A set of hyper-viscoplastic critical state models with different friction mobilisation criteria

Abstract

The approach of thermodynamics with internal variables, known as hyperplasticity, is used to develop a set of hyper-viscoplastic clay models that comply with the critical state soil mechanics and isotache viscosity. Different friction criteria of Drucker-Prager, Mohr-Coulomb, and Matsuoka-Nakai have been considered, and their conjugate features in terms of friction mobilisation and inelastic flow direction are explored. One of the distinctions of the proposed hyper-viscoplastic models regarding the existing models is having a unique friction envelope at the critical state (the paradigm of critical state soil mechanics) while adopting versatile dynamic yield surfaces and inelastic flow rules. To achieve this importance, an emphasis has been put on the practice of the stress ratio tensor (the deviatoric stress tensor per the spherical effective stress) as an essential state variable of frictional material. Along the way, some consistencies with the results and insights of studies with the discrete element method (DEM) in the literature are reported and interpreted.