Fractional plasticity for over-consolidated soft soil

The stress–strain response of over-consolidated soft soil, e.g., clay, is dependent on its pre-consolidation history and material state. In this study, a state-dependent constitutive model for over-consolidated soft soils is proposed by extending the fractional plasticity originally developed for granular soil. The state-dependent stress-dilatancy and peak failure behaviour of over-consolidated soft soil are analytically captured through stress-fractional gradient of the current yielding surface. In addition, a reference yielding surface describing the pre-consolidation history of soft soil is proposed. A combined hardening rule expressed as a function of both the incremental plastic volumetric and shear strains is suggested. To validate the proposed model, a series of drained and undrained test results of different soft soils with a wide range of over-consolidation ratios are simulated and compared. It is found that without using additional plastic potentials and state parameters, the developed fractional model can capture the state-dependent hardening and softening responses of soft soils subjected to different over-consolidation states.