Coupled systems mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Solution verification procedures for modeling and simulation of fully coupled porous media: static and dynamic behavior

  • Tasiopoulou, Panagiota (National Technical University of Athens) ;
  • Taiebat, Mahdi (Department of Civil Engineering, The University of British Columbia) ;
  • Tafazzoli, Nima (Tetra Tech EBA) ;
  • Jeremic, Boris (Department of Civil and Environmental Engineering, University of California / Earth Science Division, Lawrence Berkeley National Laboratory)
  • Received : 2014.09.25
  • Accepted : 2015.02.03
  • Published : 2015.03.25
⟨ Previous Next ⟩

Abstract

Numerical prediction of dynamic behavior of fully coupled saturated porous media is of great importance in many engineering problems. Specifically, static and dynamic response of soils - porous media with pores filled with fluid, such as air, water, etc. - can only be modeled properly using fully coupled approaches. Modeling and simulation of static and dynamic behavior of soils require significant Verification and Validation (V&V) procedures in order to build credibility and increase confidence in numerical results. By definition, Verification is essentially a mathematics issue and it provides evidence that the model is solved correctly, while Validation, being a physics issue, provides evidence that the right model is solved. This paper focuses on Verification procedure for fully coupled modeling and simulation of porous media. Therefore, a complete Solution Verification suite has been developed consisting of analytical solutions for both static and dynamic problems of porous media, in time domain. Verification for fully coupled modeling and simulation of porous media has been performed through comparison of the numerical solutions with the analytical ones. Modeling and simulation is based on the so called, u-p-U formulation. Of particular interest are numerical dispersion effects which determine the level of numerical accuracy. These effects are investigated in detail, in an effort to suggest a compromise between numerical error and computational cost.

Keywords

References

  1. Argyris, J. and Mlejnek, H.P. (1991), Dynamics of Structures. North Holland in USA Elsevier.
  2. Biot, M. (1941), "General theory of three-dimensional consolidation", J. Appl. Phys., 12(2), 155-164. https://doi.org/10.1063/1.1712886
  3. Biot, M. (1955), "Theory of elasticity and consolidation for a porous anisotropic solid", J. Appl. Phys., 26(2), 182-185. https://doi.org/10.1063/1.1721956
  4. Biot, M. (1956a), "Theory of deformation of a porous viscoelastic anisotropic solid", J. Appl. Phys., 27(5), 459-467. https://doi.org/10.1063/1.1722402
  5. Biot, M. (1956b), "Theory of propagation of elastic waves in a fluid-saturated porous solid. i. low-frequency range", J. Acoust. Soc. Am., 28(2), 168-178. https://doi.org/10.1121/1.1908239
  6. Biot, M. (15956c), "Theory of propagation of elastic waves in a fluid-saturated porous solid. ii. higher frequency range", J. Acoust. Soc. Am., 28(2), 179-191. https://doi.org/10.1121/1.1908241
  7. Bowen. R. (1980), "Incompressible porous media models by use of the theory of mixtures", Int. J. Eng. Sci., 18, 1129-1148. https://doi.org/10.1016/0020-7225(80)90114-7
  8. Bowen, R. (1982), "Compressible porous media models by use of the theory of mixtures", Int. J. Eng. Sci., 20(6), 697-735. https://doi.org/10.1016/0020-7225(82)90082-9
  9. Coussy, O. (1995), Mechanics of Porous Continua, John Wiley and Sons.
  10. Coussy, O. (2004), Poromechanics. John Wiley and Sons, Chichester.
  11. de Boer, R., Ehlers, W. and Liu, Z. (1993), "One-dimensional transient wave propagation in fluid-saturated incompressible porous media", Arch. Appl. Mech., 63(1), 59-72. https://doi.org/10.1007/BF00787910
  12. Deraemaeker, P.B.A. and Babuska, I. (1999), "Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimensions", Int. J. Numer. Meth. Eng., 46(4), 471-499. https://doi.org/10.1002/(SICI)1097-0207(19991010)46:4<471::AID-NME684>3.0.CO;2-6
  13. Ehlers, W. (1993), "Compressible, incompressible and hybrid two-phase models in porous media theories", ASME: AMD, 158, 25-38.
  14. Gajo, A. (1995), "Influence of viscous coupling in propagation of elastic waves in saturated soil", J. Geotech. Eng.- ASCE , 121(9), 636-644. https://doi.org/10.1061/(ASCE)0733-9410(1995)121:9(636)
  15. Gajo, A. and Mongiovi, L. (1995), "An analytical solution for the transient response of saturated linear elastic porous media", Int. J. Numer. Anal. Meth. Geomech., 19(6), 399-413. https://doi.org/10.1002/nag.1610190603
  16. Gajo, A., Saetta, A. and Vitaliani, R. (1994), "Evaluation of three- and two-field finite element methods for the dynamic response of saturated soil", Int. J. Numer. Meth. Eng., 37, 1231-1247. https://doi.org/10.1002/nme.1620370708
  17. Garg, S. K., Nayfeh, H. and Good, A.J. (1947), "Compressional waves in fluid-saturated elastic porous media", J. Appl. Phys., 45(5), 1968-1974. https://doi.org/10.1063/1.1663532
  18. Hiremath, M.S., Sandhu, R.S., Morland, L.W. and Wolfe, W.E. (1988), "Analysis of one-dimensional wave propagation in a fluid-saturated finite soil column", Int. J. Numer. Anal. Meth. Geomech., 12, 121-139. https://doi.org/10.1002/nag.1610120202
  19. Hughes, T. (1987), The Finite Element Method ; Linear Static and Dynamic Finite Element Analysis. Prentice Hall Inc.
  20. Ihlenburg, F. and Babuska, I. (1955), "Dispersion analysis and error estimation of Galerkin finite element methods for the Helmholtz equation", Int. J. Numer. Meth. Eng., 38, 3745-3774.
  21. Jeremic, B., Cheng, Z., Taiebat, M. and Dafalias, Y.F. (2008), "Numerical simulation of fully saturated porous materials", Int. J. Numer. Anal. Meth. Geomech., 32(13), 1635-1660. https://doi.org/10.1002/nag.687
  22. Newmark, N.M. (1959), "A method of computation for structural dynamics", J. Eng. Mech. Div.- ASCE, 85, 67-94.
  23. Oberkampf, W.L., Trucano, T.G. and Hirsch, C. (2002), "Verification, validation and predictive capability in computational engineering and physics", Proceedings of the Foundations for Verification and Validation on the 21st Century Workshop, pages 1-74, Laurel, Maryland, October 22-23 2002. Johns Hopkins University / Applied Physics Laboratory.
  24. Oden, T., Moser, R. and Ghattas, O. (2010a), "Computer predictions with quantified uncertainty, part I", SIAM News, 43(9).
  25. Oden, T., Moser, R. and Ghattas, O. (2010b), "Computer predictions with quantified uncertainty, part II", SIAM News, 43(10).
  26. Roy, C.J. and Oberkampf. W.L. (2011), "A comprehensive framework for verification, validation, and uncertainty quantification in scientific computing", Comput. Method. Appl. M., 200(25-28), 2131-2144, doi: 10.1016/j.cma.2011.03.016.
  27. Schanz, M. (2009), "Poroelastodynamics: Linear models, analytical solutions, and numerical methods", Appl. Mech. Rev. - ASME, 62, 030803-1-030803-15. https://doi.org/10.1115/1.3090831
  28. Semblat, J.F. and Brioist, J.J. (2000), "Efficiency of higher order finite elements for the analysis of seismic wave propagation", J. Sound Vib., 231(2), 460-467. https://doi.org/10.1006/jsvi.1999.2636
  29. Simon, B.R., Wu, J.S., Zienkiewicz, O.C. and Paul, D.K. (1984), "Evaluation of u - w and u - $\pi$ finite element methods for the dynamic response of saturated porous media using one-dimensional models", Int. J. Numer. Anal. Meth. Geomech., 10, 461-482.
  30. Tasiopoulou, P., Taiebat, M., Tafazzoli, N. and Jeremic, B. (2014), "On validation of fully coupled behavior of porous media using centrifuge test results", Coupled Syst. Mech., In Review.
  31. Terzaghi, K. (1923), "Die berechnung der durchlassigkeitsziffer des tones aus dem verlauf der hydrodynamischen spannungserscheinungen", Sitz. Akad. Wissen., Wien Math. Naturwiss. Kl., Abt.IIa, 132, 105-124.
  32. Terzaghi, K. (1943), Theoretical Soil Mechanics, Wiley, New York.
  33. Zienkiewicz, O.C. and Shiomi, T. (1984), "Dynamic behaviour of saturated porous media; the generalized Biot formulation and its numerical solution", Int. J. Numer. Anal. Meth. Geomech., 8, 71-96. https://doi.org/10.1002/nag.1610080106
  34. Zienkiewicz, O.C. and Taylor, R.L. (1991a), The Finite Element Method, volume 1, McGraw - Hill Book Company, fourth edition.
  35. Zienkiewicz, O.C. and Taylor, R.L. (1991b), The Finite Element Method, volume 2, McGraw - Hill Book Company, Fourth edition.

Cited by

  1. On the Validation of a Numerical Model for the Analysis of Soil-Structure Interaction Problems vol.13, pp.8, 2016, https://doi.org/10.1590/1679-78252450
  2. Comparison of numerical formulations for the modeling of tensile loaded suction buckets vol.83, 2017, https://doi.org/10.1016/j.compgeo.2016.10.026
  3. Discretization effects in the finite element simulation of seismic waves in elastic and elastic-plastic media vol.33, pp.3, 2017, https://doi.org/10.1007/s00366-016-0488-4
  4. Site Response in a Layered Liquefiable Deposit: Evaluation of Different Numerical Tools and Methodologies with Centrifuge Experimental Results vol.144, pp.10, 2018, https://doi.org/10.1061/(ASCE)GT.1943-5606.0001947
  5. Models for drinking water treatment processes vol.8, pp.6, 2015, https://doi.org/10.12989/csm.2019.8.6.489
  6. Daily influent variation for dynamic modeling of wastewater treatment plants vol.9, pp.2, 2015, https://doi.org/10.12989/csm.2020.9.2.111
  7. Seismic site response of layered saturated sand: comparison of finite element simulations with centrifuge test results vol.12, pp.1, 2015, https://doi.org/10.1186/s40703-021-00155-2