A micro-mechanical study of peak strength and critical state

Abstract

We present a micro-mechanical analysis of macroscopic peak strength, critical state, and residual strength in two-dimensional non-cohesive granular media. Typical continuum constitutive quantities such as frictional strength and dilation angle are explicitly related to their corresponding grain-scale counterparts (e.g., inter-particle contact forces, fabric, particle displacements, and velocities), providing an across-the-scale basis for a better understanding and modeling of granular materials. These multi-scale relations are derived in three steps. First, explicit relations between macroscopic stress and strain rate with the corresponding grain-scale mechanics are established. Second, these relations are used in conjunction with the non-associative Mohr–Coulomb criterion to explicitly connect internal friction and dilation angles to the micro-mechanics. Third, the mentioned explicit connections are applied to investigate, understand, and derive micro-mechanical conditions for peak strength, critical state, and residual strength.

Additional details