Fractional viscoplastic model for soils under compression

Soils in the field are often subjected to time-dependent compression, where the induced shear strength and deformation could be different upon different loading rates. To capture the rate-dependent stress-strain behaviour of soils under compression, a stress-fractional viscoplastic model is developed in this study, based on Perzyna's overstress theory. The viscoplastic flow direction of soil is modelled with a unit tensor obtained by performing fractional derivatives on the yielding surface. With the increase in the fractional order, the predicted compressive shear strength varies, and a transition from pure strain hardening to strain hardening and softening is observed. Additionally, as the strain rate increases, the predicted shear strength increases, which agrees well with the corresponding experimental observations. Further validation against a series of oedometer and triaxial test results under different strain-rate loads indicates that the fractional-order viscoplastic model can efficiently capture the rate-dependent behaviour of soils.