ORIGINAL PAPER Discrete-Element Computation of Averaged Tensorial Fields in Sand Piles Consisting of Polygonal Particles Pradip Roul • Alexander Schinner • Klaus Kassner Received: 21 August 2010 / Accepted: 25 April 2011 / Published online: 7 May 2011 Ó Springer Science+Business Media B.V. 2011 Abstract This work is a contribution to the under- standing of the mechanical properties of non-cohesive granular materials in the presence of friction and a continuation of our previous work (Roul et al. 2010) on numerical investigation of the macroscopic mechan- ical properties of sand piles. Besides previous numer- ical results obtained for sand piles that were poured from a localized source (‘‘point source’’), we here consider sand piles that were built by adopting a ‘‘line source’’ or ‘‘raining procedure’’. Simulations were carried out in two-dimensional systems with soft convex polygonal particles, using the discrete element method (DEM). First, we focus on computing the macroscopic continuum quantities of the resulting symmetric sand piles. We then show how the con- struction history of the sand piles affects their mechanical properties including strain, fabric, volume fraction, and stress distributions; we also show how the latter are affected by the shape of the particles. Finally, stress tensors are studied for asymmetric sand piles, where the particles are dropped from either a point source or a line source. We find that the behaviour of stress distribution at the bottom of an asymmetric sand pile is qualitatively the same as that obtained from an analytical solution by Didwania and co-workers (Proc R Soc Lond A 456:2569–2588, 2000). Keywords Discrete element method (DEM)  Sand pile  Representative volume element (RVE)  Stress  Strain  Fabric 1 Introduction During the last few years, extensive research has been devoted to the study of the mechanical properties of granular materials. To some extent, this is due to their importance in applications within various industrial branches such as the pharmaceutical, agricultural, geotechnical, and energy production industries. On the other hand, granular media are also interesting from a fundamental point of view—so far no generally applicable coherent theoretical description for their macro-states is available, a situation that calls for more scientific activity. In particular, the stress distribution under a sand pile has attracted much attention, based on theoretical (Bouchaud et al. 1995; Wittmer et al. 1996, 1997; Cantelaube and Goddard 1997; Didwania et al. 2000; Tejchman and Wu 2008; Claudin et al. P. Roul (&) Institute of Mathematics, Potsdam University, 14469 Potsdam, Germany e-mail: drpkroul@yahoo.com P. Roul  K. Kassner Institute of Theoretical Physics, Otto-Von-Guericke University Magdeburg, Postfach 4120, 39106 Magdeburg, Germany A. Schinner T-Systems, Dachauer Straße 665, 80995 Mu ¨nchen, Germany 123 Geotech Geol Eng (2011) 29:597–610 DOI 10.1007/s10706-011-9406-0