Geomechanics and Engineering

  • 제13권3호
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  • Pages.489-504
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  • 2017
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  • 2005-307X(pISSN)
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  • 2092-6219(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A displacement solution for circular openings in an elastic-brittle-plastic rock

  • Huang, Houxu (State Key Laboratory of Disaster Prevention and Mitigation of Explosion and Impact, PLA University of Science and Technology) ;
  • Li, Jie (State Key Laboratory of Disaster Prevention and Mitigation of Explosion and Impact, PLA University of Science and Technology) ;
  • Rong, Xiaoli (State Key Laboratory of Disaster Prevention and Mitigation of Explosion and Impact, PLA University of Science and Technology) ;
  • Hao, Yiqing (State Key Laboratory of Disaster Prevention and Mitigation of Explosion and Impact, PLA University of Science and Technology) ;
  • Dong, Xin (State Key Laboratory of Disaster Prevention and Mitigation of Explosion and Impact, PLA University of Science and Technology)
  • 투고 : 2015.11.02
  • 심사 : 2017.04.05
  • 발행 : 2017.09.25
⟨ 이전 논문 다음 논문 ⟩

초록

The localized shear and the slip lines are easily observed in elastic-brittle-plastic rock. After yielding, the strength of the brittle rock suddenly drops from the peak value to the residual value, and there are slip lines which divide the macro rock into numbers of elements. There are slippages of elements along the slip lines and the displacement field in the plastic region is discontinuous. With some restraints, the discontinuities can be described by the combination of two smooth functions, one is for the meaning of averaging the original function, and the other is for characterizing the breaks of the original function. The slip lines around the circular opening in the plastic region of an isotropic H-B rock which subjected to a hydrostatic in situ stress can be described by the logarithmic spirals. After failure, the deformation mechanism of the plastic region is mainly attributed to the slippage, and a slippage parameter is introduced. A new analytical solution is presented for the plane strain analysis of displacements around circular openings. The displacements obtained by using the new solution are found to be well coincide with the exact solutions from the published sources.

키워드

과제정보

연구 과제 주관 기관 : National Natural Science Foundation of China

참고문헌

  1. Alejano, L.R., Dono, R.A. and Veiga, M. (2012), "Platic radii and longitudinal deformation profiles of tunnels excavated in strain-softening rock masses", Tunn. Undergr. Sp. Technol., 30, 169-182. https://doi.org/10.1016/j.tust.2012.02.017
  2. Brown, E.T., Bray, J.W. and Ladanyi, B. (1983), "Ground response curves for rock tunnel", ASCE J. Geotech. Eng., 109(1), 15-39. https://doi.org/10.1061/(ASCE)0733-9410(1983)109:1(15)
  3. Carranze, T.C. (2004), "Elastoplastic solution of tunnel problems using the generalized form of Hoek-Brown failure criterion", Int. J. Rock. Mech. Min. Sci., 41(3), 629-639.
  4. Carranze, T.C. and Fairhurst, C. (1999), "The elatio-plastic response of underground excavations in rock masses that satisfy the Hoek-Brown failure criteria", Int. J. Rock. Mech. Min. Sci., 36(6), 777-809. https://doi.org/10.1016/S0148-9062(99)00047-9
  5. Eringen, A.C. and Suhubi, E.S. (1975), Elastodynamics:Finite Motions, Academic Press, New York-London.
  6. Hoek, E. and Brown, E.T. (1980), Underground Excavations in Rock, The Institution of Mining and Metallurgy, London, UK.
  7. Hoek, E., Kaiser, P.K. and Bawden, W.F. (1998), Support of Underground Excavations in Hard Rock, Balkema, Rotterdam, Netherlands.
  8. Huang, H.X., Fan, P.X., Li, J., Wang, M.Y. and Rong, X.L. (2016), "A theoretical explanation for rock core disking in triaxial unloading test by considering local tensile stress", Acta Geophys., 64(5), 430-1445.
  9. Huang, K.Z., Xue, M.D. and Lu, W.M. (2003), Tensor Analysis, TsingHua Press, Beijing, China.
  10. Jaegar, J.C. and Cook, N.G.W. (1979), Fundamental of Rock Mechanics, Champman and Hall, London, UK.
  11. Kachanov, L.M. (1971), Foundations of the Theory of Plasticity, Elsevier.
  12. Liu, X.R., Li, D.L., Wang, J.B. and Wang, Z. (2015), "Surrounding rock pressure of shallow-buried bilateral bias tunnels under earthquake", Geomech. Eng., Int. J., 9(4), 19-37.
  13. Mohammadi, M. and Tavakoli, H. (2015), "Comparing the generalized Hoek-Brown and Mohr-Coulomb failure criteria for stress analysis on the rocks failure plane", Geomech. Eng., Int. J., 9(1), 115-124.
  14. Muller, A.L., do Amaral Vargas, E. and Goncalves, C.J. (2014), "Numerical simulation of solids production in slip-lines type breakout modes using standard and Cosserat continua", J. Petrol. Sci. Eng., 122, 134-148. https://doi.org/10.1016/j.petrol.2014.06.027
  15. Park, K.H. (2014), "Similarity solution for a spherical or circular opening in elastic-strain softening rock mass", Int. J. Rock. Mech. Min. Sci., 71, 151-159.
  16. Park, K.H. and Kim, Y.J. (2006), "Analytical solution for a circular opening in an elastic-brittle-plastic rock", Int. J. Rock. Mech. Min. Sci., 43(4), 616-622. https://doi.org/10.1016/j.ijrmms.2005.11.004
  17. Qi, C.Z., Wang, M.Y., Bai, J.P. and Li, K.R. (2014), "Mechanism underlying dynamic size effect on rock mass strength", Int. J. Impact Eng., 68, 1-7. https://doi.org/10.1016/j.ijimpeng.2014.01.005
  18. Revuzhenko, A.F. and Shemyakin, E.I. (1977), "Problem of plane strain of hardening and softening plastic materials", J. Appl. Mech. Tech. Phys., 18(3), 406-420. https://doi.org/10.1007/BF00851669
  19. Sharan, S.K. (2005), "Exact and approximate solutions for displacements around circular openings in elastic-brittle-plastic Hoek-Brown rock", Int. J. Rock. Mech. Min. Sci., 42(4), 542-549. https://doi.org/10.1016/j.ijrmms.2005.03.019
  20. Serrano, A., Olalla, C. and Reig, I. (2011), "Convergence of circular tunnels in elastoplastic rock masses with non-linear failure criteria and non-associated flow laws", Int. J. Rock. Mech. Min. Sci., 48(6), 878-887. https://doi.org/10.1016/j.ijrmms.2011.06.008
  21. Van den Hoek, P.J. (2001), "Prediction of different types of cavity failure using bifurcation theory", Proceedings of the 38th Symposium of the American Rock Mechanics Association, Washington, D.C., USA, July, pp. 45-52.
  22. Vincenzo, S. and Ghassan, A.S. (2012), "Analytical solution for undrained plane strain expansion of cylindrical cavity in modified cam clay", Geomech. Eng., Int. J., 4(1), 19-37. https://doi.org/10.12989/gae.2012.4.1.019
  23. Vu, T.M., Sulem, J., Subrin, D. and Monin, N. (2013), "Semi-analytical solution for stresses and displacements in a tunnel excavated in transversely isotropic formation with non-linear behavior", Rock Mech. Rock Eng., 46(2), 213-229. https://doi.org/10.1007/s00603-012-0296-0
  24. Wang, Y. (1996), "Ground response of circular tunnel in poorly consolidated rock", ASCE J. Geotech. Eng, 122(9), 703-708. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:9(703)
  25. Wang, S.L., Zheng, H., Li, C.G. and Ge, X.R. (2011), "A finite element implementation of strain-softening rock mass", Int. J. Rock. Mech. Min. Sci., 48(1), 67-76. https://doi.org/10.1016/j.ijrmms.2010.11.001
  26. Xiao, Y., Liu, H.L., Zhu, J.G. and Shi, W.C. (2012a), "Modeling and behaviours of rockfill materials in three-dimensional stress space", Sci. China Tech. Sci., 55(10), 2877-2892. https://doi.org/10.1007/s11431-012-4979-2
  27. Xiao, Y., Liu, H. and Yang, G. (2012b), "Formulation of cross-anisotropic failure criterion for granular material", Int. J. Geomech., 12(2), 182-188. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000136
  28. Xiao, Y., Liu, H., Desai, C.S., Sun, Y. and Liu, H. (2016), "Effect of intermediate principal-stress ratio on particle breakage of rockfill material", J. Geotech. Geoenviron. Eng., 142(4), 06015017. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001433
  29. Yao, Y.P., Lu, D.C., Zhou, A.N. and Zou, B. (2004), "Generalized non-linear strength theory and transformed stress space", Sci. China Tech. Sci., 47(6), 691-709. https://doi.org/10.1360/04ye0199
  30. Zhang, Q., Jiang, B.S., Wang, S.L., Ge, X.R. and Zhang H.Q. (2012), "Elasto-plastic analysis of a circular opening in strain-softening rock mass", Int. J. Rock. Mech. Min. Sci., 50, 38-46. https://doi.org/10.1016/j.ijrmms.2011.11.011

피인용 문헌

  1. Evaluation of Excavation-Damaged Zone around Underground Tunnels by Theoretical Calculation and Field Test Methods vol.12, pp.9, 2017, https://doi.org/10.3390/en12091682