Upscaling critical state considering the distribution of meso‐structures in granular materials

Abstract

AbstractThe evolutions of meso structures of granular materials play important roles during shearing toward the critical state. This study aims to establish an extended analytical model based on a specific upscaling procedure considering the distributions of meso structures in granular materials. A general Gaussian distribution is applied when determining the relationship between meso critical state parameters and order n, and then a quantitative model of macro CSL is developed by taking the discrete case into a continuous function. The quantitative model is then related to interparticle friction μ and contact stiffness k for predicting the macro CSLs for ideal granular assemblies, and the analytical results have good agreement with DEM results. Furthermore, the influence patterns of contact properties on both meso and macro critical states are discussed in detail, which provides a roughly explanation on the variations of critical friction angle with μ.