Unified Size-Effect Law for Intact Rock
Publication: International Journal of Geomechanics
Volume 16, Issue 2
Abstract
A suite of laboratory testing was performed on Gosford sandstone samples having a range of sizes, including point-load and uniaxial compressive tests. A unified size-effect law (USEL), based on the work by Zdenek Bazant, involving fracture energy as well as fractal theories, was introduced. It was shown that USEL correlates well with the ascending and descending uniaxial compressive strength trends obtained from Gosford sandstone as well as five other rock types reported by Brian Hawkins. Fractal characteristics found to be the primary mechanism for ascending strength trends and surface flaws could be considered as a secondary mechanism. The influence of the contact area on the size-effect behavior of point-load results was investigated using a new approach. This approach was novel in the way it incorporated the load contact area. Determination of the point-load strength index using this new approach led to opposite size-effect trends compared with those observed using a conventional point-load strength index. Hence, the utilization of USEL leads to better simulation of the new point-load strength index data.
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References
Abou-Sayed, A. S., and Brechtel, C. E. (1976). “Experimental investigation of the effects of size on the uniaxial compressive strength of Cedar City quartz diorite.” The 17th U.S. Symp. on Rock Mechanics. 5D6, 1–9.
Adey, R. A., and Pusch, R. (1999). “Scale dependency in rock strength.” Eng. Geol., 53(3–4), 251–258.
Ayres da Silva, L. A., and Hennies, W. T. (1993). “A methodology for rock mass compressive strength characterization from laboratory tests.” Scale effects in rock mass, A. Pinto da Cunha, ed., Balkema, Lisbon, Portugal, 217–224.
Bazant, Z. P. (1983). “Size effect in blunt fracture: Concrete, rock, metal.” J. Eng. Mech., 518–535.
Bazant, Z. P. (1997). “Scaling of quasibrittle fracture: Hypotheses of invasive and lacunar fractality, their critique and Weibull connection.” Int. J. Frac., 83(1), 41–65.
Bazant, Z. P., and Kazemi, M. T. (1990). “Determination of fracture energy, process zone length and brittleness number from size effect, with application to rock and concrete.” Int. J. Frac., 44(1), 111–131.
Bazant, Z. P., and Planas, J. (1998). Fracture and size effect in concrete and other quasibrittle materials, CRC Press, London.
Bazant, Z. P., and Xi, Y. (1991). “Statistical size effect in quasi-brittle structures: II. Nonlocal theory.” J. Eng. Mech., 2623–2640.
Bazant, Z. P., Xi, Y., and Deid, S. G. (1991). “Statistical size effect in quasi-brittle structures: I. Is Weibull theory applicable?” J. Eng. Mech., 2609–2622.
Bieniawski, Z. T. (1968). “The effect of specimen size on the compressive strength of coal.” Int. J. Rock Mech. Min. Sci., 5(4), 325–335.
Bieniawski, Z. T. (1975). “The point-load test in geotechnical practice.” Eng. Geol., 9(1), 1–11.
Borodich, F. M. (1999). “Fractals and fractal scaling in fracture mechanics.” Int. J. Frac., 95(1–4), 239–259.
Broch, E., and Franklin, J. A. (1972). “The point-load strength test.” Int. J. Rock Mech. Min. Sci., 9(6), 669–697.
Brook, N. (1980). “Size correction for point load testing.” Int. J. Rock Mech. Min. Sci, 17(4), 231–235.
Brook, N. (1985). “The equivalent core diameter method of size and shape correction in point load testing.” Int. J. Rock Mech. Min. Sci., 22(2), 61–70.
Carpinteri, A. (1994). “Fractal nature of material microstructure and size effects on apparent mechanical properties.” Mech. Mat., 18(2), 89–101.
Carpinteri, A., Chiaia, B., and Ferro, G. (1995). “Size effects on nominal tensile strength of concrete structures: Multifractality of material ligaments and dimensional transition from order to disorder.” Mat. Struct., 28(6), 311–317.
Carpinteri, A., and Ferro, G. (1994). “Size effects on tensile fracture properties: A unified explanation based on disorder and fractality of concrete microstructure.” Mat. Struct., 27(10), 563–571.
Castelli, M., Saetta, V., and Scavia, C. (2003). “Numerical study of scale effects on the stiffness modulus of rock masses.” Int. J. Geomech., 160–169.
Cnudde, V., Boone, M., Dewanckele, J., Dierick, M., Van Hoorebeke, L., and Jacobs, P. (2011). “3D characterization of sandstone by means of X-ray computed tomography.” Geosphere, 7(1), 54–61.
Darlington, W. J., and Ranjith, P. G. (2011). “The effect of specimen size on strength and other properties in laboratory testing of rock and rock-like cementitious brittle materials.” Rock Mech. Rock Eng., 44(5), 513–529.
Dey, T., and Halleck, P. (1981). “Some aspects of size-effect in rock failure.” Geophys. Res. Lett., 8(7), 691–694.
Franklin, J. A. (1985). “Suggested method for determining point load strength.” Int. J. Rock Mech. Min. Sci., 22(2), 51–60.
Greminger, M. (1982). “Experimental studies of the influence of rock anisotropy and size and shape effects in point-load testing.” Int. J. Rock Mech. Min. Sci., 19(5), 241–246.
Griffith, A. A. (1924). “The theory of rupture.” 1st Int. Congress of Applied Mechanics, Delft, Netherlands, 55–63.
Hawkins, A. B. (1998). “Aspects of rock strength.” Bull. Eng. Geol. Environ., 57(1), 17–30.
Hiramatsu, Y., and Oka, Y. (1966). “Determination of the tensile strength of rock by a compression test of an irregular test piece.” Int. J. Rock Mech. Min. Sci., 3(2), 89–99.
Hoek, E., and Brown, E. (1980). Underground excavations in rock, Spon Press, Hertford, London.
Hoek, E., and Brown, E. T. (1997). “Practical estimates of rock mass strength.” Int. J. Rock Mech. Min. Sci., 34(8), 1165–1186.
Hoskins, J. R., and Horino, F. G. (1969). Influence of spherical head size and specimen diameters on the uniaxial compressive strength of rocks, U.S. Dept. of the Interior, Bureau of Mines, Washington, DC.
Huang, H., and Detournay, E. (2008). “Intrinsic length scales in tool-rock interaction.” Int. J. Geomech., 39–44.
Hudson, J. A., Crouch, S. L., and Fairhurst, C. (1972). “Soft, stiff and servo-controlled testing machines: A review with reference to rock failure.” Eng. Geol., 6(3), 155–189.
Hunt, D. D. (1973). “The influence of confining pressure on size effect.” M.S. thesis, Massachusetts Institute of Technology, Cambridge, MA.
ISRM (International Society of Rock Mechanics). (2007). “The complete suggested methods for rock characterization, testing and monitoring: 1974–2006 ISRM.” R. Ulusay and J. A. Hudson (eds.), Suggested methods prepared by the commission on testing methods, Compilation arranged by the ISRM Turkish National Group, Kozan ofset, Ankara.
Kim, J. K., and Eo, S. H. (1990). “Size effect in concrete specimens with dissimilar initial cracks.” Mag. Concr. Res., 42(153), 233–238.
Koifman, M. I. (1969). “Investigation of the effect of specimen dimensions and anisotropy on the strength of some coals in Donets and Kuznetsk Basin.” Mech. Prop. Rock, 118–129.
Kramadibrata, S., and Jones, I. O. (1993). “Size effect on strength and deformability of brittle intact rock.” Scale Effect in Rock Masses, A. Pinto da Cunha, ed., Balkema, Lisbon, Portugal, 277–284.
Mandelbort, B. B. (1982). The fractal geometry of nature, W. H Freeman, New York.
Mogi, K. (1962). “The influence of dimensions of specimens on the fracture strength of rocks---comparison between the strength of rock specimens and that of the earth’s crust.” Bull. Earth. Res. Inst., 40, 175–185.
Muller, J., and McCauley, J. (1992). “Implication of fractal geometry for fluid flow properties of sedimentary rocks.” Transp. Porous Media, 8(2), 133–147.
Panek, L. A., and Fannon, T. A. (1992). “Size and shape effects in point load tests of irregular rock fragments.” Rock Mech. Rock Eng., 25(2), 109–140.
Pratt, H. R., Black, A. D., Brown, W. S., and Brace, W. F. (1972). “The effect of specimen size on the mechanical properties of unjointed diorite.” Int. J. Rock Mech. Min. Sci., 9(4), 513–529.
Radlinski, A., Ioannidis, M., Hinde, A., Hainbuchner, M., Baron, M., and Rauch, H. (2004). “Angstrom-to-millimeter characterization of sedimentary rock microstructure.” J. Colloid Interface Sci., 274(2), 607–612.
Russell, A. R., and Muir Wood, D. (2009). “Point load tests and strength measurements for brittle spheres.” Int. J. Rock Mech. Min. Sci., 46(2), 272–280.
Smith, E. (1995). “Critical dimensions for scaling effects in the fracture of quasi-brittle materials.” Int. Union of Theoretical and Applied Mechanics (IUTAM) Symp. on Size-Scale Effects in the Failure Mechanisms of Materials and Structures, Politecnico di Torino, Turin, Italy.
Sufian, A., and Russell, A. R. (2013). “Microstructural pore changes and energy dissipation in Gosford sandstone during pre-failure loading using X-ray CT.” Int. J. Rock Mech. Min. Sci., 57, 119–131.
Thompson, A. (1991). “Fractals in rock physics.” Annu. Rev. Earth Planet. Sci., 19, 237–262.
Thuro, K., Plinninger, R. J., Zah, S., and Schutz, S. (2001). “Scale effect in rock strength properties: Part 2.” Rock mechanics: A challenge for society, P. Sarkka and P. Eloranta, eds., Swets & Zeitlinger, Lisse, Switzerland, 175–180.
Timoshenko, S. P., and Goodier, J. N. (1951). Theory of elasticity, McGraw-Hill, New York.
Van Mier, J. G. M. (1996). Fracture processes of concrete, CRC Press, Boca Raton, FL.
Van Mier, J. G. M., and Man, H. K. (2009). “Some notes on microcracking, softening, localization, and size effects.” Int. J. Damage Mech., 18, 283–309.
Villeneuve, M., Diederichs, M., and Kaiser, P. (2012). “Effects of grain scale heterogeneity on rock strength and the chipping process.” Int. J. Geomech., 632–647.
Vutukuri, V. S., Lama, R. D., and Saluja, S. S. (1974). Handbook on mechanical properties of rocks, Trans Tech Publications, Bay Village, OH.
Weibull, W. (1939). “A statistical theory of the strength of materials.” Ph.D. dissertation, Royal Swedish Academy of Engineering Science, Stockholm, Sweden.
Weibull, W. (1951). “A statistical distribution of function of wide applicability.” J. Appl. Mech., 18, 293–297.
Wijk, G., Rehbinder, G., and Logdstrom, G. (1978). “The relation between the uniaxial tensile strength and the sample size for Bohus granite.” Rock Mech. Rock Eng., 10(4), 201–219.
Yi, C., Zhu, H., and Liu, L. (2011). “Damage analysis for quasi-brittle materials of CT images under uniaxial compression.” Adv. Mater. Res., 170, 373–379.
Yoshinaka, R., Osada, M., Park, H., Sasaki, T., and Sasaki, K. (2008). “Practical determination of mechanical design parameters of intact rock considering scale effect.” Eng. Geol., 96(3–4), 173–186.
Zhang, Q., Zhu, H., Zhang, L., and Ding, X. (2011). “Study of scale effect on intact rock strength using particle flow modeling.” Int. J. Rock Mech. Min. Sci., 48(8), 1320–1328.
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Published In
International Journal of Geomechanics
Volume 16 • Issue 2 • April 2016
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Nov 18, 2014
Accepted: May 5, 2015
Published online: Sep 23, 2015
Discussion open until: Feb 23, 2016
Published in print: Apr 1, 2016
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