A state- and rate-dependent constitutive model for granular materials with interstitial fluid: solid-like, fluid-like behaviours and their transitions

Granular materials exhibit solid-like and fluid-like behaviour in different flow regimes, governed by intergranular frictions, collisions and viscous force from the interstitial fluid. In this paper, a state- and rate-dependent constitutive model is proposed to describe the solid-like and fluid-like behaviours in granular flows by decomposing the effective stress tensor into rate-independent and rate-dependent parts. Hypoplastic and $μ(I)$-type models are used for the rate-independent and rate-dependent parts. The Stokes number is introduced to account for interstitial fluid viscosity. Moreover, the shear-induced frictional force to capture the stress changes during rapid shearing is considered. The model is shown to capture the entire regime of granular flow and the phase transformation between solid-like and fluid-like behaviour. The model performance is demonstrated against results from the literature.