Fractal dimension in concrete and implementation for meso-simulation

A complete understanding of the geometrical structure of concrete is important. Based on the geometrical characteristics of concrete, hypothesizing that graded aggregates have a fractal effect is reasonable. In the framework of fractal theory, the fractal dimensions of aggregates and cement were clarified, and a mathematical model of the fractal dimension was formed to describe the geometrical characteristics of concrete. Two numerical meso-model groups generated by the random fractal and traditional generation method were measured and analyzed considering the gradation curve, coarse aggregate content, and weighted mean size as evaluation indices. It was verified that the evaluation indices of the numerical models with the fractal dimension of actual concrete and those of actual concrete were the same, and the numerical simulation results were consistent with theory. Based on sampling statistical analysis, the geometrical homogenization of the meso-model generated by the random fractal method was found to be satisfactory for meso-scale applications.