Unique critical state characteristics in granular media considering fabric anisotropy

The concept of the critical state in granular soils needs to make proper reference to the fabric structure that develops at critical state. This study identifies a unique property associated with the fabric structure relative to the stresses at critical state. A unique relationship between the mean effective stress and a fabric anisotropy parameter, K, defined by the first joint invariant of the deviatoric stress tensor and the deviatoric fabric tensor, is found at critical state, and is path-independent. Numerical simulations using the discrete-element method under different loading conditions and intermediate principal stress ratios identify a unique power law for this relationship. Based on the findings, a new definition of critical state for granular media is proposed. In addition to the conditions of constant stress and unique void ratio required by the conventional critical state concept, the new definition imposes the additional constraint that K reaches a unique value at critical state. A unique spatial critical state curve in the three-dimensional space K–e–p′ is found for a granular medium, the projection of which onto the e–p′ plane turns out to be the conventional critical state line. The new critical state concept provides an important reference state for a soil to reach, based on which the key concepts in the constitutive modelling of granular media, including the choice of state parameters, dilatancy relation and non-coaxiality, are reassessed, and future exploratory topics are discussed.