Abstract
Accurate quantification of roughness is important in modeling hydro-mechanical behavior of rock joints. A highly refined variogram technique was used to investigate possible existence of anisotropy in natural rock joint roughness. Investigated natural rock joints showed randomly varying roughness anisotropy with the direction. A scale dependant fractal parameter, K v, seems to play a prominent role than the fractal dimension, D r1d, with respect to quantification of roughness of natural rock joints. Because the roughness varies randomly, it is impossible to predict the roughness variation of rock joint surfaces from measurements made in only two perpendicular directions on a particular sample. The parameter D r1d × K v seems to capture the overall roughness characteristics of natural rock joints well. The one-dimensional modified divider technique was extended to two dimensions to quantify the two-dimensional roughness of rock joints. The developed technique was validated by applying to a generated fractional Brownian surface with fractal dimension equal to 2.5. It was found that the calculated fractal parameters quantify the rock joint roughness well. A new technique is introduced to study the effect of scale on two-dimensional roughness variability and anisotropy. The roughness anisotropy and variability reduced with increasing scale.
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References
N. Barton (1973) ArticleTitleReview of a new shear strength criterion for rock joints Engineering Geology 7 287–332 Occurrence Handle10.1016/0013-7952(73)90013-6
M.V. Berry Z.V. Lewis (1980) ArticleTitleOn the Weierstrass–Mandelbrot fractal function Proceedings of the Royal Society of London, Series A 370 459–484
S.R. Brown C.H. Scholz (1985) ArticleTitleBroad band width study of the topography of natural rock surfaces Journal of Geophysics Research 90 12575–12582
A. Outer ParticleDen J.F. Kaashoek H.R.G.K. Hack (1995) ArticleTitleDifficulties with using continuous fractal theory for discontinuity surfaces International Journal of Rock Mechanics and Mining Science 32 3–10 Occurrence Handle10.1016/0148-9062(94)00025-X
P.M. Dight H.K. Chiu (1981) ArticleTitlePrediction of shear behavior of joints using profiles International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts 15 303–307
J. Feder (1988) Fractals Plenum Press New York 283
N.I. Fisher T. Lewis B.J.J. Embleton (1987) Statistical Analysis of Spherical Data Cambridge University press Cambridge
S.M. Hsiung A. Ghosh M.P. Ahola A.H. Chowdhury (1993) ArticleTitleAssessment of conventional methodologies for joint roughness coefficient determination International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts 30 825–829 Occurrence Handle10.1016/0148-9062(93)90030-H
S.L. Huang S.M. Oelfke R.C. Speck (1992) ArticleTitleApplicability of fractal characterization and modeling to rock joint profiles International Journal of Rock Mechanics and Mining Science 29 89–98 Occurrence Handle10.1016/0148-9062(92)92120-2
J.K. Kodikara I.W. Johnston (1994) ArticleTitleShear behaviour of irregular triangular rock – concrete joints International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts 31 IssueID4 313–322 Occurrence Handle10.1016/0148-9062(94)90900-8
J. Krahn N.R. Morgenstern (1979) ArticleTitleThe ultimate frictional resistance of rock Discontinuities International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts 16 127–133 Occurrence Handle10.1016/0148-9062(79)91449-9
P.H.S.W. Kulatilake G. Shou T.M. Huang R.M. Morgan (1995) ArticleTitleNew peak shear strength criteria for anisotropic rock joints International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts 32 673–697 Occurrence Handle10.1016/0148-9062(95)00022-9
P.H.S.W. Kulatilake J. Um (1999) ArticleTitleRequirements for accurate quantification of self-affine roughness using the roughness-length method International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts 36 5–18 Occurrence Handle10.1016/S0148-9062(98)00170-3
P.H.S.W. Kulatilake J. Um G. Pan (1997) ArticleTitleRequirements for accurate estimation of fractal parameters for self-affine roughness profiles using the line scaling method Rock Mechanics & Rock Engineering 30 IssueID4 181–206 Occurrence Handle10.1007/BF01045716
P.H.S.W. Kulatilake J. Um G. Pan (1998) ArticleTitleRequirements for accurate quantification of self affine roughness using the variogram method International Journal of Solid Structures 35 4167–4189 Occurrence Handle10.1016/S0020-7683(97)00308-9
N.H. Maerz J.A. Franklin C.P. Bennett (1990) ArticleTitleJoint roughness measurement using shadow profiliometry International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts 27 329–344 Occurrence Handle10.1016/0148-9062(90)92708-M
A. Malinverno (1990) ArticleTitleA simple method to estimate the fractal dimension of a self-affine series Geophysical Research Letters 17 1953–1956
B.B. Mandelbrot (1967) ArticleTitleHow long is the coast of Britain? Statistical self-similarity and fractional dimension Science 156 636–638
B.B. Mandelbrot (1985) ArticleTitleSelf-affine fractals and fractal dimension Physica Scripta 32 257–260
M. Matsushita S. Ouchi (1989) ArticleTitleOn the self affinity of various curves Physica D 38 IssueID1–3 246–251 Occurrence Handle10.1016/0167-2789(89)90201-7
Miller, S.M., McWilliams, P.C. and Kerkering, J.C. (1990). Ambiguities in estimating fractal dimensions of rock fracture surfaces, In: Proc. 31st U.S. Symp. on Rock Mech., A.A. Balkema, Rotterdam, The Netherlands, pp. 471–478.
N.E. Odling (1994) ArticleTitleNatural fracture profiles, fractal dimension and joint roughness coefficients Rock Mechanics 27 135–153 Occurrence Handle10.1007/BF01020307
S. Orey (1970) ArticleTitleGaussian simple functions and Hausdorff dimension of level crossing z.Wahrscheinlichkeitstheorie verw. Gebiete 15 249–256 Occurrence Handle10.1007/BF00534922
C.Y. Poon R.S. Sayles T.A. Jones (1992) ArticleTitleSurface measurement and fractal characterization of naturally fractured rocks Journal of Physics D: Applied Physics 25 IssueID8 1269–1275 Occurrence Handle10.1088/0022-3727/25/8/019
W.L. Power T.E. Tullis (1991) ArticleTitleEuclidean and fractal models for the description of rock surface roughness Journal of Geophysical Research 96 415–424 Occurrence Handle10.1029/90JB02107
M.J. Reeves (1990) ArticleTitleRock surface roughness and frictional strength International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts 28 429–442
Rasouli, V. and Harrison, J.P. (2001) In-plane analysis of fracture surface roughness: anisotropy and scale effect in anisotropy, In: Proc. 38th U.S. Rock Mech. Symp., Washington D.C., USA, Balkema, Netherlands, pp. 777–783.
J.C. Russ (1994) Fractal Surfaces Plenum Press New York
T. Shirono P.H.S.W. Kulatilake (1997) ArticleTitleAccuracy of the spectral method in estimating fractal/spectral parameters for self-affine roughness profiles International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts 34 IssueID5 789–804
R. Tse D.M. Cruden (1979) ArticleTitleEstimating joint roughness coefficients International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts 16 303–307 Occurrence Handle10.1016/0148-9062(79)90241-9
T.H. Wu E.M. Ali (1978) ArticleTitleStatistical representation of the joint roughness International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts 15 259–262 Occurrence Handle10.1016/0148-9062(78)90958-0
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Kulatilake, P.H.S.W., Balasingam, P., Park, J. et al. Natural rock joint roughness quantification through fractal techniques. Geotech Geol Eng 24, 1181–1202 (2006). https://doi.org/10.1007/s10706-005-1219-6
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DOI: https://doi.org/10.1007/s10706-005-1219-6