Fractional Generalized Plastic Model for Rockfill

this paper extends the theory of generalised plasticity by applying the fractional differentiation approach to develop a new fractional constitutive model for rockfill. The proposed model employs a so-called fractional flow rule and applies the fractional differential operation on the yield surface to derive a new dilatancy equation. New representations of the plastic flow direction and the loading direction are provided by allowing the fractional order to equal or not equal 1.0. The current study suggests that the evolution of the relative positions between the plastic flow direction and the loading direction is influenced by the state parameter, as it alters the value of the fractional order. The fractional generalised plastic model can capture this non-orthogonal deformation characteristic without introducing an additional plastic potential function. Moreover, the proposed model features new representations of the state parameter and the plastic modulus while incorporating a limited number of material constants to simplify its formula. The model's predictions are compared with the triaxial test data of various types of rockfill under both drained and undrained conditions to verify the effectiveness of the proposed model in describing the strength and deformation characteristics of the rockfill.