基于分形理论的岩石冲击破坏分形分析

利用大直径分离式霍普金森压杆试验系统，对绢云母石英片岩和砂岩进行冲击压缩试验, 采用不同等级标准筛对岩石冲击破碎后试块进行筛分统计，运用分形几何理论，计算出冲击荷载作用下两种岩石破碎块度分布的分形维数，研究冲击速度对块度分维影响，分析两种岩石动态抗压强度随块度分维的变化关系。试验结果表明，绢云母石英片岩块度分维大部分集中在1.9~2.4之间，砂岩集中在2.5~3.0之间；两种岩石分形维数随冲击速度的升高呈上升趋势，近似线性正比关系；绢云母石英片岩动态抗压强度与块度分维无明显函数关系，砂岩动态抗压强度随块度分维的增大呈增加趋势。采用分形维数对岩石试件在冲击破碎过程中动态抗压强度的变化进行定量描述，为探索岩石动态破碎分形特征与冲击力学性能之间的内在规律，开辟新的研究途径。

Research on impact fracture of rock based on fractal theory

The impact experiment is made on the sericite-quartz schist and sandstone samples with SHPB apparatus of 100mm in diameter, and the fragment-size distribution of fragmental rocks is obtained through sieving and statistics of rock samples. Fractal dimensions of sericite-quartz schist and sandstone are calculated by using fractal geometric methods and the relationship between the dynamic compressive strength and the fractal dimensions of two rocks are analyzed. The experimental results indicate that the values of fractal dimensions of sericite-quartz schist range from 1.9 to 2.4 and the values of fractal dimensions of sandstone range from 2.5 to 3.0. The fractal dimensions of two rocks increase linearly with increasing in impact speed. However, the dynamic compressive strength of sericite-quartz schist has no obvious correlation with the fractal dimensions and the dynamic compressive strength of sandstone increases with increasing in fractal dimensions. Thus using the fractal dimensions to describe the dynamic compressive strength of two rocks may provide a new approach to investigate the inherence law between fractal characteristics and impact mechanical properties of rock materials.