The concept of representative elementary length (REL) as an effective tool to study scale effects in rock engineering problems

Davide Elmo; Doug Stead

doi:10.21701/bolgeomin.131.3.001

Authors

Davide Elmo University of British Columbia
Doug Stead University of British Columbia

DOI:

https://doi.org/10.21701/bolgeomin.131.3.001

Keywords:

Discrete fracture network approach (DFN), rock quality designation (RQD), rock mass classification systems, representative elementary length (REL), REL Ellipsoid concept

Abstract

In this paper, a discrete fracture network approach (DFN) is used to study scale effects on rock quality designation (RQD) measurements. RQD is a parameter that describes rock mass quality and represents a fundamental component of several rock mass classification systems. The results demonstrate that it is possible to define a representative elementary length (REL), above which RQD measurements represent an average indicator of rock mass quality. However, the directional bias of RQD measurements is such that the choice of REL is itself a function of the orientation of the sampling line used to estimate RQD. By considering multiple sampling directions, this paper introduces the concept of a REL Ellipsoid, whereby the normalized value of the REL along three sampling directions indicates the degree of homogeneity and isotropy of the rock mass with increase in problem scale. In the authors’ opinion, the REL Ellipsoid concept allows to better capture the nature of the 3D representative elementary volume (REV) for both isotropic and anisotropic rock masses Mapping data from a room-and-pillar mine are used in the initial validation of the proposed REL Ellipsoid concept.

Downloads

Download data is not yet available.

References

Barton, N., Lien, R., Lunde, J. 1974. Engineering classification of rock masses for the design of tunnel support. In: Rock Mechanics, 6 (4), 189-236. https://doi.org/10.1007/BF01239496

Bear, J., 2013. Dynamics of fluids in porous media. Courier Corporation. Bieniawski ZT, 1989. Engineering rock mass classification. Wiley, New York, 251 pages.

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. Int. J. Rock Mechanics and Mining Sciences, 41(1), pp. 3-19. https://doi.org/10.1016/S1365-1609(03)00025-X

Cundall, P.A. 2008. Quantifying the size effect of rock mass strength. SHIRMS 2008. Australian Centre for Geomechanics, Perth. https://doi.org/10.36487/ACG_repo/808_31

Deere, D.U. and Hendron, A.J., J., Patton, FD, and Cording, EJ (1967). Design of surface and near-surface construction in rock. In Failure and Breakage of Rock, Eighth Symposium on Rock Mechanics (pp. 237-302).

Dershowitz, W.S., Herda, H.H. 1992. Interpretation of fracture spacing and intensity. In: Proceedings of the 33rd US Rock Mechanics Symposium, Publ. 33, 757-766.

Elmo, D., Donati, D., Stead, D. 2018. Challenges in the characterization of rock bridges. Submitted to Engineering Geology. https://doi.org/10.1016/j.enggeo.2018.06.014

Elmo, D. and Stead, D., 2010. An integrated numerical modelling-discrete fracture network approach applied to the characterisation of rock mass strength of naturally fractured pillars. Rock Mechanics and Rock Engineering, 43(1), pp.3-19. https://doi.org/10.1007/s00603-009-0027-3

Elmo, D., 2006. Evaluation of a hybrid FEM/DEM approach for determination of rock mass strength using a combination of discontinuity mapping and fracture mechanics modelling, with particular emphasis on modelling of jointed pillars (Doctoral dissertation, University of Exeter).

Esmaieli, K., Hadjigeorgiou, J. and Grenon, M. 2010. Estimating geometrical and mechanical REV, based on synthetic rock mass models at Brunswick Mine. Int. J. Rock Mech. Min. Sci., 47(6), 915-926. https://doi.org/10.1016/j.ijrmms.2010.05.010

Havaej, M. and Stead, D. 2016. Investigating the role of kinematics and damage in the failure of rock slopes. Computers and Geotechnics, 78, 181-193. https://doi.org/10.1016/j.compgeo.2016.05.014

Hill, R., 1963. Elastic properties of reinforced solids: some theoretical principles. J. Mech. Phys. Solids, 11, 357-372. https://doi.org/10.1016/0022-5096(63)90036-X

Hoek, E., 2007. Practical Rock Engineering. https://www.rocscience.com/learning/hoek-s-corner.

Hoek, E., Carter, T.G. and Diederichs, M.S., 2013. Quantification of the geological strength index chart. In 47th US Rock Mechanics/Geomechanics Symposium. American Rock Mechanics Association.

Hoek, E., Kaiser P.K. and Bawden W.F. 1995. Support of underground excavations in hard rock. Rotterdam, Balkema.

Hoek, E. and Brown, E.T. 2019. The Hoek-Brown failure criterion and GSI-2018 edition. J. Rock Mech. Geotech. Eng. , In press. https://doi.org/10.1016/j.jrmge.2018.08.001

Jakubec, J. and Esterhuizen, G. 2000. Use of the mining rock mass rating (MRMR) classification: industry experience.

Palmstrom, A. 2001. In In-situ characterization of rocks. Sharma V.M. and Saxena K.R. eds. A.A. Balkema publishers, 2001, pp. 49-97.

Palmstrom, A. 2005. Underground Space Technology 20, 362-377. https://doi.org/10.1016/j.tust.2005.01.005

Pine RJ, Harrison JP (2003) Rock mass properties for engineering design. Q. J. Eng. Geol. Hydrogeol. 36, pp.5-16. https://doi.org/10.1144/1470-923601-031

Pells, P.J., Bieniawski, Z.T., Hencher, S.R., Pells, S.E. 2017. Rock quality designation (RQD): time to rest in peace. Can. Geotech. J., 54, 825-834. https://doi.org/10.1139/cgj-2016-0012

Wang, R., Elmo, D., Stead, D., Rogers, S. 2017. Characterisation of rock mass representative elementary volume using RQD and a discrete fracture network approach. In Proceedings of the 51st Int. Symp. Rock Mech., San Francisco, U.S. June 2017. Paper 760.

Zhang, W., Chen, J., Cao, Z., Wang, R. 2012. Size effect of RQD and generalized representative volume elements: A case study on an underground excavation in Baihetan dam, Southwest China. Tunnelling and Underground Space Technology 35. pp. 89-98. https://doi.org/10.1016/j.tust.2012.12.007