Basal layer of granular flow down smooth and rough inclines: kinematics, slip laws and rheology

TL;DR

This study uses simulations to analyze the basal layer dynamics in granular flows down inclined planes, revealing different regimes, slip laws, and rheological behaviors that extend current models.

Contribution

It introduces detailed simulation-based analysis of basal layer dynamics, identifying flow regimes and developing slip laws that improve understanding of granular flow rheology.

Findings

Identified three flow regimes based on roughness parameter R_a.

Developed general basal slip laws relating slip velocity to shear rate and roughness.

Showed basal layer rheology deviates from $$ rheology and aligns with Bagnold's scaling.

Abstract

Granular flow down an inclined plane is ubiquitous in geophysical and industrial applications. On rough inclines, the flow exhibits Bagnold's velocity profile and follows the so-called $\mu(I)$ local rheology. On insufficiently rough or smooth inclines, however, velocity slip occurs at the bottom and a basal layer with strong agitation emerges below the bulk, which is not predicted by the local rheology. Here, we use discrete element method simulations to study detailed dynamics of the basal layer in granular flows down both smooth and rough inclines. We control the roughness via a dimensionless parameter, $R_a$, varied systematically from 0 (flat, frictional plane) to near 1 (very rough plane). Three flow regimes are identified: a slip regime ($R_a \lesssim 0.45$) where a dilated basal layer appears, a no-slip regime ($R_a \gtrsim 0.6$) and an intermediate transition regime. In the slip regime, the kinematics profiles (velocity, shear rate and granular temperature) of the basal layer strongly deviate from Bagnold's profiles. General basal slip laws are developed which express the slip velocity as a function of the local shear rate (or granular temperature), base roughness and slope angle. Moreover, the basal layer thickness is insensitive to flow conditions but depends somewhat on the inter-particle coefficient of restitution. Finally, we show that the rheological properties of the basal layer do not follow the $\mu(I)$ rheology, but are captured by Bagnold's stress scaling and an extended kinetic theory for granular flows. Our findings can help develop more predictive granular flow models in the future.