Impact of Hydraulic Hysteresis on the Small-Strain Shear Modulus of Low Plasticity Soils

Experimental studies have observed that the small-strain shear modulus ($G_{\text{max}}$) of unsaturated soils measured during hydraulic hysteresis has a greater magnitude during imbibition than during drainage when plotted as a function of matric suction. To capture this behavior, a semiempirical model was developed to interpret the impacts of the stress state and hydraulic hysteresis on $G_{\text{max}}$ of low plasticity soils. Different from previous empirical relationships for $G_{\text{max}}$, this model incorporates elastoplastic constitutive relationships, which integrate the effects of mean effective stress and hardening because of either plastic changes in volume or changes in the degree of saturation. The effective stress is defined as the sum of the net normal stress and the product of the effective saturation and matric suction, facilitating integration of the soil-water retention curve parameters into the model. An experimental testing program involving measurement of $G_{\text{max}}$ of compacted silt during hydraulic hysteresis was used to develop data to validate a methodology for model calibration. Specifically, hysteretic trends in $G_{\text{max}}$ were defined for different mean net normal stress values using a fixed-free resonant column device with suction-saturation control. The proposed methodology to define the model parameters includes use of correlations from the literature, as well as experimental measurements of $G_{\text{max}}$ for soils in saturated conditions and during drainage. The model was found to fit the trends in experimental $G_{\text{max}}$ data with suction, degree of saturation, and effective stress during drainage, and provided adequate prediction of the $G_{\text{max}}$ data upon subsequent imbibition.