Generalization of the μ(I) rheology to account for flow type

¹ Mechanical and Civil Engineering, California Institute of Technology
² School of Engineering, Brown University

^* e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 1 December 2025

Abstract

Most existing rheological models for dense granular flow have been calibrated to simple shear flows, although in practice there are numerous different types of flows. One of the key ingredients of any granular rheological model is the flow threshold, i.e., the critical stress state which initiates the flow. In this study, we propose a generalized flow threshold informed by extensive discrete element simulations over a wide range of flow types. We propose a functional form for a generalized yield criterion accounting for the flow type through the third invariant (Lode-angle) of the stress deviator. Moreover, we generalize the conventional μ(I) form of local rheology to account for flow type dependence as a function of the inertial number.