A unified small-strain shear stiffness model for saturated and unsaturated soils

This paper presents a model for calculating the small-strain shear stiffness of saturated and unsaturated fine-grained soils as the product of a dimensionless stiffness index and four individual functions of the mean average skeleton stress, the over-consolidation ratio, the reference saturated void ratio and the degree of saturation. The main element of novelty of the model resides in the introduction of a reference saturated state, which results in a dependency of the small-strain stiffness on the degree of saturation. The reference saturated state is calculated according to a recently published constitutive law that relates the quotient between the unsaturated void ratio and the reference saturated void ratio to the degree of saturation. The model requires only two extra parameters for unsaturated states, i.e. one parameter for the volumetric behaviour and one for the stiffness behaviour. These two parameters may also be correlated to the saturated parameters, which simplifies the calibration of the model. The proposed framework is validated against laboratory experiments on three different materials resulting in generally accurate predictions compared to other published models. The good predictive capabilities and the simplicity of the formulation justify the implementation of the model into numerical codes for the analysis of geotechnical problems.