  Sand pile models are dynamical systems emphasizing the phenomenon of Self
Organized Criticality (SOC). From N stacked grains, iterating evolution rules
leads to some critical configuration where a small disturbance has deep
consequences on the system, involving numerous steps of grain fall. Physicists
L. Kadanoff et al. inspire KSPM, a model presenting a sharp SOC behavior,
extending the well known Sand Pile Model. In KSPM with parameter D we start
from a pile of N stacked grains and apply the rule: D-1 grains can fall from
column i onto the D-1 adjacent columns to the right if the difference of height
between columns i and i+1 is greater or equal to D. We propose an iterative
study of KSPM evolution where one single grain addition is repeated on a heap
of sand. The sequence of grain falls following a single grain addition is
called an avalanche. From a certain column precisely studied for D=3, we
provide a plain process describing avalanches.
