A Simple Generalized Method for Unified Constitutive Model of Clay and Sand

To consistently describe the mechanical response of sand and clay under generalized stress paths, a unified critical state constitutive model (CASM-SG) applicable to generalized loading conditions was proposed based on the unified constitutive clay and sand model (CASM) with state parameters and by employing the subloading surface theory and the transformed stress method. In the model based on the original CASM model, a plastic internal variable associated with the initial state of the soil was established by using the concept of subloading surface, and the original two-dimensional yield surface determined from triaxial compression tests was transformed into the three-dimensional stress space through the transformed stress method. A complete constitutive framework was constructed for the CASM-SG model under generalized stress conditions, including the stress dilatancy relationship and the hardening rule. Explicit expressions for the plastic modulus and the elastoplastic stiffness matrix were derived based on the consistency condition. Finally, the proposed model was employed to simulate the mechanical behavior of Hostun sand and Fujinomori clay under drained and undrained triaxial compression and extension conditions. The simulation results indicate that the CASM-SG model can accurately capture the mechanical behavior of both sand and clay under various stress paths. For Fujinomori clay, the triaxial extension strength decreases by approximately 24% compared with the triaxial compression strength, and the CASM-SG model captures this characteristic. Compared to the original CASM model, the CASM-SG model introduces two additional material parameters with clear physical interpretations, demonstrating a favorable balance between modeling accuracy and simplicity.