  When granular material is shaken vertically one observes convection, surface
fluidization, spontaneous heap formation and other effects. There is a
controversial discussion in literature whether there exists a threshold for the
Froude number $\Gamma=A_0\omega_0^2/g$ below which these effects cannot be
observed anymore. By means of theoretical analysis and computer simulation we
find that there is no such single threshold. Instead we propose a modified
criterion which coincides with critical Froude number $\Gamma_c=1$ for small
driving frequency $\omega_0$.
