On weak and strong contact force networks in granular materials

In an influential study on the micromechanical origin of stress transmission in granular materials, Radjaï et al. (1998) have proposed a division of the network of interparticle contacts into ‘weak’ and ‘strong’ contacts. This division is based on a comparison of the force at contacts with the average (over all contacts) force. They observed, from the results of a two-dimensional computer simulation of the behaviour of a system of particles, that the shear stress of the granular material is mainly carried by the strong contacts and that the anisotropy in the orientational distribution of the weak contacts is in the direction perpendicular to that of the full contact network.These findings are analytically predicted here in a qualitative sense, within a statistical framework that is based on a simple, self-similar expression for the conditional probability function for the normal force at contacts with given contact orientation.An alternative definition of weak and strong contacts is proposed here, in which the division of the contacts is based on a comparison of the force at contacts with the average force corresponding to the contact orientation. Contrary to the finding based on the definition of weak and strong contacts by Radjaï et al. (1998), with this alternative definition the pressure and the shear stress are (almost) equally carried by the weak contact network.