An analytical model for steady vertical flux through unsaturated soils with special hydraulic properties

- An analytical solution for modeling steady-state vertical flux is presented.
- The model assumes power law hydraulic conductivity and diffusivity functions.
- Algebraic expressions of practical and theoretical importance are also derived.
- It applies to positive and negative flux rates modeling infiltration and evaporation.
- It is useful for studying the effects of soil type and checking numerical schemes.

SummaryAn analytical solution for one-dimensional steady vertical flux through unsaturated homogeneous soils is presented. The model assumes power law hydraulic conductivity and diffusivity functions. The soil domain is a finite-depth flow medium overlying a water table. A steady constant flux is applied at the top boundary while a constant saturation value is specified at the bottom boundary. The general form of the analytical solution expresses implicitly the depth as function of the liquid water saturation. It can be used to model both infiltration through the soil surface and evaporation from the bottom, depending on the sign of the flux boundary value. The analytical solution takes into account the prediction of a drying front in the case of evaporation from deep water table. Algebraic expressions of practical and theoretical importance are derived in terms of soil water parameters. These expressions include the stored mass in the system at steady state as well as the drying front when it exists. The general form solution can be inverted back to obtain exact explicit solutions when the power law parameters are related. Numerical results show the effects of soil type, surface flux, capillarity, and gravity on the saturation distribution in the soil. The analytical solution is used for comparing between models, validating of numerical solutions, as well as for estimating the hydraulic parameters.