Cundall, PA, Pierce, ME & Mas Ivars, D 2008, 'Quantifying the Size Effect of Rock Mass Strength', in Y Potvin, J Carter, A Dyskin & R Jeffrey (eds), Proceedings of the First Southern Hemisphere International Rock Mechanics Symposium
, Australian Centre for Geomechanics, Perth, pp. 3-15, https://doi.org/10.36487/ACG_repo/808_31
A long-standing problem in rock mechanics is the estimation of rock mass strength. The term “rock mass” denotes a large volume of fractured rock in which yield of intact material and discontinuities (joints) must both occur for overall failure to take place. The difficulty in characterising a rock mass arises from the impossibility of testing directly (to failure) a large extent of rock. Because the proportion and configuration of the discontinuities (relative to the proportion of intact rock) determine the strength of the composite material, there is a pronounced size effect, such that large volumes appear weaker than small volumes. It is therefore important to consider the size effect in the design of large structures in rock.
Recently, a numerical approach, called synthetic rock mass (SRM), has been developed and applied in several projects. The SRM is a bonded-particle assembly representing brittle rock that contains multiple joints, each consisting of a planar array of bonds that obey a special model, the smooth joint model (SJM). The SJM allows slip and cracking at particle contacts, while respecting the given joint orientation rather than local contact orientations. Overall failure of an SRM element depends on both fracture of intact material (bond breaks) and yield of joint segments.
Results are presented from a series of numerical experiments on 3D elements of various sizes. For the first time, we are able to quantify the variation of rock mass strength as a function of size. The results are discussed in relation to empirical methods commonly used in design.
Bažant, Z.P. and Chen, E-P. (1997) Scaling of structural failure. Applied Mechanics Review, 50(10).
Bieniawski, Z.T. and Van Heerden, W.L. (1975) The significance of in situ tests on large rock specimens. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 12, pp. 101–113.
Brady, B.H.G. and Brown, E.T. (2004) Rock mechanics for underground mining, 3rd Edition. Kluwer Academic, Dordrecht.
Cai, M., Kaiser, P.K., Uno, H., Tasaka, Y. and Minami, M. (2004) Estimation of rock mass strength and deformation modulus of jointed hard rock masses using the GSI System. International Journal of Rock Mechanics and Mining Sciences, 41(1), pp. 3–19.
Cunha, A.P. (editor) (1990) Scale effects in rock mechanics. Proceedings First International Workshop on Scale Effects in Rock Masses, Loen, Norway, June, Balkema, Rotterdam, pp. 3–31.
Goodman, R.E. (1980) Introduction to rock mechanics. Wiley and Sons, New York.
Hoek, E. and Brown, E.T. (1980) Underground Excavations in Rock. London, Institution of Mining and Metallurgy.
Hoek, E. and Brown, E.T. (1997) Practical estimates of rock mass strength, International Journal of Rock Mechanics and Mining Sciences, 34(8), pp. 1165–1186.
ICSAS (Itasca Consultants S.A.S.) (2006) 3FLO, version 2.2. ICSAS, Lyon.
Itasca Consulting Group Inc. (Itasca) (2004a) UDEC (Universal Distinct Element Code), version 4.0, Itasca, Minneapolis.
Itasca Consulting Group Inc. (Itasca) (2004b) 3DEC (3-Dimensinal Distinct Element Code), version 3.0, Itasca, Minneapolis.
Itasca Consulting Group Inc. (Itasca) (2007) PFC3D (Particle Flow Code in 3 Dimensions), version 4.0, pre-release, Itasca, Minneapolis.
Jefferies, M., Lorig, L. and Alvarez, C. (2008) Influence of rock-strength spatial variability on slope stability. Continuum and Distinct Element Numerical Modeling in Geo-Engineering, Proceedings First International FLAC/DEM Symposium on Numerical Modeling, R. Hart, C. Detournay and P. Cundall (editors) 24–26 August. Minneapolis, Itasca Consulting Group (in press).
Kim, B.H., Cai, M., Kaiser, P.K. and Yang, H.S. (2007) Estimation of Block Sizes for Rock Masses with Non-persistent Joints. Rock Mechanics and Rock Engineering, 40(2), pp. 169–192.
Mas Ivars, D., Pierce, M., DeGagné, D. and Darcel, C. (2008a) Anisotropy and scale dependency in jointed rock-mass strength—A synthetic rock mass study. Continuum and Distinct Element Numerical Modeling in Geo-Engineering, Proceeding First International FLAC/DEM Symposium on Numerical Modeling, R. Hart, C. Detournay and P. Cundall (editors) 24–26 August, Minneapolis, Itasca Consulting Group (in press).
Mas Ivars, D., Potyondy, D.O., Pierce, M. and Cundall, P.A. (2008b) The smooth-joint contact model. Proceedings 8th World Congress on Computational Mechanics/5th European Congress on Computational Methods in Applied Sciences and Engineering, in press.
Mostyn, G. and Douglas, K. (2000) The shear strength of intact rock and rock masses. GeoEng 2000: An International Conference on Geotechnical and Geological Engineering (Melbourne, Australia), Vol. 1, Technomic Publishing, Lancaster, Pennsylvania, pp. 1398–1421.
Park, E-S., Martin, C.D. and Christiansson, R. (2004) Simulation of the mechanical behavior of discontinuous rock masses using a bonded-particle model. Gulf rocks 2004: Rock Mechanics Across Borders and Disciplines, D. Yale, S. Willson and A. Abou-Sayed (editors), Paper no. ARMA/NARMS 04–480.
Pierce, M., Cundall, P., Potyondy, D. and Mas Ivars, D. (2007) A synthetic rock mass model for jointed rock. Rock mechanics: Meeting society's challenges and demands, Vol. 1: Fundamentals, new technologies and new ideas, E. Eberhardt, D. Stead and T. Morrison (editors), Taylor and Francis, London, pp. 341–349.
Potyondy, D.O. and Cundall, P.A. (2004) A bonded-particle model for rock, International Journal of Rock Mechanics and Mining Sciences, 41, pp. 1329–1364.
Reyes-Montes, J., Pettitt, W. and Young, R.P. (2007) Validation of a Synthetic Rock Mass model using excavation induced microseismicity, Rock mechanics: Meeting society's challenges and demands, E. Eberhardt, D. Stead and T. Morrison (editors), Taylor and Francis Group, London, Vol. 1, pp. 365–369.
Rocha, M. (1974) Present possibilities of studying foundations of concrete dams, Advances in rock mechanics, National Academy of Sciences, Washington, D.C.
Schultz, R.A. (1996) Relative scale and the strength and deformability of rock masses. Journal of Structural Geology, 18(9), pp. 1139–1149.
Wang, C., Tannant, D.D. and Lilly, P.A. (2003) Numerical analysis of the stability of heavily jointed rock slopes using PFC2D, International Journal of Rock Mechanics and Mining Sciences, 40, pp. 415–424.
Weibull, W. (1939) A statistical theory of the strength of materials. Ingeniors Vetenskaps Akademien, Handlingar, Vol. 151–3, pp. 45–55.