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.