Continuum Modeling and Discrete Element Simulations of Elastic-Quasi-Static Granular Flow in a Compressing Slot

Abstract

The stress generated by the horizontal compression of a vertical column of granular material is investigated. The column is open at the top so that the material is free to flow upward in the slot as it is compressed. This simple geometry has interesting mechanics because both elastic and frictional regimes coexist, and it is also relevant to problems involving the insulating material in cryogenic storage tanks. Two methods are used to investigate this problem: traditional continuum modeling and discrete element simulation. The continuum model assumes that the column consists of a frictional region near the top of the column and a linearly elastic region near the bottom. Analytic solutions are obtained for each region and predictions for the location of the transition are made based on intersections of the two solutions. A discrete element simulation of the same geometry is performed to compare with the results from the continuum model. Various conditions of wall friction and particle stiffness are simulated. Based on the outcome of this comparison, we verify that in a compressing slot there are essentially two distinct regions: a frictional flow region near the top of the column that results in an exponential increase in stress with depth. This eventually saturates leading to a linear-elastic plane strain region. The location of the transition between these two regions depends on the material properties and the state of the compression.