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各种各样的统计幂定律关系经常成功地被用来描述碎屑大小分布和断口形状 (不平整度 )的分级规律 ,表明碎裂作用是一种尺度不变的作用过程。一条新的有关岩石碎裂作用破裂能量的尺度律 ,可以由分形几何以及Griffith能量平衡的概念推导出来 ,而且它与先前三条关于大小缩减或Hall Petch关系的理论是相一致的。从材料强度的观点来看 ,断口形状的分形维数是形状因子和岩石Weibull均质系数的函数。在任何一次采集中 ,如果碎屑都是致密压实的 ,那么大小分布和碎屑不平整度的分形维数是相同的。然而有些地壳碎屑在三维体积上已不再是致密压实的 ,破裂的地壳可被当作分形的多孔物质来处理。在此情况下 ,地壳碎屑形状的分形容量与地壳断口大小分布的分形维数相关 ,可以预期 ,在大地构造及地震强度的分形分析中 ,地壳断口大小分布的分形维数可作为断裂制约条件之一。
Various statistical laws of power-law relationships are often successfully used to describe the grading rules for the size distribution of crumbs and the shape of the fracture (roughness), suggesting that fragmentation is a scale-invariant process. A new scale law about the energy of rupture of rock fragmentation can be deduced from the concept of fractal geometry and Griffith energy balance, and it is consistent with the previous three theories of size reduction or Hall Petch. From the point of view of material strength, the fractal dimension of the fracture shape is a function of the shape factor and the Weibull homogeneous coefficient of the rock. In any acquisition, the fractal dimensions of size distribution and debris roughness are the same if the debris is densely compacted. However, some crustal crusts are no longer densely compacted in three-dimensional volumes, and the fractured crust can be treated as fractal porous matter. In this case, the fractal dimension of crustal crustal shape is related to the fractal dimension of crustal fracture size distribution. It is expected that the fractal dimension of crustal crush size distribution can be used as fracture condition in the fractal analysis of geotectonic and seismic intensity one.