## 1 Introduction  
An urgent task in modern construction in the Republic of Kazakhstan is to increase the durability and operational reliability of hydraulic structures and irrigation systems, on which the degree of wear reaches about 70%. Such structures operate under complex impacts from aggressive factors, including water with high mineralization, the cavitation effect of flows, and sharp daily and seasonal temperature fluctuations that involve multiple transitions through 0 \({}^{\circ}\)C during the autumn-winter period. These factors provoke the intensive development of destructive processes in the concrete matrix, contributing to leaching,carbonation, frost destruction, and the effects of salt solutions, which inevitably lead to a decrease in the strength and durability of structures [1; 2]. In light of the need to extend the service life of hydraulic structures, special attention is given to materials with improved operating characteristics, among which the use of SCC is considered a promising direction. This material is characterized by high homogeneity, structural density, and resistance to external influences. However, despite the significant potential for the use of SCC, its implementation in Kazakhstan remains limited due to insufficient scientific development, the absence of mass production of modern modified additives, a weak technological base of enterprises, and a lack of practical experience in calculating and designing structures using such materials, resulting in non-compliance with the requirements of current regulatory documents, such as SP RK EN 1992-1-1:2004 and ST RK EN 206-2017 [3]. Increasing the durability and operational reliability of structures made of SCC is possible through the use of protective coatings and polymer compositions, but these have several limitations. In particular, thin protective layers (about 0.2 mm) are susceptible to mechanical damage, which reduces their effectiveness in aggressive conditions [4]. Furthermore, while polymer compositions exhibit high resistance to external influences, their use is economically impractical in mass construction due to the high cost of components [5]. Thus, the most rational solution for enhancing the operational reliability of SCC is to modify the structure of the cement stone itself by utilizing multicomponent chemical-mineral additives that promote the formation of a dense and durable structure resistant to aggressive environments [6]. Additionally, [PERSON] et al. demonstrated that ternary binder systems combining industrial by-products (slag and manganese residue) with cement can significantly reduce environmental impact while maintaining or enhancing concrete durability [7]. Previous studies have shown that using mineral additives in heavy concretes can reduce shrinkage deformations by 20% and increase frost and water resistance by up to 25% [8]. This highlights the potential for further research into improving the performance characteristics of concrete by optimizing its microstructure and permeability. An analysis of scientific and technical literature allowed us to formulate a hypothesis that increasing the resistance of concrete to aggressive impacts can be achieved through mathematical optimization of the grain composition of the cement binder. This approach is based on forming a polydisperse structure of the cement matrix with efficient particle packing, which helps enhance the characteristics of concrete throughout its entire service life [9]. Optimization of the binder structure involves a detailed study of structure formation processes using topological analysis methods, which treat the binder as a spatial system of dispersed particles and phase formations interacting during the hydration process [10]. The most common method for studying the packing of dispersed systems is mathematical modeling using a complex sphere model, which enables the analysis of the packing density and interaction of particles of different sizes [11].