Transient Mechanical Wave Propagation in Semi-infinite Porous Media Using a Finite Element Approach with Domain Decomposition Technology

  • Andrey Terekhov
  • Arnaud Mesgouez
  • Gaelle Lefeuve-Mesgouez
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4671)


In this paper, the authors propose a numerical investigation in the time domain of the mechanical wave propagation due to an impulsional load on a semi-infinite soil. The ground is modelled as a porous saturated viscoelastic medium involving the complete Biot theory. An accurate and efficient Finite Element Method using a matrix-free technique is used. Two parallel algorithms are used: Geometrical Domain Decomposition (GDD) and Algebraic Decomposition (AD). Numerical results show that GDD algorithm has the best time. Physical numerical results present the displacements of the fluid and solid particles over the surface and in depth.


Porous Medium Parallel Algorithm Domain Decomposition Elementary Matrice Finite Element Approach 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Biot, M.A.: Theory of propagation of elastic waves in a fluid-saturated porous solid. I- Low-frequency range. The Journal of the Acoustical Society of America 28(2), 168–178 (1956)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Coussy, O.: Mécanique des milieux poreux. Ed. Technip, Paris (1991)Google Scholar
  3. 3.
    Zienkiewicz, O.C., Shiomi, T.: Dynamic behaviour of saturated porous media: the generalized Biot formulation and its numerical solution. International Journal for Numerical and Analytical Methods in Geomechanics 8, 71–96 (1984)zbMATHCrossRefGoogle Scholar
  4. 4.
    Simon, B.R., Wu, J.S.S., Zienkiewicz, O.C., Paul, D.K.: Evaluation of u-w and u-π finite element methods for the dynamic response of saturated porous media using one-dimensional models. Int. J. Numer. Anal. Methods Geomech 10, 461–482 (1986)zbMATHCrossRefGoogle Scholar
  5. 5.
    Gajo, A., Saetta, A., Vitaliani, R.: Evaluation of three and two field finite element methods for the dynamic response of saturated soil. Int. J. Numer. Anal. Methods Geomech 37, 1231–1247 (1994)zbMATHGoogle Scholar
  6. 6.
    Mesgouez, A., Lefeuve-Mesgouez, G., Chambarel, A.: Simulation of transient mechanical wave propagation in heterogeneous soils. In: Sunderam, V.S., van Albada, G.D., Sloot, P.M.A., Dongarra, J.J. (eds.) ICCS 2005. LNCS, vol. 3514, pp. 647–654. Springer, Heidelberg (2005)Google Scholar
  7. 7.
    Mesgouez, A., Lefeuve-Mesgouez, G., Chambarel, A., Fougere, D.: Numerical modeling of poroviscoelastic grounds in the time domain using a parallel approach. In: Alexandrov, V.N., van Albada, G.D., Sloot, P.M.A., Dongarra, J.J. (eds.) ICCS 2006. LNCS, vol. 3992, pp. 50–57. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Terada, K., Ito, T., Kikuchi, N.: Characterization of the mechanical behaviors of solid-fluid mixture by the homogenization method. Comput. Methods Appl. Mech. Eng. 153, 223–257 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Coussy, O., Dormieux, L., Detournay, E.: From Mixture theory to Biot’s approach for porous media. Int. J. Solids Struct. 35, 4619–4635 (1998)zbMATHCrossRefGoogle Scholar
  10. 10.
    Mesgouez, A., Lefeuve-Mesgouez, G., Chambarel, A.: Transient mechanical wave propagation in semi-infinite porous media using a finite element approach. Soil Dyn. Earth. Eng. 25, 421–430 (2005)CrossRefGoogle Scholar
  11. 11.
  12. 12.
    Hendrickson, B., Leland, R.: The Chaco User’s Guide: Version 2.0. Tech Report SAND94-2692 (1994)Google Scholar
  13. 13.
    Akbar, N., Dvorkin, J., Nur, A.: Relating P-wave attenuation to permeability. Geophysics 58(1), 20–29 (1993)CrossRefGoogle Scholar
  14. 14.
    Dvorkin, J., Nur, A.: Dynamic poroelasticity: a unified model with the squirt and the Biot mechanisms. Geophysics 58(4), 524–533 (1993)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Andrey Terekhov
    • 1
  • Arnaud Mesgouez
    • 2
  • Gaelle Lefeuve-Mesgouez
    • 2
  1. 1.Institute of Computational Mathematic and Mathematical Geophysics, Prospect Akademika Lavrentjeva, 6, Novosibirsk, 630090Russia
  2. 2.UMR Climate, Soil and Environment, University of Avignon, France, Faculté des Sciences, 33 rue Louis Pasteur, F-84000 Avignon 

Personalised recommendations