Skip to main content
SpringerLink
Log in

An algorithm for continuum modeling of rocks with multiple embedded nonlinearly-compliant joints

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

We present a numerical method for modeling the mechanical effects of nonlinearly-compliant joints in elasto-plastic media. The method uses a series of strain-rate and stress update algorithms to determine joint closure, slip, and solid stress within computational cells containing multiple “embedded” joints. This work facilitates efficient modeling of nonlinear wave propagation in large spatial domains containing a large number of joints that affect bulk mechanical properties. We implement the method within the massively parallel Lagrangian code GEODYN-L and provide verification and examples. We highlight the ability of our algorithms to capture joint interactions and multiple weakness planes within individual computational cells, as well as its computational efficiency. We also discuss the motivation for developing the proposed technique: to simulate large-scale wave propagation during the Source Physics Experiments (SPE), a series of underground explosions conducted at the Nevada National Security Site (NNSS).

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

Similar content being viewed by others

References

  1. Barton N, Bandis S, Bakhtar K (1985) Strength, deformation and conductivity coupling of rock joints. Int J Rock Mech Mining Sci Geomech Abstr 22:121–140

  2. Cook NGW (1992) Natural joints in rock: mechanical, hydraulic and seismic behaviour and properties under normal stress. Int J Rock Mech Mining Sci Geomech Abstr 29:198–223

  3. Miehe C (1996) Exponential map algorithm for stress updates in anisotropic multiplicative elastoplasticity for single crystals. Int J Numer Methods Eng 39(19):3367–3390

    Article  MATH  Google Scholar 

  4. Sahimi M (2011) Flow and transport in porous media and fractured rock: from classical methods to modern approaches. Wiley, New York

    Book  MATH  Google Scholar 

  5. Schoenberg M, Sayers CM (1995) Seismic anisotropy of fractured rock. Geophysics 60(1):204–211

    Article  Google Scholar 

  6. Birch F (1960) The velocity of compressional waves in rocks to 10 kilobars: 1. J Geophys Res 65(4):1083–1102

    Article  Google Scholar 

  7. Birch F (1961) The velocity of compressional waves in rocks to 10 kilobars: 2. J Geophys Res 66(7):2199–2224

    Article  Google Scholar 

  8. Bandis SC, Lumsden AC, Barton NR (1983) Fundamentals of rock joint deformation. Int J Rock Mech Mining Sci Geomech Abstr 20:249–268

  9. Pyrak-Nolte LJ, Myer LR, Cook NGW (1990) Transmission of seismic waves across single natural fractures. J Geophys Res Solid Earth 95(B6):8617–8638

    Article  Google Scholar 

  10. Townsend M, Prothro LB, Obi C (2012) Geology of the source physics experiment site, climax stock, Nevada National Security Site. Technical report, Nevada Test Site/National Security Technologies, LLC (United States)

  11. Vorobiev O, Ezzedine S, Antoun T, Glenn L (2015) On the generation of tangential ground motion by underground explosions in jointed rocks. Geophys J Int 200(3):1651–1661

    Article  Google Scholar 

  12. Ghaboussi J, Wilson EL, Isenberg J (1973) Finite element for rock joints and interfaces. J Soil Mech Found Div 99 (Proc Paper 10095)

  13. Desai CS, Zaman MM, Lightner JG, Siriwardane HJ (1984) Thin-layer element for interfaces and joints. Int J Numer Anal Methods Geomech 8(1):19–43

    Article  Google Scholar 

  14. Buczkowski R, Kleiber M (1997) Elasto-plastic interface model for 3d-frictional orthotropic contact problems. Int J Numer Methods Eng 40(4):599–619

    Article  MATH  Google Scholar 

  15. Jing L (2003) A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering. Int J Rock Mech Mining Sci 40(3):283–353

    Article  Google Scholar 

  16. Cundall PA (1988) Formulation of a three-dimensional distinct element model—part I. A scheme to detect and represent contacts in a system composed of many polyhedral blocks. Int J Rock Mecha Mining Sci Geomech Abstr 25:107–116

  17. Cundall PA, Hart RD (1992) Numerical modelling of discontinua. Eng Comput 9(2):101–113

    Article  Google Scholar 

  18. Hallquist JO, Goudreau GL, Benson DJ (1985) Sliding interfaces with contact-impact in large-scale Lagrangian computations. Comput Methods Appl Mech Eng 51(1–3):107–137

    Article  MathSciNet  MATH  Google Scholar 

  19. Dolbow J, Moës N, Belytschko T (2001) An extended finite element method for modeling crack growth with frictional contact. Comput Methods Appl Mech Eng 190(51):6825–6846

    Article  MathSciNet  MATH  Google Scholar 

  20. Fries T-P, Belytschko T (2010) The extended/generalized finite element method: an overview of the method and its applications. Int J Numer Method Eng 84(3):253–304

    MathSciNet  MATH  Google Scholar 

  21. Bazant ZP, Oh BH (1985) Microplane model for progressive fracture of concrete and rock. J Eng Mech 111(4):559–582

    Article  Google Scholar 

  22. Kachanov M (1992) Effective elastic properties of cracked solids: critical review of some basic concepts. Appl Mech Rev 45(8):304–335

    Article  Google Scholar 

  23. Vorobiev O (2008) Generic strength model for dry jointed rock masses. Int J Plast 24(12):2221–2247

    Article  MATH  Google Scholar 

  24. Wilkins ML (1993) Hemp 3d—a finite difference program for calculating elastic-plastic flow. Technical report, DTIC Document

  25. Vorobiev O (2012) Simple common plane contact algorithm. Int J Numer Method Eng 90(2):243–268

    Article  MathSciNet  MATH  Google Scholar 

  26. Brown SR, Scholz CH (1986) Closure of rock joints. J Geophys Res Solid Earth 91(B5):4939–4948

    Article  Google Scholar 

  27. Vorobiev O (2010) Discrete and continuum methods for numerical simulations of non-linear wave propagation in discontinuous media. Int J Numer Method Eng 83:482–507

    MATH  Google Scholar 

Download references

Acknowledgements

The authors would like to thank all members of the Computational Geosciences group at LLNL, particularly T. H. Antoun, E. B. Herbold, and M. B. Rubin, for valuable discussions. The authors wish to express their gratitude to the National Nuclear Security Administration, Defense Nuclear Nonproliferation Research and Development (DNN R&D), and the Source Physics Experiment (SPE) working group, a multi-institutional and interdisciplinary group of scientists and engineers. This work was done by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Author information

Authors and Affiliations

  1. Lawrence Livermore National Laboratory, Livermore, CA, USA

    R. C. Hurley, O. Y. Vorobiev & S. M. Ezzedine

Authors
  1. R. C. Hurley
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. Y. Vorobiev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. M. Ezzedine
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. C. Hurley.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hurley, R.C., Vorobiev, O.Y. & Ezzedine, S.M. An algorithm for continuum modeling of rocks with multiple embedded nonlinearly-compliant joints. Comput Mech 60, 235–252 (2017). https://doi.org/10.1007/s00466-017-1403-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-017-1403-6

Keywords

Search

Navigation