Simulation of the strain distribution under a two-dimensional sand pile

We study the averaged macroscopic strain tensor for a sand pile consisting of soft convex polygonal particles numerically, using the discrete-element method (DEM). First, we construct two types of "sand piles" by two different pouring protocols. Afterwards, we deform the sand piles, relaxing them under a 10% reduction of gravity. Four different types of methods, three best-fit strains and a derivative strain, are adopted for determining the strain distribution under a sand pile. The results of four different versions of strains obtained from DEM simulation are compared with each other. Moreover, we compare the vertical normal strain tensor between two types of sand piles qualitatively and show how the construction history of the piles affects their strain distribution.