Tunnel and Underground Space (터널과지하공간)

Korean Society for Rock Mechanics and Rock Engineering (한국암반공학회)
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Comparative Study on the Rock Failure Criteria Taking Account of the Intermediate Principal Stress

중간주응력을 고려한 선형 및 비선형 암석파괴조건식의 비교 고찰

  • 이연규 (군산대학교 해양건설공학과)
  • Received : 2012.01.18
  • Accepted : 2012.02.14
  • Published : 2012.02.29
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Abstract

Although the Mohr-Coulomb and Hoek-Brown failure criteria have been adopted widely in rock mechanics, they neglect the ${\sigma}_2$ effect. The result of true triaxial tests on rock samples, however, reveals that the ${\sigma}_2$ effect on strength of rocks is considerable, so that rock failure criteria taking into account the influence of ${\sigma}_2$ are necessary for the precise stability evaluation of rock structures. In this study, a new nonlinear 3-D failure criterion has been suggested by combining the Hoek-Brown criterion with the smooth octahedral shape function taken from Jiang & Pietruszczak (1988). The performance of the new criterion was assessed by comparing the strength predictions from both the suggested criterion and the corresponding linear 3-D criterion. The resulting fit of the new criterion to the true triaxial test data for six rock types taken from the literature shows that the criterion fits the experimental data very well. Furthermore, for the data sets having data taken in the low ${\sigma}_3$ range, the nonlinear failure criterion works better than the linear criterion.

암석의 파괴조건식으로 널리 이용되고 있는 Mohr-Coulomb식과 Hoek-Brown식은 중간주응력을 고려하지 못한다. 그러나 암석의 진삼축압축시험 결과에 의하면 암석의 강도는 중간주응력의 크기에 상당한 영향을 받는 것으로 알려지고 있다. 따라서 암반구조물의 정밀한 안정성 평가를 위해서는 중간주응력의 영향을 고려할 수 있는 파괴조건식이 필요하다. 이 연구에서는 Jiang & Pietruszczak(1988)이 제안한 팔면체면 단면 형상함수를 이용하여 Hoek-Brown 파괴조건식에 근사하는 새로운 3차원 비선형 암석파괴조건식을 제안하였다. 대응되는 선형파괴조건식의 강도예측 결과와 비교검토를 통해 제안한 파괴조건식의 강도예측 성능을 평가하였다. 제안한 파괴조건식을 문헌에 보고된 6개 암종의 진삼축압축시험 결과에 적합시킨 결과 매우 우수한 적합성을 얻었다. 특히, 구속압이 낮은 영역의 진삼축압축강도를 포함한 자료에 대해서는 선형 파괴조건식에 비해 뛰어난 적합성을 보였다.

Keywords

References

  1. 이연규, 2011, Mohr-Coulomb 파괴곡면에 근사하는 암석의 3차원 파괴조건식 고찰, 터널과 지하공간(한국암반공학회지), Vol. 21, pp. 93-102.
  2. 이연규, 송원경, 박철환, 최병희, 2011, 3차원 파괴조건식을 이용한 콘크리트 플러그의 안전도 평가, 터널과 지하공간(한국암반공학회지), Vol. 21, pp. 526-535.
  3. Al-Ajmi, A. M. and Zimmerman, R. W., 2005, Relation between the Mogi and the Coulomb failure criteria, Int J. Rock Mech. Min. Sci., Vol. 42, pp. 431-439. https://doi.org/10.1016/j.ijrmms.2004.11.004
  4. 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
  5. Chang, C. and Haimson, B. C., 2000a, A new true 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. Chang, C. and Haimson, B. C., 2000b, True triaxial strength and deformability of the German Continental deep drilling program (KTB) deep hole amphibolite, J. Geophys. Res., Vol. 105, pp. 18999-19013. https://doi.org/10.1029/2000JB900184
  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., Vol. 39, pp. 695-729. https://doi.org/10.1016/S1365-1609(02)00048-5
  8. Davis JC. Statistics and data analysis in geology. 3rd Ed. John Wiley & Sons; 2002.
  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. Ewy, R., 1999, Wellbore-stability predictions by use of a modified Lade criterion. SPE Drill Completion, Vol. 14(2), pp. 85-91. https://doi.org/10.2118/56862-PA
  11. Hoek., E. and Brown E. T., 1980, Underground excavations in rock, The Institution of Mining and Metallurgy, London.
  12. Hoskins, E. R., 1969, The failure of thick-walled hollow cylinders of isotropic rock, Int. J. Rock Mech. Min. Sci., Vol. 6, pp. 99-125. https://doi.org/10.1016/0148-9062(69)90030-8
  13. Issen, K. A. and Challa, V., 2008, Influence of the intermediate principal stress on the strain localization mode in porous sandstone, J. Geophys. Res., Vol. 113, B02103, doi:10.1029/2005JB004008.
  14. Matsuoka, H. and Nakai, T., 1982, A new failure criterion for soils in three-dimensional stresses, IUTAM Conf. on Deform. and Failure of Granular Mater., Delft, pp. 253-263.
  15. Mogi K., 1967, Effect of the intermediate principal stress on rock failure, J. Geophys. Res., Vol. 72, pp. 5117-5131. https://doi.org/10.1029/JZ072i020p05117
  16. Mogi, K., 1971, Fracture and flow of rocks under high triaxial compression. J. Geophys. Res., Vol. 76, pp. 1255-1269. https://doi.org/10.1029/JB076i005p01255
  17. Mogi, K., 2007, Experimental rock mechanics, Taylor & Francis.
  18. Nayak, G. C. and Zienkiewicz, O. C., 1972, Convenient forms of stress invariants for plasticity. J. Struct. Div. ASCE, Vol. 98, pp. 949-953.
  19. Jiang, J. and Pietruszczak, S., 1988, Convexity of yield loci for pressure sensitive materials, Comput. Geotech., 5, 51-63 https://doi.org/10.1016/0266-352X(88)90016-X
  20. Takahashi, M. and Koide, H., 1989, Effect of the intermediate principal stress on strength and deformation behavior of sedimentary rocks at the depth shallower than 2000m, Rock at great depth (V. Maury & D. Fourmaintraux Ed.), Vol. 1, 19-26.
  21. Tiwari, R. P. and Rao, K. S., 2006, Post failure behaviour of a rock mass under the influence of triaxial and true triaxial confinement, Engineering Geology, Vol. 84, pp. 112-129. https://doi.org/10.1016/j.enggeo.2006.01.001
  22. Willam, K. J. and Warnke, E. P., 1974, Constitutive model for triaxial behavior of concrete, Colloquium on Concrete Structures Subjected to Triaxial Stresses, ISMES Bergamo, IABSE Report, 19.
  23. Yang, X.-L., Zou, J.-F. and Sui, Z.-R., 2007, Effect of Intermediate Principal Stress on Rock Cavity Stability, J. Cent. South Univ. Technol., Vol. 14(s1), pp. 165-169. https://doi.org/10.1007/s11771-007-0237-3
  24. Yu, M.-H., Zan, Y.-W., Zhao, J. and Yoshimine, M., 2002, A unified strength criterion for rock material, Int J. Rock Mech. Min. Sci., Vol. 39, pp. 975-989. https://doi.org/10.1016/S1365-1609(02)00097-7
  25. Zhou, S., 1994, A program to model the initial shape and extent of borehole breakout. Comput. Geosci., Vol. 20, pp. 1143-1160. https://doi.org/10.1016/0098-3004(94)90068-X

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