## 3 Results and Discussion
### Autogenous Shrinkage  
Figure 10a shows the autogenous shrinkage during 24 h. In the graph, the \(y\)-axis represents the autogenous strain after the final setting. As shown in the figure, the specimens expanded before 4 h. Several researchers have reported that specimens expanded at early ages due to the generation of ettringite [49; 50; 51]. The expansion rate increased as the CNT content increased. As shown in Figure 7a, the acceleration period accelerated as the CNT content increased. This also appears to have increased the expansion rate because hydration was accelerated before 4 h. After 4 h, the specimens were contracted by autogenous shrinkage. Figure 10b shows the autogenous shrinkage during 168 h. The autogenous shrinkage decreased as the CNT content increased. Autogenous shrinkage is caused by self-desiccation, which occurs when the water in capillary pores is reduced as it is used for the hydration of cement. Therefore, a decrease in autogenous shrinkage means that more water is left in the capillary pores [42]. It was expected that the addition of CNTs would increase autogenous shrinkage due to the accelerated hydration caused by the nucleation effect of CNTs, but the experimental results were found to be opposite. CNTs bridge adjacent hydrates because they have a long geometry, as shown in Figure 1b [47; 52]. This phenomenon is referred to as the bridge effect, and it can also be observed in the SEM images of a CNT-reinforced cement composite in Figure 11 [47]. The bridge effect of CNTs is known to improve the mechanical performance of cementitious materials, such as strength [47]. Figure 10: Autogenous shrinkage of CNT-reinforced cement composites: (**a**) 24 h; (**b**) 168 h.  
Figure 9: Agglomerated CNT in CRC05. Therefore, the bridge effect of CNTs appears to have decreased autogenous shrinkage even though the hydration of OPC was accelerated by them. Many studies have been conducted to investigate the autogenous shrinkage of CNT-reinforced cement composites, but various results have been reported depending on the experimental conditions. [PERSON] et al. (2018) reported that the autogenous shrinkage of paste with silica fume (SF) increased when CNTs were added. [PERSON] and [PERSON] (2018) reported that the addition of CNTs increased autogenous shrinkage at a W/C ratio of 0.25, but it decreased deformation at a W/C ratio of 0.4. [PERSON] et al. (2018) investigated autogenous shrinkage according to the substitution rate of SF and the CNT content, and reported that the CNT content to minimize autogenous shrinkage was different depending on the substitution rate of SF. Figure 12 shows the IRH of the CNT-reinforced cement composites. IRH began to decrease after 24 h, and IRH decreased more rapidly as the CNT content increased. For CRC05, IRH decreased after approximately 12 h. The time at which IRH began to decrease was delayed as the CNT content decreased. Figure 7 also shows that hydration was accelerated as the CNT content increased, indicating that the decrease in IRH was also accelerated due to the acceleration of hydration. CRC01 and CRC03 exhibited similar IRH values until 48 h, but the IRH of CRC03 was lower than that of CRC01 after 48 h. The difference in IRH between CRC00 and CRC05 was the largest at 36 h. The difference was maintained from 36 to 144 h, but it decreased after 144 h. This indicates that the addition of CNTs accelerates the water reduction rate inside the pores due to the increase in the initial hydration rate, but its influence decreases after 144 h. The IRH of CRC05 was lower than that of CRC03 until 144 h, but they became identical after 144 h. This indicates that the effect of CNT addition on IRH decreases as age increases.