A geometric approach for natural rock blocks in engineering structures. (English) Zbl 1306.74035

Summary: The spatial positions of the discontinuities and the shapes of rock blocks that are bounded into rock masses are important features that should be taken into consideration, especially in an effort to better understand the mechanisms in which a rock fails under a load. Therefore, explicit descriptions of in situ rock mass structures are necessary in many areas of mining and construction engineering. In this paper, new geometrical classifications of two discontinuities as a construction method are developed according to the spatial orientations of the discontinuities and their locations relative to each other. Discontinuities were geometrically analyzed using a rectangular prism as an engineering structure. Thus, the geometries of the possible failure of rock blocks in engineering structures were generated and included road cuts, open slopes, and dam walls that are founded in rock media. Several basic mathematical equations and approaches derived from these equations were used. Thus, wedge forms bounded by two discontinuities and free surfaces were geometrically identified and classified. In addition, the isometric perspective method was used to better illustrate the methodology. The results obtained from two experiment fields show the effectiveness of the proposed modeling method.


74L10 Soil and rock mechanics
74R10 Brittle fracture


Swedge; LIP-RM; UDEC; Dips
Full Text: DOI


[1] Childs, E.C.: The anisotropic hydraulic conductivity of soil. J. Soil Sci. 8, 42–47 (1957)
[2] Coates, D.F.: Rock mechanics principles. Monograph 874. Canadian Dep. of Energy, Mines and Resources, Ottawa (1967)
[3] Costa, M., Coggan, J.S., Eyre, J.M.: Numerical modelling of slope behaviour at Delabole slate quarry. Int. J. Surf. Min. Reclam. Environ. 13, 11–18 (1999)
[4] El-Ramly, H., Morgenstern, N.R., Cruden, D.M.: Probabilistic slope stability analysis for practice. Can. Geotech. J. 39, 665–683 (2002)
[5] Froldi, P.: Some developments to Hoek & Bray’s formulae for the assessment of the stability in case of plane failure. Bull. Int. Assoc. Eng. Geol. 54, 91–95 (1996)
[6] de Freitas, M.H., Watters, R.J.: Some field examples of toppling failure. Géotechnique 23, 495–514 (1973)
[7] Duncan, C.W.: Toppling rock slope failures examples of analysis and stabilization. Rock Mech. Rock Eng. 13, 89–98 (1980)
[8] Goodman, R.E.: Methods of Geological Engineering in Discontinuous Rocks. West, San Francisco (1976)
[9] Goodman, R.E.: Introduction to Rock Mechanics. Wiley, New York (1980)
[10] Goodman, R.E., Shi, G.H.: Geology and rock slope stability–application of a ”keyblock” concept for rock slopes. In: Proc. 3rd Int. Conf. on Stab. in Open Pit Min. (1981)
[11] Goodman, R.E., Shi, G.H.: Block Theory and its Application to Rock Engineering. Prentice-Hall, London (1985)
[12] Hadjigeorgiou, J., Grenon, M., Lessard, J.F.: Defining in-situ block size. CIM Bull. 91, 72–75 (1998)
[13] Hocking, G.: A method for distinguishing between single and double plane sliding of tetrahedral wedges. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 13, 225–226 (1976)
[14] Hoek, E., Bray, J.W.: Rock Slope Engineering. Elsevier, New York (1991)
[15] Itasca: Itasca Software Prod., FLAC2D/3D, UDEC, 3DEC, PFC2D/3D. Itasca Consulting Group, Minneapolis (2001)
[16] Jern, M.: Determination of the in situ block size distribution in fractured rock, an approach for comparing in-situ rock with rock sieve analysis. Rock Mech. Rock Eng. 37, 391–401 (2004)
[17] LaPointe, P.R., Dershowitz, W.S., Foxford, T.: Reservoir compartmentalization, fractured reservoir discrete feature network technologies. Research report, Golder Assoc., Redmond, Washington (1997)
[18] Maerz, N.H., Germain, P.: Block size determination around underground openings using simulations. In: Franklin, J., Katsabanis, T. (eds.) Measurement of Blast Fragmentation, pp. 215–223. Balkema, Rotterdam (1996)
[19] Park, H.J., West, T.R., Woo, I.: Probabilistic analysis of rock slope stability and random properties of discontinuity parameters, Interstate Highway 40, Western North Carolina, USA. Eng. Geol. 79, 230–250 (2005)
[20] Peaker, S.M.: Development of a simple block size distribution model for the classification of rock masses. M.Sc. thesis, Univ. of Toronto (1990)
[21] Rocscience: Rocscience Software Prod., DIPS, SLIDE, ROCFALL, SWEDGE. Rocscience, Toronto (2004)
[22] Sharma, S., Raghuvanshi, T.K., Anbalagan, R.: Plane failure analysis of rock slopes, technical note. Geotech. Geolog. Eng. 13, 105–111 (1995)
[23] Snow, D.T.: A parallel plate model of fractured permeable media. Ph.D. dissertation. Univ. of California, Berkley (1965)
[24] Turanboy, A., Gökay, M.K., Ülker, E.: An approach to geometrical modelling of slope curves and discontinuities. Simul. Model. Pract. Theory 16, 445–461 (2008) · Zbl 05319594
[25] Turanboy, A., Ülker, E.: LIP-RM: an attempt at 3D visualization of in situ rock mass structures. Comput. Geosci. 12, 181–192 (2008) · Zbl 1159.86308
[26] Warburton, P.M.: Vector stability analysis of an arbitrary polyhedral rock block with any number of free faces. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 18, 415–427 (1981)
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