Small-Strain Shear Modulus Model for Saturated and Unsaturated Soils

The small-strain shear modulus depends on soil type, void ratio, stress level, and degree of saturation. Models have been proposed to describe G₀ of either saturated or unsaturated soils, yet none of them can predict G₀ for soils under both conditions. In this paper, a unified model for G₀ was proposed for soils based upon the consideration of effects of both material hardening/softening and inter-particle contact forces. These two mechanisms are characterized by degree of saturation and effective stress, respectively, as primary variables. Suction stress theory was used to determine the effective stress for soils under both saturated and unsaturated conditions. It is shown that G₀ is correlated with the soil-water retention curves of unsaturated soils by using the suction stress in the effective stress framework. The proposed model fits well for 17 soils, including those from the literature and newly tested ones under different saturation conditions and various loading conditions. A correlation between the fitting parameters of the proposed model and the inverse of the air-entry suction was found to provide good predictions of the small-strain shear modulus for unsaturated soils under various loading conditions.