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Numerical simulation of mechanisms of deformation, failure and energy dissipation in porous rock media subjected to wave stresses

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The pore characteristics, mineral compositions, physical and mechanical properties of the subarkose sandstones were acquired by means of CT scan, X-ray diffraction and physical tests. A few physical models possessing the same pore characteristics and matrix properties but different porosities compared to the natural sandstones were developed. The 3D finite element models of the rock media with varied porosities were established based on the CT image processing of the physical models and the MIMICS software platform. The failure processes of the porous rock media loaded by the split Hopkinson pressure bar (SHPB) were simulated by satisfying the elastic wave propagation theory. The dynamic responses, stress transition, deformation and failure mechanisms of the porous rock media subjected to the wave stresses were analyzed. It is shown that an explicit and quantitative analysis of the stress, strain and deformation and failure mechanisms of porous rocks under the wave stresses can be achieved by using the developed 3D finite element models. With applied wave stresses of certain amplitude and velocity, no evident pore deformation was observed for the rock media with a porosity less than 15%. The deformation is dominantly the combination of microplasticity (shear strain), cracking (tensile strain) of matrix and coalescence of the cracked regions around pores. Shear stresses lead to microplasticity, while tensile stresses result in cracking of the matrix. Cracking and coalescence of the matrix elements in the neighborhood of pores resulted from the high transverse tensile stress or tensile strain which exceeded the threshold values. The simulation results of stress wave propagation, deformation and failure mechanisms and energy dissipation in porous rock media were in good agreement with the physical tests. The present study provides a reference for analyzing the intrinsic mechanisms of the complex dynamic response, stress transit mode, deformation and failure mechanisms and the disaster mechanisms of rock media.

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  1. 1

    Jiang Y D, Zhao Y X, Liu W G, et al. Investigation on the Mechanism of Coal Bumps and Relating Experiments (in Chinese). Beijing: Science Press, 2009

  2. 2

    Lasocki S, Orlecka-Sikora B. Seismic hazard assessment under complex source size distribution of mining-induced seismicity. Tectonophys, 2008, 456: 28–37

  3. 3

    Heuze F E, Morris J P. Insights into ground shock in jointed rocks and the response of structures there-in. Int J Rock Mech Min Sci, 2007, 44: 647–676

  4. 4

    Qin S Q, Jiao J J, Tang C A, et al. Instability leading to coal bumps and nonlinear evolutionary mechanisms for a coal-pillar-and-roof system. Int J Solids Struct, 2006, 43: 7407–7423

  5. 5

    Hazzard J F, Young R P. Dynamic modelling of induced seismicity. Int J Rock Mech Min Sci, 2004, 41: 1365–1376

  6. 6

    Pan Y S, Wang L G, Zhang M T, et al. The theoretical and testing study of fault rockburst (in Chinese). Chinese J Rock Mech Engng, 1998, 17: 642–649

  7. 7

    Beamish B B, Crosd B P J. Instantaneous outbursts in underground coal mines: An overview and association with coal type. Int J Coal Geology, 1998, 35: 27–55

  8. 8

    Tang C A, Kaiser P K. Numerical simulation of cumulative damage and seismic energy release during brittle rock failure Part 1: Fundamentals. Int J Rock Mech Min Sci, 1998, 35: 123–134

  9. 9

    Fujii Y, Ishijima Y, Deguchi G. Predication of coal face rock burst and micro-seismicity in deep longwall coal mine. Int J Rock Mech Min Sci, 1997, 34: 85–96

  10. 10

    Boler F M, Billington S, Zipf R K. Seismological and energy balance constraints on the mechanism of a catastrophic bump in the Book Cliffs coal mining district, Utah, USA. Int J Rock Mech Min Sci Geomech Abstracts, 1997, 34: 27–43

  11. 11

    Xie H. Fractals in rock mechanics. A Balkema, Rotterdam, 1993

  12. 12

    Lippmann H. Keynote lecture: Mechanical considerations of bumps in coal mines. In: Proceeding 2nd Int Symp. Rockbursts and Seismicity in Mines, A Balkema, 1990

  13. 13

    Carcione J M, Helle H B, Santos J E, et al. A constitutive equation and generalized Gassmann modulus for multimineral porous media. Geophys, 2005, 70: N17–N26

  14. 14

    Sharma M D. Three-dimensional wave propagation in a general anisotropic poroelastic medium: Phase velocity, group velocity and polarization. Geophys J Int, 2004, 156: 329–344

  15. 15

    Sharma M D. Surface waves in a general anisotropic poroelastic solid half-space. Geophys J Int, 2004, 159: 703–710

  16. 16

    Wang Y S, Yu G L, Zhang Z M, et al. Review on elastic wave propagation under complex interface (Interface Layer) conditions (in Chinese). Adv Mech, 2000, 30: 378–390

  17. 17

    Crampin S. The fracture criticality of crustal rocks. Geophys J Int, 1994, 118: 428–438

  18. 18

    Vardoulakis I, Muhlhaus H B. Local rock surface instabilities. Int J Rock Mech Min Sci Geomech Abstr, 1986, 23: 379–383

  19. 19

    Kraut E A. Advances in the theory of anisotropic elastic wave propagation. Rev Geophys, 1963, 1: 401–448

  20. 20

    Biot M A. The theory of propagation of elastic waves in a fluid-saturated porous solids I. Low-frequency range, II. High frequency range. J Acoust Soc Am, 1956, 28: 168–191

  21. 21

    Ju Y, Yang Y M, Mao Y Z, et al. Laboratory investigation on mechanisms of stress wave propagations in porous media. Sci China Ser E-Tech Sci, 2009, 52: 1374–1389

  22. 22

    Lambert G, Gurevich B, Brajanovski M. Attenuation and dispersion of P-waves in porous rocks with planar fractures: Comparison of theory and numerical simulations. Geophys, 2006, 71: N41–N45

  23. 23

    Mashinskii E I. Experimental study of the amplitude effect on wave velocity and attenuation in consolidated rocks under confining pressure. J Geophys Engng, 2005, 2: 199–212

  24. 24

    Fratta D, Santamarina J C. Shear wave propagation in jointed rock: state of stress. Geotechnique, 2002, 52: 495–505

  25. 25

    Liu K X, Liu Y. Three-dimensional stress wave propagation in fluid-saturated porous media (in Chinese). Acta Mech Sinica, 2003, 35: 469–473

  26. 26

    Arntsen B, Carcione J M. Numerical simulation of the Biot slow wave in water-saturated Nivelsteiner sandstone. Geophys, 2001, 66: 890–896

  27. 27

    Kelner S, Bouchon M, Coutant O. Numerical simulation of the propagation of P waves in fractured media. Geophys J Int, 1999, 137: 197–206

  28. 28

    Cheng N. Nonlinear wave propagation in sandstone: A numerical study. Geophys, 1996, 61: 1935–1938

  29. 29

    Carcione J M. Wave propagation in anisotropic, saturated porous media: Plane-wave theory and numerical simulation. J Acoust Soc Am, 1996, 99: 2655–2666

  30. 30

    TenCate J A, Van Den Abeele K E A, Shankland T J, et al. Laboratory study of linear and nonlinear elastic pulse propagation in sandstone. J Acoust Soc Am, 1996, 100: 1383–1391

  31. 31

    Nagy G, Murakami H, Hegemier G A, et al. Experimental and analytical study of the dynamic response of low-porosity brittle rocks. J Geophys Res, 1993, 98: 22081–22094

  32. 32

    Krishnamoorthy K, Goldsmith W, Sackman J L. Measurements of wave processes in isotropic and transversely isotropic elastic rocks. Int J Rock Mech Min Sci Geomech Abstr, 1974, 11: 367–378

  33. 33

    Ju Y, Yang Y M, Song Z D, et al. A Statistical model for porous structure of rocks. Sci China Ser E-Tech Sci, 2008, 51: 2031–2039

  34. 34

    Frew D J, Forrestal M J, Chen W. A split Hopkinson pressure bar technique to determine compressive stress-strain data for rock materials. Exper Mech, 2001, 41: 40–46

  35. 35

    Dioh N N, Ivankovic A, Leevers P S, et al. Stress wave propagation effects in split Hopkinson pressure bar tests. Proc Royal Society London, Math Phys Sci-Ser A, 1995, 449: 187–204

  36. 36

    Gorham D A, Pope P H, Field J E. An improved method for compressive stress-strain measurements at very high strain rates. Proc Royal Society London, Math Phys Sci-Ser A, 1992, 438: 153–170

  37. 37

    Lindholm U S. Some experiments with split Hopkinson pressure bar. J Mech Phys Solids, 1964, 12: 317–335

  38. 38

    Davies E D H, Hunter S C. Dynamic compression testing of solids by method of split Hopkinson pressure bar. J Mech Phys Solids, 1963, 11: 155–179

  39. 39

    Wang H J. Experimental Study of Dynamic Mechanical Property and Deformation and Failure Mechanisms of Porous Rock. Dissertation of Masteral Degree. Beijing: China University of Mining & Technology, 2009. 13–38

  40. 40

    Yang Y M. Study on Modeling Porous Structures of Rocks and Mechanical Properties (in Chinese). Dissertation of Doctoral Degree. Beijing: China University of Mining & Technology, 2008. 59–84

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Correspondence to Yang Ju.

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Ju, Y., Wang, H., Yang, Y. et al. Numerical simulation of mechanisms of deformation, failure and energy dissipation in porous rock media subjected to wave stresses. Sci. China Technol. Sci. 53, 1098–1113 (2010). https://doi.org/10.1007/s11431-010-0126-0

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  • porous media
  • three-dimensional finite element model
  • rock media
  • stress wave
  • failure mechanism
  • energy dissipation