Fractional-order bounding surface model for unsaturated soils under cyclic loading

Modelling of unsaturated soil stress–strain relationships under cyclic loading with constant matric suction is a topic that is poorly addressed by the current literature. Using the theoretical framework of the bounding surface plasticity and Barcelona basic model (BBM) combined with the concept of fractional accumulated strain rate, a bounding surface model for accurately describing the unsaturated soil stress–strain relationship with constant matric suction is established here. The fractional accumulated strain rate is introduced to consider the influence of cyclic loading history. The movable mapping centre rule is used to describe the hysteresis characteristics of the dynamic stress–strain curve during the unloading process. The shape of the dynamic stress–strain curve can be described reasonably by considering the cyclic loading process as the three processes of initial loading, unloading, and reloading. The cyclic loading test data of unsaturated silt, sand, and lean clay with constant matric suction is used for parameter calibration and model validations. Results show that the proposed model can accurately capture the dynamic stress–strain relationship of unsaturated soil with constant matric suction.