The Fractal Dimension, Structure Characteristics, and Damage Effects of Multi-Scale Cracks on Sandstone Under Triaxial Compression

To study the influence of the spatial distribution and structure of multi-scale cracks on the mechanical behavior of rocks, triaxial compression tests and cyclic triaxial complete loading and unloading tests were conducted on sandstone, with real-time wave velocity monitoring and CT scan testing. The quantitative classification criteria for multi-scale cracks on sandstone were established, and the constraint effect of confining pressure was analyzed. The crack with a length less than 0.1 mm is considered a small-scale crack, 0.1–1 mm is a medium-scale crack, and larger than 1 mm is a large-scale crack. As the confining pressure increases, the spatial fractal dimension of large-scale cracks decreases, while that of medium-scale cracks increases, and that of small-scale cracks remains stable. The respective nonlinear models of the aspect ratio were established with the length and density of multi-scale cracks. The results indicate significant differences in the effects of cracks of different scales on rock damage. The distribution density of medium-scale cracks in the failed specimen is higher, which is the main reason to produce damage. The small-scale cracks mainly originate from relatively uniform initial cracks in rocks, mainly distributed in medium-density and low-density areas. The results of this research provide important insights into how to quantitatively evaluate the damage of rocks.