## 1 Introduction  
Over the past years, the demand for rapid-repair cementitious materials has increased dramatically due to the extensive construction of pavements since 1990 [1]. Cement concrete is widely used in road pavements with the advantage of high strength and long durability. However, one obstacle that hinders the fast development of cement concrete in pavements is the high difficulty and large economic cost of repairing the damaged road [1, 2]. In addition, considering the large traffic in a metropolis, such as Shanghai in China, a tiny, prolonged repair time can cause huge traffic jams [3]. Hence, it is very urgent to develop fast-setting and hardening cementitious materials used in the rapid repair of pavement [4]. The accelerator is one commonly used admixture in modern concrete to shorten the setting time and promote early strength [5, 6]. The alkali-free accelerator is widely used in civil engineering due to its advantages in maintaining long-term strength and durability [7]. Aluminum sulfate, as the most important component in the alkali-free accelerator, has attracted intensified attention due to its capability to reach the fast-setting and rapid strength development of concrete [8]. With the addition of AS, a substantial amount of Etheringite (AFt) will be formed within a quite short time; thereby, the setting time of the concrete can be significantly reduced. Apart from the rapid setting, both early and late mechanical strength can be promoted due to the fast consumption of calcium ions and accelerated cement hydration [9]. At present, most of the used repair cementitious materials are mainly prepared based on ordinary Portland cement. Considering the massive CO\({}_{2}\) emissions during the production of OPC, more low-carbon cement should be used as a rapid repair cementitious material [10]. Recently, using CSA to partially substitute OPC has become a promising method to decrease the carbon footprint of rapid-repair cementitious materials. It is estimated that the production of CSA can reduce \(\sim\)30% of CO\({}_{2}\) emissions compared to that of OPC [11]. Meanwhile, with the addition of CSA, the OPC-CSA binary blended cement exhibits the characteristics of rapid setting [12], adjustable rheological properties [13], and high sulfate resistance [14], which make them suitable to be used as rapid repair cementitious materials. However, the unsynchronized setting and hardening performance of the OPC-CSA binary blend have been found in many reports. It means that the strength development of the OPC-CSA binary blended cement was prohibited, even though the setting time can be greatly shortened [15]. Such an undesirable phenomenon restricts the widespread use of the OPC-CSA binary blend as a rapid-repair cementitious material. [PERSON] et al. reported that the slow development of strength can be mainly attributed to the depressed silicate phase hydration and the loose microstructure formed along with hydration [14]. Nowadays, the inclusion of nano-C-S-H, nano-Al\({}_{2}\)O\({}_{3}\), nano-TiO\({}_{2}\), nano-Fe\({}_{2}\)O\({}_{3}\), nano-SiO\({}_{2}\), nano-CaCO\({}_{3}\), and other nanoparticles in cementitious materials has become an effective method to promote the strength development of hardened cementitious materials, which can be attributed to the following reasons: Firstly, the silicate phase reaction can be greatly promoted through the addition of nanoparticles, which can act as the nucleation site during the hydration process of cement [16]. Moreover, the nanoparticles may react with the hydration products due to their high reactivity, which can also promote the hydration process and density the microstructure of the hardened cement paste [17]. Besides, the incorporation of nanoparticles can exert the filler effect and reduce the porosity of the hardened cement paste [18]. Among those mentioned nanoparticles, NC attracts high attention due to its low price and good capacity to enhance the early strength of hardened cement paste (HCP) [19].