Journal of Mining Engineering

Journal of Mining Engineering

Polar Graphs Presentation of Deformation Modulus in Anisotropic Blocky Rock Masses using Joint Stiffness Matrix

Document Type : research - paper

Authors
1 PhD candidate, Department of Civil Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 Assistant Professor, Department of Civil Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
3 professor Faculty of Engineering, Islamic Azad University, Science and Research Branch, Tehran, Iran
Abstract
The anisotropy in the deformational behavior of blocky rock masses has been comprehensively investigated. Uniaxial deformation modulus was selected as the key parameter. It is generally anisotropic and depends on the loading direction as well as intact rock and joint properties and joint setting. Representative volumes of blocky rock masses were numerically simulated by the discrete element method and loaded uniaxially in various directions. Then the failure mode and the deformation modulus were studied for different loading directions and for various relative joint settings. A new nonlinear stress-dependent stiffness matrix for joints was introduced and used in wich surface conditions of the joints in terms of the joint roughness coefficient (JRC) and the intact rock materials in terms of the uniaxial compressive strength (UCS) were considered. The results of the assessments are presented in the form of rose diagrams showing variations of the blocky rock mass deformation modulus that are depend on joints JRC, intact rock UCS, and the rock mass structure in term of relative joint angle. Also, the expected degree of anisotropy for various surface joint conditions and uniaxial compressive strengths of intact rock were introduced. In the geological strength index (GSI) table, results are classified such that by assigning a value to JRC for each class of the joint surface conditions, deformation modulus and degree of anisotropy corresponding to GSI values can be determined
Keywords
Subjects

Amadei, B., Savage, W.Z., 1993, Effect of joints on rock mass strength and deformability, Comprehensive rock Engineering- Principle, practice and projects. Ed: J. A. Hudson, Pergamon, Oxford, UK., 1, p. 331- 365.## Agharazi, A., Derek Martin, C.,Tannant, D, 2012, A three-dimensional equivalent continuum constitutive model for jointed rock masses containing up to three random joint sets, Geomechanics and Geoengineering: An International Journal, Vol. 7, No. 4, 227–238. ## Amadei, B., Goodman, RE, (1981), A 3-D constitutive relation for fractured rock masses, In: proceedings of the international symposium on mechanical behavior of structured media, Rotterdam: Balkema, p.249-68. ## Barton, N.R., 1976, The shear strength of rock and rock joints, Int. J. Mech. Min. Sci. & Geomech. Abstr., 13(10), 1-24. ## Barton, N., Choubey, V., 1977, The shear strength of rock joints in theory and practice, rock mechanics and rock engineering. 10, p. 1-54. ## Bieniawski, Z.T.,1978, Determining rock mass deformability- experience from case histories, Int. J. Rock Mech. Min Sic, Geomech. Abstr., p.15. ## Bandis, S C., Lumsden, A.C., and Barton, N R., 1983, Fundamentals of rock joint deformation, Int. J. Rock Mech. Min sci. & Geomech. Abstr., 20, p. 249-268. ## Barton, N.R., Bandis, S.C., 1990, Review of predictive capabilities of JRC-JCS model in engineering practice, In Rock joints, proc. int. symp. on rock joints, Loen, Norway, (eds N. Barton and O. Stephansson), 603-610. Rotterdam: Balkema. ## Bidgoli, M.N., Zhao, Z.H., Jing, L.R., 2013, Numerical evaluation of strength and deformability of fractured rock, J. Rock Mech. Gotech. Eng., 5, p.419-30. ## Cundall, P.A., 1971, A computer model for simulating progressive large scale movements in blocking rock systems, in proceedings of the symposium of the international society for rock mechanics, France. 8, p. 1-71. ## Cundall, PA., 1988, Formulation of a three dimensional distinct element model, Part I. A scheme to detect and represent contacts in a system composed of many polyhedral blocks, International Journal of Rock Mechanics and Mining Sciences 25(3), 107–16. ## Carvalho, J., 2004, Estimation of rock mass modulus, Personal Communication. ## Deere, D. U. and Miller, R.P. (1966), Engineering Classification and Index Properties for Intact Rock, Tech. Rep. No. AFWL-TR-65-116, Air Force Weapons Lab, Kirtland Air Base, New Mexico. ## Duncan, J.M., Chang, C.Y., 1970, Non- Linear analysis of stress and strain in soil, J. Soil Mech. Found. Dir. ASCE., 96, p. 1629-1655. ## Goodman, R.E., Taylor and Brekke, T.L., 1968, A model for mechanics of jointed rock, J. Soil Mech. Found. ASCE. 96, p. 637-659. ## Gerrard, C. M., 1991, The equivalent elastic properties of simplified and jointed rock masses, Proc.Int. Conf. on Computer Meth. and Advances in Geomech., Cairns, Eds: G. Beer. J. R. Brooker &J. P. Carter, Balkema, Rotterdam, 333-337. ## Gokceoglu, C., Sonmez, H., and Kayabasi, A., 2003, Predicting the deformation moduli of rock mass, Int. J. Rock Mech. Min Sci. 40, p. 701-710. ## Heuze, F. E., 1980, scale effects in the determination of rock mass strength and deformability, Rock Mech., 12, 167-192. ## Hoek, H., Brown, E.T., 1997, Practical estimates of rock mass strength, Int. J. Rock Mech. Min. Sci., 34, p. 1165-1186. ## Hoek, E., Diederichs, M.S., 2006, Empirical estimation of rock mass modulus, Int. J. Rock Mech. Min Sci., 43, p. 203-215. ## Jaeger, J.C., Cook, N.G.W., & Zimmerman, R.W., 2007, Fundamentals of mechanics, Oxford, Blackwell Publishing Ltd. ## Ivars, D.M., Pierce, M.E., & Darcel, C., et al., 2011, The synthetic rock mass approach for jointed rock mass modelling, Int. J. Rock Mech. Min Sci., 48, p. 219-44. ## Kulhawy, F.H., 1978, Geomechanical model for rock foundation settlement, J. Geotech. Engrg., ASCE, 104, p. 211-227. ## Kulatilake, P.H.S.W., Wang, S., et al., 1993, Effect of finite- size joints on the deformability of jointed rock in 3-dimensions, Int. J. Rock Mech. Min Sci., England. 30, p. 479-501. ## Khani, A., Baghbanan, A., Norouzi, A., & Hashemolhosseini, H., 2013, Effects of fracture geometry and stress on the strength of fractured rock mass, Int. J. Rock Mech. Min Sci., 60, p. 345-52. ## Min, K.B., Jing, L., 2003, Numerical determination of the equivalent elastic compliance tensor for fractured rock masses using the distinct element method, Int. J. Rock Mech. Min Sci., 40, p. 795- 816. ## Oda, M., 1988, An experimental study of the elasticity of mylonite rock with random cracks, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 25, 59-69. ## Priest, S.D.,1993, Discontinuity analysis for rock engineering, chapman & Hall. ## Robertson, A., (1970), The interpretation of geologic factors for use in slope theory, Proc. Symp.on the Theoretical Background to the Planning of Open Pit Mines, Johannesburg, South Africa, 55-71. ## Singh, B. 1973, Continuum characterization of jointed rock masses, Part 1- the constitutive equations: Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 10, p. 311-335. ## Serafim, J.L., Pereira, J.P., 1983, Consideration of the geomechanical classification of Bieniawski, Proc. Int. Symp. Eng. Geol. under- ground, Construction. Lisbon. 1, p. 33-44. ## Sonmez, H., Gokceoglu, C., & Ulusay, R., 2004, Indirect determination of the modulus of deformation of rock mass based on the GSI system, Int. J. Rock Mech. Min Sci.,1, p. 849-57. ## Goodman, RE. 1993. Engineering Geology, Rock in engineering construction. John wiley & sons, Inc. ## Scholtz, RA. 1996. Relative scale and the strength and deformability of rock messes, J. struct Geol. 18(9): 1139-1149. ## Wu, Q., Kulatilake, P.H.S.W., 2012, REV and its properties on fracture system and mechanical properties and orthotropic constitutive model for a jointed rock mass in a dam site in China, Comput. Geotech., 43, p. 124-42. ## Wang, Y., Adeyemi Emman Aladejare. 2019. Estimation of rock mass deformation modulus using indirect information multiple sources. Tunneling and underground space technology. 85,78-83. ## Yang, Z.Y., Chen, J.M., & Huang, T.H., 1998, Effect of joint sets on the strength and deformation of rock mass models, Int. J. Rock Mech. Min. Sci., 35, p. 75-84. ##
Volume 19, Issue 62
Winter 2024
Pages 61-93

  • Receive Date 18 October 2023
  • Revise Date 04 March 2024
  • Accept Date 07 May 2024