双峰土-水特征曲线分形模型及其在孔隙分类中的应用

Fractal model for bimodal soil-water characteristic curve and its application in pore classification

现有的双峰土-水特征曲线(SWCC)模型大多由单峰土-水特征曲线的经验模型衍生而来,这些模型中的参数一般没有明确的物理意义和取值范围,导致通过拟合方法确定参数大小时出现多解情况,因而从很大程度上限制了双峰SWCC的理论研究。根据毛细管理论,双峰SWCC对应于双峰孔径分布(PSD),基于此,利用Menger海绵模型对双峰PSD进行了分形描述,并以此建立了双峰SWCC的物理模型。利用该模型对20组已发表的双峰SWCC试验数据进行拟合,并与其他学者提出的模型进行对比。结果表明本文模型具有良好的拟合效果。此外,基于建立的双峰SWCC模型提出了一种孔隙分类方法,经验证,该方法所得结果较为准确,且具有应用简便、理论基础明确的优势。

Most existing bimodal soil-water characteristic curve(SWCC) models are derived from the empirical models for unimodal SWCC, in which the parameters have no clear physical meanings or value ranges generally. When the parameters are determined by these models, there are always multiple solutions, thus the theoretical researches on the bimodal SWCC are restricted to a large extent. According to the capillary theory, the bimodal SWCC is usually associated with the bimodal pore size distribution(PSD). On account of this, a fractal description method for the bimodal PSD is presented by using Menger sponge model, and a physical model for the bimodal SWCC is established. The established model is employed to fit twenty sets of published data of bimodal SWCC, and compared with the models proposed by other scholars. The results show that the proposed model has a good fitting performance. Furthermore, a method for pore classification is proposed from the established bimodal SWCC model. It is proved that the results obtained by this method are relatively accurate, with the advantages of simple application and clear theoretical basis.