  We analyze, experimentally and numerically, the steady states, obtained by
tapping, of a 2D granular layer. Contrary to the usual assumption, we show that
the reversible (steady state branch) of the density--acceleration curve is
nonmonotonous. Accordingly, steady states with the same mean volume can be
reached by tapping the system with very different intensities. Simulations of
dissipative frictional disks show that equal volume steady states have
different values of the force moment tensor. Additionally, we find that steady
states of equal stress can be obtained by changing the duration of the taps;
however, these states present distinct mean volumes. These results confirm
previous speculations that the volume and the force moment tensor are both
needed to describe univocally equilibrium states in static granular assemblies.
