A Simple and Unified Three-Dimensional Model to Describe Various Characteristics of Soils

Abstract

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.

A Simple and Unified One-Dimensional Model to Describe Various Characteristics of Soils

“…These one-dimensional models can be easily extended to three-dimensional ones by introducing the tij concept (Nakai and Mihara, 1984). The formulation of three-dimensional models is shown in another paper (Nakai et al, 2011).…”

“…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). …”

Rational modelling of elastic soil behaviour in 3D condition

“…A constitutive model which is named Suloading tij model has been proposed [6,7,8]. This model can describe soil behaviour in general 3D condition uniquely using the concept of tij [9].…”

Stress-Strain-Dilatancy Relationships of Normally Consolidated Dhaka Clay

“…The first simple model which considered the soil as an elastoplastic material is the Cam-clay model. In the Cam-clay model [12] positive dilatancy during strain hardening is not taken into consideration along with some other limitations [6] which are as follows: (i) Influence of intermediate principal stress on the deformation and strength of soil (ii) Stress path dependency on the direction of plastic strain increments (iii) Positive dilatancy during strain hardening (iv) Behavior of soil under cyclic loading (v) Soil anisotropy (vi) Influence of density and/or confining pressure on the deformation and strength (vii) Behavior of structured soil (viii) Soil anisotropy and non-coaxially (ix) Time effect and age effect (x) Unsaturated Soils.…”

“…To overcome the limitations of Cam-clay model, Subloading tij model [6] had been developed which provides a better performance in loose to dense sand and soft to stiff clay. Some of the features of the model are as follows:…”