A Unified Semiempirical Model for Small-Strain Shear Modulus of Fine-Grained Soils under Hydromechanical Loading

In recent years, several empirical and semiempirical relationships have been proposed to predict the small-strain shear modulus of unsaturated fine-grained soils along different hydraulic and mechanical loadings paths. However, a major deficiency of these relationships is the absence of a coupled linkage between hydraulic and mechanical processes that occur in unsaturated conditions. Specifically, the void ratio and effective stress are considered uncoupled, and changes in soil volume are rarely considered when implementing soil water retention curves in these equations. This study aims to address these deficiencies by discussing the coupled effect of hydraulic and mechanical processes in unsaturated soils and presenting a semiempirical model to predict the small-strain shear modulus, $G_{\max }$, of unsaturated low plasticity soils subjected to volume and effective stress changes along different mechanical and hydraulic stress paths. Predictions from this model and three other recently proposed models in the literature are compared with experimental results obtained from a series of suction-controlled bender element tests on silty soil specimens to validate the proposed model. The comparison reveals that the model proposed in this study provides more consistent predictions of the small-strain shear modulus during hydraulic hysteresis, as well as different paths of loading and unloading.