In this talk, we are concerned with the numerical simulation of granular media, characterized as a large scale discrete system, involving non smooth interactions. The numerical simulations have to be performed using contact dynamic methods (Non Smooth Contact Dynamics developed by JJ Moreau) on a fully implicit resolution of the contact forces. At a given step of evolution, all the kinematic constraints within the packing are simultaneously taken into account together with the equations of motions to determine all the contact forces in the packing. This allows to deal properly with nonlocal momentum transfers implied in multiple collisions, contrary to molecular dynamics schemes traditionally used that reduce the system evolution to a succession of binary collisions. For such problems, domain decomposition approaches, essentially developed for continuum solid mechanics, are potential interesting alternative solvers. Herein, two partitioning strategies are proposed and the associated numerical schemes are analyzed in term of convergence, computational cost and scalability property. The railway ballast topic illustrates the interest of such approach. Current works and results are presented.