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    基于分形理论研究土壤结构及其水分特征关系

    戴磊 王贵玲 何雨江

    戴磊, 王贵玲, 何雨江, 2021. 基于分形理论研究土壤结构及其水分特征关系. 地球科学, 46(9): 3410-3420. doi: 10.3799/dqkx.2020.345
    引用本文: 戴磊, 王贵玲, 何雨江, 2021. 基于分形理论研究土壤结构及其水分特征关系. 地球科学, 46(9): 3410-3420. doi: 10.3799/dqkx.2020.345
    Dai Lei, Wang Guiling, He Yujiang, 2021. The Relationship between Soil Structure and Water Characteristics Based on Fractal Theory. Earth Science, 46(9): 3410-3420. doi: 10.3799/dqkx.2020.345
    Citation: Dai Lei, Wang Guiling, He Yujiang, 2021. The Relationship between Soil Structure and Water Characteristics Based on Fractal Theory. Earth Science, 46(9): 3410-3420. doi: 10.3799/dqkx.2020.345

    基于分形理论研究土壤结构及其水分特征关系

    doi: 10.3799/dqkx.2020.345
    基金项目: 

    国家自然科学基金项目 41672249

    国家自然科学基金项目 41877201

    河北省省级科技计划项目 20374201D

    详细信息
      作者简介:

      戴磊(1983-), 男, 博士研究生, 从事多孔介质结构表征、传递过程与岩土方面研究.ORCID: 0000-0002-1692-270X.E-mail: davy202628@163.com

      通讯作者:

      王贵玲, E-mail: guilingw@163.com

    • 中图分类号: P341

    The Relationship between Soil Structure and Water Characteristics Based on Fractal Theory

    • 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(ab)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.

       

    • 图  1  采样点分布

      Fig.  1.  Schematic diagram of sampling sites distribution

      图  2  粒径分布

      曲线图为粒径频数分布;散点图为粒径累积分布

      Fig.  2.  The distribution of grain size constitutes

      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

      图  5  ab分别与D2的拟合关系

      Fig.  5.  a & b are fitted with D2, respectively

      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
      下载: 导出CSV

      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 I2 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.
      下载: 导出CSV

      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
      下载: 导出CSV

      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.
      下载: 导出CSV
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