Geomechanics and Engineering

  • 제34권3호
  • /
  • Pages.285-301
  • /
  • 2023
  • /
  • 2005-307X(pISSN)
  • /
  • 2092-6219(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Probabilistic analysis of anisotropic rock slope with reinforcement measures

  • 투고 : 2023.02.27
  • 심사 : 2023.06.29
  • 발행 : 2023.08.10
⟨ 이전 논문 다음 논문 ⟩

초록

During the construction of E75 highway through Grdelica gorge in Serbia, a major failure occurred in the zone of reinforced rock slope. Excavation was performed in highly anisotropic Paleozoic schist rock formation. The reinforcement consisted of the two rows of micropile wall with pre-stressed anchors. Forces in anchors were monitored with load cells while benchmarks were installed for superficial displacement measurements. The aim of the study is to investigate possible causes of instability considering different probability distributions of the strength of discontinuities and anchor bond strength by applying different optimization techniques for finding the critical failure surface. Even though the deterministic safety factor value is close to unity, the probability of failure is governed by variability of shear strength of anisotropic planes and optimization method used for locating the critical sliding surface. The Cuckoo search technique produces higher failure probabilities compared to the others. Depending on the assigned statistical distribution of input parameters, various performance functions of the factor of safety are obtained. The probability of failure is insensitive to the variation of bond strength. Different sampling techniques should yield similar results considering that the sufficient number of safety factor evaluations is chosen to achieve converged solution.

키워드

과제정보

This paper is funded by the Government of the Republic of Serbia (The Science Fund of the Republic of Serbia), as a part of Serbian Science and Diaspora Collaboration Program - project Rock slope stability - back analysis of failures along rock cuttings - ROCKSTAB (application number 6524757). Also, the Erasmus+ grant (EMADRID03) for the stay of Professor Svetlana Melentijevic at the University of Belgrade is acknowledged.

참고문헌

  1. Aladejare, A.E. and Akeju, V.O. (2020), "Design and sensitivity analysis of rock slope using Monte Carlo simulation", Geotech. Geol. Eng., 38, 573-585. https://doi.org/10.1007/s10706-019-01048-z.
  2. Babu, G.L. and Mukesh, M.D. (2004), "Effect of soil variability on reliability of soil slopes", Geotechnique, 54, 335-337. https://doi.org/10.1680/geot.2004.54.5.335.
  3. Barton, N. (1973), "Review of a new shear strength criterion for rock joints", Eng. Geol., 7, 287-332. https://doi.org/10.1016/0013-7952(73)90013-6.
  4. Barton, N. (1976), "The shear strength of rock and rock joints", Int. J. Rock. Mech. Min. Sci. Geomech. Abstr, 13(9), 255-279. https://doi.org/10.1016/0148-9062(76)90003-6.
  5. Barton, N. and Choubey, V. (1977), "The shear strength of rock joints in theory and practice", Rock. Mech., (10)1-2, 1-54. https://doi.org/10.1007/BF01261801.
  6. Berisavljevic, Z, Berisavljevic, D. and Zugic, Z. (2019), "Slope stability analysis of anisotropic rock masses with directional strength models", Proceedings of the 8th Int. Conf. Geotechnical Aspects in Civil Engineering, Vrnjacka Banja, November.
  7. Berisavljevic, D., Berisavljevic, Z. and Melentijevic, S. (2022), "The shear strength evaluation of rough and infilled joints and its indications for stability of rock cutting in schist rock mass", Bull. Eng. Geol. Environ., 81. https://doi.org/10.1007/s10064-022-02580-8.
  8. Box, G.P. and Wilson, K.B. (1951), "On the Experimental Attainment of Optimum Conditions", J. R. Stat. Soc., 13(1), 1-45. https://doi.org/10.1111/j.2517-6161.1951.tb00067.x.
  9. Chakraborty, R. and Dey, A. (2022), "Probabilistic slope stability analysis: state-of-the-art review and future prospects", Innov. Infrastruct. Sol., 7. https://doi.org/10.1007/s41062-022-00784-1.
  10. Cho, S.E. (2007), "Effects of spatial variability of soil properties on slope stability", Eng. Geol., 92, 97-109. https://doi.org/10.1016/j.enggeo.2007.03.006.
  11. Christian, J.T., Ladd, C.C. and Baecher, G.B. (1994), "Reliability applied to slope stability analysis", J. Geotech. Eng., 120(12). https://doi.org/10.1061/(ASCE)0733-9410(1994)120:12(2180)
  12. Design code (2013), EN 1537, Execution of special geotechnical works. Ground anchors, CEN
  13. Design code (2015), BS 8081:2015+A2:2018, Code of practice for grouted anchors, The British Standards Insitution.
  14. Duncan, J.M. (2000), "Factors of safety and reliability in geotechnical engineering", J. Geotech. Eng., 126. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:4(307)
  15. El-Ramly, H., Morgenstern, N.R. and Cruden, D.M. (2002), "Probabilistic slope stability analysis for practice", Can. Geotech. J., 39, 665-683. https://doi.org/10.1139/t02-034.
  16. Fenton, G.A. and Griffiths, D.V. (2008), Risk assessment in geotechnical engineering, John Wiley & Sons: Hoboken, N.J.
  17. Forrest, W.S. and Orr, T.L. (2010), "Reliability of shallow foundations designed to Eurocode 7", Georisk, 4(4), 186-207. https://doi.org/10.1080/17499511003646484.
  18. Gholampour, A. and Johari, A. (2019), "Reliability-based analysis of braced excavation in unsaturated soils considering conditional spatial variability", Comput. Geotech., 115. https://doi.org/10.1016/j.compgeo.2019.103163.
  19. Greco, V.R. (1996), "Efficient Monte Carlo technique for locating critical slip surface", J. Geotech. Eng., 122(7), 517-525. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:7(517).
  20. Griffiths D.V. and Fenton G.A. (2004), "Probabilistic slope stability analysis by finite elements", J. Geotech. Geoenviron. Eng., 130(5), 507-518. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:5(507).
  21. Guo, X., Sun, Q., Dias, D. and Antoinet, E. (2020), "Probabilistic assessment of an earth dam stability design using the adaptive polynomial chaos expansion", Bull. Eng. Geol. Environ., 79, 4639-4655. https://doi.org/10.1007/s10064-020-01847-2.
  22. Harr, M.E. (1987), Reliability-based design in civil engineering McGraw-Hill Inc., New York.
  23. Hassan, A.M. and Wolff, T.F. (1999), "Search algorithm for minimum reliability index of earth slopes", J. Geotech. Eng., 125(4), https://doi.org/10.1061/(ASCE)1090-0241(1999)125:4(301).
  24. Hoek, E. and Brown, E.T. (2019), "The Hoek-Brown failure criterion and GSI - 2018 edition", J. Rock Mech. Geotech. Eng., 11(3), 445-463. https://doi.org/10.1016/j.jrmge.2018.08.001.
  25. Hoek, E., Carranza-Torres, C. and Corkum, B. (2002), "Hoek-Brown criterion-2002 edition", Proceedings of the NARMS-TAC conference, Toronto, July.
  26. Huang, J., Griffiths, D.V. and Fenton, G.A. (2010), "System reliability of slopes by RFEM", Soils Found., 50(3), 343-353. https://doi.org/10.3208/sandf.50.343.
  27. Javankhoshdel, S. and Bathurst, R.J. (2016), "Influence of cross correlation between soil parameters on probability of failure of simple cohesive and c-ϕ slopes", Can. Geotech. J., 53(5), 839-853. https://doi.org/10.1139/cgj-2015-0109.
  28. Javankhoshdel, S. and Bathurst, R.J. (2014), "Simplified probabilistic slope stability design charts for cohesive and c-𝛗 soils", Can. Geotech. J., 51(9), 1033-1045. https://doi.org/10.1139/cgj-2014-0418.
  29. Javankhoshdel, S., Cami, B., Yacoub, T. and Bathurst R.J. (2019), "Probabilistic analysis of an MSE wall considering spatial variability of soil properties", Proceedings of the 8th Int. Conf. on Case Histories in Geotechnical Engineering, Philadelphia, March.
  30. Javankhoshdel, S., Luo, N. and Bathurst, R.J. (2017), "Probabilistic analysis of simple slopes with cohesive soil strength using RLEM and RFEM", Georisk, 11(3), 231-246. https://doi.org/10.1080/17499518.2016.12357122.
  31. Javankhoshdel, S., Cami, B., Mafi, R., Yacoub, T. and Bathurst, R. J. (2018), "Optimization techniques in non-circular probabilistic slope stability analysis considering spatial variability", Proceedings of the: GeoEdmonton 2018, Edmonton, Canada.
  32. Ji, J., Liao, H.J. and Low, B.K. (2012), "Modeling 2D spatial variation in slope reliability analysis using interpolated autocorrelations", Comput. Geotech., 40, 135-146. https://doi.org/10.1016/j.compgeo.2011.11.002.
  33. Jiang, T., Liu, J., Yuan, B. and Wang, S. (2011), "Influence of probability distribution of shear strength parameters on reliability-based rock slope analysis", Proceedings of the GeoHunan2011, https://doi.org/10.1061/47627(406)9.
  34. Johari, A. and Gholampour, A. (2018), "A practical approach for reliability analysis of unsaturated slope by conditional random finite element method", Comput. Geotech., 102, 79-91. https://doi.org/10.1016/j.compgeo.2018.06.004.
  35. Johari, A., Fazeli, A. and Javadi, A.A. (2013), "An investigation into application of jointly distributed random variables method in reliability assessment of rock slope stability", Comput. Geotech., 47, 42-47. https://doi.org/10.1016/j.compgeo.2012.07.003.
  36. Johari, A., Hajivand, A.K. and Binesh, S. (2020), "System reliability analysis of soil nail wall using random finite element method", Bull. Eng. Geol. Environ., 79, 2777-2798. https://doi.org/10.1007/s10064-020-01740-y.
  37. Kim, H.Y. (2013), "Statistical notes for clinical researchers: assessing normal distribution (2) using skewness and kurtosis", Restor. Dent. Endod., 38(1), 52-54. https://doi.org/10.5395/rde.2013.38.1.52.
  38. Kitch, W.A. (1994), "Deterministic and probabilistic based analyses of reinforced soil slopes", PhD Dissertation, University of Texas at Austin
  39. Kulhawy, F.H., Roth, M.J. and Grigoriu, M.D. (1991), "Some statistical evaluations of geotechnical properties", Proceedings of the 6th Int. Conf. on Applications of Statistics and Probability in Soil and Structural Engineering, Mexico City, June.
  40. Lacasse, S. and Nadim, F. (1996), "Uncertainties in characterizing soil properties", Proceedings of the Uncertainty in the Geologic Environment: From Theory to Practice, New York, July - August.
  41. Law, A.M. and McComas, M.G. (1986), "Pitfalls in the simulation of manufacturing systems", Proc. Winter Simulation Conference, Washington, D.C, December.
  42. Li, K.S. and Lumb, P. (1987), "Probabilistic design of slopes", Can. Geotech. J., 24, 520-535. https://doi.org/10.1139/t87-06.
  43. Li, S., Shangguan, Z., Duan, H., Liu, Y. and Luan, M. (2009), "Searching for critical failure surface in slope stability analysis by using hybrid genetic algorithm", Geomech. Eng., 1(1), 85-96. https://doi.org/10.12989/gae.2009.1.1.085.
  44. Li, J., Zhang, S., Liu, L., Wu, J. and Cheng, Y. (2022), "Adaptively selected autocorrelation structure-based Kriging metamodel for slope reliability analysis", Geomech. Eng., 30(2), 187-199. https://doi.org/10.12989/gae.2022.30.2.187.
  45. Li, D.Q., Zhou, C.B., Lu, W.B. and Jiang, Q.H. (2009), "A system reliability approach for evaluating stability of rock wedges with correlated failure modes", Comput. Geotech., 36(8) , 1298-1307. https://doi.org/10.1016/j.compgeo.2009.05.013.
  46. Low, B.K., Gilbert, R.B. and Wright, S.G. (1998), "Slope reliability analysis using generalized method of slices", J. Geotech. Geoenviron. Eng., 124(4), 350-362. https://doi.org/10.1061/(ASCE)1090-0241(1998)124:4(350).
  47. Low, B.K., Lacasse, S. and Nadim, F. (2007), "Slope reliability analysis accounting for spatial variation", Georisk, 1(4), 177-189. https://doi.org/10.1080/17499510701772089.
  48. Lumb, P. (1966), "The variability of natural soils", Can. Geotech. J., 3(2), 74-97. https://doi.org/10.1139/t66-009.
  49. Lumb, P. (1970), "Safety factors and the probability distribution of soil strength", Can. Geotech. J., 7(3), 225-242. https://doi.org/10.1139/t70-032.
  50. McKay, M.D., Beckman, R.J. and Conover, W.J. (1979), "A comparison of three methods for selecting values of input variables in the analysis of output from a computer code", Technometrics, 21(2), 239-245. https://doi.org/10.2307/1268522.
  51. Mostyn, G.R. and Li, K.S. (1993), "Probabilistic slope stability analysis - state-of-play" (Chapter), Probabilistic methods in geotechnical engineering, Balkema, Rotterdam.
  52. Nguyen, V.U. and Chowdhury, R.N. (1985), "Simulation for risk analysis with correlated variables", Geotechnique, 35(1), 47-58. https://doi.org/10.1680/geot.1985.35.1.47.
  53. Pearson, K. (1916), "Mathematical contributions to the theory of evolution, XIX: Second supplement to a memoir on skew variation", Philos. T. Roy. Soc. A, 216(538-548), 429-457. https://doi.org/10.1098/rsta.1916.0009.
  54. Shapiro, S.S. and Wilk, M.B. (1965), "An analysis of variance test for normality (complete samples)", Biometrika, 52(3-4), 591-611. https://doi.org/10.1093/biomet/52.3-4.591.
  55. Rafiei Renani, H., Martin, C.D., Varona, P. and Lorig, L. (2019), "Stability Analysis of Slopes with Spatially Variable Strength Properties" Rock. Mech. Rock. Eng., 52, 3791-3808. https://doi.org/10.1007/s00603-019-01828-2.
  56. Rafiei Renani H. and Martin, C.D. (2020), "Slope stability analysis using equivalent Mohr-Coulonb and Hoek-Brown criteria", Rock Mech. Rock Eng., 53(13-21). https://doi.org/10.1007/s00603-019-01889-3.
  57. GuhaRay, A. and Baidya, D.K. (2014), "Partial safety factors for retaining walls and slopes: A reliability based approach", Geomech. Eng., 6(2), 99-115. https://doi.org/10.12989/gae.2014.6.2.099.
  58. Rethati, L. (1988), Probabilistic Solutions in Geotechnics, Elsevier 
  59. Robert, C.P. and Casella, G. (2004), Monte Carlo Statistical Methods, Springer, Berlin.
  60. Rocscience (2021), "Slide2 2D Limit Equilibrium Analysis for Slopes" version 9.020. https://www.rocscience.com.
  61. Rocscience (2022), "Slide2 online user guide", https://www.rocscience.com/help/slide2/documentation.
  62. Spencer, E.E. (1967) "A method of the analysis of the stability of embankments assuming parallel inter-slice forces", Geotechnique, 17, 11-26. https://doi.org/10.1680/geot.1967.17.1.11.
  63. Tietje, O., Fitze, P. and Schneider, H.R. (2014), "Slope stability analysis based on autocorrelated shear strength parameters", Geotech. Geol. Eng., 32, 1477-1483. https://doi.org/10.1007/s10706-013-9693-8.
  64. US Army Corps of Engineers (1997), Engineering and Design: Introduction to Probability and Reliability Methods for use in Geotechnical Engineering (Technical Letter), Washington DC.
  65. Wang, L., Hwang, J.H., Luo, Z., Juang, C.H. and Xiaoz, J. (2013), "Probabilistic back analysis of slope failure - A case study in Taiwan", Comput. Geotech., 51, 12-23. https://doi.org/10.1016/j.compgeo.2013.01.008.
  66. Wang, L., Wu, C., Gu, X., Liu, H., Mei, G. and Zhang, W. (2020), "Probabilistic stability analysis of earth dam slope under transient seepage using multivariate adaptive regression splines", Bull. Eng. Geol. Environ., 79, 2763-2775 https://doi.org/10.1007/s10064-020-01730-0.
  67. Wang, L., Wu, C., Tang, L., Zhang, W., Lacasse, S., Liu, H. and Gao, L. (2020), "Efficient reliability analysis of earth dam slope stability using extreme gradient boosting method", Acta Geotech., 15, 3135-3150. https://doi.org/10.1007/s11440-020-00962-4.
  68. Wolf, T.F. (1996), "Probabilistic slope stability in theory and practice", Uncertainty in the Geologic Environment: from Theory to Practice, ASCE.
  69. Wu, T.H. and Kraft, L.M. (1970), "Safety analysis of slopes", J. Soil Mech. And Found. Div., 96(2), 609-630. https://doi.org/10.1061/JSFEAQ.0001406.
  70. Yang, X.L. and Liu, Z.A. (2018), "Reliability analysis of three-dimensional rock slope", Geomech. Eng., 15(6), 1183-1191. https://doi.org/10.12989/gae.2018.15.6.1183.
  71. Yucemen, M.S., Tang, W.H. and Ang, A.S. (1973), A Probabilistic Study of Safety and Design of Earth Slopes (Technical Report), University of Illinois at Urbana-Champaign
  72. Zhang, J., Tang, W.H. and Zhang, L. (2010), "Efficient probabilistic back-analysis of slope stability model parameters", J. Geotech. Geoenviron. Eng., 136, 99-109. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000205.
  73. Zhang, W., Gu, X., Hong, L., Han, L. and Wang, L. (2023), "Comprehensive review of machine learning in geotechnical reliability analysis: Algorithms, applications and further challenges", Appl. Soft Comput., 136. https://doi.org/10.1016/j.asoc.2023.110066
  74. Zhao, L., Jiao, K., Zuo, S., Yu, C. and Tang., G. (2020), "Pseudostatic stability analysis of wedges based on the nonlinear Barton-Bandis failure criterion", Geomech. Eng., 20(4), 287-297. https://doi.org/10.12989/gae.2020.20.4.287.
  75. Zhou, X., Chen, J., Chen, Y. et al. (2017) "Bayesian-based probabilistic kinematic analysis of discontinuity-controlled rock slope instabilities", Bull. Eng. Geol Environ., 76, 1249-1262. https://doi.org/10.1007/s10064-016-0972-5