Acta Geotechnica

, Volume 13, Issue 2, pp 267–282 | Cite as

A new incompatible mode element with selective mass scaling for saturated soil dynamics

  • P. Mira
  • A. S. Benítez
  • M. Pastor
  • J. A. Fernández Merodo
Research Paper


It is a well-known fact that addressing hydromechanical problems in saturated soils with the finite element method and equal-order interpolation formulations in displacements and pore pressures produces unstable results. Classically, stabilization has been achieved by increasing the interpolation degree of displacement with respect to pore pressure, hence fulfilling the Babuska–Brezzi condition. However, the use of quadratic elements involves high computational costs. From that point of view, the use of stabilized low-order elements is a more desirable option. Much research has been carried out in different directions in the stabilization of low-order formulations for saturated soils in quasistatic conditions, among others with the technique based on strain field enhancement through internal degrees of freedom. This article presents an alternative displacement–pore pressure formulation for saturated soil dynamics based on the enhancement of the displacement field through incompatible modes.


Dynamics Finite elements Incompatible modes Mass scaling Saturated soil 



The present work has been supported by research Grant BES-2010-036691 associated with research project BIA2009-14225-C02-02 Granted by Secretaría de Estado de Investigación of the Spanish Government.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • P. Mira
    • 1
    • 2
  • A. S. Benítez
    • 1
    • 2
  • M. Pastor
    • 2
  • J. A. Fernández Merodo
    • 2
    • 3
  1. 1.Laboratorio de Geotecnia - CEDEXCentro de Estudios y Experimentación de Obras PúblicasMadridSpain
  2. 2.Grupo M2i, E.T.S. Ingenieros de Caminos, Canales y PuertosUniversidad Politécnica de MadridMadridSpain
  3. 3.IGME Instituto Geológico y Minero de EspañaMadridSpain

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