Comparative Analysis of μ (I) and Voellmy-Type Grain Flow Rheologies in Geophysical Mass Flows: Insights from Theoretical and Real Case Studies

Abstract. The experimental-based μ(I) rheology is now prevalent to describe the movement of gravitational mass flows. Here, we reformulate μ(I) rheology as a Voellmy-type relationship to illustrate its physical implications. Through one-dimensional block modeling and a real case study, we explore the equivalence between μ(I) and widely-used Voellmy-type grain flow rheologies. Results indicate that μ(I) rheology utilizes a dimensionless inertial number to mimic contributions of granular temperature/fluctuation energy. In terms of Voellmy, the μ(I) rheolgy contains a velocity-dependent turbulent friction coefficient modelling shear thinning behavior. This turbulent friction assumes the production and decay of fluctuation energy are in balance, exhibiting no difference during accelerative and dipositional phases. The constant Coulomb friction coefficient prevents μ(I) rheology from accurately modeling the dispositional characteristics of actual mass flows. Our results highlight the strengths and limitations of both μ(I) and Voellmy rheologies, bolstering the theoretical foundation of mass flow modeling while revealing practical engineering challenges.