Three-Dimensional State-Dependent Fractional Plasticity Model for Soils

To capture the nonassociated state-dependent constitutive behavior of soils subjected to different initial densities and pressures, a novel approach, the fractional-order ($\alpha$ ) plasticity, was developed, which extends the previous $\alpha$ plasticity model for more general loading conditions by using the transformed stress method. The developed model was found to have the following key features: (1) state dependence of the three-dimensional (3D) stress-dilatancy relationship was simulated without using empirical state parameters; (2) 3D nonassociated plastic flow rule was captured without using additional plastic potentials; and (3) state-dependent plastic hardening and softening was characterized without using state parameters and plastic potentials. To validate the extended 3D model, a series of laboratory test results of different soils, for example, rockfill, sand, and clay, under different loading paths were simulated, where a good agreement between the model predictions and the corresponding test results can be found.