Multiscale Force Networks in Highly Polydisperse Granular Media

We investigate highly polydisperse packings subjected to simple shear by contact dynamics simulations. A major unsolved issue is how granular texture and force chains depend on the size polydispersity and how far they influence the shear strength. The numerical treatment was made possible by ensuring the statistical representativity of particle size classes. An unexpected finding is that the internal friction angle is independent of polydispersity. We show that this behavior is related to two mechanisms underlying the stability of force chains: (i) The class of largest particles captures strong force chains, and (ii) these chains are equilibrated by weak forces carried by increasingly smaller particles as the size span broadens. In the presence of adhesion between particles, the Coulomb cohesion increases with size polydispersity as a result of enhanced force anisotropy.

Figure 1

Internal friction $\sin {\phi }^{*}$ as a function of particle size span $s$ both from raw simulation data and as predicted by Eq. (5). The error bars indicate the standard deviation of stress fluctuations in the steady state.

Figure 2

A snapshot of a highly polydisperse packing with size span $s=0.96$: (a) the entire sample and (b) a zoom. The floating particles excluded from the force network are in white. Line thickness is proportional to normal force.

Figure 3

Probability distribution function of normal forces $f=f_n/⟨f_n⟩$ normalized by the average force $⟨f_n⟩$ for different values of size span $s$.

Figure 4

Evolution of state anisotropies as a function of the size span in the steady shear state. The error bars correspond to the standard deviation of the fluctuations in the steady state. The polar diagrams of the corresponding angular distributions (black symbols) are shown for $s=0.96$ together with their fits (red) by truncated Fourier expansions [Eq. (4)].

Figure 5

Evolution of Coulomb cohesion $c$ normalized by the average pressure in the steady state as a function of size span $s$. The error bars correspond to the standard deviation of stress fluctuations in the steady state. The inset shows the steady-state anisotropies as a function of $s$.