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An isotropic hardening elastoplastic model, named subloading ti;, has been recently proposed (Nakai and Hinokio, 2004). Three features differentiate subloading ti; model from the conventional ones: (a) the use of a modified stress space given by tensor ti;; (b) the split of the plastic strain increments in two components and (c) the use of two yield surfaces based on the concept of subloading. These three characteristics greatly improve the prediction capabilities of the model, with respect to those of the well-known Cam-clay model. However, the model formulation and implementation becomes a little more complex. In this paper the basic equations for the evolution of stresses and strains and for the evolution of the internal variables that control the size of the yield surfaces of the model are reformulated in such a way as to resemble those of any conventional elastoplastic model. This facilitates significantly the numerical integration (explicit or implicit) of the corresponding system of differential equations of the model. The present formulation also identifies the physical meaning of each concept and clearly shows where they intervene in the deduction of the elastoplastic constitutive tensors. The model is initially formulated without taking into account the plastic strain increment split, in order to emphasize the effect of adopting the subloading concept. Then the plastic split is considered using a different approach that allows writing the constitutive tensors in a simpler manner. The procedures proposed were successfully tested and all derivatives and algorithms necessary to implement the model are given in the appendices. The authors hope that these procedures make it easier for other researchers to implement and use the model as it is or to use the basic concepts in any other model.

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.

The falling cone is widely used as a laboratory test to determine the liquid limit for the characterization of clay soils. However, remolded undrained shear strength and deformability and strength parameters of critical state models can also be estimated. The objective of this paper is to show a simple methodology to determine these important parameters for engineering simulations. Controlled laboratory tests were carried out on kaolin clay samples using a cone with 30 of tip angle and 30 g of mass. Mini-vane tests were also performed to determine the remolded undrained shear strength of the samples.The experimental results were used to calibrate the Hansbo cone factor, K, from which it is possible to relate the undrained shear strength and the cone penetration for different water contents. The study shows that a calibrated cone and the proposed methodology may be

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