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, $P_{\mu}(f_t, f_n)$, for various friction coefficient $\mu$, especially when $\mu = \infty$. A universal scaling law is found to collapse the data for $\mu=0$ to $\infty$ demonstrating a link between force distribution $P_{\mu}(f_t, f_n)$ and average coordination number, $z^{\mu}_c$. The results determine $z_c^\mu$ for a finite friction coefficient, extending the constraints counting argument of isostatic granular packing to finite frictional packings.