A convertible state variable linking relative density and overconsolidation ratio for soil modeling

The mechanical behavior of clay and sand exhibits inherent state dependence, subject to the combined control of void ratio and stress. Different soil types have long relied on separate state variables to describe state dependence. In this study, a state variable Ψ capable of simultaneously reflecting void ratio and stress information is proposed by introducing a state reference line in the e -ln p coordinate system. With clay and sand considered as specific applications, Ψ is respectively specialized into an overconsolidation-ratio-dependent state variable OCR of clay using the normal consolidation line as the reference, and into a relative-density-dependent state variable D r of sand taking the loosest and densest isotropic compression lines as references. A conversion relationship between OCR and D r is then established based on the linear state reference line assumption. To further reasonably describe the nonlinear compression behavior of sand over a wide stress range, the linear loosest and densest isotropic compression lines are extended into S-type nonlinear forms. The proposed state variable is subsequently incorporated into the existing state-dependent non-orthogonal model framework and validated against monotonic loading experimental results of six clays and three sands. The results demonstrate that the proposed state variable and constitutive model can reasonably capture the state-dependent mechanical responses of clay and sand.