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Hydro-mechanical modeling of impermeable discontinuity in rock by extended finite element method

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Abstract

The extended finite element method (XFEM) is a numerical method for modeling discontinuities within the classical finite element framework. The computation mesh in XFEM is independent of the discontinuities, such that remeshing for moving discontinuities can be overcome. The extended finite element method is presented for hydro-mechanical modeling of impermeable discontinuities in rock. The governing equation of XFEM for hydraulic fracture modeling is derived by the virtual work principle of the fracture problem considering the water pressure on crack surface. The coupling relationship between water pressure gradient on crack surface and fracture opening width is obtained by semi-analytical and semi-numerical method. This method simplifies coupling analysis iteration and improves computational precision. Finally, the efficiency of the proposed method for modeling hydraulic fracture problems is verified by two examples and the advantages of the XFEM for hydraulic fracturing analysis are displayed.

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References

  1. ADACHI J I, DETOURNAY E. Plane strain propagation of a hydraulic fracture in a permeable rock [J]. Engineering Fracture Mechanics, 2008, 75(16): 4666–4694.

    Article  Google Scholar 

  2. DETOURNAY E. Propagation regimes of fluid-driven fractures in impermeable rocks [J]. International Journal of Geomechanics, 2004, 4: 35–45.

    Article  Google Scholar 

  3. GARAGASH D I. Plane-strain propagation of a fluid-driven fracture during injection and shut-in: Asymptotics of large toughness [J]. Engineering Fracture Mechanics, 2006, 73(4): 456–481.

    Article  Google Scholar 

  4. HU J, GARAGASH D I. Plane-strain propagation of a fluid-driven crack in a permeable rock with fracture toughness [J]. Journal of Engineering Mechanics, 2010, 136(9): 1152–1166.

    Article  Google Scholar 

  5. MITCHELL S L, KUSKE R, PEIRCE A P. An asymptotic framework for the analysis of hydraulic fractures: The impermeable case [J]. Journal of Applied Mechanics, 2006, 74(2): 365–372.

    Article  MathSciNet  Google Scholar 

  6. ADACHI J, SIEBRITS E, PEIRCE A, DESROCHES J. Computer simulation of hydraulic fractures [J]. International Journal of Rock Mechanics and Mining, 2007, 44(5): 739–757.

    Article  Google Scholar 

  7. SIMONI L, SECCHI S. Cohesive fracture mechanics for a multi-phase porous medium [J]. Engineering Computations, 2003, 20(5): 675–698.

    Article  MATH  Google Scholar 

  8. SECCHI S, SIMONI L, SCHREFLER B A. Mesh adaptation and transfer schemes for discrete fracture propagation in porous materials [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2007, 31(2): 331–345.

    Article  MATH  Google Scholar 

  9. SEGURA J M, CAROL I. Coupled HM analysis using zero-thickness interface elements with double nodes. Part I: Theoretical model [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2008, 32(18): 2083–2101.

    MATH  Google Scholar 

  10. BELYTSCHKO T, BLACK T. Elastic crack growth in finite elements with minimal remeshing [J]. International Journal for Numerical Methods in Engineering, 1999, 45(5): 601–620.

    Article  MathSciNet  MATH  Google Scholar 

  11. REN Qing-wen, DONG Yu-wen, YU Tian-tang. Numerical modeling of concrete hydraulic fracturing with extended finite element method [J]. Science in China Series E: Technological Sciences, 2009, 52(3): 559–565. (in Chinese)

    Article  MATH  Google Scholar 

  12. LECAMPION B. An extended finite element method for hydraulic fracture problems [J]. Communications in Numerical Methods in Engineering, 2009, 25(2): 121–133.

    Article  MathSciNet  MATH  Google Scholar 

  13. MOHAMADNEJAD T, KHOEI A R. Hydro-mechanical modeling of cohesive crack propagation in multi-phase porous media using the extended-FEM technique [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2013, 37(10): 1247–1256.

    Article  Google Scholar 

  14. MOËS N, DOLBOW J, BELYTSCHKO T. A finite element method for crack growth without remeshing [J]. International Journal for Numerical Methods in Engineering, 1999, 46 (1): 131–150.

    Article  MATH  Google Scholar 

  15. FLEMING M, CHU Y A, MORAN B. Enriched element free Galerkin methods for crack tip fields [J]. International Journal for Numerical Methods in Engineering, 1997, 40(8): 1483–1504.

    Article  MathSciNet  Google Scholar 

  16. LI Zong-li, WANG Ya-hong, REN Qing-wen. Numerical simulation model of hydraulic fracturing of rock with a single fracture under natural hydraulic power [J]. Chinese Journal of Rock Mechanics and Engineering, 2007, 26(4): 727–733. (in Chinese)

    Google Scholar 

  17. BARTON N, BANDIS S, BAKHTAR K. Strength, deformation and conductivity coupling of rock joints [J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1985, 22(3): 121–140.

    Article  Google Scholar 

  18. BARTON N, QUADROS E F. Joint aperture and roughness in the prediction of flow and groutability of rock masses [J]. International Journal of Rock Mechanics and Mining Sciences, 1997, 34(3/4): 252.e1-252.e14.

    Google Scholar 

  19. WALTERS M C, PAULINO G H, DODDS R H. Interaction integral procedures for 3-D curved cracks including surface tractions [J]. Engineering Fracture Mechanics, 2005, 72(11): 1635–1663.

    Article  Google Scholar 

  20. FLEMING M, CHU Y A, MORAN B, BELYTSCHKO T. Enriched element free Galerkin methods for crack tip fields [J]. International Journal for Numerical Methods in Engineering, 1997, 40(8): 1483–1504.

    Article  MathSciNet  Google Scholar 

  21. WU B, LI Z. Static reanalysis of structures with added degrees of freedom [J]. Communications in Numerical Methods in Engineering, 2006, 22(4): 269–281.

    Article  MathSciNet  Google Scholar 

  22. BRÜHWILER E, SAOUMA V E. Water fracture interaction in concrete-part I: Fracture properties [J]. ACI Materials Journal, 1995, 92(3): 296–303.

    Google Scholar 

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Authors and Affiliations

  1. School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    An-xing Zheng  (郑安兴) & Xian-qi Luo  (罗先启)

Authors
  1. An-xing Zheng  (郑安兴)
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  2. Xian-qi Luo  (罗先启)
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Corresponding author

Correspondence to Xian-qi Luo  (罗先启).

Additional information

Foundation item: Project(2011CB013505) supported by the National Basic Research Program of China; Project(51279100) supported by the National Natural Science Foundation of China

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Zheng, Ax., Luo, Xq. Hydro-mechanical modeling of impermeable discontinuity in rock by extended finite element method. J. Cent. South Univ. 22, 4337–4346 (2015). https://doi.org/10.1007/s11771-015-2982-z

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  • DOI: https://doi.org/10.1007/s11771-015-2982-z

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