In Refs. [20, 23, 24] the above defined
interaction law has been tested in the case of many particles in
contact at the same time. For the viscous interaction law, i.e.
the linear spring-dashpot model, energy dissipation is very
inefficient, i.e. the so-called ``detachment effect'' occurs.
The time a wave needs to propagate through a system
of size 
was found to be comparable to 
.
Thus we will measure time in units of , and velocities
in units of 
, i.e. particle size divided by the contact time,
rather corresponding to the speed of sound inside the elastic material.
Thus we have the length l as the product of
typical time and typical velocity.
Dividing Eq. 1 by kl we find that the dimensionless
deformation x/l in a static situation, i.e. y' = 0, is proportional
to the dimensionless elastic force 
. In the
gravitational field the elastic force 
scales with m g,
where m is the mass of the pile, so that 
. We
tested for several situations that our results do depend rather on
the ratio g/k, than on the specific values chosen for g or k.