Abstract: It has been recognized that the stress-dilatancy behaviour of granular soil depends on its material state. To consider such state-dependence, a variety of state parameters were suggested phenomenologically and incorporated into existing stress-dilatancy equations, e.g. Cam-clay equation, modified Cam-clay equation, by experience. In this study, a novel state-dependent stress-dilatancy equation is developed by using fractional stress gradient, where physical meaning of the fractional order is provided. The obtained stress-dilatancy ratio is determined by three factors: the fractional order, current load stress, and the distance from current stress to critical state stress. When the fractional order is larger than 1, the stress-dilatancy curve shifts from the modified Cam-clay stress-dilatancy curve towards the Cam-clay stress-dilatancy curve. However, when the fractional order is smaller than 1, the stress-dilatancy curve is located above the modified Cam-clay stress-dilatancy curve. When the fractional order is equal to 1, the proposed stress-dilatancy curve coincides with the modified Cam-clay curve. To validate the proposed approach, a state-dependent fractional plasticity model for sand soils is established by using the proposed stress-dilatancy equation. Then, a series of drained and undrained triaxial compression tests on sand and rockfill with different initial states is simulated and compared, from which a good agreement between the model simulations and the corresponding test results can be observed. Comparison with the model predictions of the UH sand model indicates that the UH model gives better prediction.

Key words: fractional calculus, plasticity, constitutive model, state dependence, sand