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Vibro-Injection Pile Installation in Sand: Part I—Interpretation as Multi-material Flow

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Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 77))

Abstract

The installation of vibro-injection piles into saturated sand has a significant impact on the surrounding soil and neighboring buildings. It is generally characterized by a multi-material flow with large material deformations, non-stationary and new material interfaces, and by the interaction of the grain skeleton and the pore water. Part 1 in this series of papers is concerned with the mathematical and physical modeling of the multi-material flow associated with vibro-injection pile installation. This model is the backbone of a new multi-material arbitrary Lagrangian-Eulerian (MMALE) numerical method presented in Part 2.

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References

  1. Aubram, D.: Differential geometry applied to continuum mechanics. In: Veröffentlichungen des Grundbauinstitutes der Technischen Universität Berlin, vol. 44. Shaker, Aachen (2009)

    Google Scholar 

  2. Aubram, D.: An arbitrary Lagrangian-Eulerian method for penetration into sand at finite deformation. In: Veröffentlichungen des Grundbauinstitutes der Technischen Universität Berlin, vol. 62. Shaker, Aachen (2013)

    Google Scholar 

  3. Aubram, D.: Three-scale hybrid mixture theory for geomechanical multi-material flow (submitted for publication)

    Google Scholar 

  4. Aubram, D., Rackwitz, F., Savidis, S.A.: An ALE finite element method for cohesionless soil at large strains: computational aspects and applications. In: Benz, T., Nordal, S. (eds.) Proceedings 7th European Conference on Numerical Methods in Geotechnical Engineering (NUMGE), pp. 245–250. CRC Press, Boca Raton (2010)

    Google Scholar 

  5. Belytschko, T., Liu, W.K., Moran, D.: Nonlinear Finite Elements for Continua and Structures. Wiley, Chichester (2000)

    MATH  Google Scholar 

  6. Bennethum, L.S., Cushman, J.H.: Multiscale, hybrid mixture theory for swelling systems. 1. Balance laws. Int. J. Eng. Sci. 34, 125–145 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  7. Bennethum, L.S., Weinstein, T.: Three pressures in porous media. Transp. Porous Media 54, 1–34 (2004)

    Article  MathSciNet  Google Scholar 

  8. Bennethum, L.S.: Compressibility moduli for porous materials incorporating volume fraction. J. Eng. Mech. 132, 1205–1214 (2006)

    Article  Google Scholar 

  9. Bennethum, L.S.: Theory of flow and deformation of swelling porous materials at the macroscale. Comput. Geotech. 34, 267–278 (2007)

    Article  Google Scholar 

  10. Benson, D.J.: Computational methods in Lagrangian and Eulerian hydrocodes. Comput. Methods Appl. Mech. Eng. 99, 235–394 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  11. Benson, D.J.: A mixture theory for contact in multi-material Eulerian formulations. Comput. Methods Appl. Mech. Eng. 140, 59–86 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  12. Biot, M.A.: General theory of three-dimensional consolidation. J. Appl. Phys. 12, 155–164 (1941)

    Article  MATH  Google Scholar 

  13. Biot, M.A., Willis, D.G.: The elastic coefficients of the theory of consolidation. J. Appl. Mech. 24, 594–601 (1957)

    MathSciNet  Google Scholar 

  14. Bouré, J.A., Delhaye, J.M.: General equations and two-phase flow modeling, Sect. 1.2. In: Hetsroni, G. (ed.) Handbook of Multiphase Systems. Hemisphere Publishing Corporation, Washington (1982)

    Google Scholar 

  15. Bouré, J.A.: Two-phase flow models: the closure issue. Multiph. Sci. Technol. 3(1–4), 3–30 (1987)

    Article  Google Scholar 

  16. Bowen, R.M.: Compressible porous media models by use of the theory of mixtures. Int. J. Eng. Sci. 20(6), 697–735 (1982)

    Article  MATH  Google Scholar 

  17. Colella, P., Glaz, H.M., Ferguson, R.E.: Multifluid algorithms for Eulerian finite difference methods (1997) (unpublished manuscript)

    Google Scholar 

  18. De Boer, R.: Theory of Porous Media. Springer, Berlin (2000)

    Book  MATH  Google Scholar 

  19. Steinmann, Paul: Elasticity. In: Steinmann, Paul (ed.) . LAMM, vol. 2, pp. 287–364. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  20. Drew, D.A.: Mathematical modeling of two-phase flow. Annu. Rev. Fluid Mech. 15, 261–291 (1983)

    Article  Google Scholar 

  21. Drumheller, D.S.: A theory for dynamic compaction of wet porous solids. Int. J. Solids Struct. 23, 211–237 (1987)

    Article  Google Scholar 

  22. Ehlers, W.: Grundlegende Konzepte in der Theorie Poröser Medien. Technische Mechanik 16, 63–76 (1996)

    Google Scholar 

  23. Hirt, C.W., Amsden, A.A., Cook, J.L.: An arbitrary Lagrangian-Eulerian computing method for all flow speeds. J. Comput. Phys. 14, 227–253 (1974)

    Article  MATH  Google Scholar 

  24. Kapila, A.K., Menikoff, R., Bdzil, J.B., Son, S.F., Stewart, D.S.: Two-phase modeling of deflagration-to-detonation transition in granular materials: reduced equations. Phys. Fluids 13, 3002–3024 (2001)

    Article  Google Scholar 

  25. Koning, H.L.: Some observations on the modulus of compressibility of water. In: Proceedings European Conference on Soil Mechanics and Foundation Engineering-Problems of Settlement and Compressibility of Soils, Sect. 1, Wiesbaden, Germany, pp. 33–36. Deutsche Gesellschaft für Erdund Grundbau e.V. (1963)

    Google Scholar 

  26. Lewis, R.W., Schrefler, B.A.: The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media, 2nd edn. Wiley, Chichester (1998)

    MATH  Google Scholar 

  27. Malvern, L.E.: Introduction to the Mechanics of a Continuous Medium. Prentice Hall Inc, New Jersey (1969)

    Google Scholar 

  28. Marsden, J.E., Hughes, T.J.R.: Mathematical Foundations of Elasticity. Dover Publications, New York (1994)

    Google Scholar 

  29. Miller, G.H., Puckett, E.G.: A high-order Godunov method for multiple condensed phases. J. Comput. Phys. 128, 134–164 (1996)

    Article  MATH  Google Scholar 

  30. Miller, D.S., Zimmerman, G.B.: An algorithm for time evolving volume fractions in mixed zones in Lagrangian hydrodynamics calculations. Russian J. Phys. Chem. B 3, 117–121 (2009)

    Article  Google Scholar 

  31. Murrone, A., Guillard, H.: A five equation reduced model for compressible two phase flow problems. J. Comput. Phys. 202, 664–698 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  32. Nikolinakou, M.A., Whittle, A.J., Savidis, S.A., Schran, U.: Prediction and interpretation of the performance of a deep excavation in Berlin sand. J. Geotech. Geoenviron. Eng. 137(11), 1047–1061 (2011)

    Article  Google Scholar 

  33. Niemunis, A., Herle, I.: Hypoplastic model for cohesionless soils with elastic strain range. Mech. Cohesive-Frictional Mater. 2, 279–299 (1997)

    Article  Google Scholar 

  34. Rackwitz, F., Savidis, S.A.: Numerische Untersuchungen zum Tragverhalten von Zugpfählen in Berliner Sand. Bauingenieur 79(9), 375–383 (2004)

    Google Scholar 

  35. Savidis, S.A., Aubram, D., Rackwitz, F.: Arbitrary Lagrangian-Eulerian finite element formulation for geotechnical construction processes. J. Theor. Appl. Mech. 38(1–2), 165–194 (2008)

    MathSciNet  Google Scholar 

  36. Shashkov, M.: Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes. Int. J. Numer. Methods Fluids 56(8), 1497–1504 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  37. Stewart, H.B., Wendroff, B.: Two-phase flow: models and methods. J. Comput. Phys. 56, 363–409 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  38. Truesdell, C., Toupin R.A.: Encyclopedia of physics. In: Bd. III/1: The Classical Field Theories, pp. 226–793. Springer, Heidelberg (1960)

    Google Scholar 

  39. Truesdell, C., Noll, W.: The Non-Linear Field Theories of Mechanics, 3rd edn. Springer, Berlin (2004)

    Book  Google Scholar 

  40. Vitali, E., Benson, D.J.: An extended finite element formulation for contact in multi-material arbitrary Lagrangian-Eulerian calculations. Int. J. Numer. Methods Eng. 67, 1420–1444 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  41. von Wolffersdorff, P.-A.: A hypoplastic relation for granular materials with a predefined limit state surface. Mech. Cohesive-Frictional Mater. 1, 251–271 (1996)

    Article  Google Scholar 

  42. Whitaker, S.: The transport equations for multi-phase systems. Chem. Eng. Sci. 28, 139–147 (1973)

    Article  Google Scholar 

  43. Whitaker, S.: Flow in porous media iii: deforming media. Transp. Porous Media 1, 127–154 (1986)

    Article  Google Scholar 

  44. Wriggers, P.: Nonlinear Finite Element Methods. Springer, Berlin (2008)

    MATH  Google Scholar 

  45. Zienkiewicz, O.C., Shiomi, T.: Dynamic behaviour of saturated porous media: the generalized Biot formulation and its numerical solution. Int. J. Numer. Analyt. Methods Geomech. 8, 71–96 (1984)

    Article  MATH  Google Scholar 

  46. Zienkiewicz, O.C., Chan, A.H.C., Pastor, M., Schrefler, B.A., Shiomi, T.: Computational Geomechanics-With Special Reference to Earthquake Engineering. Wiley, Chichester (1999)

    MATH  Google Scholar 

  47. Zienkiewicz, O.C., Taylor, R.L.: The Finite Element Method, vol. 3, 5th edn. Butterworth-Heinemann, Oxford (2000)

    Google Scholar 

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Acknowledgments

The presented work was carried out under the financial support from the German Research Foundation (DFG; grants SA 310/26-1 and SA 310/26-2) as part of the DFG Research Unit FOR 1136, which is gratefully acknowledged. We thank our colleagues in this research unit for several fruitful discussions about our work.

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Aubram, D., Rackwitz, F., Savidis, S.A. (2015). Vibro-Injection Pile Installation in Sand: Part I—Interpretation as Multi-material Flow. In: Triantafyllidis, T. (eds) Holistic Simulation of Geotechnical Installation Processes. Lecture Notes in Applied and Computational Mechanics, vol 77. Springer, Cham. https://doi.org/10.1007/978-3-319-18170-7_5

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  • DOI: https://doi.org/10.1007/978-3-319-18170-7_5

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