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arXiv · 2003.06912

On unsteady flows of pore pressure-activated granular materials

Anna Abbatiello·Miroslav Bulíček·Tomáš Los·Josef Málek·Ondřej Souček
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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.

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Anna Abbatiello, Miroslav Bulíček, Tomáš Los, Josef Málek, Ondřej Souček. 2020-03-15. On unsteady flows of pore pressure-activated granular materials. https://doi.org/10.1007/s00033-020-01424-3

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