Consequences of the tij-concept and a new modeling approach

Abstract

Abstract The strength and the dilatancy of soils are largely influenced by the choice of the stress and strain increment variables. Cam-clay like models that use extended Mises strength criterion cannot consider the effect of intermediate principal stress properly and give unrealistic strength under generalized three-dimensional stresses except triaxial compression condition. Nakai and Mihara proposed a modified stress tensor ( t ij ) based on the Spatially Mobilized Plane (SMP) concept that uses Matsuoka–Nakai strength criterion to consider the influence of intermediate principal stress on the strength and the dilatancy of soils. Matsuoka–Nakai strength criterion is a convex surface on the π -plane in the ordinary stress space and satisfies Mohr–Coulomb criterion under axisymmetric conditions (triaxial compression and extension). Using the t ij -concept, isotropic and kinematic hardening clay and sand models have been proposed and experimentally verified. Recent investigations have revealed inconsistency of the t ij -concept with the critical state concept used in the original and modified Cam-clay models. In this paper the inconsistency of the t ij -concept with the critical state concept is pointed out first, then a modeling approach has been introduced, which virtually can adopt any strength criterion in a consistent way to incorporate the critical state concept. It is shown that the proposed stress and strain increment quantities are properly work conjugate. A compact stress–dilatancy relation is also introduced using the proposed stress and strain increment quantities, which gives a continuous and smooth plastic potential and has control over the stiffness of the model predictions.