Constitutive Theory for Sand Based on the Concept of Critical Fabric Surface

Abstract

A novel theoretical framework for the interpretation and modeling of the critical-state behavior of granular soils is proposed in this paper. The theory is built upon the hypothesis that the fabric state of granular assemblies is attracted by a critical fabric surface under continuous shearing. A fabric ratio-stress ratio relation and a fabric-porosity relation are proposed based on recent discrete element modeling (DEM) experimental results. It follows that the existence of a critical-state line in the conventional e-p-q space can be derived by combining the aforementioned elements, offering a new perspective on the critical-state phenomenon. Simple fabric evolution laws are proposed to capture the first-order features of the stress-strain-fabric behaviors of granular soils. The basic evolution laws are then enhanced to capture the behavior of natural sand. The computed results agree well with the data from Toyoura sand under a wide range of pressure and density conditions. This exploratory study reveals a promising pathway to integrate various microstructure information in the continuum modeling of granular soils. The generality and limitations of the model is also discussed at the end of this paper.