## 1 Introduction  
Carbon nanotubes (CNTs) are widely used owing to their mechanical, electrical, and thermal properties [1; 2; 3]. The electrical conductivity of CNTs is similar to that of metallic materials. Their yield strength ranges from 10 to 60 GPa, and their modulus of elasticity ranges from 0.3 to 1 TPa [4; 5]. Mixed with other materials, CNTs make it possible to create conducting pathways in composites even with a low content as they have high aspect ratios (between 10 and 1000) [6]. Several studies have also been conducted in the field of construction to apply CNTs to cement composites [7]. Previous studies focused on the effects of CNTs on the mechanical properties of cement composites, such as compressive, flexural, and tensile strengths [7; 8; 9; 10; 11]. In addition, a few other studies have been conducted on the heating and self-sensing properties of cement composites using the electromagnetic properties of CNTs [5; 12; 13; 14; 15; 16; 17]. To use CNT-reinforced cement composites in the field, their hydration and shrinkage properties need to be investigated; several researchers have conducted studies on such properties. [PERSON] and [PERSON] [18] reported that CNTs accelerate the early age hydration of cement, which is related to the nucleation effect of CNTs. They also reported that CNTs form homogeneous networks inside cement composites as fillers and that they play the role of an entangled mesh that supports hydration products. [PERSON] et al. [19] evaluated the interaction between CNTs and hydrate ions and explained the interaction between Ca\({}^{2+}\) and CNTs based on the binding mechanism. They also experimentally revealed that the C-S-H gel concentration was increased by CNTs [19]. [PERSON] et al. [20] reported that CNTs improve the toughness of cement composites as they serve as bridges between hydration products. [PERSON] et al. [21] reported that CNTs accelerate the generation of C-S-H or CH by providing nucleation sites with respect to cement hydration. [PERSON] et al. [22] investigated the mechanical properties of CNT-reinforced cement composites. They reported that CNTs improve the mechanical properties of cement composites because the microstructure of CNTs-reinforced cement composites become denser than normal cement composites. To improve the self-heating performance of CNT-reinforced cement composites, the homogeneity of the conducting pathways formed by CNTs inside the matrix must be ensured. Adding aggregate into the matrix interferes with the interconnectivity of CNTs and has an adverse effect on the conductive network, thereby increasing the electrical resistance [23]. In addition, cement composites with a low water-to-binder ratio increase the dispersibility of CNTs, thereby improving the electrical conductivity [24; 25]. Therefore, high-strength cement paste with a low water-to-cement (W/C) ratio is likely to be subjected to cracking at early ages due to the occurrence of high autogenous shrinkage [26; 27]. [PERSON] et al. [28] reported that the induction period decreased and the heat flow increased when 0.25% CNT was added compared to the cement weight. The authors also reported that CNTs accelerated the hydration of cement by affecting the nucleation of C-S-H and improving water availability around the CNTs. The accelerated cement hydration may increase the autogenous shrinkage. However, CNTs play the role of an entangled mesh that supports hydration products by forming homogeneous networks inside cement composites as fillers [18]. This increases the resistance to autogenous shrinkage by increasing the stiffness between the hydration products [29; 30]. [PERSON] et al. [31] investigated effect of CNTs on early autogenous shrinkage of cement paste. They also reported that the early autogenous shrinkage of cement paste decreased by adding CNTs because CNTs accelerated the hydration of cement composites. As mentioned above, many studies have been conducted on multifunctional concrete such as self-sensing concrete in which CNTs are applied to concrete.