A simple gradation-state-dependent model for granular materials

Abstract

This paper proposes a gradation-state-dependent constitutive model to capture the granular materials' mechanical behaviours considering the granular crushing's influence. Firstly, a gradation evolution law is developed to reflect the change in grain size distribution (GSD) with the growth of stress levels, and then, based on the evolution law, the elastic compliance matrix is modified to reflect the effects of particle breakage. Secondly, as the critical state line (CSL) exhibits gradation dependence, a novel method is developed to describe the family of CSLs under different fixed gradations. Subsequently, by combining the gradation evolution law with the CSL equation, the paper explains the steepening of the slope of the critical state line when the crushing is activated. With the improvement of CSL, the material's shear dilatancy and contraction properties are better reflected, assisting in establishing a plastic compliance matrix. Employing the derived elastic and plastic compliance matrix, the elastic–plastic model reflecting the influence of gradation and state effects is established and verified with a series of experimental and discrete element method (DEM) simulation results.