The effects of interparticle cohesion on the collapse of granular columns

TL;DR

This work addresses how interparticle cohesion alters gravity-driven collapse of granular columns in two geometries by introducing a bulk cohesive number $\mathrm{Co}$ that compares macroscopic cohesion to particle weight. The authors compare two cohesion sources—pendular-state wet grains and polymer-coated grains—across axisymmetric (3D) and channelized (2D) geometries, and they demonstrate that final deposit morphologies follow the same scaling structure as cohesionless cases, with $\mathrm{Co}$ mainly shifting prefactors. They quantify cohesion via yield-strength measurements to define $\mathrm{Co}$ and show data collapse across geometries, supported by an alternative interpretation $\mathrm{Co}=\ell_c/d$, where $\ell_c=\tau_y/(\phi\rho g)$. The study provides a unifying framework connecting bulk cohesion to particle-scale forces, enabling cross-comparison of cohesive granular systems in geophysical and industrial contexts and suggesting extensions to broader cohesion ranges and numerical modeling.

Abstract

The presence of interparticle cohesion can drastically change the behavior of granular materials. For instance, powders are challenging to handle, and one can make a sandcastle using wet grains. In this study, we report experimental results for columns of model cohesive grains collapsing under their own weight in air and spreading on a rough horizontal surface. The effects of two different sources of interparticle cohesion on two collapse geometries are compared and rationalized in a common framework. Grains are made cohesive by adding a small amount of water, such that they are in the pendular state, or by applying a polymer coating. The effects of cohesion are reported for a cylindrical column that spreads unconfined axisymmetrically and a confined rectangular column that flows in a single direction. A dimensionless number, comparing macroscopic cohesive strength to particle weight, is shown to capture the effects of cohesion on the final morphology. To this end, a characterization of the cohesive strength of the granular materials is obtained, independent of the physical source of cohesion at the particle scale. Such a framework allows for a common description of cohesive granular materials with different sources of cohesion.

Figures (9)

• Figure 1: (a) Schematic of the 3D axisymmetric experimental apparatus. A hollow cylinder is first filled with a granular material, then the cylindrical shell is rapidly lifted, which allows the grains to spread axisymmetrically on a horizontal surface under their own weight ,as illustrated by the dashed lines. (b) Side view of the 3D axisymmetric setup showing the initial dimensions of the cylindrical column $H_0$ and $R_0$, and the final height $H_{\infty}$ and runout $R_{\infty}$ of the relaxed pile. (c) Side view of the 2D channelized setup showing the initial dimensions of the rectangular column $H_0$ and $L_0$, and the final deposit of final height $H_{\infty}$ and runout distance $\Delta L_{\infty} = L_{\infty} - L_0$. The horizontal bottom surfaces for both cases are coated with one layer of glued grains.
• Figure 2: (a) Inset: Schematic of the inclined plane setup. By changing the height $h$, the weight $W$ can be changed and controlled. Main figure: Shear and normal stresses $\tau$ and $\sigma$, respectively, corresponding to each failure experiment for all the tested grains. The best fits of the yield curves, which are shown in solid lines, are used to estimate the yield stress $\tau_{\rm y}$ and the friction coefficient $\mu$ using the Mohr-Coulomb failure criterion from Eq. \ref{['eq:Coulomb_Cohesion']}. (b) Measured volume fraction $\phi$ from the shear cell experiments for our range of grains as a function of $\mathrm{Co}$ [as defined in Eq. \ref{['eq:Co_Stress']}]. $\phi$ is averaged from all the trials, and the standard deviation from this average is the associated uncertainty. The evolution of the friction coefficient $\mu$ and the yield stress $\tau_{\rm y}$ as a function of $\mathrm{Co}$ are shown in (c) and (d), respectively. The uncertainties in both subfigures show the variation of fits.
• Figure 3: Side profiles of the cylindrical column collapsing axisymmetrically for various initial aspect ratios, $a$, and cohesions, $\mathrm{Co}$, taken every 0.03 s. (a) $a = 0.5$, (b) $a = 2$ and (c) $a = 10$. For each $a$, we report collapses with cohesionless grains, i.e., $\mathrm{Co}$ = 0, a medium cohesion with $\mathrm{Co}$ = 8.1 and with our most cohesive grains with $\mathrm{Co}$ = 20. The corresponding videos are available in supplemental materials.
• Figure 4: Time evolution of the spreading radius for the axisymmetric collapse of cylindrical columns after triggering the withdrawal of the confining cylinder. (a) $a = 0.5$, (b) $a=2.0$, and (c) $a=10$ for our full range of cohesion. These cases correspond to the evolutions shown in Fig. \ref{['fig:Fig3_TimeSeries']} with additional intermediate cohesion values.
• Figure 5: A top view of the relaxed piles for a selection of aspect ratios $a$ and cohesive numbers $\mathrm{Co}$. (a) $\mathrm{Co}=0$, with a trace of the initial cylindrical column of radius $R_0 =$ 4.2 cm shown. (b) and (c) correspond to moderate cohesions for wet grains ($\mathrm{Co}$ = 7.5) and CCGM ($\mathrm{Co}$ = 8.1), respectively, and lead to similar results. (d) $\mathrm{Co}$ = 20 corresponds to the most cohesive grains used in this study. A common scale bar is shown, corresponding to 10 cm.