Fractional-order plasticity model for sand-silt mixtures

The sand-silt mixtures, as common heterogeneous soils, are ubiquitous in nature and geotechnical engineering, and their particle contact state and mechanical properties are significantly affected by the factors such as density, stress level and fines content. In order to comprehensively describe the complex mechanical properties of the sand-silt mixtures within the fines content threshold (F_C$<$F_Cthre), the plastic flow rules that can uniformly describe association and non-association are determined based on the fractional calculus theory. Using the concept of equivalent skeleton void ratio, the equivalent skeleton state parameter is embedded in the dilatancy equation and plastic modulus, and then a fractional-order plasticity model considering the fines content and state-dependent behavior is established. The comparison between the predicted results and the experimental data shows that the proposed fractional-order plasticity model can effectively reflect the strain-softening (strain-hardening) and dilatancy (contraction) behaviors of the sand-silt mixtures under drained conditions. Meanwhile, the key characteristics of undrained conditions, such as flow and non-flow behaviors, can also be reasonably described.