Experimental and Numerical Studies of Saturation Overshoot during Infiltration into a Dry Soil

Downward infiltration of water into almost dry soil, when there is no ponding at the soil surface, often occurs in the form of fingers, with saturation overshoot at the finger tips. While this is well known, there is still uncertainty about the exact saturation pattern within fingers. We performed a series of one-dimensional water infiltration experiments into a dry soil to study the non-monotonicity of the saturation. We observed that saturation showed a non-monotonic behavior as a function of time. The overshoot was somewhat plateau shaped at relatively low flow rates but was quite sharp at higher flow rates. Two mathematical models, referred to as the extended standard (ESD) model and the interfacial area (IFA) model, were used to simulate the experimental results. Both models were based on extended forms of the Richards equation by including a dynamic capillary term. In the ESD model, standard equations for hysteresis were used. In the IFA model, the specific interfacial area was introduced to simulate hysteresis. Parameter values for both models were obtained from preliminary experiments or using empirical formulas. Only one parameter, the dynamic capillarity coefficient tau, was optimized to model saturation overshoot. While the ESD model did not reproduce the form of saturation overshoot for any combination of parameter values, the IFA model could provide good agreement with the data. To our knowledge, this is the first time where a combination of the IFA model and the dynamic capillarity equation has been used to simulate a set of experiments.