岩石破碎体的粒度分布与分形

SIZE AND FRACTAL DISTRIBUTIONS OF ROCK FRAGMENTS

本文系统研究了分形破碎体的筛上、筛下分布规律及其与一些典型粒度公式的关系，讨论了它们的理论基础和破碎机理。证明，仅在尺度范围足够宽，且D＜3时，分形分布才与指数α＜3的G-S分布一致；D＞3时符合筛上幂律分布；分形分布不可能与指数分布一致。Welbull分布，对数正态分布等仅在特殊情况下与分形分布一致。分形方法更好地反映了破碎的本质。分析结果表明，矿山岩石破碎体，包括天然砂，基本上符合分形规律。

By studing systematically the distribution laws of percentages retained or passing of fractalfragments,and discussing the relations between the fractal and some typical granularity formulas and theitpossible generating mechanisms,we have given a demostraion as follows. Only if D<3,the fractal distribution with a fairly broad range is consistent with the G-S distribution of whith exponential α<3,and for D>3,it is consistent with a power-law distritution of percentages retained,but it is unlikcly relatcd to the exponcntial distribution. The Wcibull distribution,log-normal distribution etc. are equivalent to the fractal only for exceptionaI cases. Fractal theories can reflect the nature of rock frangmentation better. Analysis results show that fragments of mine rocks,including natural sand,mainly fit in the fractal distribution.