Tunnel and Underground Space (터널과지하공간)

Korean Society for Rock Mechanics and Rock Engineering (한국암반공학회)
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Application of Slip-line Method to the Evaluation of Plastic Zone around a Circular Tunnel

원형터널 주변의 소성영역 평가를 위한 slip-line 해석법 활용

  • Lee, Youn-Kyou (Department of Coastal Construction Engineering, Kunsan National University)
  • 이연규 (군산대학교 건축.해양건설융합공학부)
  • Received : 2022.09.28
  • Accepted : 2022.10.17
  • Published : 2022.10.31
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Abstract

The generalized Hoek-Brown (GHB) criterion, which is recognized as one of the standard failure conditions for rock mass, is specialized for rock engineering applications and covers a wide range of rock mass conditions. Accordingly, many research efforts have been devoted to the incorporation of this criterion into the stability analysis of rock structures. In this study, the slip-line analysis method, which is a kind of elastoplastic analysis method, is combined with the GHB failure criterion to derive analytical equations that can easily calculate the plastic radius and stress distribution in the vicinity of the circular tunnel. In the process of derivation of related formulas, it is assumed that the behavior of rock mass after failure is perfectly plastic and the in-situ stress condition is hydrostatic. In the formulation, it is revealed that the plastic radius can be calculated analytically using the two respective tangential friction angles corresponding to the stress conditions at tunnel wall and elastic-plastic boundary. It is also shown that the plastic radius and stress distribution calculated using the derived analytical equations coincide with the results of Lee & Pietruszczak's numerical method published in 2008. In the latter part of this paper, the influence of the quality of the rock mass on the size of the plastic zone, the stress distribution, and the change of the tangential friction angle was investigated using the derived analytical equations.

암반의 표준 파괴기준식의 하나로 인정받고 있는 일반화된 Hoek-Brown (GHB) 식은 암반공학적 활용에 특화되어 있으며 넓은 범위의 암반조건을 고려할 수 있다. 이에 따라 암반 구조물의 안정성 해석과정에서 GHB 식을 적극적으로 활용하기 위한 많은 연구 노력이 진행 중이다. 이 연구에서는 탄소성 해석법의 일종인 slip-line 해석법을 GHB 파괴기준식과 결합하여 원형터널 주변의 소성반경과 응력분포를 간편하게 계산할 수 있는 해석적 수식들을 유도하였다. 관련 수식 유도과정에서는 파괴 후 거동으로 완전 소성 거동을 가정하였고, 초기지압은 정수압 상태로 가정하였다. 이 연구를 통하여 소성반경은 터널 벽면과 탄성-소성 경계면에 대응되는 두 접선 마찰각을 이용하여 해석적으로 계산할 수 있음을 밝혔다. 또한 유도한 해석 식들을 이용하여 계산한 소성반경과 응력분포는 2008년에 발표된 Lee & Pietruszczak의 수치해석적 방법의 결과와 일치함을 보였다. 이 논문의 후반부에서는 유도한 해석 식을 활용하여 암반의 양호도가 소성영역의 크기, 응력분포, 접선마찰각의 변화에 미치는 영향을 분석하였다.

Keywords

Acknowledgement

이 논문은 정부(과학기술정보통신부)의 재원으로 한국연구재단의 지원을 받아 수행된 연구임(No.2021R1F1A1048311).

References

  1. Alonso, E., Alejano, L.R., Varas, F., Fdez-Manin, G., and Carranza-Torres, C., 2003, Ground response cureves for rock masses exhibiting strain-softening behaviour, Int. J. Numer. Anal. Meth. Geomech., 27, 1153-85. https://doi.org/10.1002/nag.315
  2. Brady, B.H.G and Brown, E.T., 2004, Rock mechanics for underground mining (3rd ed.), Kluwer Academic Publishers, Boston.
  3. Brown, E.T., Bray, J.W., Ladanyi, B., and Hoek, E., 1983, Ground response curves for rock tunnels, ASCE J. Geotech. Eng. Div., 109(1), 15-39. https://doi.org/10.1061/(ASCE)0733-9410(1983)109:1(15)
  4. Carranza-Torres, C. and Fairhurst, C., 1999, The elasto-plastic response of underground excavation in rock masses that satisfy the Hoek-Brown failure criterion, Int. J. of Rock Mech. & Min. Sci., 36, 777-809. https://doi.org/10.1016/S0148-9062(99)00047-9
  5. Carranza-Torres, C., 2004, Elasto-plastic solution of tunnel problems using the generalized form of the Hoek-Brown failure criterion, Int. J. of Rock Mech. & Min. Sci., 41(Supp. 1), 1-11.
  6. Carter, J.P., Booker, J.R., and Yeung, S.K., 1986, Cavity expansion in cohesive frictional soils, Geotechnique, 36, 349-58. https://doi.org/10.1680/geot.1986.36.3.349
  7. Das, B.M, 1997, Principles of geotechnical engineering (4th Ed.), PWS Publishing Company, Boston.
  8. Davis, R.O. and Selvadurai, A.P.S., 2002, Plasticity and Geomechanics, Cambridge University Press, New York.
  9. Hoek, E. and Brown, E.T., 1980, Underground excavations in rock, Institution of Mining and Metallurgy, London
  10. Hoek, E. and Brown, E.T., 1997, Practical estimation of rock mass strength, Int. J. of Rock Mech. & Min. Sci., 34(8), 1165-86. https://doi.org/10.1016/S1365-1609(97)80069-X
  11. Hoek, E., Carranza-Torres, C., and Corkum, B., 2002, Hoek-Brown failure criterion - 2002 Edition, Proc. NARM-TAC Conf., Toronto, 1, 267-273.
  12. Hoek, E., Marinos, P., and Benissi, M., 1998, Applicability of the geological strength index (GSI) classification for very weak and sheared rock mass, The case of the Athens Schist Formation, Bull. Eng. Geol. Env., 57, 151-60. https://doi.org/10.1007/s100640050031
  13. Kumar, P., 1998, Shear failure envelope of Hoek-Brown criterion for rock mass, Tunn. Undergr. Space Technol., 13(4), 453-58. https://doi.org/10.1016/S0886-7798(98)00088-1
  14. Lee, Y.K. and Pietruszczak, S., 2008, A new numerical procedure for elasto-plastic analysis of a circular opening excavated in a strain-softening rock mass, Tunn. Undergr. Sp. Tech., 23(5), 588-599. https://doi.org/10.1016/j.tust.2007.11.002
  15. Lee, Y.-K. and Pietruszczak, S., 2017, Analytical representation of Mohr failure envelope approximating the generalized Hoek-Brown failure criterion, Int. J. of Rock Mech. & Min. Sci., 100, 90-9. https://doi.org/10.1016/j.ijrmms.2017.10.021
  16. Lee, Y.-K. and Pietruszczak, S., 2021, Limit Equilibrium Analysis Incorporating the Generalized Hoek-Brown Criterion, Rock. Mech. Rock Eng., 54, 4407-18. https://doi.org/10.1007/s00603-021-02518-8
  17. Lee, Y.K., 2018, Approximate Shear Strength Formula Implied in the Generalized Hoek-Brown Failure Criterion, Tunnel & Underground Space (J. Korean Soc. Rock Mech.), 28(5), 426-41.
  18. 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. https://doi.org/10.1016/j.ijrmms.2014.07.003
  19. 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
  20. Serrano, A., Ollala, 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, 1013-18. https://doi.org/10.1016/S1365-1609(00)00028-9
  21. Sharan, S.K., 2008, Analytical solutions for stresses and displacements around a circular opening in a generalized Hoek-Brown rock, Int. J. Rock Mech. & Min., 45(1), 78-85. https://doi.org/10.1016/j.ijrmms.2007.03.002
  22. Sofianos, A.I., 2003, Tunnelling Mohr-Coulomb strength parameters for rock masses satisfying the generalized Hoek-Brown criteiron, Int. J. of Rock Mech. & Min. Sci., 40, 435-40. https://doi.org/10.1016/S1365-1609(03)00017-0
  23. Wang, R. and Skirrow, R., 2008, Slip line solution by spreadsheet, Proc. GeoEdmonton'08: 61st Canadian Geotech. Conf., Edmonton, 382-7.