Unified 3D critical state bounding‐surface plasticity model for soils incorporating continuous plastic loading under cyclic paths. Part I: Constitutive relations

The unified three‐dimensional (3D) critical state bounding‐surface plasticity model g UTS enables clays, silts and sands to be treated within a single framework. Furthermore, loose and dense states of a particular soil subjected to a wide range of confinements are viewed as a single material defined by the same set of constants. The model is able to handle both monotonic and complex cyclic paths including those involving a rotation of the principal stress directions. The model incorporates the following features: combined use of radial and deviatoric mapping rules and the use of an apparent normal consolidation line for sands; use of a non‐associated flow rule where the ratio of the rates of volumetric plastic strain to deviatoric plastic strain is a function only of the ratio of deviatoric to mean effective stresses and the Lode angle; adoption of a bi‐linear critical state line projected onto the plane of the void ratio versus logarithm of mean effective stress; inclusion of a sub‐elliptic, or super‐elliptic, segment in the plastic dilatancy surface for stress ratios less than critical; use of elliptic segments in the deviatoric planes; movement of the projection centre in the deviatoric mapping region and incorporation of a plastic stiffening effect for cyclic paths which repeatedly load in the same deviatoric direction.