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Geometrical and material non-linear analysis of fully and partially saturated porous media

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Porous Media

Abstract

A formulation for a partially saturated porous medium undergoing large elastic or elasto-plastic deformations is presented. The porous material is treated as a multiphase continuum with the pores of the solid skeleton filled by water and air, this last one at constant pressure. This pressure may either be the atmospheric pressure or the cavitation pressure. The governing equations at macroscopic level are derived in a spatial and a material setting. Solid grains and water are assumed to be incompressible at the microscopic level. The elasto-plastic behaviour of the solid skeleton is described by the multiplicative decomposition of the deformation gradient into an elastic and a plastic part. The effective stress state is limited by the Drucker-Prager yield surface. The water is assumed to obey Darcy’s law. Numerical examples of the Liakopoulos’ test and of strain localization of dense or loose sand and of clay under undrained conditions conclude the paper.

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References

  1. Armero, F.: Formulation and Finite Element Implementation of a Multiplicative Model of Coupled Poro-Plasticity at Finite Strains under Fully Saturated Conditions. Computer Methods Appl. Mech. Engrg. 171 (1999), 205–241.

    MathSciNet  MATH  Google Scholar 

  2. Bluhm, J., de Boer, R.: The Volume Fraction Concept in the Porous Media Theory. ZAMM 77 (1997), 8, 563–577.

    Article  MathSciNet  MATH  Google Scholar 

  3. de Boer, R.: Theory of Porous Media: Highlight in Historical Development and Current State. Springer-Verlag, Berlin 2000.

    Google Scholar 

  4. de Boer, R., Ehlers, W., Kowalski, S., Plischka, J.: Porous media-a survey of different approaches. Forschungsberichte aus dem Fachbereich Bauwesen der Universität Essen, 54, Essen 1991.

    Google Scholar 

  5. Bolzon, G., Schrefler, B. A., Zienkiewicz, O. C.: Elastoplastic soil constitutive laws generalized to partially saturated states. Géotechnique 46 (1996), 279289.

    Google Scholar 

  6. Borja, R. I., Alarcon, E.: A Mathematical Framework for Finite Strain Elastoplastic Consolidation. Part 1: Balance Laws, Variational Formulation, and Linearization. Computer Meth. Appl. Mech. Engrg. 122 (1995), 145–171.

    Article  MathSciNet  MATH  Google Scholar 

  7. Borja, R. I., Tamagnini, C.: Numerical Implementation of a Mathematical Model for Finite Strain Elastoplastic Consolidation. In Owen, D. R. J., Onate, E., Hinton, E. (eds.): Computational Plasticity — Fundamentals and Applications, CIMNE, Barcelona 1997, pp. 1631–1640.

    Google Scholar 

  8. Ciarlet, P. G.: Mathematical Elasticity. Volume I: Three-Dimensional Elasticity. Elsevier Science, 1988.

    MATH  Google Scholar 

  9. Diebels, S., Ehlers, W.: Dynamic Analysis of a Fully Saturated Porous Medium Accounting for Geometrical and Material Non-linearities. Int. J. Numer. Meth. Eng. 39 (1996), 81–97.

    Article  MATH  Google Scholar 

  10. Diebels, S., Ehlers, W., Ellsiepen, P., Volk, W.: On the Regularization of Shear Band Phenomena in Liquid-saturated and Empty Soils. In Brillard, A., Ganghoffer, J. F. (eds.): Proc. Euromech Colloquium 378 on Nonlocal Aspects in Solid Mechanics, University of Mulhouse 1998, pp. 58–63.

    Google Scholar 

  11. Drucker, D. C., Prager, W.: Soil Mechanics and Plastic Analysis or Limit Design. Quart. Appl. Math. 10 (1952), 2, 157–165.

    MathSciNet  MATH  Google Scholar 

  12. Ehlers, W., Eipper, G.: Finite Elastic Deformation in Liquid-Saturated and Empty Porous Solids. Transport in Porous Media 34 (1999), 179–191.

    Article  MathSciNet  Google Scholar 

  13. Gawin, D., Sanavia, L., Scherfler, B. A.: Cavitation Modelling in Saturated Geomaterials with Application to Dynamic Strain Localization. Int. J. Num. Methods in Fluids 27 (1998), 109–125.

    Article  MATH  Google Scholar 

  14. Gray, W. G., Hassanizadeh, M.: Unsaturated Flow Theory including Interfacial Phenomena. Water Resources Res. 27 (1991), (8), 1855–1863.

    Article  Google Scholar 

  15. Hassanizadeh, M., Gray, W. G.: General Conservation Equations for Multiphase System: 1. Averaging technique. Adv. Water Res. 2 (1979), 131–144.

    Article  Google Scholar 

  16. Hassanizadeh, M., Gray, W. G.: General Conservation Equations for Multi-Phase System: 2. Mass, Momenta, Energy and Entropy Equations. Adv. Water Res. 2 (1979), 191–201.

    Article  Google Scholar 

  17. Hassanizadeh, M., Gray, W. G.: General Conservation Equations for Multi-Phase System: 3. Constitutive Theory for Porous Media Flow. Adv. Water Res. 3 (1980), 25–40.

    Article  Google Scholar 

  18. Jeremic, B., Runesson, K., Sture, S.: Finite Deformation Analysis of Geomaterials. Int. J. Numer. Anal. Meth. Geomech. 25 (2001), 741–756.

    Article  Google Scholar 

  19. Lee, E. H.: Elastic-Plastic Deformation at Finite Strains. J. Appl. Mech. 1 (6) (1969).

    Google Scholar 

  20. Lewis, R. W., Schrefler, B. A.: The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media. John Wiley and Sons, Chichester 1998.

    MATH  Google Scholar 

  21. Liakopoulos, A. C.: Transient flow through unsaturated porous media. Ph. D. Thesis, University of California, Berkeley 1965.

    Google Scholar 

  22. Marsden, J. E., Hughes, T. J. R.: Mathematical Foundations of Elasticity. Prentice-Hall, Englewood Cliffs 1983.

    MATH  Google Scholar 

  23. Meroi, E., Schrefler, B. A., Zienkiewicz, O. C.: Large Strain Static and Dynamic Semi-Saturated Soil Behaviour. Int. J. Num. Analytical Methods Geomech. 19 (2) (1995), 81–106.

    Article  MATH  Google Scholar 

  24. Miehe, C.: Computation of Isotropic Tensor Functions. Comm. Num. Meth. Eng. 9 (1993), 889–896.

    Article  MATH  Google Scholar 

  25. Mokni, M., Desrues, J.: Strain Localization Measurements in Undrained Plane-strain Biaxial Tests on Hostun RF Sand. Mech. Cohes-Frict. Mater. 4 (1998), 419–441.

    Google Scholar 

  26. Nemat-Nasser, S.: On Finite Plastic Flow of Crystalline Solids and Geomaterials. Transactions of ASME. 50 (1983), 1114–1126.

    Article  MATH  Google Scholar 

  27. Peters, J. F., Lade, P. V., Bro, A.: Shear Band Formation in Triaxial and Plane Strain tests. In Donaghe, R. T., Chaney, R. C., Silver, M. L. (eds.): Advanced Triaxial Testing of Soil and Rock, ASTM STP 977, Am. Soc. Testing and Materials, Philadelphia 1988, p. 604.

    Chapter  Google Scholar 

  28. Reese, S.: Elastoplastic Material Behaviour with Large Elastic and Large Plastic Deformation. ZAMM Z. Angew. Math. Mech. 77 (1997), 277–278.

    Google Scholar 

  29. Sanavia, L., Schrefler, B. A., Stein, E., Steinmann, P.: Modelling of localization at finite inelastic strain in fluid saturated porous media. In Ehlers, W. (ed.): IUTAM Symposium on Theoretical and Numerical Methods in Continuum Mechanics of Porous Materials. Kluwer, Dordrecht 2001, pp. 239–244.

    Google Scholar 

  30. Sanavia, L., Schrefler, B. A., Steinmann, P.: A mathematical and numerical model for finite elastoplastic deformations in fluid saturated porous media. In Capriz, G., Ghionna, V. N. Giovine, P. (eds.): Modeling and Mechanics of Granular and Porous Materials, Series of Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Boston (in print), pp. 297–346. Also UKL-LTM Report J2001–10, University of Kaiserslautern, Germany, Chair of Applied Mechanics.

    Google Scholar 

  31. Sanavia, L., Schrefler, B. A., Steinmann, P.: A formulation for an unsaturated porous medium undergoing large inelastic strains. Computational Mechanics (in print). Also UKL-LTM Report J2001–12 University of Kaiserslautern, Germany, Chair of Applied Mechanics.

    Google Scholar 

  32. Schrefler, B. A., Sanavia, L., Majorana, C. E.: A Multiphase Medium Model for Localization and Postlocalization Simulation in Geomaterials. Mech. Cohes.Frict. Mater. 1 (1996), 95–114.

    Article  Google Scholar 

  33. Schrefler, B. A., Simoni, L.: A unified approach to the analysis of saturated-unsaturated elastoplastic porous media. In Proc. Numerical Methods in Geomechanics, Balkema, 1988.

    Google Scholar 

  34. Simo, J. C., Taylor, R.: Consistent Tangent Operators for Rate-Independent Elastoplasticity. Comp. Meth. Applied Mech. Eng. 48 (1985), 101–118.

    Article  MATH  Google Scholar 

  35. Simo, J. C.: Numerical Analysis and Simulation of Plasticity. In Ciarlet, P. G., Lions, J. L. (eds.): Numerical Methods for Solids, Part 3, Vol. 6 of Handbook of Numerical Analysis, North-Holland, 1998.

    Google Scholar 

  36. Simo, J. C., Hughes, T. J. R.: Computational Inelasticity. Springer-Verlag, 1998.

    Google Scholar 

  37. Steinmann, P.: A finite element formulation for Strong Discontinuities in Fluid-Saturated Porous Media. Mech. Cohes.-Frict. Mater. 4 (1999), 133–152.

    Google Scholar 

  38. Vardoulakis, J., Sulem J.: Bifurcation Analysis in Geomechanics. Blakie Academic and Professional, London 1995.

    Google Scholar 

  39. Wriggers, P.: Continuum Mechanics, Non-linear Finite Element Techniques and Computational Stability. In Stein, E. (ed.): Progress in Computational Analysis of Inelastic Structures, CISM Courses and Lectures No. 321, Springer-Verlag, Wien 1993.

    Google Scholar 

  40. Zhang, H. W., Sanavia, L., Schrefler, B. A.: An Internal Length Scale in Strain Localization of Multiphase Porous Media. Mech. Cohes.-Frict. Mater. 4 (1999), 433–460.

    Google Scholar 

  41. Zhang, H. W., Sanavia, L., Schrefler, B. A.: Numerical analysis of dynamic strain localization in initially water saturated dense sand with a modified generalized plasticity model. Comp. Struct. 79 (2000), 441–459.

    Article  Google Scholar 

  42. Zienkiewicz, O. C., Chan, A., Pastor, M., Schrefler, B. A., Shiomi T.: Computational Geomechanics with special Reference to Earthquake Engineering. John Wiley and Sons, Chichester 1999.

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Structural and Transportation Engineering, University of Padua, 35131, Padua, Italy

    Lorenzo Sanavia & Bernhard A. Schrefler

  2. Chair of Applied Mechanics, University of Kaiserslautern, 67653, Kaiserlautern, Germany

    Paul Steinmann

Authors
  1. Lorenzo Sanavia
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  2. Bernhard A. Schrefler
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  3. Paul Steinmann
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Editor information

Editors and Affiliations

  1. Institut für Mechanik (Bauwesen), Lehrstuhl II, Universität Stuttgart, Pfaffenwaldring 7, D-70569, Stuttgart, Germany

    Wolfgang Ehlers

  2. Institut für Mechanik, Universität Essen, Universitätsstr. 15, D-45141, Essen, Germany

    Joachim Bluhm

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© 2002 Springer-Verlag Berlin Heidelberg

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Sanavia, L., Schrefler, B.A., Steinmann, P. (2002). Geometrical and material non-linear analysis of fully and partially saturated porous media. In: Ehlers, W., Bluhm, J. (eds) Porous Media. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04999-0_12

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  • DOI: https://doi.org/10.1007/978-3-662-04999-0_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-07843-9

  • Online ISBN: 978-3-662-04999-0

  • eBook Packages: Springer Book Archive

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