We propose an alternative approach to count the microscopic static configurations of granular packs under gravity by considering arches. This strategy obviates the problem of filtering out configurations that are not mechanically stable, opening the way for a range of granular models to be studied via ensemble theory. Following this arch-based approach, we have obtained the exact density of states for a 2D, non-interacting rigid arch model of granular assemblies. The calculated arch size distribution and volume fluctuations show qualitative agreement with realistic simulations of tapped granular beds. We have also validated our calculations by comparing them with the analytic solution for the limiting case of a quasi-1D column of frictionless disks.
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