论我国特殊土粒度分布的分形结构

Fractal Structure of Granularity Distribution of Regional Soils in China

本文根据分形几何学理论,研究了我国黄土、膨胀土、红土三类特殊土的粒度成分特征,发现在双对数坐标下粒度含量与粒径之间呈直线关系,表明粒度分布具分形结构。根据该直线的斜率b,由公式D=3-b可求得相应的分维。计算结果表明,三类特殊土的分维界于2～3之间,且红土的分维大于膨胀土,黄土最小。分维是描述该系统的一个序参量,其大小反映了作为自组织系统的土体的本质特征,分维大,自组织程度高,土体演化处于高级阶段。本文还讨论了分维与分选程度、孔隙特征及结构特征的关系。在此基础上,指出分维是描述粘性土粒度特征,进行粘性土工程分类的一个合适的指标。

The granularity characteristics of loess, laterite and expansive soil in China are studied according to the fractal geometry. It is found that there is a linear relationship between the accumulative granularity content and the grain size in log-log plot, and it's slope b can be used to calculate the relative fractal dimension D by the equation D = 3 - b. Results show that the D of regional soils changes from 2 to 3, and the D of laterite is the largest and loess is the lowest. Further, the D may be taken as the series-parameter, which describes the soil system as a self-organization one. The higher the value of D, the greater the degree of the self-organization, correspondingly, the evolution of the soil is in the higher stage. Correlations between fractal dimension and sorting or grading, pore-size distribution, microstruc-ture characteristics are discussed respectively. It is concluded that the fractal dimension is a better index for the description of granularity characteristics and the classification of cohesive soils.