Abstract: When solving the water infiltration problem in unsaturated soils, the hydraulic function is a function of water content or suction, which makes the equation governed by hydraulic function exhibits strong nonlinear characteristics resulting in the difficulty of solving the horizontal infiltration problem. Based on the assumption that the water flow in soil medium follows the path of time - consuming extreme value, a time functional was introduced, and the horizontal infiltration problem was transformed into a functional extreme value problem based on a variational principle. By solving Euler-Lagrange equation and combining with the boundary conditions, the explicit analytical solution of the nonlinear transient horizontal infiltration problem was obtained. Combined with the Brooks-Corey hydraulic function, the distribution of volume water content of this type of soils in the unsaturated state was explicitly solved. By calculating the water horizontal infiltration laws of four different types of soil samples through theoretical and numerical methods, the results obtained by the solution matched well with the existing results and numerical results, verifying the effectiveness of the method. The results show that the distribution of volume water content has a power function against location distance and wetting front distance ratio, and the power exponent depends on the shape parameter of soil water characteristic curve. Initial conditions and boundary conditions had different effects on the distribution of volumetric water content.

Key words: horizontal infiltration, variational method, Euler-Lagrange equation, Brooks-Corey model