Abstract
Characterization of a jointed rock mass is a fundamental step in the design of a geotechnical engineering project. In this paper, fractal descriptions for joint properties and discrete fracture network (DFN) modelling for a field rock mass are presented. Based on the field investigation in an open-pit mine, traditional probability density functions are used to describe the distributions of joint orientation, spacing and trace length. A special meshing method of Schmidt projection is firstly introduced to calculate the fractal dimension for joint orientation. Comparison between the Fisher parameter and the fractal dimension suggests that the latter is a better indicator since it contains more information on the joint orientation (i.e. joint number and dispersion level). Then, the calculation procedures of the fractal dimensions for joint spacing and trace length are provided, and the corresponding fractal probability density functions are deduced by introducing the minimum spacing/trace length value and the fractal dimension value. Based on fractal analysis, the DFN module embedded in 3DEC 5.0 is used to reconstruct the field rock mass. Considering the limitations of traditional distribution functions and the complexity associated with field joint data, the fractal geometry theory could serve as a more rational tool to delineate the discontinuous, non-homogenous and anisotropic features for rock materials.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bagde MN, Raina AK, Chakraborty AK, Jethwa JL (2002) Rock mass characterization by fractal dimension. Eng Geol 63(1):141–155. https://doi.org/10.1016/S0013-7952(01)00078-3
Chen JP, Wang Q, Gu XM, Fan JH (2007). Fractal dimension of orientation pole distribution for rock mass joints. Chinese Journal of Rock Mechanics and Engineering 26(3): 501–508, DOI: 1000–6915(2007)03–0501–08 (in Chinese)
Ehlen J (2000) Fractal analysis of joint patterns in granite. Int J Rock Mech Min Sci 37(9):909–922. https://doi.org/10.1016/S1365-1609(00)00027-7
Ge YF, Kulatilake PHSW, Tang HM, Xiong CR (2014) Investigation of natural rock joint roughness. Comput Geotech 55:290–305. https://doi.org/10.1016/j.compgeo.2013.09.015
Hammah RE, Curran JH (1998) Fuzzy cluster algorithm for the automatic identification of joint sets. Int J Rock Mech Min Sci 35(7):889–905. https://doi.org/10.1016/S0148-9062(98)00011-4
Han XD, Chen JP, Wang Q, Li YY, Zhang W, Yu TW (2016) A 3D fracture network model for the undisturbed rock mass at the Songta dam site based on small samples. Rock Mech Rock Eng 49(2):611–619. https://doi.org/10.1007/s00603-015-0747-5
He SD, Li YR, Aydin A (2018) A comparative study of UDEC simulations of an unsupported rock tunnel. Tunn Undergr Space Technol 72:242–249. https://doi.org/10.1016/j.tust.2017.11.031
Itasca (2013) 3 Dimensional Distinct Element Code, version 5.0. Itasca Consulting Group, Inc, Minnesota
Ivanova VM, Sousa R, Murrihy B, Einstein HH (2014) Mathematical algorithm development and parametric studies with the GEOFRAC three-dimensional stochastic model of natural rock fracture systems. Comput Geosci 67(3):100–109. https://doi.org/10.1016/j.cageo.2013.12.004
Kulatilake PHSW (1985) Fitting fisher distributions to discontinuity orientation data. J Geol Educ 33(5):266–269. https://doi.org/10.5408/0022-1368-33.5.266
Kulatilake PHSW, Wathugala DN, Stephansson O (1993) Joint network modelling with a validation exercise in Stripa mine, Sweden. Int J Rock Mech Mining Sci Geomech Abstracts 30(5):503–526. https://doi.org/10.1016/0148-9062(93)92217-E
Kulatilake PHSW, Fiedler R, Panda BB (1997) Box fractal dimension as a measure of statistical homogeneity of jointed rock masses. Eng Geol 48(3–4):217–229. https://doi.org/10.1016/S0013-7952(97)00045-8
Kulatilake PHSW, Balasingam P, Park J, Morgan R (2006) Natural rock joint roughness quantification through fractal techniques. Geotech Geol Eng 24(5):1181. https://doi.org/10.1007/s10706-005-1219-6
Lei QH, Latham JP, Tsang CF (2017) The use of discrete fracture networks for modelling coupled geomechanical and hydrological behaviour of fractured rocks. Comput Geotech 85:151–176. https://doi.org/10.1016/j.compgeo.2016.12.024
Liu RC, Jiang YJ, Li B, Wang XS (2015) A fractal model for characterizing fluid flow in fractured rock masses based on randomly distributed rock fracture networks. Comput Geotech 65:45–55. https://doi.org/10.1016/j.compgeo.2014.11.004
Oda M (1988) A method for evaluating the representative elementary volume based on joint survey of rock masses. Can Geotech J 25(3):440–447. https://doi.org/10.1139/t88-049
Odling NE (1997) Scaling and connectivity of joint systems in sandstones from western Norway. J Struct Geol 19(10):1257–1271. https://doi.org/10.1016/S0191-8141(97)00041-2
Mandelbrot BB (1983) The fractal geometry of nature. W.H. freeman. In: San Francisco
Ni PP, Wang SH, Wang CG, Zhang SM (2017) Estimation of REV size for fractured rock mass based on damage coefficient. Rock Mech Rock Eng 50(3):555–570. https://doi.org/10.1007/s00603-016-1122-x
Priest SD, Hudson JA (1976) Discontinuity spacings in rock. Int J Rock Mech Mining Sci Geomech Abstracts 13(5):135–148. https://doi.org/10.1016/0148-9062(76)90818-4
Priest SD (1993) Discontinuity analysis for rock engineering. Chapman and Hall, London
Sen Z, Kazi A (1984) Discontinuity spacing and RQD estimates from finite length scanlines. Int J Rock Mech Mining Sci Geomech Abstracts 21(4):203–212. https://doi.org/10.1016/0148-9062(84)90797-6
Song SY, Sun FY, Zhang W, Chen JP, Xu PH, Niu CC et al (2017) Identification of structural domains by considering multiple discontinuity characteristics: a case study of the Songta dam. Bull Eng Geol Environ:1–10. https://doi.org/10.1007/s10064-017-1024-5
Velde B, Dubois J, Moore D, Touchard G (1991) Fractal patterns of fractures in granites. Earth Planet Sci Lett 104(1):25–35. https://doi.org/10.1016/0012-821X(91)90234-9
Wang CL, Gao AS, Shi F, Hou XL, Ni PP, Ba DY (2019) Three-dimensional reconstruction and growth factor model for rock cracks under uniaxial cyclic loading/unloading by X-ray CT. Geotech Test J 42(1):117–135. https://doi.org/10.1520/GTJ20170407
Warburton PM (1980) A stereological interpretation of joint trace data. Int J Rock Mech Mining Sci Geomech Abstracts 17(4):181–190. https://doi.org/10.1016/0148-9062(80)91084-0
Zhan JW, Xu PH, Chen JP, Wang Q, Zhang W, Han XD (2017) Comprehensive characterization and clustering of orientation data: a case study from the Songta dam site, China. Eng Geol 225:3–18. https://doi.org/10.1016/j.enggeo.2017.01.010
Zhang W, Chen JP, Cao ZX, Wang RY (2013) Size effect of RQD and generalized representative volume elements: a case study on an underground excavation in Baihetan dam, Southwest China. Tunnell Underground Space Technol Incorpor Trenchless Technol Res 35(3):89–98. https://doi.org/10.1016/j.tust.2012.12.007
Zheng J, Deng JH, Yang XJ, Wei JB et al (2014) An improved Monte Carlo simulation method for discontinuity orientations based on fisher distribution and its program implementation. Comput Geotech 61(3):266–276. https://doi.org/10.1016/j.compgeo.2014.06.006
Acknowledgements
This research is supported by the National Natural Science Foundation of China (grant nos. 51578164, 51678547, 51878634, 51878185), the China Postdoctoral Science Foundation Funded Project (grant nos. 2016 M600711 2017 T100664). The Research Funds provided by MOE Engineering Research Center of Rock-Soil Drilling & Excavation and Protection (grant no. 201402), and the Fundamental Research Funds for the Central Universities-Cradle Plan for 2015 (grant no. CUGL150411) are also acknowledged. Special thanks go to the reviewers for their valuable comments.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, L., Wu, W., El Naggar, M.H. et al. Characterization of a jointed rock mass based on fractal geometry theory. Bull Eng Geol Environ 78, 6101–6110 (2019). https://doi.org/10.1007/s10064-019-01526-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10064-019-01526-x