A Model for Rock Fragment Size Based on Crack Propagation Dynamics
摘要
The size of rock fragments serves as a critical indicator reflecting the degree of fragmentation, which has significant implications for the design and optimization of engineering blasting parameters. Currently, research on fragment size has relied predominantly on geometric, statistical, and energy-based methods; however, studies from the perspective of fracture dynamics are lacking. In this context, based on fracture mechanics theory, this study investigates the propagation and coalescence patterns of wing cracks under dynamic loading. By combining this with materials mechanics, a stability analysis of rock pillars is conducted, leading to the establishment of a predictive model for fragment size. This study investigates the effects of the strain rate and initial crack concentration on the cumulative mass distribution, morphological characteristics, and average fragment size of fragments. The results indicate that an increase in the strain rate leads to the coalescence of smaller-scale cracks, ultimately resulting in specimen failure. A power-law relationship between the strain rate and the size of coalescing cracks is derived through a fitting process. As the strain rate increases, both the cumulative number of fragments and the cumulative mass curves shift to the left, indicating a decrease in fragment size with increasing strain rate. The cumulative mass curve of fragments follows a power-law distribution, and its logarithm exhibits a linear pattern. Statistical analysis of the fragment shapes indicates that the aspect ratio is independent of the strain rate. As the initial crack concentration increases, the strain rate required for crack coalescence decreases. There is a negative correlation between the strain rate and average fragment size. Model validation revealed that this model is reasonable, revealing the mechanism of dynamic fragmentation and providing theoretical support for engineering design.