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Mathematical Problems in Engineering
Volume 2016, Article ID 4256079, 12 pages
http://dx.doi.org/10.1155/2016/4256079
Research Article

Free Finite Element Approach for Saturated Porous Media: Consolidation

ETSI Caminos, Technical University of Madrid, Profesor Aranguren s/n, 28040 Madrid, Spain

Received 4 March 2016; Accepted 8 May 2016

Academic Editor: Giovanni Garcea

Copyright © 2016 M. M. Stickle et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. W. G. Gray and C. T. Miller, Introduction to the Thermodynamically Constrained Averaging Theory for Porous Medium Systems, Springer, Berlin, Germany, 2014.
  2. M. Pastor, T. Blanc, B. Haddad et al., “Depth averaged models for fast landslide propagation: mathematical, rheological and numerical aspects,” Archives of Computational Methods in Engineering, vol. 22, no. 1, pp. 67–104, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. R. I. Borja and J. A. White, “Continuum deformation and stability analyses of a steep hillside slope under rainfall infiltration,” Acta Geotechnica, vol. 5, no. 1, pp. 1–14, 2010. View at Publisher · View at Google Scholar · View at Scopus
  4. R. de Boer, Trends in Continuum Mechanics of Porous Media, Springer, Berlin, Germany, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  5. O. C. Zienkiewicz and T. Shiomi, “Dynamic behaviour of saturated porous media: the generalized Biot formulation and its numerial solution,” International Journal for Numerical and Analytical Methods in Geomechanics, vol. 8, no. 1, pp. 71–96, 1984. View at Publisher · View at Google Scholar · View at Scopus
  6. O. C. Zienkiewicz, A. H. C. Chan, M. Pastor, D. K. Paul, and T. Shiomi, “Static and dynamic behaviour of soils: a rational approach to quantitative solutions. I. Fully saturated problems,” Proceedings of the Royal Society of London, vol. 429, no. 1877, pp. 285–309, 1990. View at Publisher · View at Google Scholar · View at Scopus
  7. O. C. Zienkiewicz, A. H. C. Chan, M. Pastor, B. A. Schreer, and T. Shiomi, Computational Geomechanics with Special Reference to Earthquake Engineering, John Wiley & Sons, Chichester, UK, 1999.
  8. S. Diebels and W. Ehlets, “Dynamic analysis of a fully saturated porous medium accounting for geometrical and material non-linearities,” International Journal for Numerical Methods in Engineering, vol. 39, no. 1, pp. 81–97, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  9. S. Breuer, “Quasi-static and dynamic behavior of saturated porous media with incompressible constituents,” Transport in Porous Media, vol. 34, no. 1, pp. 285–303, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. C. Li, R. I. Borja, and R. A. Regueiro, “Dynamics of porous media at finite strain,” Computer Methods in Applied Mechanics and Engineering, vol. 193, no. 36–38, pp. 3837–3870, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. R. W. Lewis and B. A. Schreer, The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media, John Wiley & Sons, Chichester, UK, 1998.
  12. J. Planas, I. Romero, and J. M. Sancho, “B free,” Computer Methods in Applied Mechanics and Engineering, vol. 217–220, pp. 226–235, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. A. K. Gupta and B. Mohraz, “A method of computing numerically integrated stiffness matrices,” International Journal for Numerical Methods in Engineering, vol. 5, no. 1, pp. 83–89, 1972. View at Publisher · View at Google Scholar · View at Scopus
  14. T. J. R. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Dover, 2000.
  15. O. C. Zienkiewicz and R. Taylor, The Finite Element Method—The Basics, Butterworth Heinemann, Woburn, Mass, USA, 2000.
  16. D. M. Pedroso, “A consistent u-p formulation for porous media with hysteresis,” International Journal for Numerical Methods in Engineering, vol. 101, no. 8, pp. 606–634, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. R. de Boer, W. Ehlers, and Z. Liu, “One-dimensional transient wave propagation in fluid-saturated incompressible porous media,” Archive of Applied Mechanics, vol. 63, no. 1, pp. 59–72, 1993. View at Publisher · View at Google Scholar · View at Scopus
  18. B. A. Schrefler, “Mechanics and thermodynamics of saturated/unsaturated porous materials and quantitative solutions,” Applied Mechanics Reviews, vol. 55, no. 4, pp. 351–388, 2002. View at Publisher · View at Google Scholar · View at Scopus
  19. J. A. White and R. I. Borja, “Stabilized low-order finite elements for coupled solid-deformation/fluid-diffusion and their application to fault zone transients,” Computer Methods in Applied Mechanics and Engineering, vol. 197, no. 49-50, pp. 4353–4366, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  20. M. Pastor, O. C. Zienkiewicz, T. Li, X. Li, and M. Huang, “Stabilized finite elements with equal order of interpolation for soil dynamics problems,” Archives of Computational Methods in Engineering, vol. 6, no. 1, pp. 3–33, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  21. B. Markert, Y. Heider, and W. Ehlers, “Comparison of monolithic and splitting solution schemes for dynamic porous media problems,” International Journal for Numerical Methods in Engineering, vol. 82, no. 11, pp. 1341–1383, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  22. O. C. Zienkiewicz, C. T. Chang, and P. Bettess, “Drained, undrained, consolidating and dynamic behaviour assumptions in soils,” Geotechnique, vol. 30, no. 4, pp. 385–395, 1980. View at Publisher · View at Google Scholar · View at Scopus
  23. M. A. Biot, “General theory of three-dimensional consolidation,” Journal of Applied Physics, vol. 12, no. 2, pp. 155–164, 1941. View at Publisher · View at Google Scholar · View at Scopus
  24. D. S. Jeng and J. R. C. Hsu, “Wave-induced soil response in a nearly saturated sea-bed of finite thickness,” Geotechnique, vol. 46, no. 3, pp. 427–440, 1996. View at Publisher · View at Google Scholar · View at Scopus