Unified constitutive model for granular–fluid mixture in quasi-static and dense flow regimes

Most granular materials encountered in nature and industry lie either in the quasi-static regime or the intermediate dense flow regime. Debris materials are a typical granular material with viscous interstitial fluid and show solid-like behaviors before failure and fluid-like behaviors after failure. Based on Bagnold’s pioneering work on granular–fluid flows, we propose a framework for constitutive model development, which has an additive form. Based on this framework, a unified constitutive model for granular–fluid material in the quasi-static and dense flow regimes is developed. The main intergranular interactions and granular–fluid interactions controlling the mechanical behaviors are taken into account using the Mohr–Coulomb model and a Bagnold-type relation. Dry granular flows in three simple configurations, i.e., plain shear, vertical chute flow and flow on an inclined plane, are studied. Analytical solutions based on the presented unified model are obtained. Comparisons between results from the presented model and the $$\mu (I)$$ model indicate that the explicit partition of frictional and collisional stress components provides insights into dense granular flows. In addition, the new model is used to predict the stress–strain relations in two annular shear tests. The applicability and advantages of the unified model are discussed.