Transport in Porous Media

, Volume 120, Issue 2, pp 271–285 | Cite as

A Simple Hysteretic Constitutive Model for Unsaturated Flow

  • Mariangeles Soldi
  • Luis Guarracino
  • Damien Jougnot


In this paper, we present a constitutive model to describe unsaturated flow that considers the hysteresis phenomena. This constitutive model provides simple mathematical expressions for both saturation and hydraulic conductivity curves, and a relationship between permeability and porosity. The model is based on the assumption that the porous media can be represented by a bundle of capillary tubes with throats or “ink bottles” and a fractal pore size distribution. Under these hypotheses, hysteretic curves are obtained for saturation and relative hydraulic conductivity in terms of pressure head. However, a non-hysteretic relationship is obtained when relative hydraulic conductivity is expressed as a function of saturation. The proposed relationship between permeability and porosity is similar to the well-known Kozeny–Carman equation but depends on the fractal dimension. The performance of the constitutive model is tested against different sets of experimental data and previous models. In all of the cases, the proposed expressions fit fairly well the experimental data and predicts values of permeability and hydraulic conductivity better than others models.


Constitutive model Unsaturated flow Hysteresis phenomena Saturation Hydraulic conductivity 



The authors thank the editor and two anonymous reviewers for their careful assessment of our work and the valuable comments and suggestions that helped to greatly improve the manuscript.


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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  • Mariangeles Soldi
    • 1
  • Luis Guarracino
    • 1
  • Damien Jougnot
    • 2
  1. 1.Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La PlataConsejo Nacional de Investigaciones Científicas y TécnicasLa PlataArgentina
  2. 2.UPMC Univ Paris 06, CNRS, EPHE, UMR 7619 METISSorbonne UniversitesParisFrance

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