- Volume 22 Issue 3
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)
- Received : 2012.06.11
- Accepted : 2012.06.21
- Published : 2012.06.30
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.
Joint roughness;Fractional Brownian profile;Random midpoint displacement method;Fractal parameters;Statistical parameters
Supported by : 부경대학교
- 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.
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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.
- 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
- 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.
- 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
- 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.
- 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
- 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
- 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.
- 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
- 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.
- 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.
- 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
- 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
- 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
- Reeves M. J., 1990, Rock surface roughness and frictional strength, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., Vol. 28, pp. 429-442.
- 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.
- 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
- 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.
- 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
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