Hydrodynamic disconnectivity between surface water and groundwater is common in arid environments. It is also prone to affect shallow streams in wetter climate. Sediment layers with low permeability, owing to clogging, for instance, reduce hydrodynamic connectivity. The resistance of this clogging layer, results in unsaturated infiltration, which is characterized by the non-linear Richards equation. Either due to lack of field information, parsimony regarding computational resources or mere misunderstanding of the system, infiltration is often assumed saturated or drastically simplified in hydrogeological models. Here we show the existence of three simple generic asymptotic solutions to the unsaturated problem of vertical steady-state infiltration through a clogged profile, which we associate to three regimes: one dominated by the clogging layer, one by the underlying sediments and one depending on both layers. We also argue that infiltration rate roughly grows linearly with ponding depth. These observations motivate a refined definition of clogging potentially helpful in model selection as well as two novel approximate infiltration formulas. Our refined generic analytic framework is useful to better understand and formalize infiltration.