Minimum number of samples required for uniaxial compressive strength of heterogeneous sandstone with breccia clasts

The heterogeneity in breccia content and geometry significantly influences the variability of the mechanical properties of sandstone containing breccia clasts. However, previous studies have often neglected the distribution of breccia geometry, resulting in inaccurate assessments of mechanical behavior. To investigate mechanical properties and determine the minimum number of samples for testing, particle-shape indices were introduced to quantify breccia geometry and its statistical distribution. Using laboratory experiments and numerical simulations, we developed a model that incorporates breccia content and the distribution of breccia geometry. The study explored the effects of breccia area, slenderness, and roughness on the mechanical properties of sandstone containing breccia clasts, along with their impact on the minimum sample number. The findings reveal a strong positive correlation between breccia content and fine length with the uniaxial compressive strength of sandstone containing breccia clasts, with Pearson correlation coefficients of 0.87 and 0.62, respectively. In contrast, breccia roughness exhibited a weaker correlation, with a Pearson coefficient of 0.31. Increasing the variability of the fine length of the breccia significantly elevated the minimum sample number, while variability in breccia roughness had no significant effect. Although the area of individual breccia particles did not alter the minimum required sample number, it contributed to an increase in the uniaxial compressive strength of the sandstone with breccia clasts. This study reveals the underlying causes of the variability in the mechanical properties of sandstone containing breccia clasts and establishes a dynamic approach to determine the minimum sample number, which was found to be 14. The proposed method achieved a relative error of less than 2% in predicting the uniaxial compressive strength. These findings provide valuable insights into evaluating mechanical properties and determining its minimum required sample number.