A Bethe lattice representation for sandpiles
  Avalanches in sandpiles are represented throughout a process of percolation in a Bethe lattice with a feedback mechanism. The results indicate that the frequency spectrum and probability distribution of avalanches resemble more to experimental results than other models using cellular automata simulations. Apparent discrepancies between experiments are reconciled. Critical behavior is here expressed troughout the critical properties of percolation phenomena. 
Oscar Sotolongo-Costa, Alexei Vazquez and J.C. Antoranz