Power series solution for ponded infiltration on sloping surfaces

SummaryRecently it has been shown that the Philip power series solution can also be applied for falling head ponded infiltration (Mollerup and Hansen, 2007) or more generally for variable head (VH) ponded infiltration on flat surfaces (Mollerup, 2007). In this study, it is shown that the power series solution can also be applied for VH ponded infiltration on sloping surfaces. Numerical simulations have been made for a Guelph Loam. For a VH scenario, the power series solution was compared with a 2D FEM-solution of Richards' equation with good agreement. Using the developed series solutions, a VH scenario was compared with constant head (CH) simulations with both a ponding depth of zero and the average ponding depth as used in the VH simulations. Especially the latter gave small differences in the cumulative infiltration compared with the VH results. Simulations showed that cumulative infiltration normal to the slope as function of time is decreasing with increasing slope angles for similar vertical ponding depths, corresponding to equal amount of surface water on a given horizontal slope section. In contrast, the infiltration on a given projected horizontal area increases with the slope angle.

► A power series solution for infiltration on sloping surfaces is presented. ► The theory can be applied variable head ponded infiltration. ► For a scenario the power series solution is compared with a 2D FEM-solution. ► A variable head scenario is compared with constant head scenarios. ► The effect of slope angle is investigated.