## 1 Introduction  
Cement mortar and concrete are among the most widely used, durable and reliable materials in modern construction; therefore, improving their structure and properties has always been one of the main priorities of construction materials science. Currently, there is a wide variety of technical possibilities for modifying the cement-based composites and improving their physical and mechanical characteristics. These include decreasing the water-to-cement ratio [1, 2], increasing the binder fineness [3, 4], using plasticizers [5, 6], varying the hardening conditions [7], introducing the various types of fiber [8, 9, 10], etc. Moreover, many researchers around the world have claimed that the application of nano-sized additives can significantly improve the properties of the cement-based materials by affecting the processes of their structural formation [11, 12, 13]. In practice, the creation of favorable conditions for the effective hydration of Portland cement is achieved by adding the additives that have high activity due to the large surface area and the ability to compact the cement matrix structure [14, 15]. The presence of nano-sized particles in the hardening mineral matrix stimulates the formation of the layer of hydration products on their surface. Here, the further recrystallization of hydration products into larger crystal blocks is limited due to the high surface energy of nanoparticles. This provides the conditions for creating the high-density and defect-free structure that unites the conglomerate and gives it high density and strength. Furthermore, it rearranges the pore structure of the cement gel and ettringle towards smaller sized pores and promotesthe intensive formation of lower based calcium silicate hydrates [16] that increase the strength of cement matrix. Recently, carbon-based nanomaterials such as carbon black, isostatic graphite, graphene oxide, graphene nanoplates, carbon nanotubes and fibers have gained wide popularity in the field of construction composites modification [17; 18; 19]. In addition, many researchers believe that a promising direction in the modification of concretes and mortars is the use of nano-dispersed oxide systems SiO\({}_{2}\), Al\({}_{2}\)O\({}_{3}\), Fe\({}_{2}\)O\({}_{3}\), CaO that are similar in composition and structure to the products of cement hydration [20; 21; 22]. An example of such materials can be micro- and nanosilica, metakaolin fly ash, granulated blast furnace slag as well as synthetic additives--fumed silica, nanosilica, colloidal silica, etc. [23; 24; 25; 26]. At the same time, it is necessary to strive for the maximum reduction of the material cost while increasing the physical and mechanical characteristics. The cost of using carbon and synthetic silica-containing nano-sized materials, even considering their very low amount, is several times higher than the cost of natural silica-based additives as well as the wastes from various industries. The combined use of additives of different genesis can also be preferable as the mechanism of their influence on the processes of structural formation of the material has different natures [27; 28; 29]. It creates their synergistic effect on the processes of cement hydration and hardening, leading to the creation of composites with unique physical and mechanical characteristics. Namely, silicon-based additives introduced into the composition of the material are able to bind calcium hydroxide into low-basic calcium silicate hydrates C-S-H, which are characterized by increased strength. At the same time, carbon nanoparticles can change the morphology of cement hydration products, contributing to the compaction of the structure, which, in turn, leads to a strength increase [30; 31; 32]. Thereby, the purpose of this study is to develop a complex additive that combines both carbon nanoparticles and a silicon-based additive.