On probability distributions of contact force magnitudes in loaded dense granular media

This paper discusses possible models for probability distributions of contact force magnitudes in loaded granular media. Many authors have studied such distributions, based on experiments with real particles as well as simulations in 2D and 3D. This has led to various and partly contradicting suggestions for the form of those distributions, which are described in the present paper. Its new theoretical investigations start from the empirically justied assumption that the components of contact forces follow exponential distributions with a certain dependence structure. This leads to distributions of force magnitudes similar to Gamma distributions with shape parameters depending on space dimension, which is in good agreement to results from experiments and numerical simulations. Also the analytical and statistical difficulties of the problem of determination of distributions of force magnitudes are discussed. [PUBLICATION ABSTRACT]