  We consider the stability of a porous medium submitted to a steady-state flow
with free-boundary. Assuming some hypotheses, it is possible to implement the
kinematic method by using an approximate pressure field bounding the true
pressure field from below. We are interested in finding such approximate
pressure fields and in proving that they bound the true pressure field from
below without knowing the true pressure field. We use fields which are
solutions of a problem with relaxed conditions with regard to the real problem.
Under a uniqueness condition of the solution of a weak formulation of the
problem, such fields are lower bounds for the true pressure field. Finally, we
give the example of a vertical dam.
