Erodible, granular beds are fragile

Abstract

Geophysical flows that involve the transport of grains and the shearing of colloids and non-Brownian suspensions often take place above a substrate composed of the same particles that can be incorporated into the flow. Despite the importance of understanding such erodible beds to the phrasing of appropriate boundary conditions for the solution of continuum models, a rigorous definition of the erodible bed and the constitutive relations for the stresses within it are still lacking. Here, we use discrete-element simulations to show that the intense, intermittent forming and breaking of contact chains marks the transition to the erodible bed at a critical solid volume fraction, as in shear jamming of steady, homogeneous flows. However, the compressible, collisional flow that confines the bed is not strong enough to insure the stability of the contact network, resulting in a bulk stiffness that is three orders of magnitude less than in shear jamming.