Acta Geotechnica

, Volume 9, Issue 5, pp 903–934 | Cite as

Modeling the hydro-mechanical responses of strip and circular punch loadings on water-saturated collapsible geomaterials

  • WaiChing SunEmail author
  • Qiushi Chen
  • Jakob T. Ostien
Research Paper


A stabilized enhanced strain finite element procedure for poromechanics is fully integrated with an elasto-plastic cap model to simulate the hydro-mechanical interactions of fluid-infiltrating porous rocks with associative and non-associative plastic flow. We present a quantitative analysis on how macroscopic plastic volumetric response caused by pore collapse and grain rearrangement affects the seepage of pore fluid, and vice versa. Results of finite element simulations imply that the dissipation of excess pore pressure may significantly affect the stress path and thus alter the volumetric plastic responses.


Bearing capacity Cap plasticity Excess pore pressure Hydro-mechanical coupling Poromechanics Stabilized procedure 



Thanks are due to Professor Bernhard Schrefler for fruitful discussion. We are very grateful for the comprehensive reviews and insightful suggestions provided by the anonymous reviewers. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.


  1. 1.
    Abellan M-A, de Borst R (2006) Wave propagation and localisation in a softening two-phase medium. Comput Methods Appl Mech Eng 195(37–40):5011–5019Google Scholar
  2. 2.
    Andrade JE, Borja RI (2006) Capturing strain localization in dense sands with random density. Int J Numer Methods Eng 67(11):1531–1564CrossRefzbMATHGoogle Scholar
  3. 3.
    Arnold DN (1990) Mixed finite element methods for elliptic problems. Comput Methods Appl Mech Eng 83(1-3):281–312CrossRefGoogle Scholar
  4. 4.
    Babuška I (1973) The finite element method with Lagrangian multipliers. Numerische Mathematik 20:179–192Google Scholar
  5. 5.
    Bathe K-J (2001) The inf-sup condition and its evaluation for mixed finite element methods. Comput Struct 79(2):243–252Google Scholar
  6. 6.
    Bear J (1972) Dynamics of fluids in porous media. Elsevier Publishing Company, New York, NYzbMATHGoogle Scholar
  7. 7.
    Belytschko T, Liu WK, Moran B (2000) Nonlinear finite elements for continua and structures. Wiley, West Sussex, England Google Scholar
  8. 8.
    Biot MA (1941) General theory of three dimensional consolidation. J Appl Phys 12(2):155–164CrossRefzbMATHGoogle Scholar
  9. 9.
    Bochev PB, Dohrmann CR, Gunzburger MD (2006) Stabilization of low-order mixed finite elements for the Stokes equations. SIAM J Numer Anal 44(1):82–101Google Scholar
  10. 10.
    Borja RI (2013) Plasticity: Modeling & Computation. Springer, BerlinGoogle Scholar
  11. 11.
    Borja RI, Alarcón E (1995) A mathematical framework for finite strain elastoplastic consolidation part 1: Balance laws, variational formulation, and linearization. Comput Methods Appl Mech Eng 122(1–2):145–171Google Scholar
  12. 12.
    Brezzi F, Douglas J, Marini LD (1985) Two families of mixed finite elements for second order elliptic problems. Numerische Mathematik. 47:217–235Google Scholar
  13. 13.
    Chapelle D, Bathe KJ (1993) The inf-sup test. Comput Struct 47(4–5):537–545Google Scholar
  14. 14.
    Coussy O (2004) Poromehcanics. Wiley, West Sussex, EnglandGoogle Scholar
  15. 15.
    de Souza Neto EA, Perić D, Owen DRJ (2008) Computational Methods for Plasticity. Wiley, Ltd, ISBN 9780470694626Google Scholar
  16. 16.
    DiMaggio FL, Sandler IS (1971) Material model for granular soils. J Eng Mech Div 97:935–950Google Scholar
  17. 17.
    Dolarevic S, Ibrahimbegovic A (2007) A modified three-surface elasto-plastic cap model and its numerical implementation. Comput Struct 85:419–430CrossRefGoogle Scholar
  18. 18.
    Fossum AF, Fredrich JT (2000) Cap plasticity models and compactive and dilatant pre-failure deformation. In: Girard J, Liebman M, Breeds C, Doe T (eds) Pacific rocks 2000: rock around the rim. Seattle, WA, Taylor & Francis pp 1169–1176Google Scholar
  19. 19.
    Foster CD, Regueiro RA, Fossum AF, Borja RI (2005) Implicit numerical integration of a three-invariant, isotropic/kinematic hardening cap plasticity model for geomaterials. Comput Methods Appl Mech Eng 194:5109–5138CrossRefzbMATHGoogle Scholar
  20. 20.
    Gamage K, Screaton E, Bekins B, Aiello I (2011) Permeability–porosity relationships of subduction zone sediments. Mar Geol 279(1):19–36CrossRefGoogle Scholar
  21. 21.
    Grueschow E, Rudnicki JW (2005) Elliptic yield cap constitutive modeling for high porosity sandstone. Int J Solids Struct 42:4574–4587CrossRefzbMATHGoogle Scholar
  22. 22.
    Jeremic B, Cheng Z, Taiebat M, Dafalias Y (2008) Numerical simulation of fully saturated porous materials. Int J Numer Anal Methods Geomech 32(13):1635–1660Google Scholar
  23. 23.
    Karaoulanis FE (2013) Implicit numerical integration of nonsmooth multisurface yield criteria in the principal stress space. Arch Comput Methods Eng 20:263–308 Google Scholar
  24. 24.
    Ling HI, Liu H (2003) Pressure-level dependency and densification behavior of sand through generalized plasticity model. J Eng Mech 129(8):851–860CrossRefGoogle Scholar
  25. 25.
    Moran B, Ortiz M, Shih CF (1990) Formulation of implicit finite-element methods for multiplicative finite deformation plasticity. Int J Numer Methods Eng. 29(3):483–514Google Scholar
  26. 26.
    Mota A, Sun W, Ostien JT, Foulk JW, Long KN (2013) Lie-group interpolation and variational recovery for internal variables. Comput Mech (in press)Google Scholar
  27. 27.
    Nur A, Byerlee JD (1971) An exact effective stress law for elastic deformation of rock with fluids. J Geophys Res 76(26):6414–6419Google Scholar
  28. 28.
    Prevost JH (1982) Nonlinear transient phenomena in saturated porous media. Comput Methods Appl Mech Eng. 30(1):3–18Google Scholar
  29. 29.
    Prevost JH, Høeg K (1976) Reanalysis of simple shear soil testing. Can Geotech J 13(4):418–429CrossRefGoogle Scholar
  30. 30.
    Regueiro RA, Foster CD (2011) Bifurcation analysis for a rate-sensitive, non-associative, three-invariant, isotropic/kinematic hardening cap plasticity model for geomaterials: Part I. small strain. Int J Numer Anal Methods Geomech 35:201–225CrossRefzbMATHGoogle Scholar
  31. 31.
    Rice JR, Cleary MP (1976) Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents. Rev Geophys 14(2):227–241Google Scholar
  32. 32.
    Rudnicki JW, Rice JR (1975) Conditions for the localization of deformation in pressure-sensitive dilatant materials. J Mech Phys Solids 23(6):371–394CrossRefGoogle Scholar
  33. 33.
    Sandler IS, Rubin D (1979) An algorithm and a modular subroutine for the cap model. Int J Numer Anal Methods Geomech 3:173–186CrossRefzbMATHGoogle Scholar
  34. 34.
    Schulze O, Popp T, Kern H (2001) Development of damage and permeability in deforming rock salt. Eng Geol 61(2):163–180CrossRefGoogle Scholar
  35. 35.
    Simo JC, Hughes TJR (1986) On the variational foundations of assumed strain methods. ASME J Appl Mech 53:51–54MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Simon BR, Wu JS-S, Zienkiewicz OC, Paul DK (1986) Evaluation of u–w and u − π finite element methods for the dynamic response of saturated porous media using one-dimensional models. Int J Numer Anal Methods Geomech. 10(5):461–482Google Scholar
  37. 37.
    Skempton AW (1954) The pore-pressure coefficient a and b. Geotechnique 4(4):143–147CrossRefGoogle Scholar
  38. 38.
    Sloan SW, Abbo AJ, Sheng DC (2001) Refined explicit integration of elastoplastic models with automatic error control. Eng Computations 18:121–154CrossRefGoogle Scholar
  39. 39.
    Stefanov YP, Chertov MA, Aidagulov GR, Myasnikov AV (2011) Dynamics of inelastic deformation of porous rocks and formation of localized compaction zones studied by numerical modeling. J Mech Phys Solids 59(11):2323–2340MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Stevenson DL (1978) Salem limestone oil and gas production in the Keenville field, Wayne County, Illinois. Department of registration and education, state of IllinoisGoogle Scholar
  41. 41.
    Sun W (2013) A unified method to predict diffuse and localized instabilities in sands. Geomech Geoeng Int J 8(2):65–75CrossRefGoogle Scholar
  42. 42.
    Sun W, Andrade JE, Rudnicki JW, Eichhubl P (2011) Connecting microstructural attributes and permeability from 3d tomographic images of in situ shear-enhanced compaction bands using multiscale computations. Geophys Res Lett 38(10):L10302CrossRefGoogle Scholar
  43. 43.
    Sun W, Kuhn M, Rudnicki JW (2013a) A multiscale DEM-LBM analysis on permeability evolutions inside a dilatant shear band. Acta Geotech 8:465–480Google Scholar
  44. 44.
    Sun W, Ostien JT, Salinger A (2013b) A stabilized assumed deformation gradient finite element formulation for strongly coupled poromechanical simulations at finite strain. Int J Numer Anal Methods Geomech. doi: 10.1002/nag.2161
  45. 45.
    Sun WC, Andrade JE, Rudnicki JW (2011) Multiscale method for characterization of porous microstructures and their impact on macroscopic effective permeability. Int J Numer Methods Eng 88(12):1260–1279MathSciNetCrossRefzbMATHGoogle Scholar
  46. 46.
    Swan CC, Seo YK (2000) A smooth, three-surface elasto-plastic cap model: rate formulation, integration algorithm and tangent operators. Research report, University of IowaGoogle Scholar
  47. 47.
    Terzaghi K, Peck RB, Mesri G (1996) Soil mechanics in engineering practice. Wiley-Interscience, New York, NYGoogle Scholar
  48. 48.
    Tu X, Andrade Jose E, Chen Q (2009) Return mapping for nonsmooth and multiscale elastoplasticity. Comput Methods Appl Mech Eng. 198:2286–2296CrossRefzbMATHGoogle Scholar
  49. 49.
    Van Langen H, Vermeer PA (1991) Interface elements for singular plasticity points. Int J Numer Anal Methods Geomech 15(5):301–315CrossRefGoogle Scholar
  50. 50.
    Wang B, Popescu R, Prevost JH (2004) Effects of boundary conditions and partial drainage on cyclic simple shear test results-a numerical study. Int J Numer Anal Methods Geomech 28(10):1057–1082CrossRefzbMATHGoogle Scholar
  51. 51.
    White JA, Borja RI (2008) Stabilized low-order finite elements for coupled solid-deformation/fluid-diffusion and their application to fault zone transients. Comput Methods Appl Mech Eng 197(49):4353–4366CrossRefzbMATHGoogle Scholar
  52. 52.
    Wriggers P (2010) Nonlinear finite element methods. Springer-Verlag, Berlin, Heidelberg Google Scholar
  53. 53.
    Xia K, Masud A (2006) New stabilized finite element method embedded with a cap model for the analysis of granular materials. J Eng Mech 132(3):250–259CrossRefGoogle Scholar
  54. 54.
    Yang Y, Aplin AC (2007) Permeability and petrophysical properties of 30 natural mudstones. J Geophys Res Solid Earth (1978–2012) 112(B03206):1–14Google Scholar
  55. 55.
    Zhang HW, Schrefler BA (2001) Uniqueness and localization analysis of elastic plastic saturated porous media. Int J Numer Anal Methods Geomech 25(1):29–48Google Scholar

Copyright information

© Springer-Verlag (outside the USA)  2013

Authors and Affiliations

  1. 1.Department of Civil Engineering and Engineering MechanicsColumbia UniversityNew YorkUSA
  2. 2.Glenn Department of Civil EngineeringClemson UniversityClemsonUSA
  3. 3.Mechanics of Materials DepartmentSandia National LaboratoriesLivermoreUSA

Personalised recommendations