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A simple and uniˆed constitutive model for soils, considering various eŠects such as the in‰uences of density, bonding, time dependent behavior and others, is presented in this paper. The elastoplastic behavior of over consolidated non-structured soils under a one-dimensional stress condition isˆrstly presented by introducing a state variable that represents the in‰uence of density (stage I). To describe the one-dimensional stress-strain behavior of structured soils, attention is focused on density and bonding as the main factors that aŠect the response of this type of soil, because it can be considered that soil a skeleton structure which is in a looser state than that of a normally consolidated soil is formed by bonding eŠects (stage II). Furthermore, a simple method is presented which allows for other soil characteristics to be considered, such as time and temperature dependency, and the eŠect of suction in unsaturated soils. Experimental observations show that the normally consolidated line (NCL) in the void ratio-stress relation (e.g., e-ln s curve) shifts depending on the change of strain rate, temperature, suction and others (stage III). The validation of the model at stages I and II is demonstrated by simulating one-dimensional consolidation tests for normally consolidated, over consolidated and natural clays. The applicability of the model at stage III is veriˆed not only by the simulations of time-dependent behavior of clays in one-dimensional element tests but also by the soil-water coupledˆnite element analysis of oedometer tests as a boundary value problem. The extension from one-dimensional models to three-dimensional models is easily achieved by deˆning the yield function using stress invariants instead of one-dimensional stress s' and by assuming an appropriate ‰ow rule in stress space. The details of the modeling in general three-dimensional stress conditions will be described in another paper (Nakai et al., 2011).

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A simple and uniˆed 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 in‰uence of intermediate principal stress on the deformation and strength of soils, and the positive and negative soil dilatancy. Firstly, theˆrst step in extending any kind of one-dimensional model to a three-dimensional one is explained in detail: the signiˆcance of tij concept and its stress invariants (tN and tS) is explained and compared with the idea of ordinary stress invariants ( p and q) 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 diŠerent void ratios and for over consolidated and natural clays under drained and undrained conditions. The model in stage III is veriˆed by simulations of shear tests with diŠerent 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.