Consequences of the tij-concept and a new modeling approach

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 pi-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. (C) 1998 Elsevier Science Ltd. All rights reserved.