黏性土粒径分布的多重分形特性及土-水特征曲线的预测研究

土壤粒径分布的分形特性常由单一分维数来描述,这一分形参数可作为土-水特征曲线模型中的常数。但实验证据显示,单一分维数不足以描述某些黏性土在整个粒径范围土粒的分形分布。为了评估粒径分布的多重分形参数预测土-水特征曲线的效能,对3个黏土样实测粒径分布和土-水特征曲线,研究粒径分布的多重分形特性,并利用分形模型预测土-水特征曲线。研究发现,在较为宽泛的粒径范围,土的粒径分布存在3个不同分维数的土粒区域,分维数的大小与土粒区域的粒径大小有关。粒径越大的区域,分维数越大;利用不同区域的分维数预测土-水特征曲线并与实测结果比较,显示模型预测对多重分形参数较为敏感,采用大粒径区域分维数的计算结果与实测数据甚为吻合。虽然多重分形参数精确描述了土粒的分形分布,但在预测土-水特征曲线时应考虑粒径分布分形标度性质的差异。

Predicting soil-water characteristic curve from multi-fractal particle-size distribution of clay

The fractal behavior of soil particle-size distribution (PSD) is characterized by a single fractal dimension,which is related to constants of models for soil-water characteristic curve (SWCC). However,experimental evidence shows that a single fractal parameter is not sufficient to characterize a fractal distribution for the entire range of soil particle sizes. In order to evaluate multi-fractal parameters potentially capability for prediction of SWCC,a series of PSD and SWCC tests was conducted for three clay samples to investigate multi-fractal PSDs behavior and prediction of SWCC model. It was found that three domains with different fractal dimension characterize the soil PSD within a wide size range. The magnitude of multi-fractal parameter is related to particle size. Large fractal dimension corresponds to the domains with large particle size. The prediction results obtained from the fractal dimension in each domain are compared with the measured data. The model to predict SWCC is shown to be sensitive to the value of multi-fractal parameters. The measured data is well agreement with model result obtained from the fractal dimension in domains with large particle size. The results indicate that although the multi-fractal parameters can accurately characterize soil PSDs, the differences in scaling properties of soil PSDs should be considered in predicting SWCC.