  We propose an alternative approach to count the microscopic static
configurations of granular packs under gravity by considering arches. This
strategy simplifies 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 two-dimensional 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
with the analytic solution for the limiting case of a quasi-one-dimensional
column of frictionless disks.
