A fractional-order two-surface plasticity model for over-consolidated clays and its application to deep gallery excavation

This paper proposes a novel fractional-order two-surface constitutive model for over-consolidated clays within the framework of the fractional plasticity and bounding surface theories. It incorporates the stress-fractional operator of the loading surface into isotropic and progressive hardening rules, thus obtaining an incremental stress–strain relation without an explicit plastic flow rule. The proposed fractional-order model can replicate the main features of over-consolidated clays well, including stiffness non-linearity, the occurrence of plastic strains before high peak strength, non-associativity, weak/strong dilatancy, and cyclic behavior. In model simulations on a set of element tests along different loading paths on natural Boom clay and remolded Fujinomori clay, the proposed model reveals better agreement than the modified Cam-Clay model (MCC). Next, the fractional-order model, ACC-2 model and MCC model are implemented via a user-defined material subroutine in ABAQUS with an explicit integration scheme based on the forward modified Euler method with automatic sub-stepping and error control. The different models are then applied to the fully coupled two-dimensional hydromechanical modeling of the excavation of two deep underground galleries in natural Boom clay. The results ultimately verify the validity and applicability of the proposed model.