A single-stress elasto-plastic triaxial model for saturated and unsaturated soils

Abstract This paper presents a constitutive model for predicting the behaviour of saturated and unsaturated soils under compression and shearing, utilising a single-stress elasto-plastic framework. The model extends the scaled stress concept from isotropic to triaxial stress states, enabling a unified approach to modelling both saturated and unsaturated soils under general loading conditions. Central to the model is a capillary bonding function, which leads to the definition of a unified normal compression line (UNCL) for both saturated and unsaturated soils, relating the void ratio to the mean scaled stress in a semi-logarithmic plane. This UNCL is integrated into the modified Cam-Clay model for saturated soils by replacing the effective stress with the scaled stress to account for partial saturation. In particular, the deviatoric scaled stress is defined using the same scaling factor applied to isotropic stress states. To further enhance the model, an alternative yield function is also introduced to improve the prediction of volumetric strains at critical state. The proposed constitutive framework has been validated against four distinct sets of triaxial tests on fine-grained soils, ranging from clays to silts, under constant suction. The results confirm the robustness of the model, showing that the scaled stress variable effectively normalises the behaviour of both saturated and unsaturated soils under isotropic and deviatoric loading conditions. The flexibility in positioning the unified critical state line (UCSL) generally enhances the prediction of volumetric behaviour during shearing across varying suction levels.