Numerical simulations of dense granular media lead, for various situations, to model the grains as rigid bodies, and to consider contact with friction for the interactions between grains (monuments, masonry, blocky rocks, geomaterial, ballasts, powders...) The dynamical evolution of such a collection of rigid bodies is non smooth, and dedicated numerical methods are available. When the number of grains is large (and the number of interactions even larger), the simulations are computationally intensive. In such cases, domain decomposition (DD) is expected to be an efficient computationally tool. The most efficient DD methods for mechanical problems are multilevel schemes, but for the granular dynamics with rigid grains, no elliptical operators are involved, and the classical coarse space designs are not directly applicable. Indeed, even without coarse space, some monolevel DD methods may exhibit a behavior similar to scalability. Though embedding a coarse space problem may be useful for deriving a numerical homogeneous constitutive law of a granular media, it is not obvious that the convergence rate will be significantly improved for such a problem, for which dynamics and non-smooth features may dominate the numerical behavior. Preliminary results lead to an indicator of convergence that does not exhibit clearly a lack of scalability for a mono-level domain decomposition method. An enriched version of the domain decomposition strategy will be described and tested according to these topics.