## 3 Properties of Multifunctional Cemertitious Composites
### Percolation Threshold  
The primary factor influencing the performance of multifunctional cementitious composites is the concentration of electrically conductive fillers [131]. Achieving optimal performance in multifunctional cementitious composites requires careful consideration of the percolation threshold value during specimen fabrication [132]. The percolation threshold represents the range where electrical resistivity experiences a significant reduction with the inclusion of conductive fillers, as illustrated in Figure 9 [92]. From Figure 9, it is apparent that electrical resistivity variations with the inclusion of conductive fillers are not considerable within zone A (insulation phase) [133]. However, beyond zone A and within zone B, there is a drastic drop in electrical resistivity with the inclusion of conductive fillers [134]. Towards the end of zone B, the impact of conductive fillers on reducing electrical resistivity decreases due to the congestion of direct contacts and conductive pathways [61]. Consequently, in zone C (the electron conductive-dominated phase), the further inclusion of conductive fillers does not significantly reduce electrical resistance, indicating that the optimal concentration of conductive fillers should be within the percolation zone (zone B) [135]. Figure 9: Influence of conductive filler concentration on electrical resistivity; A = insulation phase; B = percolation zone; C = electron conductive-dominated phase [92], published by Elsevier (2015). In zone A, the direct contact between conductive fillers is not significant, resulting in poor conductive pathways. Due to the low concentration of conductive fillers, the conductive mechanism in region A is primarily based on tunneling effects (electron hopping) in dry conditions and tunneling effects (electron hopping) and ion conduction in wet conditions [136]. The tunneling effect relies on the distance between conductive fillers and typically occurs when the distance is less than 10 nm. Therefore, in dry conditions, the electrical resistivity of self-sensing cementitious composites containing electrically conductive fillers below the percolation threshold is very high due to weak tunneling effects caused by the large distance between conductive fillers [137]. However, in wet conditions, the electrical resistivity of electrically conductive cementitious composites containing conductive fillers below the percolation threshold can considerably decrease due to ion conduction in the pore solution [138]. In other words, in wet conditions, the electrical mechanism of electrically conductive cementitious composites within zone A is based on ion conduction and tunneling effects. In zone B (percolation threshold), in dry conditions, the conductive mechanism is based on tunneling effects and direct conduction, resulting in considerably low electrical resistivity [139]. In zone B, the distance between conductive fillers is significantly small, leading to strong tunneling effects (electron hopping). Towards the end of zone B, tunneling effects considerably improve due to the very small distance between conductive fillers and the well-formed conductive pathways originating from direct contact between conductive fillers. In wet conditions, in region B, the conductive mechanism is based on ionic conduction, tunneling effects, and direct contact with conductive fillers [140]. In region B, therefore, the effects of moisture content on electrical resistivity are not considerable due to strong tunneling effects and direct contact with conductive fillers. In zone C, the conductive mechanism is primarily based on the direct contact with conductive fillers due to the high concentration of these fillers [141]. Consequently, the effects of moisture content (ionic conduction) on the electrical resistivity of self-sensing cementitious composites, when the content of conductive fillers exceeds the percolation threshold, are not significant [142].