## 1 Introduction  
Incorporating carbon-based materials, such as carbon nanotube (CNT), carbon black, and carbon fiber (CF) into a cement composite enhances its conductivity to that of a semiconductor. Conductive cement composites have novel applications in the field of construction, such as self-sensing [1; 2; 3; 4; 5; 6; 7], self-heating [8; 9; 10], and electromagnetic shielding [11; 12]. Among the aforementioned materials, CNT, and carbon black are nanoscale fillers. Such fillers are too small to be dispersed in cement composites. Hence, the dispersion techniques of sonication [13; 14; 15; 16; 5; 17], surface treatment [13; 16; 17; 18; 19], or both [13; 16; 17], are necessary. Otherwise, the agglomerated fillers may cause mechanical and electric faults in cement composites due to the van der Waals interaction. CFs can be dispersed relatively easily, compared with nanoscale fillers because CFs are micrometers in diameter and millimeters in length. Since the dispersion of CFs can be improved simply by incorporating silica future [20; 21; 22; 23], the above-mentioned dispersion techniques may not be required. In previous studies, the percolation threshold of CF was reported to be approximately between 0.5%and 1.0% [11; 21; 22; 24; 25; 26; 27], while those of carbon nanotubes and carbon black were reported to be approximately 1.0% [5; 28; 29] and 7.22-11.39% [30], respectively. In other words, CFs are more efficient in forming electric pathways in cement composites [31]. Several researchers showed that incorporating 0.1% CF into a cement composite with 0.5% CNT resulted in a stable electrical conductivity [23] and outstanding self-sensing performance [4]. In particular, [PERSON] et al. [4] reported the feasibility of replacing 0.5% CNT with 0.1% CF for improving the self-sensing performance. Owing to the relatively low unit cost of CF (approximately 19% of CNT [4]), mass production of CF is more suitable than that of nanoscale fillers. Thus, CF has been applied to the reinforcements of various types for concrete structures such as CF reinforced polymer (CFRP) sheet [32; 33], grid [34; 35], rebar [36; 37] and so on. Additionally, since commercial CF is produced by chopping a CF bundle with thousand monofilaments, it is possible to be produced in various lengths. Generally, long CFs are more difficult to be dispersed than short CFs [38]. Such poor dispersion serves as mechanical drawbacks [39]. Thus, short CF is preferred due to this dispersion problem [40; 41]. Several researchers have investigated the effects of CF length on the electrical conductivity, and they have agreed that the longer the CF, the higher the electrical conductivity of the cement composite [21; 42; 43]. This is because the contact probability of each CF filament increases as the length of CF increases. However, if the CF filament is long, a wide electrode spacing may be required. If the electrode spacing is narrow, there is not sufficient space for the CF to be dispersed. Although most researchers have studied only the influence of the CF length on the electrical conductivity of cement composites, they did not consider the effects of electrode spacing. Generally, to measure the electrical properties of a cement composite, the electrodes are set based on the two- or four-probe configurations [44; 45]. The former configuration is conceptually simple: two electrodes inserted in a cement composite serve as current (sources) and voltage (sense) terminals. However, the measurement of the resistance in the two-probe method can be overestimated because the resistance includes the contact resistance arising from the interface between the electrode and cement composite [44; 45]. This overestimation is considerably large for a high resistance range. On the contrary, in a four-probe configuration, the current (source) and voltage (sense) terminals operate separately; the voltage is measured from the inner electrodes, while the current flows between the outer electrodes.