Breakage-Dependent Fractional Plasticity Model for Sands

Particle breakage could significantly influence the shear strength, volumetric deformation, stress-dilatancy relationship, and plastic-flow rule of crushable sands. A breakage-dependent fractional-plasticity (BDFP) model was proposed in this paper to capture the evolution of the stress-strain relationship for crushable sands by using a general plastic-flow rule, which is obtained from the Riemann-Liouville fractional derivative on the modified Cam-Clay yield surface and the incorporation of the breakage-dependent void-ratio-pressure state parameter in the framework of a kinetic breakage-dependent critical state line. The BDFP model can well predict the state- and breakage-dependent strength and deformation of crushable sands. Specifically under higher confining pressures, the prediction for the evolution of the volumetric strain of crushable sands by the BDFP model is much better than that by the model not considering particle breakage.