Computer Estimation of JRC Index Using Function Moments
Abstract
The paper deals with a shape of geological discontinuities. This shape significantly affects the stability of rock massifs. The joint roughness coefficient (JRC) is one of the main shape indicators but the methods of its estimation are based on the empirical analysis of fracture curves in present. We propose a new mathematically correct theory of automatic estimation of the JRC. It shows that determination of the JRC should be based not only on subjective experience, but objective shape characteristics should be used as well. The moment method is one of the possibilities. The principal moments of a fracture surface and the elongation of so called equimomental ellipse can be determined as the possible characteristics of the shape of a fracture surface. The paper introduces a software which is able to reconstruct a 3D profile of a scanned surface and to assign its JRC index automatically.
References
Abu-Mostafa, Y. S., and Psaltis, D. Image normalization by complex moments. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1 (1985), 46–55.
Amanloo, F., and Hosseinitoudeshki, V. The effect of joint roughness coefficient (jrc) and joint compressive strength (jcs) on the displacement of tunnel. International Research Journal of Applied and Basic Sciences, Science Explorer Publications 4, 8 (2013), 2216–2224.
Barnsley, M. F., Devaney, R. L., Mandelbrot, B. B., Peitgen, H.-O., Saupe, D., Voss, R. F., Fisher, Y., and McGuire, M. The science of fractal images, vol. 1. Springer, 1988.
Barton, N. Review of a new shear-strength criterion for rock joints. Engineering Geology 7, 4 (1973), 287–332.
Barton, N. Shear strength criteria for rock, rock joints, rockfill and rock masses: Problems and some solutions. Journal of Rock Mechanics and Geotechnical Engineering 5, 4 (2013), 249–261.
Barton, N., and Choubey, V. D. The shear strength of rock joints in theory and practice. Rock mechanics 10 (1977), 1–54.
Crespo, J. F., Crespo, J. F., Lopes, G. A., and Aguiar, P. M. Principal moments for efficient representation of 2d shape. In 2009 16th IEEE International Conference on Image Processing (ICIP) (2009), IEEE, pp. 1085–1088.
Du, S., Hu, Y., Hu, X., and Guo, X. Comparison between empirical estimation by jrc-jcs model and direct shear test for joint shear strength. Journal of Earth Science 22, 3 (2011), 411–420.
Fournier, A., Fussell, D., and Carpenter, L. Computer rendering of stochastic models. Communications of the ACM 25, 6 (1982), 371–384.
Ha, V. H., and Moura, J. M. Efficient 2d shape orientation. In Proceedings 2003 International Conference on Image Processing (Cat. No. 03CH37429) (2003), vol. 1, IEEE, pp. I–225.
Han, F.-s., and Tang, C.-a. Numerical investigation for anisotropy of compressive strength of rock mass with multiple natural joints. Journal of Coal Science and Engineering (China) 16, 3 (2010), 246–248.
Li, Y., Wang, J., Jung, W., and Ghassemi, A. Mechanical properties of intact rock and fractures in welded tuff from newberry volcano. In Proceedings of 37th Workshop on Geothermal Reservoir Engineering, Stanford, CA (2012), vol. 30.
Lin, J.-C. Universal principal axes: an easy-toconstruct tool useful in defining shape orientations for almost every kind of shape. Pattern Recognition 26, 4 (1993), 485–493.
Mandelbrot, B. B., and Mandelbrot, B. B. The fractal geometry of nature, vol. 1. WH freeman New York, 1982.
Marola, G. On the detection of the axes of symmetry of symmetric and almost symmetric planar images. IEEE Transactions on Pattern Analysis and Machine Intelligence 11, 1 (1989), 104–108.
Martisek, D. The two-dimensional and three-dimensional processing of images provided by conventional microscopes. Scanning: The Journal of Scanning Microscopies 24, 6 (2002), 284–296.
Martisek, D., and Druckm¨ullerov´a, H. Multifocal image processing. Mathematics for Applications 3, 1 (2014), 77–90.
Martisek, D., and Prochazkova, J. The analysis of rock surface asperities. MENDEL Journal 24, 1 (2018), 135–142.
Martisek, D., Proch´azkov´a, J., and Ficker, T. High-quality three-dimensional reconstruction and noise reduction of multifocal images from oversized samples. Journal of Electronic Imaging 24, 5 (2015), 053029.
Nakagawa, M., Jiang, Y., Kawakita, M., Yamada, Y., and Akiyama, Y. Evaluation of mechanical properties of natural rock joints for discontinuous numerical analysis. In Proc. ISRM Int. Symp. 3rd ARMS (2004), Millpress.
Prasad, V. S. N., and Yegnanarayana, B. Finding axes of symmetry from potential fields. IEEE Transactions on Image Processing 13, 12 (2004), 1559–1566.
Prudencio, M., and Van Sint Jan, M. Strength and failure modes of rock mass models with non-persistent joints. International Journal of Rock Mechanics and Mining Sciences 44, 6 (2007), 890–902.
Rafek, A. G., and Goh, T. L. Correlation of joint roughness coefficient (jrc) and peak friction angles of discontinuities of malaysian schists. Earth Science Research 1, 1 (2012), 57.
Rodrigues, J. J., Aguiar, P. M., and Xavier, J. M. Ansig—an analytic signature for permutation-invariant two-dimensional shape representation. In 2008 IEEE Conference on Computer Vision and Pattern Recognition (2008), IEEE, pp. 1–8.
Shen, D., Ip, H., Cheung, K., and Teoh, E. K. Symmetry detection by generalized complex (gc) moments: a close-form solution. IEEE Transactions on Pattern Analysis and Machine Intelligence 21, 5 (1999), 466–476.
Singh, M., and Singh, B. High lateral strain ratio in jointed rock masses. Engineering Geology 98, 3-4 (2008), 75–85.
Starha, P., Prochazkova, J., and Martisek, D. The reconstruction of the object surface using confocal microscope with hyperchromatic lens. MENDEL Journal 24, 1 (2018), 129–134.
Teh, C.-H., and Chin, R. T. On image analysis by the methods of moments. IEEE Transactions on pattern analysis and machine intelligence 10, 4 (1988), 496–513.
Zuni´c, J., Kopanja, L., and Fieldsend, J. E. Notes on shape orientation where the standard method does not work. Pattern Recognition 39, 5 (2006), 856–865.
Copyright (c) 2021 MENDEL
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
MENDEL open access articles are normally published under a Creative Commons Attribution-NonCommercial-ShareAlike (CC BY-NC-SA 4.0) https://creativecommons.org/licenses/by-nc-sa/4.0/ . Under the CC BY-NC-SA 4.0 license permitted 3rd party reuse is only applicable for non-commercial purposes. Articles posted under the CC BY-NC-SA 4.0 license allow users to share, copy, and redistribute the material in any medium of format, and adapt, remix, transform, and build upon the material for any purpose. Reusing under the CC BY-NC-SA 4.0 license requires that appropriate attribution to the source of the material must be included along with a link to the license, with any changes made to the original material indicated.
