## 1 Introduction  
Cementitious materials play a vital role in the construction industry [1, 2]. Their complexity has not limited their range of applications. Concrete possesses many advantageous features, such as ease of production, low cost, high durability, versatility in molding, and energy efficiency [1, 2, 3]. In the past several decades, researchers have sought to enhance the physical properties of cementitious materials by utilizing nanomaterials [1, 2, 4, 5, 6, 7, 8, 9]. A cement-based nanocomposites, which harness the advantages of nanomaterials, have attracted the attention of numerous researchers throughout the world [4, 5, 6, 7, 8]. Ultra-fine additives of cement-based materials include nano-silica (NS), carbon nanotubes (CNTs), nanoclay, and nano-Al\({}_{2}\)O\({}_{3}\), and these additives have been the research subjects of numerous studies [5, 9, 10, 11, 12]. It was determined that NS introduces several beneficial characteristics when it is incorporated into cement, such as a reduction of the setting time and an increase in the calcium hydration products at early ages principally stemming from high pozzolanic reactivity with an exceptional surface area [13, 14, 15]. CNTs have remarkable characteristics due to their graphitic layers composed of carbon-carbon sp\({}^{2}\) bonding, which leads to a high stiffness and axial strength [16]. When they are embedded in cementitious materials, they contribute to enhancements in the mechanical characteristics due to the pore-filling and bridging effects between the cement hydration products [9; 17; 18]. Nanoclay, also known as nano-metakaolin, is a silica-based product. It produces calcium silicate hydrate (C-S-H) gel by reacting with calcium hydroxide (CH) and enhances the early strength, resistance to alkali-silica reactions, and sulfate resistance when incorporated into concrete [9; 17]. Nano-Al\({}_{2}\)O\({}_{3}\) was also introduced to cementitious materials, resulting in enhancements in the mechanical characteristics, such as the modulus of elasticity, compressive strength, and split tensile strength [18; 19]. These effects were attributed to high pozzolanic activity, which other inorganic nanomaterials exhibit [18]. Among those nanomaterials, NS and CNTs are most commonly chosen by researchers to impart outperforming physical characteristics to cement-based materials [10; 19]. Both NS and CNTs can fill in the pores and decrease the pore diameters [11; 14; 20; 21]. Furthermore, it is expected that NS may produce finer hydration products to enhance the anchorage of CNTs in the cement matrix. Meanwhile, it is often reported that CNTs are likely to agglomerate due to electrostatic attraction, and this results in deterioration in the physical characteristics of the resultant composites [1; 22]. Multiple studies have demonstrated that silica materials help to distribute CNTs in cementitious materials [22; 23; 24; 25; 26]. Thus, it is expected that the presence of NS may improve the distribution uniformity of CNTs. The representative studies in which NS and CNTs were utilized are summarized. [PERSON] et al., 2010 examined the influence of the multi-walled carbon nanotube (MWNT) length on the flexural strengths of cementitious composites and concluded that the strength enhancement rate accomplished using long MWNTs (10-100 nm) with a content of 0.025-0.048 wt.% was comparable to that accomplished using short MWNTs (10-30 nm) with a content of 0.08 wt.% [27]. [PERSON] et al., 2015 utilized a novel dispersion agent, Pluronic F-127, to distribute single-walled carbon nanotubes (SWNTs) [28]. They also experimentally examined the optimal dosage of the agent and carried out flexural and compressive strength tests that showed enhancements of 7% and 19% after 28 d of curing, respectively, by incorporating 0.1% SWNT [28]. [PERSON] et al., 2017 demonstrated that mechanical and electro-mechanical properties were enhanced by incorporations of MWNT and silica future [29].