Force measurements on static granular materials.

A method for measuring normal forces under a granular packing is introduced. A high precision electronic balance is used to measure normal forces on individual beads at the bottom of a granular material. Due to the high sensitivity of this setup the normal forces on individual beads without applying any external load on the system were measured. From these measurements the distribution of forces, the response to small perturbations at grain level and the spatial correlation between normal forces were investigated at the bottom of the packing. The distribution function is consistent with a power law with an exponent alpha=0.3 for small forces. At large forces a crossover to an exponential decay is observed with a decay constant beta=1.8. Small amplitude spatial correlations were observed in the normal forces at the bottom of the pile, and the radial pressure distribution was dependent of the different filling procedures. Finally we report on systematic relaxations in the measured weight as a function of time on single grains at the bottom of the packing after perturbing the system.