Application of fractal analysis in civil engineering: aggregate size distribution, surface damage detection, and crack propagation monitoring

Fractal geometry has emerged as a robust alternative to Euclidean geometry for characterizing irregular and complex structures, and its significance in civil engineering has increased with advances in computational tools. This study evaluates the effectiveness of fractal analysis in three domains: (i) aggregate particle size distribution, (ii) fracture surface characterization of fiber-reinforced mortars, and (iii) crack propagation monitoring in reinforced concrete beams. Initially, image-based fractal analysis of an aggregate pile produced granulometric curves that closely matched the sieve analysis results, with only minor deviations observed in the finer fractions. In the second stage, three-point bending tests on chopped glass fiber-reinforced mortars demonstrated an inverse correlation between flexural strength and fractal dimension, where specimens with higher strength exhibited lower fractal dimensions (1.64–1.84). Finally, the propagation of a dominant shear crack in a 2 m reinforced concrete beam was analyzed under four-point bending. The fractal dimension increased from approximately 1.05 at crack initiation to 1.31 at collapse, indicating that it may capture damage evolution more sensitively than displacement measurements. The findings suggest that fractal dimension can serve as a promising quantitative parameter for structural damage monitoring. In addition to laboratory applications, the method shows potential for rapid post-earthquake assessment of debris and for aggregate characterization in field conditions where experimental facilities are limited. This study highlights the versatility of fractal analysis and its potential as a complementary tool for structural health monitoring in civil engineering.