Convection and motion in 2-d embankments under cyclic boundary conditions

TL;DR

This paper investigates grain motion in a 2D embankment under cyclic forcing, revealing conditions for stable periodic flow, localized flow regions, and the onset of bulk convection, supported by theoretical modeling and experimental comparison.

Contribution

It introduces a Coulomb-type model to analyze flow stability and flow localization in 2D embankments under cyclic boundary conditions, highlighting when bulk convection occurs.

Findings

No periodic solutions for high friction parameters.

Flow localization occurs at free surface, near wall, and in yield band.

Bulk convection arises when periodic solutions are unstable.

Abstract

The motion of grains in a 2d embankment under periodic horizontal forcing is studied theoretically using Coulomb-type modelling. Periodic conditions are used to determined the inclination of the free surface. It is shown that no periodic solution can be found in some domain of the bulk- and wall- friction parameters larger than 30 degrees. When a stable periodic solution exists, we show that the finite amplitude of motion leads to generate a flow localised (i) at the free surface, (ii) near the bulldozer wall and (iii) in the yield band; this may enforce a bulk convection too. At last, we argue why bulk convection is generated when the periodic solution is not stable. Results are compared to experimental data. Pacs # : 5.40.-a ; 5.45.-a ; 45.70.-n ; 62.20.-x ; 83.50.V