Structural evolution of a granular pack under manual tapping

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 ($\varphi$), 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 $\varphi$ allows us to posit a linear relation between the total force of the granular pack ($F_{tot}^{\ast }(\tau )$) and $\varphi (\tau )$.

7 pages, 11 figures

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