Acta Mechanica

, Volume 225, Issue 8, pp 2435–2448 | Cite as

Wave propagation in unsaturated porous media

  • Holger Steeb
  • Patrick S. Kurzeja
  • Stefan M. Schmalholz


We present a simple macroscopical three-phase model describing wave propagation in partially saturated porous media. The model consists of a continuous non-wetting phase and a continuous wetting phase and is an extension of classical biphasic (Biot-type) models. The framework is based on kinematics, balance equations and well-known constitutive equations for single- and multi-phase continua. The final set of linearised equations gives information about the physical behaviour of three compressional waves and one shear wave. Among others, information about phase velocities, damping and displacements of the single constituents can be determined for arbitrary variations of input parameters like saturation or angular frequency (ω). The physical processes are investigated and explained by an example of Massilon sandstone filled with air and water. For the quasi-static limit case, i.e. \({\omega \mapsto 0}\), the results of the model are identical with the phase velocity obtained with the well-known Gassmann–Wood limit. The model focuses on systems with a liquid and a gas phase. It is shown that the grain compressibility can be neglected in this case, and the amount of material parameters as well as the complexity reduces significantly compared to other three-phase approaches. This makes the well-adapted model suitable for direct application in the vadose zone or partially saturated laboratory samples with a gas phase and a liquid phase. The final model is characterised by low computational effort, general validity for application from geophysics over engineering up to biomedicine and flexibility for use of extended empirical and theoretical relationships.


Porous Medium Phase Velocity Bulk Modulus Capillary Pressure Vadose Zone 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Wien 2014

Authors and Affiliations

  • Holger Steeb
    • 1
  • Patrick S. Kurzeja
    • 1
  • Stefan M. Schmalholz
    • 2
  1. 1.Institute of MechanicsRuhr-University BochumBochumGermany
  2. 2.Institute of Earth Sciences, Bâtiment GeopolisUniversity of LausanneLausanneSwitzerland

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