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 analyse various structural quantities. These include the packing fraction ($ϕ$), force per disk ($F_d$) and force chain segment length ($l$) as a function of the tapping number ($τ$). 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 $τ$ for force per disk, the force chain segment length shows no dependence on $τ$. The $τ$ dependence of $F_d$ and $ϕ$ allows us to posit a linear relation between the total force of the granular pack ($F_{tot}^*(τ)$) and $ϕ(τ)$.

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