터널과지하공간 (Tunnel and Underground Space)

  • 제23권3호
  • /
  • Pages.219-227
  • /
  • 2013
  • /
  • 1225-1275(pISSN)
  • /
  • 2287-1748(eISSN)
한국암반공학회 (Korean Society for Rock Mechanics and Rock Engineering)
권호 표지
DOI QR코드

DOI QR Code

비선형 암석 파괴조건식의 접선 마찰각과 점착력의 중간주응력 의존성

Dependency of Tangential Friction Angle and Cohesion of Non-linear Failure Criteria on the Intermediate Principal Stress

  • 이연규 (군산대학교 해양과학대학 해양건설공학과) ;
  • 최병희 (한국지질자원연구원 지구환경연구본부)
  • 투고 : 2013.05.06
  • 심사 : 2013.05.23
  • 발행 : 2013.06.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Mohr-Coulomb 파괴조건식은 암반구조물의 설계에 활발히 이용되고 있지만 암석의 비선형 강도특성과 중간주응력이 강도에 미치는 영향을 고려할 수 없다는 단점을 가지고 있다. 이러한 단점을 극복하기 위하여 Hoek-Brown 파괴조건식이 제안되었으며 최근 중간주응력의 영향을 고려할 수 있는 여러 3-D 파괴조건식들이 제안되고 있다. 그러나 아직까지도 많은 암반공학적 설계과정에서 Mohr-Coulomb 파괴조건식을 이용하여 암반의 파괴 가능성이 평가되고 있고 대부분의 현장 기술자들도 내부마찰각과 점착력으로 암반의 강도특성을 이해하는데 익숙하다. 그러므로 Mohr-Coulomb 파괴조건식에 비해 개선된 비선형 혹은 3-D 파괴조건식의 접선마찰각 및 접선점착력이 구해지면 기존의 Mohr-Coulomb 파괴조건식을 활용하는 틀 안에서 개선된 파괴조건식들의 장점을 이용하는 것이 가능하다. 본 연구에서는 접선마찰각과 접선점착력을 응력불변량으로 표시하는 방법을 제시하고 이를 일반화된 Hoek-Brown 파괴조건식과 Hoek-Brown 파괴조건식을 3-D로 확장시킨 HB-WW 파괴조건식에 적용하였다. 또한 파괴조건식의 중간주응력 의존성을 3차원 주응력 공간에서 기하학적으로 해석하는 새로운 접근법을 제안하였다. 제안된 방법의 실행 사례를 통해 HB-WW 파괴함수의 접선마찰각과 접선점착력은 2-D 파괴함수의 경우와 달리 중간주응력의 크기에 상당한 영향을 받음을 보였다.

Although Mohr-Coulomb failure criterion has limitations in that it is a linear criterion and the effect of the intermediate principal stress on failure is ignored, this criterion has been widely accepted in rock mechanics design. In order to overcome these shortcomings, the Hoek-Brown failure criterion was introduced and recently a number of 3-D failure criteria incorporating the effect of the intermediate principal stress on failure have been proposed. However, in many rock mechanics designs, the possible failure of rock mass is still evaluated based on Mohr-Coulomb criterion and most of practitioners are accustomed to understanding the strength of rock mass in terms of the internal friction angle and cohesion. Therefore, if the equivalent Mohr-Coulomb strength parameters of the advanced failure criteria are calculated, it is possible to take advantage of the advanced failure criteria in the framework of the Mohr-Coulomb criterion. In this study, a method expressing the tangential Mohr-Coulomb strength parameters in terms of the stress invariant is proposed and it is applied to the generalized Hoek-Brown criterion and the HB-WW criterion. In addition, a new approach describing the geometric meaning of the ${\sigma}_2$-dependency of failure criteria in 3-D principal stress space is proposed. Implementation examples of the proposed method show that the influence of the intermediate principal stress on the tangential friction angle and cohesion of the HB-WW criterion is considerable, which is not the case for the 2-D failure criterion.

키워드

참고문헌

  1. Al-Ajmi, A.M. and Zimmerman, R.W., 2006, Stability analysis of vertical boreholes using the Mogi-Coulomb failure criterion, Int J. Rock Mech. Min. Sci., 43, 1200-1211. https://doi.org/10.1016/j.ijrmms.2006.04.001
  2. Balmer, G., 1952, A general analytical solution for Mohr's envelope. American Society of Testing and Materials Vol. 52, pp. 1260-1271.
  3. Benz, T., Schwab, R., Kauther, R.A. and Vermeer, P.A., 2008, A Hoek-Brown criterion with intrinsic material strength factorization, Int. J. Rock Mech. Min. Sci., Vol. 45, pp. 210-222. https://doi.org/10.1016/j.ijrmms.2007.05.003
  4. Benz, T. and Schwab, R., 2008, A quantitative comparison of six rock failure criteria, Int J. Rock Mech. Min. Sci., 45, 1176-1186. https://doi.org/10.1016/j.ijrmms.2008.01.007
  5. Chang, C. and Haimson, B.C., 2000, A new triaxial cell for testing mechanical properties of rock and its use to determine rock strength and deformability of Westerly granite, Int. J. Rock Mech. Min. Sci., Vol. 37, pp. 285-296. https://doi.org/10.1016/S1365-1609(99)00106-9
  6. Choi, S.O. and Deb, D., 2005, Supplementation of generalized Hoek-Brown Yield surface through the singularity adjustment in elastic-plastic analysis, Geosytem Engineering, Vol. 8, No. 2, pp. 43-50. https://doi.org/10.1080/12269328.2005.10541235
  7. Colmenares, L.B. and Zoback, M.D., 2002, A statistical evaluation of intact rock failure criteria constrained by polyaxial test data for five different rocks, Int J. Rock Mech. Min. Sci., 39, 695-729. https://doi.org/10.1016/S1365-1609(02)00048-5
  8. Deb, D. and Choi, S.O., 2005, Comparison between direct and indirect implementation of generalized Hoek and Brown failure criterion in numerical analysis procedure, J. Korean Soc. Rock Mech. (Tunnel and Underg. Space), Vol. 15, No. 3, pp. 228-235.
  9. Drucker, D. and Prager, W., 1952, Soil mechanics and plastic analysis or limit design. Q. Appl. Math., Vol. 10, pp. 157-165. https://doi.org/10.1090/qam/48291
  10. Hoek, E. and Brown, E.T., 1980, Underground excavation in rock, Institute of Mining and Metallurgy, London.
  11. Hoek, E., 1990, Estimating Mohr-Coulomb friction and cohesion values from the Hoek-Brown failure criterion. Int. J. Rock Mech. Min. Sci., Vol. 27, No. 3, pp. 227-229.
  12. Hoek, E., Carranza-Torres and C., Corkum, B., 2002, Hoek-Brown criterion - 2002 edition. Proc NARMS-TAC Conf, Toronto, Vol. 1, pp. 267-273.
  13. Lee, Y.-K., 2011, Study on a 3-dimensional rock failure criterion approximating to Mohr-Coulomb surface, Korean Soc. Rock Mech. (Tunnel and Underg. Space), Vol. 21, No. 2, pp. 93-102.
  14. Lee, Y.-K., Song, W.-K., Park, C. and Choi, B.-H., 2011, Stability analysis of concrete plugs using a 3-D failure criterion, Korean Soc. Rock Mech. (Tunnel and Underg. Space), Vol. 21, No. 6, pp. 526-535.
  15. Lee, Y.-K. and Choi, B.-H., 2012, Equivalent friction angle and cohesion of the generalized Hoek-Brown failure criterion in terms of stress invariants, Korean Soc. Rock Mech. (Tunnel and Underg. Space), Vol. 22, No. 6, pp. 462-470. https://doi.org/10.7474/TUS.2012.22.6.462
  16. Lee, Y.-K. and Jeon, S., 2009, Homogenization of elastic cracks in Hoek-Brown rock, J. Korean Soc. Rock Mech. (Tunnel and Underg. Space), Vol. 19, No. 2, pp. 158-166.
  17. Lee, Y.-K., 2012, Comparative study on the rock failure criteria taking account of the intermediate principal stress, Korean Soc. Rock Mech. (Tunnel and Underg. Space), Vol. 22, No. 1, pp. 12-21. https://doi.org/10.7474/TUS.2012.22.1.012
  18. Lee, Y.-K., Pietruszczak, S. and Choi, B.-H., 2012, Failure criteria for rocks based on smooth approximations to Mohr-Coulomb and Hoek-Brown failure functions, Int. J. Rock Mech. & Min. Sci., Vol. 56, pp. 146-160. https://doi.org/10.1016/j.ijrmms.2012.07.032
  19. Lee, Y.-K. and Bobet, A., 2013, Instantaneous friction angle and cohesion of 2-D and 3-D Hoek-Brown failure criterion in terms of stress invariants, Rock Mech. Rock Eng., DOI: 10.1007/s00603-013-0423-6.
  20. Marinos, P. and Hoek, E., 2000, GSI: a geologically friendly tool for rock mass strength estimation. Proc. Int. Conf. on Geotechnical & Geological Engineering, GeoEng 2000, Melbourne, pp. 1422-1442.
  21. Mogi, K., 2007, Experimental rock mechanics, Taylor & Francis.
  22. Nayak, G.C. and Zienkiewicz, O.C., 1972, Convenient forms of stress invariants for plasticity. J. Struct. Div. ASCE, Vol. 98, pp. 949-953.
  23. Willam, K.J. and Warnke, E.P., 1972, Constitutive model for triaxial behavior of concrete, Colloquium on Concrete Structures Subjected to Triaxial Stresses, ISMES Bergamo, IABSE Report, 19.