Beyond critical state : a critical-state hydrodynamic model (CSHM) for solid-fluid phase transition of clay

Abstract

Clay's solid-fluid phase transition, a key cause of geohazards like landslides and debris flows, remains notoriously difficult to model due to its coupled frictional yielding and strain-rate-dependent fluidization. Its complexity poses a substantial challenge to constitutive modeling. For the first time, this study proposes a novel critical-state hydrodynamic model (CSHM), which efficiently captures clay's nonlinear solid-fluid phase transition by integrating quasi-static and viscous stress components in a unified framework. The quasi-static stress is described by a critical-state-based elastoplastic model, representing the solid-like behavior. In contrast, the viscous stress is described using a novel hydrodynamics-based rheological model that captures the fluid-like behavior by introducing a state variable termed “clay temperature”. The quasi-static component captures key aspects including nonlinear elasticity, stress dilatancy, and critical state, whereas the proposed viscous component describes shear-heating or shear-cooling rheology. Subsequently, extensive element simulations are employed to evaluate the new CSHM. Finally, validation against experimental data demonstrates that the CSHM accurately captures the clay's solid-to-fluid phase transition. The analyses reveal that: (i) While sand undergoes a shear-induced heating phase transition and is well described by the existing kinetic theory, clay exhibits shear-cooling, which our novel model accurately captures. (ii) Clay's phase transition is characterized by two transitional points (critical-state point and viscous-stress-dominant point) and three different regimes (solid-like, transitional, and fluid-like). (iii) Unlike the traditional HB model, a 2D model describing stress in the fluid-like state, the CSHM is a 3D full-range phase transition model that captures evolution from initial to critical state, and eventually fluid-like state.