When a sandpile relaxes under vibration, it is known that its measured angle
of repose is bistable in a range of values bounded by a material-dependent
maximal angle of stability; thus, at the same angle of repose, a sandpile can
be stationary or avalanching, depending on its history. In the nearly jammed
slow dynamical regime, sandpile collapse to a zero angle of repose can also
occur, as a rare event. We claim here that fluctuations of {\it dilatancy} (or
local density) are the key ingredient that can explain such varied phenomena.
In this work, we model the dynamics of the angle of repose and of the density
fluctuations, in the presence of external noise, by means of coupled stochastic
equations. Among other things, we are able to describe sandpile collapse in
terms of an activated process, where an effective temperature (related to the
density as well as to the external vibration intensity) competes against the
configurational barriers created by the density fluctuations.Comment: 15 pages, 1 figure. Minor changes and update