  We prepare static granular beds under gravity in different stationary states
by tapping the system with pulsed excitations of controlled amplitude and
duration. The macroscopic state---defined by the ensemble of static
configurations explored by the system tap after tap---for a given tap intensity
and duration is studied in terms of volume, V, and force moment tensor, \Sigma.
In a previous paper [Pugnaloni et al., Phys. Rev. E 82, 050301(R) (2010)], we
reported evidence supporting that such macroscopic states cannot be fully
described by using only V or \Sigma, apart from the number of particles N. In
this work, we present an analysis of the fluctuations of these variables that
indicates that V and \Sigma may be sufficient to define the macroscopic states.
Moreover, we show that only one of the invariants of \Sigma is necessary, since
each component of \Sigma falls onto a master curve when plotted as a function
of Tr(\Sigma). This implies that these granular assemblies have a common shape
for the stress tensor, even though it does not correspond to the hydrostatic
type. Although most results are obtained by molecular dynamics simulations, we
present supporting experimental results.
