  We investigate mathematical properties of the system of nonlinear partial
differential equations that describe, under certain simplifying assumptions,
evolutionary processes in water-saturated granular materials. The
unconsolidated solid matrix behaves as an ideal plastic material before the
activation takes place and then it starts to flow as a Newtonian or a
generalized Newtonian fluid. The plastic yield stress is non-constant and
depends on the difference between the given lithostatic pressure and the
pressure of the fluid in a pore space. We study unsteady three-dimensional
flows in an impermeable container, subject to stick-slip boundary conditions.
Under realistic assumptions on the data, we establish long-time and large-data
existence theory.
