Structural Evolution of a Granular Pack under Manual Tapping

We experimentally study a two-dimensional (2D) granular pack of photoelastic disks subject to vertical manual tapping. Using bright-and dark-field images, we employ gradient-based image analysis methods to analyze various structural quantities. These include the packing fraction (phi), force per disk (F-d), and force chain segment length (l) as functions of the tapping number (tau). The increase in the packing fraction with the tapping number is found to exponentially approach an asymptotic value. An exponential distribution is observed for the cumulative numbers of both the force per disk F-d : N-cum(F-d) = A(F) exp(-F-d/F-0), and the force chain segment length l : N-cum(l) = A(l) exp(-l/l(0)). Whereas the coefficient A(F) varies with tau for F-d, l shows no dependence on tau. The tau dependences of F-d and phi allow us to posit a linear relationship between the total force of the granular pack F-tot* (tau) and phi(tau).