Distribution of contact forces in a homogeneous granular material of identical spheres under triaxial compression

Abstract

The distribution P(F) of contact forces F in a homogeneous isotropic disordered granular sample subject to uniform triaxial stress field is studied using a model where forces propagate and collide. Collisions occur at grain and obey given rules which allow satisfying local static equilibrium. Analogy with Boltzmann's equation of density evolution is drawn and used to derive the parameters that control the distribution Ps(F) of contact forces F in the stationary state in case of a packing of mono-disperse spheres. Using symmetry argument and mean field approximation, it is found that stationarity is achieved when the density Ps(F) of force can be written as the product of exponentials of quantities whose sums are preserved during collisions. This introduces 3 parameters in 2d and 6 in 3d which are the mean force components {Fxo, Fyo, Fzo}, and the mean torques of the force on a grain {Mxo, Myo, Mzo} >. Astonishingly, it seems that the theory cannot include distribution of contact orientation implicitly. Extension of the model is possible with some care to case of anisotropic packing. Pacs # : 5.40 ; 45.70 ; 62.20 ; 83.70.Fn