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

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