Tunnel and Underground Space (터널과지하공간)

Korean Society for Rock Mechanics and Rock Engineering (한국암반공학회)
권호 표지
DOI QR코드

DOI QR Code

Generation of Roughness Using the Random Midpoint Displacement Method and Its Application to Quantification of Joint Roughness

랜덤중점변위법에 의한 거칠기의 생성 및 활용에 관한 연구

  • Seo, Hyeon-Kyo (Department of Energy Resources Engineering, Pukyong National University) ;
  • Um, Jeong-Gi (Department of Energy Resources Engineering, Pukyong National University)
  • 서현교 (부경대학교 에너지자원공학과) ;
  • 엄정기 (부경대학교 에너지자원공학과)
  • Received : 2012.06.11
  • Accepted : 2012.06.21
  • Published : 2012.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

Quantification of roughness plays an important role in modeling strength deformability and fluid flow behaviors of rock joints. A procedure was suggested to simulate joint roughness, and characteristics of the roughness was investigated in this study. Stationary fractional Brownian profiles with known input values of the fractal parameter and other profile properties were generated based on random midpoint displacement method. Also, a procedure to simulate three dimensional roughness surface was suggested using the random midpoint displacement method. Selected statistical roughness parameters were calculated for the generated self-affine profiles to investigate the attribute of roughness. Obtained results show that statistical parameters applied in this study were able to consider correlation structure and amplitude of the profiles. However, effect of data density should be tackled to use statistical parameters for roughness quantification.

거칠기에 대한 정량화는 암석 절리의 강도 및 변형, 수리특성 등을 연구함에 있어서 매우 중요하다. 이 연구는 절리 거칠기를 모사하고 거칠기의 속성을 고찰하였다. 프랙털 파라미터와 프로파일 특성치를 입력변수로 설정하여 랜덤중점변위법에 기반한 이차원적 정상성 브라운 프로파일이 생성되었다. 또한, 랜덤중점변위법을 사용하여 삼차원적 거칠기 면을 모사하는 절차가 제시되었다. 이 연구의 거칠기 모사기법은 절리 거칠기와 관련된 해석적 연구를 수행하기 위한 요소 기술로 활용될 수 있다. 자기유사 거칠기 프로파일에 대하여 통계적 거칠기 파라미터를 적용한 결과 미소 거칠기의 기울기와 관련된 $Z_2$, $SL_{ave}$, $SD_{SL}$ 등의 통계적 파라미터는 상관구조, 진폭 등의 거칠기 속성을 고려할 수 있으나 측점간격의 변화에 영향을 받는 것으로 나타났다.

Keywords

References

  1. Bae, K. Y. and C. I. Lee, 2002, Development of a 3D roughness measurement system of rock joint using laser type displavement meter, Tunnel and Underground Space, Vol. 12, pp. 268-276.
  2. Barton, N., 1973, Review of a new shear strength criterion for rock joints. Engrg. Geology 7, pp. 287-332. https://doi.org/10.1016/0013-7952(73)90013-6
  3. Barton, N. and V. Choubey, 1977, The shear strength of rock joints in theory and practice, Rock Mechanics (Springer-Verlag), Vol. 10, pp. 1-54. https://doi.org/10.1007/BF01261801
  4. Brown, S. R. and C. H. Scholz, 1985, Broad band width study of the topography of natural rock surfaces, J. Geophys. Res. 90, pp. 12575-12582. https://doi.org/10.1029/JB090iB14p12575
  5. Den Outer, A., J. F. Kaashoek and H. R. G. K. Hack, 1995, Difficulties with using continuous fractal theory for discontinuity surfaces, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., Vol. 32, pp. 3-10. https://doi.org/10.1016/0148-9062(94)00025-X
  6. Dight P. M. and H. K. Chiu, 1981, Prediction of shear behavior of joints using profiles, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., Vol. 18, pp. 369-386. https://doi.org/10.1016/0148-9062(81)90002-4
  7. Fournier A., D. Fussel and L. Carpenter L, 1982, Computer rendering of stochastic models, Commun. ACM., Vol. 25, pp. 371-384. https://doi.org/10.1145/358523.358553
  8. Fox C. G., 1987, An inverse Fourier transform algorithm for generating random signals of a specified spectral form, Comput. Geosci., Vol. 13, pp. 369-374. https://doi.org/10.1016/0098-3004(87)90009-4
  9. Hsiung S. M., D. D. Kans, M. P. Ahola, A. H Chowdhury and A. Ghosh, 1994, Laboratory characterization of rock joints, Center for Nuclear Waste Regulatory Analyses, U.S. Nuclear Regulatory Commission, pp. 71-113.
  10. Huang, S. L., S. M. Oelfke and R. C Speck, 1992, Applicability of fractal characterization and modeling to rock joint profiles, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., Vol. 29, pp. 89-98. https://doi.org/10.1016/0148-9062(92)92120-2
  11. Jones R. A. and B. Guirguis, 1979, Spectral analysis applied to the characterization of a surface profile, 3rd Int. Conf. on Appl. of Prob. & Stat. for Soil & Structural Engr., Vol. 1, pp. 39-45.
  12. Kodikara J. K. and I. W. Johnston, 1994, Shear behavior of irregular triangular rock concrete joints, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., Vol. 31, pp. 313-322. https://doi.org/10.1016/0148-9062(94)90900-8
  13. Krahn J. and N. R Morgenstern, 1979, The ultimate frictional resistance of rock discontinuities, Int. J. Rock Mech. Min. Sci., Vol. 16, pp. 127-133.
  14. Kulatilake P. H. S. W., G. Shou, T. H Huang and R. M Morgan, 1995, New peak shear strength criteria for anisotropic rock joints, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., Vol. 32, pp. 673-697. https://doi.org/10.1016/0148-9062(95)00022-9
  15. Lee Y. H., J. R. Carr, D. J Barr and C. T Haas, 1990, The fractal dimension as a measure of the roughness of rock discontinuity profiles, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., Vol. 27, pp. 453-464. https://doi.org/10.1016/0148-9062(90)90998-H
  16. Lee, D. H., S. J. Lee and S. O. Choi, 2011, A study on a 3D roughness analysis of rock joints based on surface angularity, Tunnel and Underground Space, Vol. 21, pp. 494-507.
  17. Malinverno A., 1990, A simple method to estimate the fractal dimension of a self affine series, Geophysical Research Letters, Vol. 17, pp. 1953-1956. https://doi.org/10.1029/GL017i011p01953
  18. Maerz N. H., J. A. Franklin and C. P Bennett, 1990, Joint roughness measurement using Shadow Profilometry, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., Vol. 27, pp. 329-343.
  19. Miller S. M., P. C McWilliams and J. C Kerkering, 1990, Ambiguities in estimating fractal dimensions of rock fracture surfaces, Proc. 31st U.S. Symp. on Rock Mech., pp. 471-478.
  20. Odling N. E., 1994, Natural fracture profiles, fractal dimension and joint roughness coefficients, Rock Mech. & Rock Engrg., Vol. 27, pp. 135-153. https://doi.org/10.1007/BF01020307
  21. Park, J. W., Y. K. Lee, J. J. Song and B. H. Choi, 2012, A new coefficient for three dimensional quantification of rock joint roughness, Tunnel and Underground Space, Vol. 22, pp. 106-119. https://doi.org/10.7474/TUS.2012.22.2.106
  22. Power W. L. and T. E. Tullis, 1991, Euclidean and fractal models for the description of rock surface roughness, J. Geophys. Res., Vol. 96, pp. 415-424. https://doi.org/10.1029/90JB02107
  23. Reeves M. J., 1990, Rock surface roughness and frictional strength, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., Vol. 28, pp. 429-442.
  24. Saupe D., 1988, Algorithms for random fractals, The Science of Fractal Images(edited by Peitgen H-O and D. Saupe), Springer Verlag, New York, pp. 71-113.
  25. Tse R. and D. M Cruden, 1979, Estimating Joint Roughness Coefficients, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., Vol. 16, pp. 303-307. https://doi.org/10.1016/0148-9062(79)90241-9
  26. Voss R. F., 1988, Fractals in nature: from characterization to simulation, The Science of Fractal Images(edited by Peitgen H-O and D. Saupe), Springer Verlag, New York, pp. 71-113.
  27. Wu T. H. and E. M. Ali, 1978, Statistical representation of joint roughness, Int. J. Rock Mech. Min. Sci. Abstr., Vol. 15, pp. 259-262. https://doi.org/10.1016/0148-9062(78)90958-0

Cited by

  1. Development of a New Method for the Quantitative Generation of an Artificial Joint Specimen with Specific Geometric Properties vol.11, pp.2, 2019, https://doi.org/10.3390/su11020373