Study of the water vertical infiltration path in unsaturated soil based on a variational method: application of power function distribution of D(θ)

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Abstract
The classical Richards Equation of water infiltration in unsaturated soil is a partial differential equation, which is nonlinear and difficult to obtain analytical solution. Taking time as the least action variable, the infiltration path as a functional of time is established based on Richards Equation. The vertical infiltration problem of unsaturated soil under gravity is transformed into the functional extremum problem, and solved by Euler-Lagrange Equation. The results show that the diffusion coefficient D(θ) has a function relationship with the depth of wetting front. When the type of diffusion coefficient is known, the moisture content of wetting front at specified depth, the moisture content of the farthest wetting front and the maximum entropy distribution of soil moisture content can be obtained at the optimal path. Taking the optimal path as the standard, the accuracy of solving Richards Equation by Boltzmann transformation and linear transformation is tested.
Funding Information
  • the Natural Science Foundation of Jiangxi Provincial Department of Science and Technology (20202BABL204066)
  • the Natural Science Foundation of Jiangxi Provincial Department of Education (GJJ180954)

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