Fractal model of the strength of lightweight concrete based on volcanic tuff taking into account the scale effect

The study proposes a fractal model based on B. Mandelbrot's geometry. Mandelbrot geometry to describe the scale effect in concrete. It has been experimentally established that under-loading concrete undergoes degradation of its structure, which is expressed in the sequential destruction of fractals at different scale levels. It was found that the scale reduction leads to an increase in concrete strength: 20x20x20 mm specimens showed the highest strength among all four compositions (23.3-25.3 MPa). The average density of tuff concrete was also investigated: the smallest specimens had a density of 1961.3 kg/m³, while the largest specimens had a density of 1974.2 kg/m³, which is explained by the heterogeneity of the structure and pore distribution. The water permeability of concrete, evaluated through air permeability, showed that specimens with higher air permeability (30.2-30.5 s/cm³) had better water resistance (W14). These data indicate a correlation between air permeability and water resistance, which may be due to the denser structure and improved pore distribution. The study of air permeability makes it possible to predict the durability of concrete structures when exposed to moisture, as well as to improve the quality of building materials and reduce the cost of their operation.