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

Abstract

ABSTRACT The classical Richards equation of water infiltration in unsaturated soil is a partial differential equation, which is non-linear and difficult to solve analytically. Taking time as the variable with the least action, the infiltration path as a function of time is established based on the Richards equation. The vertical infiltration problem of unsaturated soil under gravity is transformed into the functional extremum problem, and solved with the Euler-Lagrange equation. The results show that the diffusion coefficient D(θ) has a functional relationship with the depth of the wetting front. When the type of diffusion coefficient is known, the moisture content of the wetting front at a 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 the Richards equation by Boltzmann transformation and linear transformation is tested.