沙粒粗糙度和粒径分布的分形特性

提出了一种度量沙粒粗糙度和沙粒粒径分布的分形维数的计算方法，用分规法和周长面积法度量沙粒平面剖面线的不规则性，用Ｗｅｉｂｕｌｌ分布模型分析研究沙粒粒径分布的规律。结果表明：沙粒的表面粗糙度越大，其分形维数越大；沙粒组成中的细沙越多，其分形维数越大。同时表明分形几何可用于不规则图形和破碎模型的定量研究。

Fractal Analysis of the Roughness and Grading of Sands

An evaluation of fractal dimensions of both physical particle roughness and grain size distribution of sand is made. The divider and area perimeter fractal dimensions are used to quantify the roughness of planar profiles of individual sand grains, and the Weibull model is used to describe the grading of sand. The results indicate that the rougher the sand profiles, the higher the corresponding fractal dimensions, and the higher the fragmentation fractal dimensions, the higher the relative percentage of fine sands in the size distribution. The results also show that the fractal theory is applicable to quantify the irregularity of sand surface and grain size distribution.