Critical-State Fractional Model and Its Numerical Scheme for Isotropic Granular Soil Considering State Dependence

Abstract

Many elastoplastic models have been proposed to model the stress–strain behavior of granular soils. However, due to the dependence of stress-dilatancy on the material state, different model parameters are often needed to model the constitutive behavior of granular soils under different initial states. In this study, an attempt is made to develop a state-dependent fractional plasticity model by using the fractional-order Cambridge stress-dilatancy equation, in which detailed numerical approximations of the model are provided for further potential application. To validate the proposed model as well as the numerical solution, a series of triaxial test results on a number of different granular soils, including rockfill, sand, and ballast, is simulated. A good agreement between the model predictions and the corresponding test results is observed.