Numerical Investigations of Blockiness of Fractured Rocks Based on Fracture Spacing and Disc Diameter
Publication: International Journal of Geomechanics
Volume 20, Issue 3
Abstract
Some numerical models treat masses of rock as assemblages of isolated blocks, whereas others treat them as continuous material. It needs to be determined at what level a rock is cut into assemblages of discrete blocks by fractures. This paper used a parameter to measure the degree to which rocks form an assemblage of blocks; is a dimensionless number in the range and is defined as the ratio of the aggregated volume of individual blocks in the investigated domain to the total volume of the rock mass in the investigated domain. The quantitative description scheme for fracture spacing and persistence suggested by the International Society for Rock Mechanics (ISRM) was used to construct different types of fractured rocks to conduct investigations into blockiness. Seventy-seven different types of fracture networks were studied. The fractures investigated covered all the fracture spacing and persistence ratings suggested by the ISRM. Based on the blockiness of the 77 samples, an analytical function was established to describe the relationship between the blockiness and the fracture spacing () and fracture disc diameter (). The resulting function is an S-shaped curve.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
This study was financially supported by the National Nature Science Foundation of China (Nos. 41802248 and 40772208), the Fundamental Research Funds for the Central Universities (No.2652018180), and the Beijing Excellent Talent Training Project (No. 2016000020124G111).
References
Aler, J., J. Du Mouza, and M. Arnould. 1996. “Measurement of the fragmentation efficiency of rock mass blasting and its mining applications.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 33 (2): 125–139. https://doi.org/10.1016/0148-9062(95)00054-2.
Bieniawski, Z. T. 1989. Engineering rock mass classification. New York: Wiley.
Biner, S. B. 1996. “A finite element method analysis of the role of interface behavior in the creep rupture characteristics of a discontinuously reinforced composite with sliding grain boundaries.” Mater. Sci. Eng. A-Struct. Mater. Prop. Microstruct. Process. 208 (2): 239–248. https://doi.org/10.1016/0921-5093(95)10045-8.
Chen, G., Y. Ohnishi, and T. Ito. 1998. “Development of high-order manifold method.” Int. J. Numer. Anal. Methods Geomech. 43 (4): 685–712. https://doi.org/10.1002/(SICI)1097-0207(19981030)43:4%3C685::AID-NME442%3E3.0.CO;2-7.
Chen, Q., C. Wei, W. Niu, D. Chen, C. Feng, and Q. Fan. 2014. “Stability classification of roadway roof in fractured rock mass based on blockiness theory.” [In Chinese.] Rock Soil Mech. 35 (10): 2901–2908. https://doi.org/10.16285/j.rsm.2014.10.026.
Cundall, P. A. 1988. “Formulation of a three-dimensional distinct element model—Part 1. A scheme to detect and represent contacts in a system composed of many polyhedral blocks.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 25 (3): 107–116. https://doi.org/10.1016/0148-9062(88)92293-0.
Deere, D. U. 1963. “Technical description of rock cores for engineering purposes.” Rock Mech. Eng. Geol. 1 (1): 17–22.
Doughty, C., R. Salve, and J. S. Y. Wang. 2002. “Liquid-release tests in unsaturated fractured welded tuffs. II: Numerical modeling.” J. Hydrol. 256 (1–2): 80–105. https://doi.org/10.1016/S0022-1694(01)00521-2.
Elmouttie, M. K., G. Krahenbuhl, G. V. Poropat, and I. Kelso. 2014. “Stochastic representation of sedimentary geology.” Rock Mech. Rock Eng. 47 (2): 507–518. https://doi.org/10.1007/s00603-013-0411-x.
Elmouttie, M. K., and G. V. Poropat. 2012. “A method to estimate in situ block size distribution.” Rock Mech. Rock Eng. 45 (3): 401–407. https://doi.org/10.1007/s00603-011-0175-0.
Empereur-Mot, L., and T. Villemin. 2003. “OBSIFRAC: Database-supported software for 3D modeling of rock mass fragmentation.” Comput. Geosci. 29 (2): 173–181. https://doi.org/10.1016/S0098-3004(02)00079-1.
Fallah, N., M. Cross, G. Taylor, and C. Bailey. 2000. “Comparison of finite element and finite volume methods application in geometrically nonlinear stress analysis.” Appl. Math. Modell. 24 (7): 439–455. https://doi.org/10.1016/S0307-904X(99)00047-5.
Goodman, R. E., and G. Shi. 1985. Block theory and its application to rock engineering. Englewood Cliffs, NJ: Prentice Hall.
Harrison, J. P., and J. A. Hudson. 2000. Engineering rock mechanics. Part 2: Illustrative workable examples. Oxford, UK: Pergamon.
Heliot, D. 1988. “Generating a blocky rock mass.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 25 (3): 127–138. https://doi.org/10.1016/0148-9062(88)92295-4.
Hoek, E., P. K. Kaiser, and W. F. Bawden. 1995. Support of underground excavation in hard rock. Rotterdam, Netherlands: A.A. Balkema.
Huang, H., B. Lecampion, and E. Detournay. 2013. “Discrete element modeling of tool-rock interaction I: Rock cutting.” Int. J. Numer. Anal. Methods Geomech. 37 (13): 1913–1929. https://doi.org/10.1002/nag.2113.
Hudson, J. A., and S. D. Priest. 1979. “Discontinuity and rock mass geometry.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 16 (6): 339–362. https://doi.org/10.1016/0148-9062(79)90001-9.
Ikegawa, Y., and J. A. Hudson. 1992. “A novel automatic identification system for three-dimensional multi-block systems.” Eng. Comput. 9 (2): 169–179. https://doi.org/10.1108/eb023856.
ISRM (International Society for Rock Mechanics). 1978. “Suggested methods for the quantitative description of discontinuities in rock masses.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 15 (6): 319–368. https://doi.org/10.1016/0148-9062(78)91472-9.
Jing, L. 2000. “Block construction for three-dimensional discrete element models of fractured rocks.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 37 (4): 645–659. https://doi.org/10.1016/S1365-1609(00)00006-X.
Jing, L. 2003. “A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering.” Int. J. Rock Mech. Min. Sci. 40 (3): 283–353. https://doi.org/10.1016/S1365-1609(03)00013-3.
Jing, L., and J. A. Hudson. 2002. “Numerical methods in rock mechanics.” Int. J. Rock Mech. Min. Sci. 39 (4): 409–427. https://doi.org/10.1016/S1365-1609(02)00065-5.
Jing, L., and O. Stephansson. 1994. “Topological identification of block assemblage for jointed rock masses.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 31 (2): 163–172. https://doi.org/10.1016/0148-9062(94)92807-X.
Kalenchuk, K. S., M. S. Diederichs, and S. McKinnon. 2006. “Characterizing block geometry in jointed rockmasses.” Int. J. Rock Mech. Min. Sci. 43 (8): 1212–1225. https://doi.org/10.1016/j.ijrmms.2006.04.004.
Kim, B. H., M. Cai, P. K. Kaiser, and H. S. Yang. 2007. “Estimation of block sizes for rock masses with non-persistent joints.” Rock Mech. Rock Eng. 40 (2): 169–192. https://doi.org/10.1007/s00603-006-0093-8.
Kulatilake, P. H. S. W., D. N. M. Wathugala, and O. Stephansson. 1993. “Joint network modeling with a validation exercise in Strip mine, Sweden.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 30 (5): 503–526. https://doi.org/10.1016/0148-9062(93)92217-E.
Lambert, C., K. Thoeni, A. Giacomini, D. Casagrande, and S. Sloan. 2012. “Rockfall hazard analysis from discrete fracture network modeling with finite persistence discontinuities.” Rock Mech. Rock Eng. 45 (5): 871–884. https://doi.org/10.1007/s00603-012-0250-1.
Lin, D., C. Fairhurst, and A. M. Starfield. 1987. “Geometrical identification of three-dimensional rock block system using topological techniques.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 24 (6): 331–338. https://doi.org/10.1016/0148-9062(87)92254-6.
Long, J. C. S., and D. M. Billaux. 1987. “From field data to fracture network modeling: An example incorporating spatial structure.” Water Resour. Res. 23 (7): 1201–1216. https://doi.org/10.1029/WR023i007p01201.
Lu, J. 2002. “Systematic identification of polyhedral blocks with arbitrary joints and faults.” Comput. Geotech. 29 (1): 49–72. https://doi.org/10.1016/S0266-352X(01)00018-0.
Mondali, M., A. Abedian, and S. Adibnazari. 2005. “FEM study of the second stage creep behavior of Al6061/SiC metal matrix composite.” Comput. Mater. Sci. 34 (2): 140–150. https://doi.org/10.1016/j.commatsci.2004.12.063.
Oda, M. 1982. “Fabric tensor for discontinuous geological materials.” Soils Found. 22 (4): 96–108. https://doi.org/10.3208/sandf1972.22.4_96.
Ohnishi, Y., and Q. Yu. 2001. “3D block analyses for fractured rock.” In Computer methods and advances in geomechanics, edited by Desai, et al. 577–580. Rotterdam, Netherlands: A.A. Balkema.
Pahl, P. J. 1981. “Estimating the mean length of discontinuity traces.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 18 (3): 221–228. https://doi.org/10.1016/0148-9062(81)90976-1.
Powrie, W. 1997. Soil mechanics: Concept and applications. London: E & FN Spon.
Priest, S. D. 2004. “Determination of discontinuity size distribution from scan-line data.” Rock Mech. Rock Eng. 37 (5): 347–368. https://doi.org/10.1007/s00603-004-0035-2.
Priest, S. D., and J. Hudson. 1976. “Discontinuity spacing in rock.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 13 (5): 135–148. https://doi.org/10.1016/0148-9062(76)90818-4.
Shi, G. 1989. “Discontinuous deformation analysis: A new numerical model for the statics and dynamics of block systems.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of California, Berkeley.
Starzec, P., and J. Andersson. 2002. “Application of two-level factorial design to sensitivity analysis of keyblock statics from fracture geometry.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 39 (2): 243–255. https://doi.org/10.1016/S1365-1609(02)00026-6.
Tsesarsky, M., E. Gal, and E. Machlav. 2013. “3D global–local finite element analysis of shallow underground caverns in soft sedimentary rock.” Int. J. Rock Mech. Min. Sci. 57 (Jan): 89–99. https://doi.org/10.1016/j.ijrmms.2012.07.034.
Wang, L. G., S. Yamashita, F. Sugimoto, C. Pan, and G. Tan. 2003. “A Methodology for predicting the in situ size and shape distribution of rock blocks.” Rock Mech. Rock Eng. 36 (2): 121–142. https://doi.org/10.1007/s00603-002-0039-8.
Warburton, P. M. 1980. “A stereological interpretation of joint trace data.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 17 (4): 181–190. https://doi.org/10.1016/0148-9062(80)91084-0.
Warburton, P. M. 1981. “Vector stability analysis of an arbitrary polyhedral rock block with any number of free faces.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 18 (5): 415–427. https://doi.org/10.1016/0148-9062(81)90005-X.
Warburton, P. M. 1983. “Application of a new computer model for reconstructing blocky block geometry analysis single block stability and identifying keystones.” In Proc., 5th Int. Congress on Rock Mechanics, F225–F230. Rotterdam, Netherlands: A.A. Balkema.
Wu, J. H., Y. Ohnishi, and S. Nishiyama. 2005. “A development of the discontinuous deformation analysis for rock fall analysis.” Int. J. Numer. Anal. Methods Geomech. 29 (10): 971–988. https://doi.org/10.1002/nag.429.
Xia, L., M. Li, Y. Chen, Y. Zheng, and Q. Yu. 2015. “Blockiness level of rock mass around underground powerhouse of three gorges project.” Tunnelling Underground Space Technol. 48 (Apr): 67–76. https://doi.org/10.1016/j.tust.2015.02.002.
Xia, L., X. Liu, and Q. Yu. 2010. “Determining representative elementary volume of fractured rock mass based on blockiness analysis.” [In Chinese.] Rock Soil Mech. 31 (12): 3992–3997. https://doi.org/10.16285/j.rsm.2010.12.048.
Xia, L., Y. Zheng, and Q. Yu. 2016. “Estimation of the REV size for blockiness of fractured rock masses.” Comput. Geotech. 76 (Jun): 83–92. https://doi.org/10.1016/j.compgeo.2016.02.016.
Yu, Q. 2000. “Analyses for fluid flow and solute transport in discrete fracture network.” Ph.D. thesis, Dept. of Civil Engineering, Kyoto Univ.
Yu, Q., Y. Ohnishi, G. Xue, and D. Chen. 2009. “A generalized procedure to identify three-dimensional rock blocks around complex excavations.” Int. J. Numer. Anal. Methods Geomech. 33 (3): 355–375. https://doi.org/10.1002/nag.720.
Zhang, L., and H. H. Einstein. 2000. “Estimating the intensity of rock discontinuities.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 37 (5): 819–837. https://doi.org/10.1016/S1365-1609(00)00022-8.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 20 • Issue 3 • March 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Mar 1, 2019
Accepted: Aug 13, 2019
Published online: Jan 2, 2020
Published in print: Mar 1, 2020
Discussion open until: Jun 2, 2020
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.