On the Formulation of Multiphase Porous Geomaterials

  • Fusao OkaEmail author
  • Sayuri Kimoto
Conference paper
Part of the Springer Series in Geomechanics and Geoengineering book series (SSGG)


For partially saturated soils, several stress variables have been used such as the net stress, Bishop stress, generalized Bishop stress and skeleton stress have been used. For elastic behavior of water saturated geomaterials, Biot developed a theory of porous media which is equivalent to the elastic water saturated model with the effective stress with the so-called Biot constant. On the other hand, for inelastic response, the applicability of the effective stress with Biot constant has not yet well been studied. In this study, the authors present the formulation of two phase and three-phase geomaterials based on the continuum thermodynamics with internal variables. It has been found that the effective stress with Biot coefficient is obtained for elastic two-phase materials, and the skeleton stress with Biot constant can be derived for three-phase materials such as partially saturated soil.


Multi-phase geomaterials Skeleton stress Unsaturated soil 


  1. 1.
    Biot, M.A., Willis, D.G.: The elastic coefficients of the theory of consolidation. J. Appl. Mech. 24, 594–601 (1957)MathSciNetGoogle Scholar
  2. 2.
    Kimoto, S., Oka, F., Morimoto, Y.: The effective stress concept and the evaluation of changes in pore air pressure under jacketed isotropic compression tests for dry sand based on 2-phase porous theory. Int. J. Num. Anal. Methods Geomech. 41, 1894–1907 (2017). Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Lab. 3, 138-1 Association for Disaster Prevention ResearchEmeritus of Kyoto UniversitySakyo-kuJapan
  2. 2.Department of Civil and Earth Resources EngineeringKyoto UniversityKyotoJapan

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