Dilatancy of two-dimensional disk packing

Earth and Environmental Sciences, Nagoya University - Tikusa, Nagoya 464-8601, Japan

^a sirono@eps.nagoya-u.ac.jp

Received: 6 July 2011
Accepted: 12 September 2011

Abstract

Dilatancy is numerically determined for a two-dimensional disk packing with a uniform radius distribution between 0.1 and 0.5 in dimensionless units. The minimum expansion of the packing decreases with a power-law exponent of −2.1 as the number of disks increases. By identifying a set of packed disks moving cooperatively, different rearrangements can be distinguished. The average number of distinct rearrangements exceeds two, irrespective of the number of disks. These results imply that tightly packed disks can rearrange continuously from one configuration to another.