Elastoplastic modelling of mechanical behavior of rocks with fractional-order plastic flow

•A fractional plasticity model without using plastic potential is developed for rocks.•The fractional order is originally related to volumetric compression/dilation transition.•A unified plastic hardening/softening function is introduced for complete mechanical response.•The model is validated on both soft and brittle rocks under conventional triaxial compressions. The progressive transition in volumetric deformation from compression to dilation has been widely observed in rock-like materials under compressive stresses. This paper attempts to develop a fractional plasticity model for rocks by incorporating such volumetric compression/dilation transition state. Firstly, a fractional-order plastic flow rule suitable for describing soft rocks is proposed without using plastic potential. A unified hardening/softening function is introduced with the equivalent plastic shear strain as hardening variable. The fractional constitutive model is then adapted for brittle rocks. Comparisons between the fractional plastic model and some existing associated/non-associated plastic models demonstrate that the present model is capable of capturing correctly the transition state of volume compaction and dilation. Validations against experimental results from conventional triaxial compression tests indicate that the model allows to predict the main mechanical behaviors of rocks under different confining pressures.