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Influences of different grain size contents on soil-water characteristic curve of unsaturated laterite based on fractal theory
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摘要: 颗粒级配是影响土-水特征曲线的主要因素之一，探讨这个问题对研究非饱和土的渗流和强度特性具有重要价值。以江西红土为研究对象，人工配制5组颗粒级配不同的土样，基于分形理论研究其分形特征及其分维数，结合滤纸法试验测量土样的土-水特征曲线并求得其特征值，然后分析各特征值与分维数之间的关系。结果表明：对于不同颗粒级配的土-水特征曲线，同一体积含水率下细土颗粒含量越多的土样其基质吸力越大；粗细土颗粒含量不同的土样均具有较好的分形特征；颗粒级配定量指标均随分维数的增加呈现出先增后减的规律；且分维数随着细粒土含量的减少而降低，进气值和残余基质吸力值均随分维数的增大而提高。说明可运用分维数讨论颗粒级配对土-水特征曲线的影响。Abstract: The contents of different particle sizes in soil are one of the main factors that affect the soil-water characteristic curve. It is of great practical value to study and analyze the seepage and strength problems of the unsaturated soil. In this paper, taking the laterite in Jiangxi Province as the research object, the soil samples having different contents of coarse and fine particles are prepared in five groups. And some studies of the fractal characteristics and fractal dimension D of the fractal theory are carried out on the basis of the fractal theory. The soil-water characteristic curves of soil samples are measured by filter paper method, and their characteristic values have been obtained. Then, the relationship between the characteristic values and the fractal dimension D is discussed and analyzed. The relevant testing with analysis results shows that for the soil-water characteristic curves with different particle size distributions, the greater the soil matrix suction of the soil samples with the same volume moisture content, the greater the fine soil matrix suction. The soil samples with different soil particle sizes have better fractal characteristics. It is feasible to analyze the influences of the particle size on the soil-water characteristic curves by the fractal dimension D. The quantitative indexes of the gradation of grain, Cu and Cc, show the law of increasing first and then decreasing with the increase of the fractal dimension D. And the fractal dimension D will decrease with the decrease of the fine soil content, and both the inlet values and the residual matrix suction values will increase with the increase of the fractal dimension D.
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Key words:
- fractal theory /
- particle content /
- filter paper method /
- SWCC /
- fractal dimension
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图 2 不同颗粒粒径含量下土－水特征曲线
Figure 2. Soil-water characteristic curves with different particle size distributions
图 3 土-水特征曲线中各点的定义
Figure 3. Definition of each point in soil-water characteristic curves
图 5 级配定量指标及关键粒径与分维数D的关系
Figure 5. Relationship curves between Cu, Cc, critical grain size and fractal dimension D
图 6 土-水特征曲线特征值与分维数D的关系
Figure 6. Relationships between characteristic values of soil-water characteristic curves and fractal dimension D
表 1 各土样在Fredlund & Xing1模型中的拟合参数及特征值
Table 1. Fitting parameters and characteristic values of each soil sample in Fredlund & Xing1 model
土样编号 模型参数a 模型参数n 模型参数m 复相关系数R 2 进气值/kPa 残余基质吸力/kPa S1 1 998.334 2 0.438 9 1.778 6 0.99 49.35 1 415 560.48 S2 11 443.032 4 0.392 0 3.299 2 0.98 39.22 995 364.59 S3 4 035.887 5 0.384 9 2.582 4 0.98 27.89 167 390.89 S4 15 469.104 8 0.377 7 4.476 3 0.99 14.27 120 102.49 S5 678.771 8 0.434 2 1.990 3 0.98 11.94 59 583.64 
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