On unsteady flows of pore pressure-activated granular materials

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.

Automated summary

The study focused on investigating mathematical properties of the system of nonlinear partial differential equations that describe evolutionary processes in water-saturated granular materials. It was found that the unconsolidated solid matrix behaves as an ideal plastic material before activation and then flows as a Newtonian or a generalized Newtonian fluid. The plastic yield stress is non-constant and depends on the difference between lithostatic pressure and pressure of the fluid in pore space, with research conducted on unsteady three-dimensional flows subject to stick-slip boundary conditions in an impermeable container.