Statistical-mechanical characteristics of dense planar granular systems

We demonstrate the use of a structural and statistical characterisation method on two types of planar disc packs. One is a very dense pack of mean coordination number 5.20 and the other of mean coordination number 4.0. Except for constraining the mean coordination number in the latter one, the different pack types were constructed by the same deposition process and had the same disc size distribution, for a fair statistical comparison. We show that the two types converge to limit statistics and that these limit statistics are different. We analyse the limit statistics and compare between both types of packs, demonstrating that the differences are directly related to the difference in the mean coordination numbers. We then find quantitatively the difference between the (inverse) compactivities of the two pack types: . This explicit result supports strongly the validity of Edwards approach and underpins it as a useful tool to characterise granular systems quantitatively. In particular, it also paves the way to quantify the elusive compactivity.