A simple and unified model to describe some features of soil behavior in one dimensional condition is presented in another related paper (Nakai et al., 2011). In the present paper, this one-dimensional model is extended to describe not only the soil features explained in the related paper three-dimensionally (3D), but also to explain other soil features found in multi-dimensional conditions, such as shear behavior considering the influence of intermediate principal stress on the deformation and strength of soils, and the positive and negative soil dilatancy. Firstly, the first step in extending any kind of one-dimensional model to a three-dimensional one is explained in detail: the significance of tij
concept and its stress invariants (tN
) is explained and compared with the idea of ordinary stress invariants (p
) used in the Cam clay model. Then, the advanced elastoplastic relations (stages I to III) in the one-dimensional condition presented in the related paper are re-formulated as three-dimensional models—e.g., a model for over consolidated soil, a model for structured soil and a model which considers time-dependent behavior. The three-dimensional models for over consolidated soil (stage I) and structured soil (stage II) are formulated so as to coincide with the subloading tij
model developed by Nakai and Hinokio (2004) and by Nakai (2007), respectively. The validity of the models in stage I and stage II is checked by simulations of various shear tests for sands with different void ratios and for over consolidated and natural clays under drained and undrained conditions. The model in stage III is verified by simulations of shear tests with different strain rates, and by simulating creep tests and others, not only for normally consolidated clay but also for non-structured and structured over consolidated clays under drained and undrained conditions.
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