Structural evolution of a granular pack under manual tapping

TL;DR

This study investigates how a 2D granular pack's structure evolves under manual tapping, revealing exponential approaches to steady states in packing fraction and force distributions, with some quantities unaffected by tapping number.

Contribution

It introduces a detailed experimental analysis of structural and force chain evolution in a granular pack under manual tapping, highlighting exponential behaviors and independence of certain parameters from tapping.

Findings

Packing fraction approaches an asymptote exponentially.

Force per disk and force chain length follow exponential distributions.

Force chain segment length remains unaffected by tapping number.

Abstract

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 analyse various structural quantities. These include the packing fraction ($\phi$), force per disk ($F_d$) and force chain segment length ($l$) as a function of the tapping number ($\tau$). The increase in packing fraction with tapping number is found to exponentially approach an asymptotic value. An exponential distribution is observed for both the cumulative numbers of force per disk $F_d$ : $N_{cum}(F_d) = A_F \exp (-\frac{F_d}{F_0})$, and force chain segment length $l$ : $N_{cum}(l) = A_l \exp (-\frac{l}{l_0})$. Whereas the coefficient ${A_F}$ varies with $\tau$ for force per disk, the force chain segment length shows no dependence on $\tau$. The $\tau$ dependence of $F_d$ and $\phi$ allows us to posit a linear relation between the total force of the granular pack ($F_{tot}^*(\tau)$) and $\phi(\tau)$.