Advertisement

Significance and Usefulness of the tij Concept

  • Teruo NakaiEmail author
Conference paper
Part of the Springer Series in Geomechanics and Geoengineering book series (SSGG)

Abstract

Constitutive models formulated using the stress invariants (p and q) cannot describe uniquely the deformation and strength of geomaterials under three principal stresses [1]. Then, the concept of tij has been proposed to describe uniquely the stress-strain behaviors in general three-dimensional (3D) stress conditions [2]. This concept was found out from the idea that the frictional law essentially governs soil behavior. Since the formulation of elastoplastic model using this concept was described in the previous papers [3, 4], the meaning of this concept and its usefulness are presented in this paper.

Keywords

Constitutive modeling Spatially mobilized plane Concept of tij 

References

  1. 1.
    Schofield, A.N., Wroth, C.P.: Critical State Soil Mechanics. McGrow-Hill, London (1968)Google Scholar
  2. 2.
    Nakai, T., Mihara, Y.: A new mechanical quantity for soils and its application to elastoplastic constitutive models. Soils Found. 24(2), 82–94 (1984)CrossRefGoogle Scholar
  3. 3.
    Nakai, T., Hinokio, T.: A simple elastoplastic model for normally and over consolidated soils with unified material parameters. Soils Found. 44(2), 53–70 (2004)CrossRefGoogle Scholar
  4. 4.
    Nakai, T.: Constitutive Modeling of Geomaterials: Principles and Applications. CRC Press, Boca Raton (2012)CrossRefGoogle Scholar
  5. 5.
    Murayama, S.: A theoretical consideration on a behavior of sand. In: Proceedings of IUTAM Symposium on Rheology and Soil Mechanics, Grenoble, pp. 146–159 (1964)Google Scholar
  6. 6.
    Matsuoka, H., Nakai, T.: Stress-deformation and strength characteristics of soil under three different principal stresses. Proc. JSCE 232, 59–70 (1974)Google Scholar
  7. 7.
    Oda, M.: The mechanism of fabric changes during compressional deformation of sand. Soils Found. 12(2), 1–18 (1972)CrossRefGoogle Scholar
  8. 8.
    Satake, M.: Anisotropy in ground and soil materials. Tsuchi Kiso 32(11), 5–12 (1984, in Japanese)Google Scholar
  9. 9.
    Satake, M.: Fabric tensor in granular materials. In: Proceedings of IUTAM Conference on Deformation and Failure of Granular Materials, Delft, pp. 63–68 (1982)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Geo-Research Institute and Chubu UniversityNagoyaJapan

Personalised recommendations