DOI QR코드

DOI QR Code

Preliminary numerical study on long-wavelength wave propagation in a jointed rock mass

  • Chong, Song-Hun (Department of Civil Engineering, Sunchon National University) ;
  • Kim, Ji-Won (Department of Civil and Environmental Engineering, KAIST) ;
  • Cho, Gye-Chun (Department of Civil and Environmental Engineering, KAIST) ;
  • Song, Ki-Il (Department of Civil Engineering, Inha University)
  • Received : 2020.01.17
  • Accepted : 2020.03.17
  • Published : 2020.05.10

Abstract

Non-destructive exploration using elastic waves has been widely used to characterize rock mass properties. Wave propagation in jointed rock masses is significantly governed by the characteristics and orientation of discontinuities. The relationship between spatial heterogeneity (i.e., joint spacing) and wavelength for elastic waves propagating through jointed rock masses have been investigated previously. Discontinuous rock masses can be considered as an equivalent continuum material when the wavelength of the propagating elastic wave exceeds the spatial heterogeneity. However, it is unclear how stress-dependent long-wavelength elastic waves propagate through a repetitive rock-joint system with multiple joints. A preliminary numerical simulation was performed in in this study to investigate long-wavelength elastic wave propagation in regularly jointed rock masses using the three-dimensional distinct element code program. First, experimental studies using the quasi-static resonant column (QSRC) testing device are performed on regularly jointed disc column specimens for three different materials (acetal, aluminum, and gneiss). The P- and S-wave velocities of the specimens are obtained under various normal stress levels. The normal and shear joint stiffness are calculated from the experimental results using an equivalent continuum model and used as input parameters for numerical analysis. The spatial and temporal sizes are carefully selected to guarantee a stable numerical simulation. Based on the calibrated jointed rock model, the numerical and experimental results are compared.

Keywords

Acknowledgement

Supported by : National Research Foundation of Korea (NRF)

This research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Ministry of Science and ICT (MSIT) (No.2017R1A5A 1014883). The second author was supported by the Korea Ministry of Land, Infrastructure and Transport (MOLIT) as 「Innovative Talent Education Program for Smart City」.

References

  1. Brady, B.H. and Brown, E.T. (1993), Rock Mechanics: For Underground Mining, Springer Science & Business Media. Berlin, Germany.
  2. Biggs, J.M. (1964), Introduction to Structural Dynamics, McGraw-Hill, New York, U.S.A.
  3. Cai, J. and Zhao, J. (2000), "Effects of multiple parallel fractures on apparent attenuation of stress waves in rock masses", Int. J. Rock Mech. Min. Sci., 37(4), 661-682. https://doi.org/10.1016/S1365-1609(00)00013-7.
  4. Cha, M. and Cho, G.C. (2007), "Compression wave velocity of cylindrical rock specimens: Engineering modulus interpretation", Jpn. J. Appl. Phys., 46(7S), 4497. https://doi.org/10.1143/JJAP.46.4497.
  5. Cha, M., Cho, G.C. and Santamarina, J.C. (2009), "Long-wavelength P-wave and S-wave propagation in jointed rock masses", Geophysics, 74(5), E205-E214. https://doi.org/10.1190/1.3196240.
  6. Chai, S., Li, J., Zhang, Q., Li, H. and Li, N. (2016), "Stress wave propagation across a rock mass with two non-parallel joints", Rock. Mech. Rock. Eng., 49(10), 4023-4032. https://doi.org/10.1007/s00603-016-1068-z.
  7. Cook, N.G. (1992). "Natural joints in rock: mechanical, hydraulic and seismic behaviour and properties under normal stress", Int. J. Rock Mech. Min. Sci., 29(3), 198-223. https://doi.org/10.1016/0148-9062(92)93656-5.
  8. Fratta, D. and Santamarina, J. (2002), "Shear wave propagation in jointed rock: State of stress", Geotechnique, 52(7), 495-505. https://doi.org/10.1680/geot.2002.52.7.495.
  9. Goodman, R.E. (1989), Introduction to Rock Mechanics, Wiley, New York, U.S.A.
  10. Howie, J.A. and Amini, A. (2005), "Numerical simulation of seismic cone signals", Can. Geotech. J., 42(2), 574-586. https://doi.org/10.1139/t04-120.
  11. Itasca, C. (2013), 3DEC, Software, Version 5.0, Minneapolis, Minnesota, U.S.A.
  12. Ju, Y., Sudak, L. and Xie, H. (2007), "Study on stress wave propagation in fractured rocks with fractal joint surfaces", Int. J. Solids Struct., 44(13), 4256-4271. https://doi.org/10.1016/j.ijsolstr.2006.11.015.
  13. Kim, J.W., Chong, S.H. and Cho, G.C. (2018), "Experimental characterization of stress-and strain-dependent stiffness in grouted rock nasses", Materials. 11(4), 524. https://doi.org/10.3390/ma11040524.
  14. Li, H., Liu, T., Liu, Y., Li, J., Xia, X. and Liu, B. (2016), "Numerical modeling of wave transmission across rock masses with nonlinear joints", Rock. Mech. Rock. Eng., 49(3), 1115-1121. https://doi.org/10.1007/s00603-015-0766-2.
  15. Li, J., Li, H., Jiao, Y., Liu, Y., Xia, X. and Yu, C. (2014), "Analysis for oblique wave propagation across filled joints based on thin-layer interface model", J. Appl. Geophys., 102, 39-46. https://doi.org/10.1016/j.jappgeo.2013.11.014
  16. Li, J., Ma, G. and Zhao, J. (2010), "An equivalent viscoelastic model for rock mass with parallel joints", J. Geophys. Res. Solid Earth, 115(B3). https://doi.org/10.1029/2008JB006241.
  17. Li, J.C., Wu, W., Li, H., Zhu, J. and Zhao, J. (2013), "A thin-layer interface model for wave propagation through filled rock joints", J. Appl. Geophys., 91 31-38. https://doi.org/10.1016/j.jappgeo.2013.02.003.
  18. Mindlin, R.D. (1960), Waves and Vibrations in Isotropic, Elastic Plates, in Structural Mechanics. Pergamon Press, New York, U.S.A., 199-232.
  19. Mohd-Nordin, M.M., Song, K.I., Cho, G.C. and Mohamed, Z. (2014), "Long-wavelength elastic wave propagation across naturally fractured rock masses", Rock Mech. Rock Eng., 47(2), 561-573. https://doi.org/10.1007/s00603-013-0448-x.
  20. Perino, A., Zhu, J., Li, J., Barla, G. and Zhao, J. (2010), "Theoretical methods for wave propagation across jointed rock masses", Rock Mech. Rock Eng., 43(6), 799-809. https://doi.org/10.1007/s00603-010-0114-5.
  21. Perino, A. and Barla, G. (2015), "Resonant column apparatus tests on intact and jointed rock specimens with numerical modelling validation", Rock Mech. Rock Eng., 48(1), 197-211. https://doi.org/10.1007/s00603-014-0564-2.
  22. Pyrak‐Nolte, L.J., Myer, L.R. and Cook, N.G. (1990), "Transmission of seismic waves across single natural fractures", J. Geophys. Res. Solid Earth, 95(B6), 8617-8638. https://doi.org/10.1029/JB095iB06p08617.
  23. Robertsson, J.O., Blanch, J.O. and Symes, W.W. (1994), "Viscoelastic finite-difference modeling", Geophysics, 59(9), 1444-1456. https://doi.org/10.1190/1.1443701.
  24. Saenger, E.H., Gold, N. and Shapiro, S.A. (2000), "Modeling the propagation of elastic waves using a modified finite-difference grid", Wave Motion, 31(1), 77-92. https://doi.org/10.1016/S0165-2125(99)00023-2.
  25. Sansalone, M. and Carino, N.J. (1986), "Impact-echo: A method for flaw detection in concrete using transient stress waves", NBSIR 86-3452, US Department of Commerce, National Bureau of Standards, National Engineering Laboratory, Center for Building Technology, Structures Division, U.S.A.
  26. Schoenberg, M. (1980), "Elastic wave behavior across linear slip interfaces", J. Acoust. Soc. Am., 68(5), 1516-1521. https://doi.org/10.1121/1.385077.
  27. Schoenberg, M. and Muir, F. (1989), "A calculus for finely layered anisotropic media", Geophysics, 54(5), 581-589. https://doi.org/10.1190/1.1442685.
  28. Schoenberg, M. and Sayers, C.M. (1995), "Seismic anisotropy of fractured rock", Geophysics, 60(1), 204-211. https://doi.org/10.1190/1.1443748.
  29. Tao, M., Chen, Z., Li, X., Zhao, H. and Yin, T. (2016), "Theoretical and numerical analysis of the influence of initial stress gradient on wave propagations", Geomech. Eng., 10(3), 285-296. https://doi.org/10.12989/gae.2016.10.3.285.
  30. Villiappan, S. and Murti, V. (1984), "Finite element constraints in the analysis of wave propagation problem", UNICV Report No.48, R-218, School of Civil Engineering, University of New South Wales, Australia.
  31. Wang, R., Hu, Z., Zhang, D. and Wang, Q. (2017), "Propagation of the stress wave through the filled joint with linear viscoelastic deformation behavior using time-domain recursive method", Rock Mech. Rock Eng., 50(12), 3197-3207. https://doi.org/10.1007/s00603-017-1301-4.
  32. White, J.E. (1983), Underground Sound: Application of Seismic Waves, Elsevier Science Publishing Company Inc, Amsterdam, The Netherlands.
  33. Wu, N., Liang, Z., Li, Y., Qian, X. and Gong, B. (2019), "Effect of confining stress on representative elementary volume of jointed rock masses", Geomech. Eng., 18(6), 627-638. https://doi.org/10.12989/gae.2019.18.6.627.
  34. Zerwer, A., Cascante, G. and Hutchinson, J. (2002), "Parameter estimation in finite element simulations of Rayleigh waves", J. Geotech. Geoenviron. Eng., 128(3), 250-261. https://doi.org/10.1061/(ASCE)1090-0241(2002)128:3(250).
  35. Zhao, X., Zhao, J., Cai, J. and Hefny, A.M. (2008), "UDEC modelling on wave propagation across fractured rock masses", Comput. Geotech., 35(1), 97-104. https://doi.org/10.1016/j.compgeo.2007.01.001
  36. Zhu, J., Deng, X., Zhao, X. and Zhao, J. (2013), "A numerical study on wave transmission across multiple intersecting joint sets in rock masses with UDEC", Rock. Mech. Rock. Eng., 46(6), 1429-1442. https://doi.org/10.1007/s00603-012-0352-9.
  37. Zhu, J., Zhao, X., Wu, W. and Zhao, J. (2012), "Wave propagation across rock joints filled with viscoelastic medium using modified recursive method", J. Appl. Geophys., 86, 82-87. https://doi.org/10.1016/j.jappgeo.2012.07.012.

Cited by

  1. Theoretical model for the shear strength of rock discontinuities with non-associated flow laws vol.24, pp.4, 2020, https://doi.org/10.12989/gae.2021.24.4.307
  2. Development of Equivalent Stress- and Strain- Dependent Model for Jointed Rock Mass and Its Application to Underground Structure vol.25, pp.12, 2021, https://doi.org/10.1007/s12205-021-0616-6