Roughness Research of Center Profile Curve on Rock Fracture Surface Based on Statistical Method
- 1 School of Mathematics, Nanjing Normal University, Taizhou College, Taizhou, China
- 2 State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology, Beijing, China
- 3 Faculty of Science, Jiangsu University, Zhenjiang, China
- 4 Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang, China
Abstract
In order to research roughness of rock fracture surfaces whether to depend on scale effect, Brazil discs were fractured under tensile and compression stresses in Brazil split test with MTS (Mechanics Test Systems) and a laser profilometer was used to scan rock fracture surfaces and coordinates datum of central profile were acquired. A figure of the central profile was plotted through the coordinates datum. A certain line segment length is regarded as a step length, which is called scale and the scale length is taken to connect pairs of closer peak points on the profile curve. The directional dis tribution of every scale ’ s normal vector is analy z ed by statistics and normal hypothesis test. Finally, some statistics of sample degrees datum are compared with other ones and reach a conclusion that roughness of center profile curve de pends on scale effect. The distribution of degrees more and more approximate s normal distribution along with increase of scale .
- N. Barton and V. Choubey, “The Shear Strength of Rock Jounts in Theory and Practice,” Rock Mechanics, Vol. 1977, Vol. 10, No. 2, pp. 1-45. doi:10.1007/BF01261801
- N. Barton, “Review of a New Shear Strength Criterion for Rock Joints,” Engineering Geology, Vol. 7, No. 4, 1973, pp. 287-332. doi:10.1016/0013-7952(73)90013-6
- R. Tse and D. M. Cruden, “Estimating Joint Roughness Coefficients,” International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, Vol. 16, No. 5, 1979, pp. 303-307. doi:10.1016/0148-9062(79)90241-9
- N. H. Maerz, J. A. Franklin and C. P. Bennett, “Joint Roughness Measurement Using Shadow Profilometry,” International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, Vol. 27, No. 5, 1990, pp. 329-343. doi:10.1016/0148-9062(90)92708-M
- K. Falconer and W. G. Yang, “Fractal Geometry Mathematical Foundations and Applications,” 2nd Edition, Posts & Telecom Press, Beijing, 2007.
- Y. H. Zhang, H. W. Zhou and H. P. Xie, “Improved Cubic Covering Method for Fractal Dimensions of a Fracture Surface of Rock,” Chinese Journal of Rock Mechanics and Engineering, Vol. 24, No. 17, 2005, pp. 3192- 3196.
- H. P. Xie, H. Q. Sun, Y. Ju, et al., “Study on Generation of Rock Surfaces by Using Fractal Interpolation,” International Journal of Solid and Structure, Vol. 38, No. 32-33, 2001, pp. 5765-5787. doi:10.1016/S0020-7683(00)00390-5
- H. P. Xie, J.-A. Wang and M. A. Kwa Niewski, “Multifractal Characterization of Rock Fracture Surfaces,” International Journal of Rock Mechanics Mining Sciences, Vol. 36, No. 1, 1999, pp. 19-27. doi:10.1016/S0148-9062(98)00172-7
- S. C. Bandis, A. C. Lumsden and N. R. Barton, “Fundamentals of Rock Joint Deformation,” International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, Vol. 20, No. 6, 1983, pp. 249-268. doi:10.1016/0148-9062(83)90595-8
- P. H. S. W. Kulatilake, G. Shou, T. H. Huang and R. M. Morgan, “New Peak Shear Strength Criteria for Anisotropic Rock Joints,” International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, Vol. 32, No. 7, 1995, pp. 673-697. doi:10.1016/0148-9062(95)00022-9
- H. W. Zhou and H. Xie, “Anisotropic Characterization of Rock Fracture Surfaces Subjected to Profile Analysis,” Physics Letters A, Vol. 325, No. 5-6, 2004, pp. 355-362. doi:10.1016/j.physleta.2004.04.006
- W. Gao, “Mechanics of Rock,” Peking University Press, Beijing, 2010.