  We describe the asymptotic behaviour of a filtration problem from a
contaminated porous medium to a non-contaminated porous medium through thin
vertical fissures of fixed height h>0, of random thinness of order {\epsilon}
and which are $\epsilon$-periodically distributed. We compute the limit
velocity of the flow and the limit flux of pollutant at the interfaces between
the two porous media and the intermediate one.
