On unsteady flows of pore pressure-activated granular materials
Abstract
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.
Cite
@article{arxiv.2003.06912,
title = {On unsteady flows of pore pressure-activated granular materials},
author = {Anna Abbatiello and Miroslav Bulíček and Tomáš Los and Josef Málek and Ondřej Souček},
journal= {arXiv preprint arXiv:2003.06912},
year = {2020}
}