Skip to main content
SpringerLink
Log in

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

  • Research Paper
  • Published:
Acta Geotechnica Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31
Fig. 32
Fig. 33
Fig. 34
Fig. 35
Fig. 36
Fig. 37
Fig. 38
Fig. 39
Fig. 40

Similar content being viewed by others

References

  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):5011–5019

    Google Scholar 

  2. Andrade JE, Borja RI (2006) Capturing strain localization in dense sands with random density. Int J Numer Methods Eng 67(11):1531–1564

    Article  MATH  Google Scholar 

  3. Arnold DN (1990) Mixed finite element methods for elliptic problems. Comput Methods Appl Mech Eng 83(1-3):281–312

    Article  Google Scholar 

  4. Babuška I (1973) The finite element method with Lagrangian multipliers. Numerische Mathematik 20:179–192

    Google Scholar 

  5. Bathe K-J (2001) The inf-sup condition and its evaluation for mixed finite element methods. Comput Struct 79(2):243–252

    Google Scholar 

  6. Bear J (1972) Dynamics of fluids in porous media. Elsevier Publishing Company, New York, NY

    MATH  Google Scholar 

  7. Belytschko T, Liu WK, Moran B (2000) Nonlinear finite elements for continua and structures. Wiley, West Sussex, England

  8. Biot MA (1941) General theory of three dimensional consolidation. J Appl Phys 12(2):155–164

    Article  MATH  Google Scholar 

  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):82–101

    Google Scholar 

  10. Borja RI (2013) Plasticity: Modeling & Computation. Springer, Berlin

  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):145–171

    Google Scholar 

  12. Brezzi F, Douglas J, Marini LD (1985) Two families of mixed finite elements for second order elliptic problems. Numerische Mathematik. 47:217–235

    Google Scholar 

  13. Chapelle D, Bathe KJ (1993) The inf-sup test. Comput Struct 47(4–5):537–545

    Google Scholar 

  14. Coussy O (2004) Poromehcanics. Wiley, West Sussex, England

  15. de Souza Neto EA, Perić D, Owen DRJ (2008) Computational Methods for Plasticity. Wiley, Ltd, ISBN 9780470694626

  16. DiMaggio FL, Sandler IS (1971) Material model for granular soils. J Eng Mech Div 97:935–950

    Google Scholar 

  17. Dolarevic S, Ibrahimbegovic A (2007) A modified three-surface elasto-plastic cap model and its numerical implementation. Comput Struct 85:419–430

    Article  Google Scholar 

  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 1169–1176

  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 194:5109–5138

    Article  MATH  Google Scholar 

  20. Gamage K, Screaton E, Bekins B, Aiello I (2011) Permeability–porosity relationships of subduction zone sediments. Mar Geol 279(1):19–36

    Article  Google Scholar 

  21. Grueschow E, Rudnicki JW (2005) Elliptic yield cap constitutive modeling for high porosity sandstone. Int J Solids Struct 42:4574–4587

    Article  MATH  Google Scholar 

  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):1635–1660

    Google Scholar 

  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. Ling HI, Liu H (2003) Pressure-level dependency and densification behavior of sand through generalized plasticity model. J Eng Mech 129(8):851–860

    Article  Google Scholar 

  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):483–514

    Google Scholar 

  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)

  27. Nur A, Byerlee JD (1971) An exact effective stress law for elastic deformation of rock with fluids. J Geophys Res 76(26):6414–6419

    Google Scholar 

  28. Prevost JH (1982) Nonlinear transient phenomena in saturated porous media. Comput Methods Appl Mech Eng. 30(1):3–18

    Google Scholar 

  29. Prevost JH, Høeg K (1976) Reanalysis of simple shear soil testing. Can Geotech J 13(4):418–429

    Article  Google Scholar 

  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 35:201–225

    Article  MATH  Google Scholar 

  31. Rice JR, Cleary MP (1976) Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents. Rev Geophys 14(2):227–241

    Google Scholar 

  32. Rudnicki JW, Rice JR (1975) Conditions for the localization of deformation in pressure-sensitive dilatant materials. J Mech Phys Solids 23(6):371–394

    Article  Google Scholar 

  33. Sandler IS, Rubin D (1979) An algorithm and a modular subroutine for the cap model. Int J Numer Anal Methods Geomech 3:173–186

    Article  MATH  Google Scholar 

  34. Schulze O, Popp T, Kern H (2001) Development of damage and permeability in deforming rock salt. Eng Geol 61(2):163–180

    Article  Google Scholar 

  35. Simo JC, Hughes TJR (1986) On the variational foundations of assumed strain methods. ASME J Appl Mech 53:51–54

    Article  MathSciNet  MATH  Google Scholar 

  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):461–482

    Google Scholar 

  37. Skempton AW (1954) The pore-pressure coefficient a and b. Geotechnique 4(4):143–147

    Article  Google Scholar 

  38. Sloan SW, Abbo AJ, Sheng DC (2001) Refined explicit integration of elastoplastic models with automatic error control. Eng Computations 18:121–154

    Article  Google Scholar 

  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):2323–2340

    Article  MathSciNet  MATH  Google Scholar 

  40. Stevenson DL (1978) Salem limestone oil and gas production in the Keenville field, Wayne County, Illinois. Department of registration and education, state of Illinois

  41. Sun W (2013) A unified method to predict diffuse and localized instabilities in sands. Geomech Geoeng Int J 8(2):65–75

    Article  Google Scholar 

  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):L10302

    Article  Google Scholar 

  43. Sun W, Kuhn M, Rudnicki JW (2013a) A multiscale DEM-LBM analysis on permeability evolutions inside a dilatant shear band. Acta Geotech 8:465–480

    Google Scholar 

  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. 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):1260–1279

    Article  MathSciNet  MATH  Google Scholar 

  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 Iowa

  47. Terzaghi K, Peck RB, Mesri G (1996) Soil mechanics in engineering practice. Wiley-Interscience, New York, NY

  48. Tu X, Andrade Jose E, Chen Q (2009) Return mapping for nonsmooth and multiscale elastoplasticity. Comput Methods Appl Mech Eng. 198:2286–2296

    Article  MATH  Google Scholar 

  49. Van Langen H, Vermeer PA (1991) Interface elements for singular plasticity points. Int J Numer Anal Methods Geomech 15(5):301–315

    Article  Google Scholar 

  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):1057–1082

    Article  MATH  Google Scholar 

  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):4353–4366

    Article  MATH  Google Scholar 

  52. Wriggers P (2010) Nonlinear finite element methods. Springer-Verlag, Berlin, Heidelberg

  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):250–259

    Article  Google Scholar 

  54. Yang Y, Aplin AC (2007) Permeability and petrophysical properties of 30 natural mudstones. J Geophys Res Solid Earth (1978–2012) 112(B03206):1–14

  55. Zhang HW, Schrefler BA (2001) Uniqueness and localization analysis of elastic plastic saturated porous media. Int J Numer Anal Methods Geomech 25(1):29–48

    Google Scholar 

Download references

Acknowledgements

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.

Author information

Authors and Affiliations

  1. Department of Civil Engineering and Engineering Mechanics, Columbia University, 500 West 120th Street, New York, NY, 10027, USA

    WaiChing Sun

  2. Glenn Department of Civil Engineering, Clemson University, 101 Sikes Avenue, Clemson, SC, 29634, USA

    Qiushi Chen

  3. Mechanics of Materials Department, Sandia National Laboratories, 7011 East Avenue, Livermore, CA, 94550, USA

    Jakob T. Ostien

Authors
  1. WaiChing Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qiushi Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jakob T. Ostien
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to WaiChing Sun.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sun, W., Chen, Q. & Ostien, J.T. Modeling the hydro-mechanical responses of strip and circular punch loadings on water-saturated collapsible geomaterials. Acta Geotech. 9, 903–934 (2014). https://doi.org/10.1007/s11440-013-0276-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11440-013-0276-x

Keywords

Search

Navigation