General Infiltration Law for Structured Soils from the Porous Media Momentum Equation and Its Simplification for Horton’s Law

Abstract

Infiltration and overland flow, as a pair of watershed process, are fundamental in hydrology. Infiltration is even more fundamental because without an accurate infiltration model, it is impossible to model overland flow accurately. However, the current infiltration theory, based on the Richards theory, is self-contradictory, though it has been used for more than nine decades. This is because Richards used the Darcy–Buckingham law to describe infiltration dynamics and thus neglected the effect of infiltration acceleration, whereas his result shows that the acceleration is not negligible, at least in the initial phase, which is against his premise. We call this self-contradiction the “Richards paradox.” To resolve this paradox, we have to consider the acceleration in infiltration dynamic equations. We then replace the Darcy–Buckingham law with the porous media momentum equation in this research, which leads to a new infiltration theory and a simple general infiltration law (GIL). Theoretically, this GIL is valid for laminar, transitional, and turbulent infiltrations. Practically, this law reduces to Horton’s law for laminar infiltration. In addition, this new theory explains why the Green–Ampt equation fails in the initial phase of infiltration. After that, the proposed GIL, together with its simplification of Horton’s law, is tested with field data and compared with the Richards theory. Finally, the application, limitations, and research needs of the proposed method are briefly described. It is expected that this research, together with the general unit hydrograph model for both overland flow and subsurface flow, will provide a deep understanding of the watershed process and an advanced tool for watershed modeling. The current infiltration theory based on the Richards theory from laboratory tests does not agree with data from field soils that are heterogeneous and have macropores and pore networks. The widely used Horton’s empirical law agrees with field data well but is not supported by rigorous fundamental physical laws. This research filled this theory–practice gap by applying the porous media continuity and momentum equations to infiltration dynamics and obtained a simple general infiltration law, which reduces to Horton’s law for laminar infiltration. The proposed law can be applied for simulations of infiltration process in hydrology, soil sciences, agricultural and civil engineering, irrigation design, soil and water conservation, and even chemical and food engineering.