Fractal indexing of rock strength data for safer geo-environmental assessments

This study presents a novel approach to evaluating the reliability of rock strength data by integrating specimen geometry, mechanical behavior, and fractal analysis. Fifteen marble core specimens with length-to-diameter (L/D) ratios of ~ 2.0, 2.5, and 3.0 were tested under uniaxial compression to determine key mechanical parameters: uniaxial compressive strength (UCS), elastic modulus (E), and Poisson’s ratio (ν). Axial stress–strain curves were subjected to box-counting fractal analysis to derive fractal dimension (Df) values, thereby quantifying the complexity of deformation. To assess data consistency across specimen groups, a new dimensionless metric—Fractal-Integrated Strength Index (FISI)—was developed by combining the means and variabilities of UCS, E, and Df. The results revealed that specimens with L/D ≈ 2.5 yield the most stable and representative mechanical responses, whereas L/D ≈ 2.0 samples exhibit significant variability. These findings emphasize the critical influence of specimen geometry on test reliability and highlight the potential of fractal-based metrics in enhancing data robustness. The proposed FISI index provides a practical basis for geotechnical assessments in urban geo-environmental projects, where consistent mechanical characterization is key to sustainable and safe construction.