On a formula finding fractal dimension

Abstract

Purpose: The article is devoted to the determination of the fractal dimension of cellular concrete, in particular foam concrete, and the further clarification of the relationship between fractal dimension and porosity and average density of cellular concrete. Design/methodology/approach: In the theoretical description of disordered systems, the fundamentals of fractal theory are actively used, which allow obtaining statistical indicators of chaotic natural and artificially disordered systems, which include cellular concrete. The parameters of the pore structure are difficult to quantify by conventional methods because of the complexity and irregularity of the pore structure due to their random distribution. Findings: Formulas for calculating the fractal dimension and average density of highly porous material are calculated and proposed. The formula for calculating the average density takes into account the density of the material between the pore walls. Research limitations/implications: The calculation of the fractal dimension is one of the main factors affecting the practical application of the theory of fractals, a natural problem arises on a theoretical basis to justify these calculations. Practical implications: The formulas proposed in this work for calculating the fractal dimension and density of a highly porous structure improve research on methods for producing substances with a controlled fractal structure, which will help create materials with unusual mechanical properties, density, and porosity. Originality/value: The formula for calculating the fractal dimension obtained in the work improves the well-known Hausdorff-Bezikovich formula. On the other hand, it makes it possible to obtain a highly porous structure with a given density of the material under study.