The transport of small particles in soil voids is a common problem in construction. Filtering determines the creation of foundations by pumping liquid grout and building watertight walls in the soil. A 1-D model of depth filtration for a slurry in a porous medium is considered. It is assumed that the velocity of the carrier liquid is high enough to detach the deposited particles from the carcass of the porous medium. To take into account the effect of sediment lifting, the particle release function is introduced into the standard filtration model. For the filtration model with deposit release, analytic solutions are found at the inlet of the porous sample and at the concentration front. An asymptotics near the concentration front and a traveling wave solution are constructed.