The mechanical behaviors of rockfills exhibit strain-softening and dilative features

which is also influenced by the pressure

loading paths and density. In this paper

a new fractional sub-loading surface model for rockfills is proposed based on the critical state mechanism

which is a typical double yield surfaces model. In the p-q plane

the current and reference stress points are located on the sub-loading surface and the reference yield surface

respectively. The relative position between the sub-loading surface and reference yield surface is controlled by the void ratio difference ?. Compared with the state parameter ?

? is able to account for the effect of loading paths additionally. The proposed model is able to account for the extent between the plastic flow direction and the loading direction without introducing a plastic potential function. A fractional plastic flow rule is developed by applying the Caputo fractional stress operator on the yield function

which provides a unified description for the associated and non-associated plastic flow rules. The formula of the proposed model is quite simple and the included seven model parameters can be determined through laboratory tests conveniently. The model predictions were compared with the drained triaxial test results of Tacheng rockfill under the conditions of various initial void ratios and confining pressures. A good agreement between the model predictions and experimental results is obtained

which indicates that the proposed model is capable of describing the stress-strain curves and deformation features of Tacheng rockfill. In addition

the effect of initial void ratios on the critical state line in the e-lnp plane is also captured by the proposed model.