State-Dependent Model Incorporating Particle Breakage for Rockfill Material Established by Fractional Calculus

Particle breakage and material state highly affect the dilatancy, strength, and stress–strain behavior of rockfill material, which should be considered reasonably in constitutive modeling. Fractional calculus is an efficient way to build a constitutive model for materials, and some fractional-order models were proposed to simulate the state-dependent constitutive behavior of rockfill material; however, particle breakage was neglected in these models. For filling this research gap, a fractional-order constitutive model considering both particle breakage and material state is proposed in this paper, in which the Caputo fractional derivative is adopted. In the proposed model, a general formulation for the peak stress ratio is developed by incorporating the particle breakage index and the critical state parameter, and a dilatancy relationship incorporating particle breakage is used to determine the plastic flow direction. Additionally, the loading direction is derived by introducing the Caputo fractional derivative, and the plastic modulus is established by considering particle breakage and material state. Drained triaxial test results of different rockfill materials are simulated for the capability demonstration of the proposed model, and it can be observed that the stress–strain and volume change behavior of rockfill material are predicted accurately, including plastic dilation and contraction, strain hardening, and postpeak strain softening features.