From force distribution to average coordination number in frictional granular matter

We study the joint probability distribution of normal and tangential frictional forces in jammed granular media, Pμ(ft,fn), for various values of the friction coefficient μ, especially when μ=∞. A universal scaling law is found to collapse the data for μ=0 to ∞, demonstrating a link between the force distribution Pμ(ft,fn) and the average coordination number, zcμ. The results determine zcμ for a finite friction coefficient, extending the constraint-counting argument of isostatic granular packing to finite frictional packings.