Predicting Joint Roughness Coefficients Using Fractal Dimension of Rock Joint Profiles

Abstract:

The Joint Roughness Coefficients, JRC, is presented Barton and Choubey in 1977. A series of different rock joint profiles were reconstructed by means of the independent cut method (Voss, 1988) using the programs written by MATLAB language. The reconstructed joint profiles have different amplitude and roughness. JRC values of the joint profiles were calculated on the basis of an empirical formula founded by Tse & Cruden in 1979 using measure interval space 0.5mm on the profiles. The fractal dimension values of the joint profile were calculated by means of stick-measuring methods suggested by Xu in 1996. The relationships between JRC and fractal dimension for all joint profiles were analyzed and exist strong correlations. A new empirical equation describing the relationships was established based on nonlinear fitting analysis and can predict JRC values accurately.

• Periodical: Applied Mechanics and Materials (Volumes 170-173)
• Pages: 443-448
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.170-173.443
• Online since: May 2012
• Authors: Hong Fa Xu, Pei Sheng Zhao, Chao Fu Li, Quan Tong
• Keywords: Empirical Equation, Fractal Curves, Fractal Dimension, JRC, Rock Joint

References

[1] N. Barton, V. Choubey: The shear strength of rock joints in theory and practice. Rock Mechanics Vol. 10, No.1-2 (1977), pp.1-54.

DOI: 10.1007/bf01261801

[2] Y.H Lee. J.R. Carr, D.J. Bars, C.J. Haas. The fractal dimension as a measure of the roughness of rock discontinuity profiles. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 27 (1990), 453-464.

DOI: 10.1016/0148-9062(90)90998-h

[3] S.L. Huang, S.M. Oelfke and R.C. Speck: Applicability of fractal characterization and modelling to rock joint profiles. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts Vol.29, No.2 (1992), pp.89-98.

DOI: 10.1016/0148-9062(92)92120-2

[4] N. E. Odling: Natural fracture profiles, fractal dimension and joint roughness coefficients. Rock Mech. Rock Engng Vol.27, No.3(1994), pp.135-153.

DOI: 10.1007/bf01020307

[5] H.P. Xie: Fractal description of rock joints. Chinese Journal of Geotechnical Engineering Vol.17, No.1 (1995), pp.18-23. (In Chinese)

[6] P. H. S. W. Kulatilake and J. Um: Requirements for accurate quantification of self-affine roughness using the roughness–length method. International Journal of Rock Mechanics and Mining Sciences Vol.36, No.1 (1999), pp.5-18.

DOI: 10.1016/s0148-9062(98)00170-3

[7] A. Den Outer, J. F. Kaashoek, H. R. G. K. Hack: Difficulties with using continuous fractal theory for discontinuity surfaces. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. Vol.32, No.1 (1995), pp.3-9.

DOI: 10.1016/0148-9062(94)00025-x

[8] I. Karatzas and S.E. Shreve: Brownian Motion and Stochastic Calculus, 2nd Edition. (Springer-Verlag New York, Inc., 1991).

[9] L. Decreusefond, A.S. Üstünel: Stochastic Analysis of the Fractional Brownian Motion. Potential Analysis Vol.10, No.2(1999), pp.177-214.

[10] M.V. Berry, Z.V. Lewis: On the Weierstrass-Mandelbrot fractal function. Proceedings of the Royal Society. Series A, Vol.370(1980), pp.459-484.

[11] Poon, C. Y., Sayles, R. S., Jones, T. A.: Surface measurement and fractal characterization of naturally fractured rocks. J. Phys. D: Applied Phys. 25(1992), pp.1269-1275.

DOI: 10.1088/0022-3727/25/8/019

[12] Voss, R. Fractals in nature. In: Peitgen, H., Saupe D. (eds.) The science of fractal images, Springer, New York Berlin Heidelberg, (1988), pp.21-69.

[13] R. Tse, D.M. Cruden: Estimating joint roughness coefficients. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. Vol.16(1979), pp.303-307.

[14] H.F. Xu: Fractal characters and calculation of fractal dimension of joints surface. In: 4th Academic Conference of Chinese Society for Rock Mechanics & Engineering (1996), Beijing, Chinese Science and Technology Press, pp.111-117. (In Chinese).

[15] H.F. Xu, Y.R. Li, X.Y. Liu, et al: Fractal simulation of joint profiles and relationship between IRC and fractal dimension. Chinese Journal of Rock Mechanics and Engineering, Vol.21, No.11(2002), pp.1663-1666. (In Chinese).