## 2 Materials and Methods  
The research involved both theoretical and applied methods. The theoretical aspect was grounded in mathematical principles, considering mathematics, construction materials science, and colloid chemistry, along with analysis and modeling. This facilitated a deeper exploration of the topology of dispersed systems and a comparison of results with those from previous research groups, concentrating on the durability and operational reliability of SCC. The applied research aimed to validate the theoretical hypothesis regarding the feasibility of using polydisperse binders in SCC. Experiments were carried out to evaluate the theoretical conclusions about the durability and operational reliability of the resulting SCC, as well as to process and document the results obtained in accordance with standards. All materials used in the study were sourced and produced in Kazakhstan. All studies and tests adhered to the regulatory documentation in effect in Kazakhstan. The study aimed to determine the optimal polyfractional composition, based on the cement clinker component, which achieves maximum or near-maximum spatial packing of polyfractional binder particles, thereby contributing to the transformation of the physical and mechanical properties of SCC. To verify the scientific hypothesis and achieve the aim of improving the structure and performance properties of SCC through the use of technology to optimize its most vulnerable component--cement stone--based on the principle of polydisperse structure formation and utilizing modern three-dimensional modeling algorithms, a set of research tasks was established as follows [14]:  
* A computational validation of the potential to obtain a hardened cement matrix with an ordered fine crystalline structure by controlling the binder (cement) composition with varying dispersity and high packing density;
* Laboratory studies of concrete samples of SCC with variable compositions of polyfractional cement focused on identifying the optimal composition regarding the bifurcation processes of the physical and mechanical properties of concrete. The research included two consecutive stages: a preliminary stage of the study and the main stage. During the preliminary studies, the following works were carried out:  
* Mathematical modeling of the packing density of polyfractional compositions to identify the most efficient dispersed cement powders;  
Figure 1: Covering with circles in two-dimensional space: polygons and elementary cells in cubic or hexagonal packing [12]. * Preliminary assessment of the strength of SCC based on the most efficient dispersed powders to select the most prospective compositions for the subsequent main research. During the main studies, laboratory tests were carried out, including an assessment of the following physical and mechanical properties of concrete:
* X-ray phase analysis;
* Evaluation of compressive and bending strength;
* Evaluation of water saturation (absorption);
* Evaluation of water permeability;
* Evaluation of frost resistance;
* Evaluation of chemical resistance. The composition of self-compacting concrete C35/45, developed at the Temirbeton-1 plant, is based on quick-hardening Portland cement with an additive content of no more than 5%, and was used as a reference sample. According to the basic characteristics required for SCC, the material has the following rheological indicators: workability class of the mixture SF2 (670 mm) and viscosity class VF2 (14 s), according to [15]. Since the proposed composition includes only polyc fractional cement (instead of standard cement), the rheological properties were not considered as evaluation criteria. The composition of the reference sample is presented in Table 1.  
Portland cement clinker supplied by Standard Cement LLP (Shymkent, Kazakhstan) was used in the studies.