The Relationship between Soil Structure and Water Characteristics Based on Fractal Theory
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摘要: 为定量获得土壤结构对其水力性质的指示作用，室内实验选用华北平原子牙河流域原状土样为研究对象，用张力计法和激光粒度分析仪分别测定土壤水分特征曲线和样品粒度分布，基于分形理论计算土壤粒度分布的分形维数，采用实验测定与模型验证相结合的方法对水分特征曲线进行分析.结果表明，土壤颗粒粒度分布在[10 μm，50 μm]区间内的分段分维值是表征土壤粒度累积分布显著上升段特征的关键参数，与0~80 kPa吸力范围内的土壤水分特征曲线幂函数模型拟合参数(a、b)有极显著相关关系.研究区内土壤水分特征曲线以分形形式表达的幂函数模型为：θ=100.78×(3-D)S(D-3)/3，利用土壤结构分形特征能够有效指示其水力性质.Abstract: In order to understand the indicative effect of soil structure on its hydraulic properties, undisturbed soil samples from the Ziya-River basin in the North China plain were selected as the research objects. The soil water characteristic curve was measured by tension meter method, and the particle size distribution of soil samples was measured by laser particle size analyzer. The fractal dimension of soil particle size distribution was calculated based on fractal theory. Soil water characteristic curve was analyzed by experimental measurement and model verification. The fractal dimension of soil particle size distribution in the range of[10 μm, 50 μm] is the key parameter to characterize the characteristics of the significant rising section of soil particle size distribution, which is significantly correlated with the fitting parameters (a, b) of the power function model of soil water characteristic curve in the suction range of 0-80 kPa. The power function model expressed by the fractal form of soil water characteristic curve in the study area is: θ=100.78×(3-D)S(D-3)/3, and the fractal characteristics of soil structure can effectively indicate its hydraulic properties.
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Key words:
- soil /
- fractal theory /
- soil particle size distribution /
- soil water characteristic curve /
- hydrogeology
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图 3 正定采样点S1分维拟合图
x轴为$\lg \frac{{{d_i}}}{{{d_{\max }}}}$；y轴为$\lg \frac{{V\left({\delta ＜ {d_i}} \right)}}{{{V_0}}}$
Fig. 3. Fractal dimension fitting diagram of ZD sampling (S1)
图 4 流域内不同位置采样剖面土壤水分特征曲线
Fig. 4. SWCC curves at different sampling positions and soil depths
表 1 采样点地理位置
Table 1. Geographical data of soil sampling locations
地理位置 样品编号 坐标 高程(m) 取样深度(m) 地貌 ZD S1 114°34'36.10"E, 38°08'14.10"N 73 0.43~0.53 山前平原 S2 0.9~1.0 S3 1.40~1.50 JZ S4 115°17'55.42"E, 37°34'58.09"N 27 0.87~0.97 冲积平原 S5 1.1~1.2 HJ S6 116°07'55.00"E, 38°23'53.00"N 13 0.67~0.77 冲积平原 S7 1.25~1.35 DC S8 116°37'37.30"E, 38°39'32.88"N 7 0.7~0.8 冲积平原 S9 0.87~0.97 YGD S10 117°32'24.00"E, 39°00'48.00"N 2 0.5~0.6 滨海平原 S11 0.7~0.8 YF S12 117°34'12.70"E, 38°59'25.43"N 2 0.35~0.45 滨海平原 S13 0.6~0.7 S14 0.96~1.06 
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表 2 采样点分段分维数
Table 2. Subsection fractal dimension of sampling point
采样点 编号 粒径特征区间(μm) 分段分维数 I1段 I2段 D1 D2 ZD S1 5~30 10~50 2.000 3 2.365 2 S2 5~30 10~50 2.039 6 2.194 3 S3 5~30 10~50 2.365 8 2.679 1 JZ S4 5~30 10~50 0.963 3 1.445 2 S5 5~30 10~50 2.262 9 2.739 3 HJ S6 5~30 10~50 1.780 7 2.164 0 S7 5~30 10~50 1.238 4 1.639 6 DC S8 5~30 10~50 2.380 9 2.790 6 S9 5~30 10~50 1.970 0 2.402 4 YGD S10 5~30 10.000~42.603 2.614 2 2.872 8 S11 5~30 10.00~38.93 2.740 3 2.918 0 YF S12 5~30 10.000~35.573 2.757 2 2.922 9 S13 5~30 10.000~35.573 2.771 5 2.926 3 S14 5~30 10.00~38.93 2.783 3 2.925 7 注：对于最大粒径小于50 μm的粒度分布，取粒径最大值作为区间右边界，如滨海新区的S10~S14采样点.
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表 3 不同采样点下幂函数经验公式拟合结果
Table 3. The fitting results of empirical formula in different sampling points
采样点 编号 幂函数参数拟合结果 a b R2 ZD S1 56.455 3 -0.162 38 0.916 6 S2 70.747 4 -0.315 4 0.922 7 S3 55.502 7 -0.330 1 0.950 0 JZ S4 180.803 6 -0.529 1 0.767 5 S5 77.985 9 -0.213 4 0.850 5 HJ S6 114.335 7 -0.412 3 0.979 2 S7 213.844 1 -0.534 9 0.987 7 DC S8 44.891 58 -0.147 88 0.973 3 S9 52.983 8 -0.150 55 0.949 8 YGD S10 42.066 2 -0.047 56 0.945 7 S11 47.767 4 -0.038 6 0.937 3 YF S12 39.325 6 -0.116 05 0.966 9 S13 40.956 4 -0.048 6 0.981 8 S14 49.236 3 -0.060 2 0.947 8
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表 4 土壤结构分维与土-水特征曲线拟合参数的Pearson相关系数
Table 4. Pearson correlation coefficient between FDs and SWCC fitting parameters
项目 D D1 D2 a -0.494 -0.89** -0.901** b 0.16 0.901** 0.906** 注：**表明在p < 0.01水平上极显著相关.
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