DOI QR코드

DOI QR Code

Theoretical model for the shear strength of rock discontinuities with non-associated flow laws

  • Galindo, Ruben (Department of Geotechnical Engineering, Technical University of Madrid) ;
  • Andres, Jose L. (Department of Geotechnical Engineering, Technical University of Madrid) ;
  • Lara, Antonio (Department of Geotechnical Engineering, Technical University of Madrid) ;
  • Xu, Bin (Department of Civil Engineering, College of Civil Engineering and Architecture, Zhejiang University) ;
  • Cao, Zhigang (Department of Civil Engineering, College of Civil Engineering and Architecture, Zhejiang University) ;
  • Cai, Yuanqiang (Department of Civil Engineering, College of Civil Engineering and Architecture, Zhejiang University)
  • 투고 : 2020.05.06
  • 심사 : 2021.01.28
  • 발행 : 2021.02.25

초록

In an earlier publication (Serrano et al. 2014), the theoretical basis for evaluating the shear strength in rock joints was presented and used to derive an equation that governs the relationship between tangential and normal stresses on the joint during slippage between the joint faces. In this paper, the theoretical equation is applied to two non-linear failure criteria by using non-associated flow laws, including the modified Hoek and Brown and modified Mohr-Coulomb equations. The theoretical model considers the geometric dilatancy, the instantaneous friction angle, and a parameter that considers joint surface roughness as dependent variables. This model uses a similar equation structure to the empirical law that was proposed by Barton in 1973. However, a good correlation with the empirical values and, therefore, Barton's equation is necessary to incorporate a non-associated flow law that governs breakage processes in rock masses and becomes more significant in highly fractured media, which can be induced in a rock joint. A linear law of dilatancy is used to assess the importance of the non-associated flow to obtain very close values for different roughness states, so the best results are obtained for null material dilatancy, which considers significant changes that correspond to soft rock masses or altered zones of weakness.

키워드

참고문헌

  1. Alejano, L.R. and Alonso E. (2005), "Considerations of the dilatancy angle of rocks and rock masses", Int. J. Rock Mech. Sci. Geomech. Abstr., 42(4), 481-487. https://doi.org/10.1016/j.ijrmms.2005.01.003.
  2. Archambault, G., Roleau, A., Daigneault, R. and Flamand, R. (1993), "Progresive failure of rock masses by a self similar anastomosing process of rupture at all scales and its scale effects on their shear strength", Proceedings of the 2nd International Workshop on Scale Effects in Rock Masses, Lisboa, Portugal, June.
  3. Asadollahi, P. (2009), "Stability analysis of a single three dimensional rock block: effect of dilatancy and high-velocity water jet impact", Ph.D. Dissertation, University of Texas, Austin, Texas, U.S.A.
  4. Barton, N. (1973), "Review of a new shear strength criterion for rock joints", Eng. Geol., 7, 287-332. https://doi.org/10.1016/0013-7952(73)90013-6.
  5. Barton, N. and Bandis, S. (1982), "Effects of block size on the shear behavior of jointed rock", Proceedings of the 23rd US Symposium on Rock Mechanics, Berkeley, California, U.S.A., August.
  6. Belem, T. (2016), "Quantitative parameters of primary roughness for describing the morphology of surface discontinuities at various scales ", Geomech. Eng., 11(4), 515- 530. https://doi.org/10.12989/gae.2016.11.4.515.
  7. Belem, T., Souley, M. and Homand F. (2007), "Modelling surface rougness degradation of rock joint wall during monotonic and cyclic shearing", Acta Geotech., 2(4), 227-248. https://doi.org/10.1007/s11440-007-0039-7.
  8. Chong, S., Kim, J., Cho, G. and Song, K. (2020), "Preliminary numerical study on long-wavelength wave propagation in a jointed rock mass", Geomech. Eng., 21(3), 227- 236. https://doi.org/10.12989/gae.2020.21.3.227.
  9. Fairhurst, C. (2003), "Stress determination in rock: A brief history and review", Int. J. Rock Mech. Min. Sci., 40(7-8), 957-973. https://doi.org/10.1016/j.ijrmms.2003.07.002.
  10. Gens, A., Carol, I. and Alonso, E.E. (1990), "A constitutive model for rock joints, formulation and numerical implementation", Comput. Geotech. 9, 3-20. https://doi.org/10.1016/0266-352X(90)90026-R.
  11. Grasselli, G. and Egger, P. (2003), "Constitutive law for the shear strength of rock joints based on three-dimensional surface parameters", Int. J. Rock Mech. Min. Sci., 40(1), 25-40. https://doi.org/10.1016/S1365-1609(02)00101-6.
  12. Heuze, F.E. and Barbour, T.G. (1982) "New models for rock joints and interfaces", J. Geotech. Eng. Div., 108(5), 757-76. https://doi.org/10.1061/(ASCE)0733-9410(1983)109:7(1011).
  13. Hoek, E. and Brown, E.T. (1997), "Practical estimates of rock mass strength", Int. J. Rock Mech. Sci. Geomec. Abstr., 34(8), 1165-1187. https://doi.org/10.1016/S1365-1609(97)80069-X.
  14. Hoek, E., Carranza-Torres, C. and Corkum B. (2002), "Hoek-Brown failure criterion - 2002 Edition", Proceedings of the NARMS-TAC 2002, Mining Innovation and Technology, Toronto, Canada, July.
  15. Hoek, E., Marinos, P. and Benissi, M. (1998), "Applicability of the geological strength index (GSI) classification for weak and sheared rock masses; The case of the Athens schist formation", B. Eng. Geol. Environ., 57(2), 151-160. https://doi.org/10.1007/s100640050031.
  16. Hu, W. and Lin, H. (2018), "Non-linear shear strength criterion for a rock joint with consideration of friction variation", Geotech. Geol. Eng., 36(6), 3731-3741. https://doi.org/10.1007/s10706-018-0567-y.
  17. Huang, S.L., Oelfke, S.M. and Speck, R.C. (1992), "Applicability of fractal characterization and modelling to rock joint profile", Int. J. Rock Mech. Min. Sci., 29, 89-98. https://doi.org/10.1016/0148-9062(92)92120-2.
  18. Jaeger, J.C. (1971), "Friction of rocks and stability of rock slopes", Geotecnique 21(2), 97-34. https://doi.org/10.1680/geot.1971.21.2.97.
  19. Ladanyi, B. and Archambault, G. (1969), "Simulations of the shear behavior of a jointed rock mass", Proceedings of the 11th US Symposium on Rock Mechanics, Berkeley, California, U.S.A. June.
  20. Lee, Y.H., Carr, J.R., Barr, D.J. and Haas, C.J. (1990), "The fractal dimension as a measure of the roughness of rock discontinuity profiles", Int. J. Rock Mech. Min. Sci., 27, 453-464. https://doi.org/10.1016/0148-9062(90)90998-H.
  21. Leichnitz, W. (1985), "Mechanical properties of rock joints", Int. J. Rock Mech. Min. Sci., 22(5), 313-321. https://doi.org/10.1016/0148-9062(85)92063-7.
  22. Lin, H., Hu, W., Chen, Y., Cao, R., Wang, Y., Yong, R. and Du, S. (2020), "Shear resistance of rock joint under nonuniform normal stress", Adv. Mater. Sci. Eng., 1-8. https://doi.org/10.1155/2020/9316482.
  23. Muralha, J. (1995), Fractal Dimension of Joint Roughness Surfaces, Balkema, Rotterdam, The Netherlands.
  24. Patton, F.D. (1966), "Multiple modes of shear failure in rock", Proceedings of the 1st Congress of International Society of Rock Mechanics, Lisboa, Portugal, September.
  25. Plesha, M.E. (1987), "Constitutive models for rock discontinuities with dilatancy and surface degradation", Int. J. Numer. Anal. Meth. Geomech., 11(4), 345-362. https://doi.org/10.1002/nag.1610110404.
  26. Qiu, X., Plesha, M.E, Huang, X. and Haimson, B.C. (1993), "An investigation of the mechanics of rock joints-part II: Analytical investigation", Int. J. Rock Mech. Min. Sci., 30(3), 271-287. https://doi.org/10.1016/0148-9062(93)92730-E.
  27. Saeb, S. and Amadei, B. (1992), "Modeling rock joints under shear and normal loading", Int. J. Rock Mech. Min. Sci., 29(3), 267-278. https://doi.org/10.1016/0148-9062(92)93660-C.
  28. Samadhiya, N.K., Viladkar, M.N. and Al-Obaydi, M.A. (2008) "Three-dimensional joint/interface element for rough undulating major discontinuities in rock masses", Int. J. Geomech., 8(6), 327-335. https://doi.org/10.1061/(ASCE)1532-3641(2008)8:6(327).
  29. Schneider, H.J. (1976), "The friction and deformation behavior of rock joints", Rock Mech. Rock Eng., 8(3), 169-184. https://doi.org/10.1007/BF01239813.
  30. Serrano, A. and Olalla, C. (1994), "Ultimate bearing capacity of rock masses", Int. J. Rock Mech. Min. Sci., 31(2), 93-106. https://doi.org/10.1016/0148-9062(94)92799-5.
  31. Serrano, A., Olalla, C. and Galindo, R.A. (2014), "Micromechanical basis for shear strength of rock discontinuities", Int. J. Rock Mech. Min Sci., 70, 33-46. https://doi.org/10.1016/j.ijrmms.2014.02.021.
  32. Serrano, A., Olalla, C. and Gonzalez, J. (2000), "Ultimate bearing capacity of rock masses based on the modified Hoek-Brown criterion", Int. J. Rock Mech. Min. Sci., 37(6), 1013-1018. https://doi.org/10.1016/S1365-1609(00)00028-9.
  33. Singh, M., Raj, A. and Singh, B. (2011), "Modified Mohr-Coulomb criterion for non-linear triaxial and polyaxial strength of intact rocks", Int. J. Rock Mech. Min. Sci., 48(4), 546-555. https://doi.org/10.1016/j.ijrmms.2011.02.004.
  34. Singh, M. and Singh, B. (2012), "Modified Moh-Coulomb criterion for non-linear triaxial and polyaxial strength of jointed rocks", Int. J. Rock Mech. Min. Sci., 51, 43-52. https://doi.org/10.1016/j.ijrmms.2011.12.007.
  35. Tse, R. and Cruden, D.M. (1979), "Estimating joint roughness coefficients", Int. J. Rock Mech. Min. Sci., 16(5), 303-307. https://doi.org/10.1016/0148-9062(79)90241-9.
  36. Veermer, P.A and De Borst, R. (1984), "Non-associated plasticity for soils, concrete and rock", Heron, 29(3). https://doi.org/10.1016/0148-9062(79)90241-9.
  37. Xie, H., Wang, J.A. and Kwasniewski, M.A. (1999), "Multifractal characterization of rock fracture surfaces", Int. J. Rock Mech. Min. Sci., 36, 19-27. https://doi.org/10.1016/S0148-9062(98)00172-7.
  38. Zhang, X., Yi, B., Jiang, Q., Feng, X. and Chen, N. (2017), "Evaluation models for the peak shear-strength and shear-resistance components of rough rock joints", J. Test. Eval., 45(6), 20170134. https://doi.org/10.1520/JTE20170134.
  39. Zhao, L., Jiao, K., Zuo, S., Yu, C. and Tang, G. (2020), "Pseudo-static stability analysis of wedges based on the nonlinear Barton-Bandis failure criterion", Geomech. Eng., 20(4), 287-297. https://doi.org/10.12989/gae.2020.20.4.287.