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Numerical Verification for Plane Failure of Rock Slopes Using Implicit Joint-Continuum Model

내재적 절리-연속체 모델을 이용한 암반사면 평면파괴의 수치해석적 검증

  • Shin, Hosung (Dept. of Civil & Environmental Engrg., Univ. of Ulsan)
  • 신호성 (울산대학교 건설환경공학부)
  • Received : 2020.12.18
  • Accepted : 2020.12.28
  • Published : 2020.12.31

Abstract

Embedded joints in the rock mass are a major constituent influencing its mechanical behavior. Numerical analysis requires a rigorous modeling methodology for the rock mass with detailed information regarding joint properties, orientation, spacing, and persistence. This paper provides a mechanical model for a jointed rock mass based on the implicit joint-continuum approach. Stiffness tensors for rock mass are evaluated for an assemblage of intact rock separated by sets of joint planes. It is a linear summation of compliance of each joint sets and intact rock in the serial stiffness system. In the application example, kinematic analysis for a planar failure of rock slope is comparable with empirical daylight envelope and its lateral limits. Since the developed implicit joint-continuity model is formulated on a continuum basis, it will be a major tool for the numerical simulations adopting published plenteous thermal-hydro-chemical experimental results.

암반내의 절리는 암반의 전체적인 역학적 거동에 중요한 역할을 한다. 암반에 대한 수치해석은 절리면의 역학적 물성, 방향성, 간격 그리고 연속성을 정교하게 모델링할수 있어야 한다. 본 논문의 내재적 절리-연속체 접근법은 절리군을 포함한 암반의 역학적 모델을 제시한다. 암반에 대한 강성 텐서는 온전한 암석과 절리군의 역학적 특성으로부터 산정하였다. 이는 온전한 암석과 절리군에 대한 연속적 강성 시스템의 컴플라이언스 텐서 합으로부터 산정할 수 있다. 암반사면의 평면파괴에 대한 수치해석은 기존의 daylight envelope과 측면한계를 적용하는 경험적인 방법과 상당히 일치함을 확인하였다. 개발된 내재적 절리-연속체 모델은 연속체 기반으로 수식화되어 기존의 절리에 대한 열-수리-화학적 실험적 결과들을 실제 수치해석에 적용할수 있을 것이다.

Keywords

References

  1. Agharazi, A., Martin, C.D., and Tannant, D.D. (2012), "A Three Dimensional Equivalent Continuum Constitutive Model for Jointed Rock Masses Containing up to Three Random Joint Sets", Geomech. Geoeng.: An Int. J., Vol.7, No.4, pp.227-238. https://doi.org/10.1080/17486025.2012.714476
  2. Amadei, B. and Goodman, R.E. (1981), "A 3-D Constitutive Relation for Fractured Rock Masses", Proceedings of the international symposium on mechanical behaviour of structured media, pp.249-268.
  3. Bagheri, M.A. and Settari, A. (2006), "Effects of Fractures on Reservoir Deformation and Flow Modeling", Can. Geotech. J., 43, pp.574-586. https://doi.org/10.1139/t06-024
  4. Barton, N., Bandis, S., and Shinas, C. (2001), "Engineering Criterion of Rock Mass Strength", Proceedings of the fourth Hellenic conference on geotechnical and geo-environmental engineering, 1, pp.115-122.
  5. Brideau, M.A., Chauvin, S., Andrieux, P., and Stead, D. (2012), "Influence of 3D Statistical Discontinuity Variability on Slope Stability Conditions", Landslides and engineered slopes: Protecting Society through improved understanding, pp.587-593.
  6. Cai, M. and Horii, H. (1992), "A Constitutive Model of Highly Jointed Rock Masses", Mech. Mater., Vol.13, No.3, pp.217-246. https://doi.org/10.1016/0167-6636(92)90004-W
  7. Desai, C.S., Zamman, M.M., Lightner, J.G., and Siriwardane, H.J. (1984), "Thin Layer Element for Interfaces and Joints", Int J Numer Anal Methods Geomech., 8, pp.19-43. https://doi.org/10.1002/nag.1610080103
  8. Duncan, C.W. and Christopher, W.M. (2010), Rock Slope Engineering: Civil and Mining, 4th Edition, p.388.
  9. Gan, Q. and Elsworth, D. (2016), "A Continuum Model for Coupled Stress and Fluid Flow in Discrete Fracture Networks", Geomech Geophys Geo-Energy Geo-Resour, Vol.2, No.1, pp.43-61. https://doi.org/10.1007/s40948-015-0020-0
  10. Goodman, R. and Shi, G. (1985), Block theory and its application to rock engineering, Prentice-Hall International, p.338.
  11. Goodman, R.E., Taylor, R.L., and Brekke, T.L. (1968), "A Model for the Mechanics of Jointed Rock", J. Soil Mech. Div. ASCE., 94(SM3), pp.637-659. https://doi.org/10.1061/JSFEAQ.0001133
  12. Grujovic, N., Divac, D., Zivkovic, M., Slavkovic, R., Milivojevic, N., Milivojevic, V., and Rakic, D. (2013), "An Inelastic Stress Integration Algorithm for a Rock Mass Containing Sets of Discontinuities", Acta Geotech, 8, pp.265-278. https://doi.org/10.1007/s11440-012-0194-3
  13. Hoek, E. and Londe, P. (1974), "The design of rock slopes and foundations", General Report on Theme III. Proc.
  14. Hoek, E. and Bray, J.D. (1981), Rock Slope Engineering, 3rd Edition, CRC Press, p.368.
  15. Huang, T.H., Chang, C.S., and Yang, Z.Y. (1995), "Elastic Moduli for Fractured Rock Mass", Rock Mechanics and Rock Engineering, Vol.28, No.3, pp.135-144. https://doi.org/10.1007/BF01020148
  16. Hudson, J.A. and Harrison, J.P. (2000), Engineering rock mechanics: An introduction to the principles, Elsevier, p.444.
  17. Jaeger, J.C., Cook, N.G.W., and Zimmerman, R.W. (2007), Fundamentals of Rock Mechanics, 4th edition, Blackwell, p.475.
  18. Lee, S.H., Lough, M.F., and Jensen, C.L. (2001), "Hierarchical Modeling of Flow in Naturally Fractured Formations with Multiple Length Scales", Water Resources Research, 37, pp.443-455. https://doi.org/10.1029/2000WR900340
  19. Lei, Q. (2016), Characterisation and modelling of natural fracture networks: Geometry, geomechanics and fluid flow, Imperial College, PhD Thesis.
  20. Lisle, R.J. (2004), "Calculation of the Daylight Envelope for Plane Failure of Rock Slopes", Geotechnique, Vol.54, No.4, pp.279-280. https://doi.org/10.1680/geot.2004.54.4.279
  21. Liu, X., Han, G., Wang, E., Wang, S., and Nawnit, K. (2018), "Multiscale Hierarchical Analysis of Rock Mass and Prediction of its Mechanical and Hydraulic Properties", Journal of Rock Mechanics and Geotechnical Engineering, Vol.10, No.4, pp.694-702. https://doi.org/10.1016/j.jrmge.2018.04.003
  22. Maghous, S., Bernaud, D., Fre'ard, J., and Garnier, D. (2008), "Elastoplastic behaviour of Jointed Rock Masses as Homogenized Media and Finite Element Analysis", International Journal of Rock Mechanics and Mining Sciences, 45, pp.1273-1286. https://doi.org/10.1016/j.ijrmms.2008.01.008
  23. Oda, M. (1986), "An Equivalent Continuum Model for Coupled Stress and Fluid Flow Analysis in Jointed Rock Masses", Water Resour Res., Vol.22, No.13, pp.1845-1856. https://doi.org/10.1029/WR022i013p01845
  24. Pluimers, S.B. (2015), Hierarchical fracture modeling approach, Delft University of Technology, Ph.D Thesis.
  25. Rafeh, F., Mroueh, H., and Burlon, S. (2015), "Equivalent continuum model accounting for anisotropy in chalk by means of embedded joint sets", Computer Methods and Recent Advances in Geomechanics, Oka, Murakami, Uzuoka & Kimoto (Eds.) Taylor & Francis Group.
  26. Samadhiya, N.K., Viladkar, M.N., and Al-Obaydi, M.A. (2008), "Numerical Implementation of Anisotropic Continuum Model for Rock Masses", International Journal of Geomechanics, ASCE, Vol.8, No.2, pp.157-161. https://doi.org/10.1061/(ASCE)1532-3641(2008)8:2(157)
  27. Shin, H. and Santamarina, J. (2019), "An Implicit Joint-continuum Model for the Hydro-mechanical Analysis of Fractured Rock Masses", International Journal of Rock Mechanics and Mining Sciences, 119, pp.140-148. https://doi.org/10.1016/j.ijrmms.2019.04.006
  28. Sitharam, T.G., Sridevi, J., and Shimizu, N. (2001), "Practical Equivalent Continuum Characterization of Jointed Rock Masses", Int J Rock Mech Min Sci, 38, pp.437-448. https://doi.org/10.1016/S1365-1609(01)00010-7
  29. Son, M., Lee, W.K., and Hwang, Y.C. (2014), "Estimation of Elastic Modulus of Jointed Rock Mass under Tunnel Excavation Loading", Journal of the Korean Geotechnical Society, Vol.30, No.7, pp.17-26. https://doi.org/10.7843/KGS.2014.30.7.17
  30. Stead, D., Eberhardt, E., and Coggan, J. (2006), "Development in the Characterization of Complex Rock Slope Deformation and Failure Using Numerical Modeling Techniques", Engineering Geology, 83, pp.217-235. https://doi.org/10.1016/j.enggeo.2005.06.033
  31. Twiss, R.J. and Moores, E.M. (2007), Structural Geology, second ed. W.H. Freeman and Company, p.736.
  32. Wang, T.T. and Huang, T.H. (2009), "A Constitutive Model for the Deformation of a Rock Mass Containing Sets of Ubiquitous Joints", Int. J. Rock Mech. Min. Sci., Vol.46, No.3, pp.521-530. https://doi.org/10.1016/j.ijrmms.2008.09.011