A critical state model for sand and overconsolidated clay with unified hardening

This paper develops a unified critical state model that is applicable to sands of varying densities, and overconsolidated clays, termed as the CASM-SU. A unified hardening parameter is introduced to the original hardening law of the Clay and Sand model with subloading surface, i.e., the CASM-S, where the effects of the unified hardening parameter on the Hvorslev peak stress ratio is well considered. A Lade-based transformed stress method is incorporated to represent intermediate-principal-stress effects without adding an independent parameter. The newly developed CASM-SU shares seven physical parameters with the classical CASM, without introducing a new model parameter u that is given by the CASM-S. This parameter lacks physical meaning, which needs mathematical fitting. A forward Euler integration algorithm is employed for numerical implementation, and the model is validated against drained and undrained tests on clays with various overconsolidation ratios and sands with different relative densities. The comparisons demonstrate that the CASM-SU accurately captures the stress–strain and volumetric responses of both soil types and significantly improves the prediction of peak tensile and compressive strength. The proposed formulation provides a physically based and unified constitutive framework for modelling the behaviour of sands and clays within the critical state framework.