Hi,
Just few comments based on the previous discussion:
1) Are you running a Richards-based model with a steady-state solution? If so, I would highly recommend to use the transient mode. It is very hard to solve the non-linearity of the Richards' Equation under a steady-state solution.
2) It seems to me that model is solving fine. The fact that you see a "second" water table at the top, it reflects the typical wetting front propagation in an unsaturated medium. Ideally over the time, if recharge decreases, you may see the movement of this "second" phreatic level down to the regional water level. If the recharge is very large, eventually you will see that model becomes completely saturated after several iterations, therefore it will reach a topography-like phreatic surface.
3) Material properties: Are you sure that such van Genuchten values correspond to the assigned conductivity? As indicated in item 2, it seems to me that water is moving very slow. A higher conductivity necessarily does mean fast water movement, if van Genuchten properties are not the adequate. So, please make double-check.
4) You may try to decrease the non-linearity by means of using the Modified Van Genuchten relationship and assuming a linear form (i.e. what you named before as "sigma").