Force chains as the link between particle and bulk friction angles in granular material

Abstract:

From initial motion of sediment in rivers, to landslides and rock fall, predictions of granular transport typically rely on a Mohr-Coulomb failure criterion in which resistance to motion is parameterized by a friction angle. Empirically determined friction angles are generally large and variable when applied to the movement of a single grain as in fluvial transport, but are generally smaller and more consistent when applied to effectively infinite numbers of grains as in soil mechanics. We propose that these two end member definitions of friction angle are linked by transmission of force along grain to grain contacts (i.e. granular force chains) over length scales of 1 to ~ 20 grain diameters. A numerical model based on the statistics of individual grain-pocket friction angles, targeted physical experiments, and discrete element modeling all demonstrate that the maximum stable angle of granular material on a rough bed decreases by up to 15° as the number of potentially unstable particles increases. Decreased stability with increasing number of grains occurs as force chains become longer and more effective at dislodging downslope grains. The average friction angle for an assembly of particles therefore emerges directly from the statistics of the individual grain-pocket friction angles and is distinct from the sliding coefficient of friction acting between grains. Small clusters of grains abound at the earth’s surface, and we suggest that force chains are important for a wide variety of subaerial and subaqueous sediment transport processes.