  In this work, we consider a mathematical model for flow in a unsaturated
porous medium containing a fracture. In all subdomains (the fracture and the
adjacent matrix blocks) the flow is governed by Richards' equation. The
submodels are coupled by physical transmission conditions expressing the
continuity of the normal fluxes and of the pressures. We start by analyzing the
case of a fracture having a fixed width-length ratio, called $\varepsilon > 0$.
Then we take the limit $\varepsilon \to 0$ and give a rigorous proof for the
convergence towards effective models. This is done in different regimes,
depending on how the ratio of porosities and permeabilities in the fracture,
respectively matrix scale with respect to $\varepsilon$, and leads to a variety
of effective models. Numerical simulations confirm the theoretical upscaling
results.
