Influence of Soil Heterogeneity and Gravity Fingers on Unsaturated Flow During Infiltration–Evaporation Cycle

Water infiltration in the vadose zone is a transient and unstable process influenced by several factors, including the non-linearity of soil hydraulic properties, rapidly changing boundary conditions, root growth, hysteresis, and soil heterogeneity. As a result, infiltration is often non-uniform and develops into preferential flow. This complex phenomenon, commonly manifested as gravity fingers, originates from wetting-front instabilities and saturation overshoot, the latter being a prerequisite for finger formation.

Experimental studies have consistently shown that infiltration into both homogeneous and heterogeneous soils frequently produces preferential pathways in the form of fingers. However, simulations of unsaturated flow typically rely on the Richards equation, which accounts only for local capillary pressure and therefore fails to reproduce preferential flow patterns. Alternative formulations have been proposed to overcome this limitation, such as the model by Cueto-Felgueroso et al. (2020), which incorporates non-local capillary effects.

In this work, we investigate unsaturated flow under infiltration–evaporation cycles, explicitly considering soil heterogeneity and the formation of gravity fingers. Our objective is to improve the modeling of infiltration and evaporation processes in soils, to better predict water flow behavior, and to characterize the impact of soil heterogeneity, non-linear properties, and gravity fingers on these processes. We are comparing two modeling approaches: the traditional Richards equation and the fourth-order spatial derivative model proposed by Cueto-Felgueroso et al. (2020). Flow is solved using the finite element library FEniCS, and soil heterogeneity is represented by Gaussian random permeability fields with varying correlation lengths and variances.

Keywords: infiltration and evaporation cycles, unsaturated flow, heterogeneity, gravity fingers, finite element method.

References

Luis Cueto-Felgueroso, Marı́a José Suarez-Navarro, Xiaojing Fu, and Ruben Juanes. Numerical simulation of unstable preferential flow during water infiltration into heterogeneous dry soil. Water, 12(3):909, 2020.