土壤颗粒的分形特征及其应用

本文应用土壤颗粒的质量分布原理来描述土壤颗粒的分形特征。通过对10种土壤颗粒的机械组成进行分析,分别计算出它们的分形维数（D=2.489～2.896）,并分析了其与土壤质地之间的关系。同时对土壤颗粒分形维数与所对应土壤的幂函数型水分特征曲线的拟合分形维数进行比较分析,建立了二者之间的相关关系。结果表明:分形维数的大小反映了土壤质地中粘粒、粉粒和砂粒含量的变化,随粘粒含量的增多分形维数增大,随砂粒含量的增多分形维数减小;同时土壤颗粒分形维数与所对应的水分特征曲线的拟合分形维数呈现出良好的一致性,因而对所研究的土壤而言,可应用土壤颗粒的质量分形维数结合幂函数模型来估算土壤水分特性曲线。

FRACTAL PROPERTY OF SOIL PARTICLE SIZE DISTRIBUTION AND ITS APPLICATION

Numerous studies have shown that soil particle size distribution( PSD) , mass distribution, surface distribution and pore size distribution are fractals, which are generally described with fractal geometry. In this paper, the fractal properties of ten types of soils from loamy sand to clay were investigated with the method developed by Tyler and Wheatcraft(1992) on the basis of accumulative mass distribution of soil particles. Sieving data sets of the above mentioned ten soils were used to calculate fractal dimension which ranged from 2.489 to 2.896, and relationship between fractal dimension of PSD and soil texture was analyzed. Meanwhile the fractal dimension of PSD was compared with the fitted fractal dimension calculated from the calibration of the power-law expression of the corresponding soil water retention function developed with Menger sponge, and the mathematical relationship between them was therefore established. Results indicated that the fractal dimension of PSD increased with clay content but decreased with sand content, and the fractal dimension of PSD was approximately the same as and in linear relationship with the fractal dimension of the power-law expression for the soil water retention function. This implies that the soil water retention properties can be predicted by the power-law function in combination with the mass based fractal dimension of PSD.