Mixed formulation for an easy and robust numerical computation of sorptivity

Sorptivity is one of the most important parameters for the quantification of water infiltration into soils. proposed a specific formulation to derive sorptivity as a function of the soil water retention and hydraulic conductivity functions, as well as initial and final soil water contents. However, this formulation requires the integration of a function involving hydraulic diffusivity, which may be undefined or present numerical difficulties that cause numerical misestimations. In this study, we propose a mixed formulation that scales sorptivity and splits the integrals into two parts: the first term involves the scaled degree of saturation, while the second involves the scaled water pressure head. The new mixed formulation is shown to be robust and well-suited to any type of hydraulic function - even with infinite hydraulic diffusivity or positive air-entry water pressure heads - and any boundary condition, including infinite initial water pressure head, h -> -infinity. Lastly, we show the benefits of using the proposed formulation for modeling water into soil with analytical models that use sorptivity.