Tunnel and Underground Space (터널과지하공간)

Korean Society for Rock Mechanics and Rock Engineering (한국암반공학회)
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Improving the Accuracy of the Mohr Failure Envelope Approximating the Generalized Hoek-Brown Failure Criterion

일반화된 Hoek-Brown 파괴기준식의 근사 Mohr 파괴포락선 정확도 개선

  • Youn-Kyou Lee (Department of Coastal Construction Engineering, Kunsan National University)
  • 이연규 (국립군산대학교 해양건설공학과)
  • Received : 2024.07.30
  • Accepted : 2024.08.14
  • Published : 2024.08.31
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Abstract

The Generalized Hoek-Brown (GHB) criterion is a nonlinear failure criterion specialized for rock engineering applications and has recently seen increased usage. However, the GHB criterion expresses the relationship between minimum and maximum principal stresses at failure, and when GSI≠100, it has disadvantage of being difficult to express as an explicit relationship between the normal and shear stresses acting on the failure plane, i.e., as a Mohr failure envelope. This disadvantage makes it challenging to apply the GHB criterion in numerical analysis techniques such as limit equilibrium analysis, upper-bound limit analysis, and the critical plane approach. Consequently, recent studies have attempted to express the GHB Mohr failure envelope as an approximate analytical formula, and there is still a need for continued interest in related research. This study presents improved formulations for the approximate GHB Mohr failure envelope, offering higher accuracy in predicting shear strength compared to existing formulas. The improved formulation process employs a method to enhance the approximation accuracy of the tangential friction angle and utilizes the tangent line equation of the nonlinear GHB failure envelope to improve the accuracy of shear strength approximation. In the latter part of this paper, the advantages and limitations of the proposed approximate GHB failure envelopes in terms of shear strength prediction accuracy and calculation time are discussed.

일반화된 Hoek-Brown (GHB) 식은 암반공학적 활용에 특화된 비선형 파괴기준식이며 최근 활용 빈도가 증가하고 있다. 그러나 GHB 식은 파괴 시점의 최소주응력과 최대주응력의 관계식이며 GSI≠100이면 파괴면에 작용하는 수직응력과 전단응력의 명시적 관계식 즉, Mohr 파괴포락선식으로 표현이 어렵다는 단점을 가지고 있다. 이 단점으로 인해 GHB 식을 한계평형해석, 상계한계해석, 임계평면법 등과 같은 수치해석기법에 적용하는 것이 쉽지 않다. 이에 따라 최근 GHB Mohr 파괴포락선을 근사적인 해석식으로 표현하려는 연구가 시도되고 있으며 관련 연구에 대한 지속적 관심이 여전히 필요하다. 이 연구에서는 기존 식보다 전단강도 예측 정확도가 높은 근사 GHB Mohr 파괴포락선 수식화 방법을 제시하였다. 개선된 수식화 과정에서는 접선마찰각의 근사 정확도를 높이는 방법과 비선형 GHB 파괴포락선의 접선식을 활용하여 전단강도 근사값의 정확도를 높이는 방법이 이용되었다. 이 논문의 후반부에서는 전단강도 예측 정확성과 계산시간 측면에서 제안된 근사 GHB 파괴포락선들의 장단점을 논의하였다.

Keywords

Acknowledgement

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

References

  1. AlKhafaji, H., Imani, M., and Fahimifar, A., 2020, Ultimate bearing capacity of rock mass foundations subjected to seepage forces using modified Hoek-Brown criterion, Rock Mech. Rock Eng., 53, 251-268.  https://doi.org/10.1007/s00603-019-01905-6
  2. Brady, B.H.G., and Brown, E.T., 2004, Rock Mechanics for Underground Mining, 3rd Ed., Kluwer Academic Publishers.
  3. Chen, W.F., 2008, Limit analysis and soil plasticity, J.Ross Publishing Inc. 
  4. Hoek, E., and Brown, E.T., 1980, Underground Excavations in Rock. London: Institution of Mining and Metallurgy. 
  5. Hoek, E., and Marinos, P., 2007, A brief history of the development of the Hoek-Brown failure criterion, Soils and Rocks, 2, 1-13.  https://doi.org/10.28927/SR.302085
  6. Hoek, E., 1983, Strength of jointed rock masses, Geotechnique, 33(3), 187-223.  https://doi.org/10.1680/geot.1983.33.3.187
  7. Hoek, E., Carranza-Torres, C., and Corkum, B., 2002, Hoek-Brown failure criterion - 2002 Edition, Proc. NARM-TAC Conf., Toronto, 1(1), 267-273. 
  8. Imani, M., and Aali, R., 2020, Effects of embedment depath of foundations on ultimate bearing capacity of rock masses, Geotech. Geol. Eng., 38, 6511-6528.  https://doi.org/10.1007/s10706-020-01452-w
  9. Kumar, P., 1998, Shear failure envelope of Hoek-Brown Criterion for Rockmass, Tunn. Undergr. Space Technol., 13(4), 453-458.  https://doi.org/10.1016/S0886-7798(98)00088-1
  10. Lee, Y.K., and Pietruszczak, S., 2017, Analytical representation of Mohr failure envelope approximating the generalized Hoek-Brown failure criterion, Int. J. Rock Mech. Min. Sci., 100, 90-99.  https://doi.org/10.1016/j.ijrmms.2017.10.021
  11. Lee, Y.K., and Pietruszczak, S., 2021, Limit Equilibrium Analysis Incorporating the Generalized Hoek-Brown Criterion, Rock Mech. Rock Eng., 54(9), 4407-4418,.  https://doi.org/10.1007/s00603-021-02518-8
  12. Lee, Y.K., and Pietruszczak, S., 2024, A procedure for assessing the orientation of failure plane in transversely isotropic rocks, Rock Mech. Rock Eng., (Online First). 
  13. Lee, Y.K., 2014, Relationship between tangential cohesion and friction angle implied in the generalized Hoek-Brown failure criterion, Tunnel & Underground Space, 24(5), 366-372.  https://doi.org/10.7474/TUS.2014.24.5.366
  14. Lee, Y.K., 2018, Approximate shear strength formula implied in the generalized Hoek-Brown failure criterion, Tunnel & Underground Space, 28(5), 426-441. 
  15. Lee, Y.K., 2021, Calculation of factor of safety for plane failure of rock slope utilizing the nonlinear Mohr envelope, J. Korean Soc. Min. Energy Res. Eng., 58(4), 290-299.  https://doi.org/10.32390/ksmer.2021.58.4.290
  16. Marinos, P., and Hoek, E., 2000, GSI: a geologically friendly tool for rock mass strength estimation, Proc. GeoEng2000 Int. conf. Geotech. Geol. Eng. Melbourne, 1422-1446. 
  17. Park, D., and Michalowski, R.L., 2019, Roof stability in deep rock tunnels, Int. J. Rock Mech. Min. Sci., 124, 104139. 
  18. Park, D., and Michalowski, R.L., 2021, Three-dimensional stability assessment of slopes in intact rock governed by the Hoek-Brown failure criteiron, Int. J. Rock Mech. Min. Sci., 137, 104522. 
  19. Park, D., 2023, Infinite rock slope analysis with Hoek-Brown failure criterion, Rock Mech. Rock Eng., 56(9), 6919-6928.  https://doi.org/10.1007/s00603-023-03431-y
  20. Pietruszczak, S., and Mroz, Z., 2001, On failure criteria for anisotropic cohesive-frictional materials, Int. J. Numer. Anal. Meth. Geomech., 25(5), 509-524.  https://doi.org/10.1002/nag.141
  21. Rojat, F., Labiouse, V., and Mestat, P., 2015, Improved analytical solutions for the response of underground excavation in rock mass satisfying the generalized Hoek-Brown failure criterion, Int. J. Rock Mech. Min. Sci., 79, 193-204.  https://doi.org/10.1016/j.ijrmms.2015.08.002
  22. Shen, J., Karakus, M., and Xu, C., 2012a, Direct expressions for linearization of shear strength envelopes given by the Generalized Hoek-Brown criterion using genetic programming, Comput. Geotech., 44, 139-146.  https://doi.org/10.1016/j.compgeo.2012.04.008
  23. Shen, J., Priest, S.D., and Karakus, M., 2012b, Determination of Mohr-Coulomb shear strength parameters from Generalized Hoek-Brown criterion for slope stability analysis, Rock Mech. Rock Eng., 45, 123-129.  https://doi.org/10.1007/s00603-011-0184-z
  24. Sofianos, A.I., and Nomikos, P.P., 2006, Equivalent Mohr-Coulomb and generalized Hoek-Brown strength parameters for supported axisymmetric tunnels in plastic or brittle rock, Int. J. Rock Mech. Min. Sci., 43(5), 683-704.  https://doi.org/10.1016/j.ijrmms.2005.11.006
  25. Ucar, R., 1986, Determination of shear failure envelope in rock masses, J. Geotech. Eng. Div. ASCE, 112(3), 303-315.  https://doi.org/10.1061/(ASCE)0733-9410(1986)112:3(303)
  26. Wyllie, D.C., 2017, Rock slope engineering, 5th Ed., CRC Press, Baca Raton. 
  27. Yang, X.L., and Yin, J.H., 2005, Upper bound solution for ultimate bearing capacity with a modified Hoek-Brown failure criterion, Int. J. Rock Mech. Min. Sci., 42(4), 550-560.  https://doi.org/10.1016/j.ijrmms.2005.03.002
  28. Yang, X.L., Li, L., and Yin, J.H., 2004, Stability analysis of rock slopes with a modified Hoek-Brown failure criterion, Int. J. Num. Anal. Meth. Geomech., 28, 181-190.  https://doi.org/10.1002/nag.330