Fractional consistency two-surface viscoplastic modeling of unsaturated soils

Experimental evidence obtained from reservoir slope soils and embankment fills indicates that unsaturated soils exhibit a measurable time-dependency, which highlights more comprehensive consideration in the constitutive modeling. In this paper, we present a novel two-surface viscoplastic model for unsaturated soils within the theoretical framework of fractional consistency viscoplasticity and bounding/subloading surface theory. Formulated in terms of two constitutive variables-the generalized Bishop’s stress and bonding variable ( ξ ), hydro-mechanical hardening, and the modified isotach viscosity with the exponential formed creep coefficient, are systematically incorporated in a hierarchical framework to characterize the hardening/softening responses of unsaturated soils. Then, by rigorously enforcing the consistency condition of the loading surface, a complete incremental constitutive relation integrating stress, strain, matric suction, and strain rate is developed. The robustness and predictive accuracy of the proposed model are subsequently demonstrated through the model performance and model verification against experimental results obtained from four distinct unsaturated soils, namely, Baijiabao landslide soil, reconstituted London clay, Qianjiangping landslide soil, and a compacted clayey silty soil-subjected to various loading paths, including isotropic and triaxial creep tests, CRS oedometric-relaxation tests, strain rate-controlled monotonic triaxial compression tests, and multistage triaxial cyclic tests. The results demonstrate that the proposed model effectively captures the complex rate-dependent behaviors of unsaturated soils.