hop through the non-conductive (cement mortar) area between the fibers, while conductivity is created in the cement mortar. As the volume fraction of fibers keeps increasing, a region appears in which the flow of electrons rapidly increases. Such a phenomenon is called a percolation  
Figure 11: The effect of fiber volume fractions on the compressive strength of developed conductive CFRCM, SFRCM versus PM specimens. phenomenon, and the time at which percolation starts or the state of fibers at this time is called a percolation threshold [58]. That is, the percolation threshold refers to the dosages in the state in which a continuous conductive pathway is secured through the contact between adjacent conductive internal particles (fibers). The most important of the state quantities at the percolation threshold are the volume fraction of fibers. Table 7 shows the average electrical conductivity (\(\sigma\)) measurement results of the developed conductive FRCM and PM according to the fiber volume fractions at each age (28, 56, and 91 days) and are also compared in Figure 12. As shown in Table 7 and Figure 12, the electrical conductivity slightly increased as the volume fraction of steel fibers increased compared to PM, but overall, the electrical conductivity did not improve significantly even if steel fibers were added up to 1.25%. It is thus made clear that the electrical conductivity could not be significantly improved in SFRCM containing steel fibers because the steel fibers used in this study could not form conductive pathways. In contrast, Figure 12 displays that the percolation transition region for CFRCM exhibits a so-called S-curve. It can be seen here that CFRCM reveals the onset of conductive pathways formation between 0.3% and 0.4% fibers, thereby increasing the conductivity. In particular, when the volume fraction of carbon fibers exceeds 0.4%, the percolation phenomenon takes place, rapidly increasing the electrical conductivity, and the carbon fibers start to come into contact and form a conductive pathway, thus greatly increasing the conductivity. However, the volume fraction of carbon fibers showed a gradual increase by 0.5-0.6%, and the ratio decreased somewhat since a conductive path was already formed. The reason for the decrease in the electrical conductivity of CFRCM in the region following the percolation phenomenon is thought to result from the occurrence of voids due to the mixing of a large dosage of fibers and from fiber ball phenomenon in which fibers aggregate with each other and, consequently, the amount of voids increases. The detected percolation threshold for CFRCM used in this study was 0.4% in terms of securing electrical conductivity, showing the optimal dosage of carbon fiber. Therefore, the upper limit of the percolation threshold may determine the optimal dosage of carbon fiber for the electrical conductivity of CFRCM. These findings have also been reported in previous studies [59; 60]. As shown in Table 7, for example, the average electrical conductivity of PM (plain mortar mix) at the age of 28, 56, and 91 days was about \(1.05\times 10^{-4}\) S/cm, \(8.66\times 10^{-5}\) S/cm, and \(6.18\times 10^{-5}\) S/cm, respectively, and that of SFRCM containing 1.25% fiber (Steel125 mix) was about \(7.94\times 10^{-4}\) S/cm, \(5.51\times 10^{-4}\) S/cm, and \(3.57\times 10^{-4}\) S/cm, respectively.