Fractional Derivative Statistical Damage Model of Unsaturated Expansive Soil Based on Unified Hydraulic Effect

Unsaturated expansive soil is widely distributed in China and has complex engineering properties. This paper proposes the unified hydraulic effect shear strength theory of unsaturated expansive soil based on the effective stress principle, swelling force principle, and soil–water characteristics. Considering the viscoelasticity and structural damage of unsaturated expansive soil during loading, a fractional hardening–damage model of unsaturated expansive soil was established. The model parameters were established on the basis of the proposed calculation method of shear strength and the triaxial shear experiment on unsaturated expansive soil. The proposed model was verified by the experimental data and a traditional damage model. The proposed model can satisfactorily describe the entire process of the strain-hardening law of unsaturated expansive soil. Finally, by investigating the damage variables of the proposed model, it was found that: (a) when the values of confining pressure and matric suction are close, the coupling of confining pressure and matric suction contributes more to the shear strength; (b) there is a damage threshold for unsaturated expansive soil, and is mainly reflected by strength criterion of infinitesimal body; (c) the strain hardening law of unsaturated expansive soil is mainly reflected by fractional derivative operator.