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Understanding the percolation process of water in unsaturated soils during rainfall is crucial. A mathematical model representing the movement of water in unsaturated soils was established on the basis of the one-dimensional Richards’ equation and the fractional-derivative Darcy model. By assuming that the soil-water characteristic curve can be described by the Gardner model, a semi-analytical solution was derived. The solution was verified through the finite element software COMSOL Multiphysics (COMSOL). The effects of fractional order α on percolation process and the efficiency of the fractional model were investigated.

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Semi-analytical Solution of Temporal Fractional Percolation Process in Unsaturated Soils

  • 会议论文

  • 发表日期：

    2025年

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  • Jidong Mao,
  • Jianguo Zheng,
  • Wei Shi,
  • Yongtang Yu,
  • Tao Zeng

摘要

Understanding the percolation process of water in unsaturated soils during rainfall is crucial. A mathematical model representing the movement of water in unsaturated soils was established on the basis of the one-dimensional Richards’ equation and the fractional-derivative Darcy model. By assuming that the soil-water characteristic curve can be described by the Gardner model, a semi-analytical solution was derived. The solution was verified through the finite element software COMSOL Multiphysics (COMSOL). The effects of fractional order α on percolation process and the efficiency of the fractional model were investigated.