Grain volume distribution alters the critical phenomena in complex granular systems

Abstract

The grain size distribution (GSD) plays an important role in the mechanical properties of amorphous disordered systems and complex granular materials. Varying GSD causes segregation issues and alters critical behaviors. This work used the discrete element method (DEM) to investigate the rheological and critical behaviors of sheared granular flows with various GSDs. The results show that, while a unified rheological relation can be obtained, a characteristic length scale, which is associated with the contact probability and can be obtained from any GSD, is embedded within such a polydisperse disordered system. We further acquire a correlation function between critical solid fractions and dimensionless grain volume distributions. This work elucidates the effect of particle volumes on the rheology and micromechanics of dry granular systems and provides further insights in better incorporating the influence of other particle properties into a unified framework, which is helpful and critical for the corresponding engineering and geophysical problems.

Figures (6)

• Figure 1: Rheological behaviors: (a-c) The $\mu_{\mathrm{eff}}\sim I_{ca}$ and $\phi_s\sim I_{ca}$ relationships plotted for systems with size distribution D1, D2, and D3, where $I_{ca}$ is the conventional inertial number that uses system averaged particle diameter as the characteristic length. The inset of (b) shows the relationship between two length scales, $d_{ac}$ and $d_{aw}$, where $d_{ac}$ is the average particle diameter calculated based on contact number of each particle and $d_{aw}$ is the average particle diameter calculated based on volume of each particle. (e-f) The $\mu_{\mathrm{eff}}\sim I_{cw}$ and $\phi_s\sim I_{cw}$ relationships plotted for systems with size distribution D1, D2, and D3, where $I_{cw}$ is the new dimensionless number calculated with $d_{aw}$. Inset of (d) presents a simulation snapshop, and the inset of (f) is the relationship between $\phi_s/\phi_c$ and the proposed new inertial number $I_{cw}$ (see Equation \ref{['eq:Icw']}.
• Figure 2: Relationship between the effective viscosity of granular systems, $\eta_{\mathrm{eff}}=\tau/\dot{\gamma}$, and the solid fraction, $\phi_s$. In the inset of this figure, we change the horizontal and vertical axes into $|\phi_s - \phi_c|$ and ${\eta_{\mathrm{eff}}}^{-1/1.3}$, respectively. The dashed line represents a linear relationship.
• Figure 3: (a) Histogram of the number of contact while changing $I_{cw}$. This figure only plots data from the system of D3 and $\eta_s = 1.0$. (b) The $Z_c\sim \phi_s$ relationship for systems with different GSDs, and $Z_c$ is the average coordination number. (c) The volume percentage of particles with only 0 or 1 contact is plotted against $I_{cw}$. (d) Relationship between the dimensionless granular temperature, $T_g/(\dot{\gamma}d_{aw})^2$, and $\phi_s$ (inset: $T_g/(\dot{\gamma}d_{aw})^2\sim|\phi_c - \phi_s|$). (e) The relationship between $\phi_c$ and the dimensionless index of the grain volume distribution, $I_{GVD}$.
• Figure 4: (a) The time evolution of the shear stress, $\tau$, pressure, $\sigma_n$, and the solid fraction, $\phi_s$. (b) the profile of particle velocities in the $x-$direction, $V_{px}$. The inset of (b) shows the configuration of a simple shear simulation of the granular system.
• Figure 5: (a-d) show both the PDF and CDF of different GSDs for particle size ranging from 1 to 10 cm, while (c) and (f) show the PDF and CDF for systems with $d_p\in [3.16, 10]$ cm. In Figs. (g,h), we plot the rheological properties of systems with $d_p\in [3.16, 10]$ cm.