Geomechanics and Engineering

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The expanded LE Morgenstern-Price method for slope stability analysis based on a force-displacement coupled mode

  • Deng, Dong-ping (School of Civil Engineering, Central South University) ;
  • Lu, Kuan (School of Civil Engineering, Central South University) ;
  • Wen, Sha-sha (School of Civil Engineering, Central South University) ;
  • Li, Liang (School of Civil Engineering, Central South University)
  • Received : 2020.08.03
  • Accepted : 2020.10.26
  • Published : 2020.11.25
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Abstract

Slope displacement and factor of safety (FOS) of a slope are two aspects that reflect the stability of a slope. However, the traditional limit equilibrium (LE) methods only give the result of the slope FOS and cannot be used to solve for the slope displacement. Therefore, developing a LE method to obtain the results of the slope FOS and slope displacement has significance for engineering applications. Based on a force-displacement coupled mode, this work expands the LE Morgenstern-Price (M-P) method. Except for the mechanical equilibrium conditions of a sliding body adopted in the traditional M-P method, the present method introduces a nonlinear model of the shear stress and shear displacement. Moreover, the energy equation satisfied by a sliding body under a small slope displacement is also applied. Therefore, the double solutions of the slope FOS and horizontal slope displacement are established. Furthermore, the flow chart for the expanded LE M-P method is given. By comparisons and analyses of slope examples, the present method has close results with previous research and numerical simulation methods, thus verifying the feasibility of the present method. Thereafter, from the parametric analysis, the following conclusions are obtained: (1) the shear displacement parameters of the soil affect the horizontal slope displacement but have little effect on the slope FOS; and (2) the curves of the horizontal slope displacement vs. the minimum slope FOS could be fitted by a hyperbolic model, which would be beneficial to obtain the horizontal slope displacement for the slope in the critical state.

Keywords

Acknowledgement

The research described in this paper was financially supported by the National Natural Science Foundation of China (Grant No. 51608541) and the Natural Science Foundation of Hunan Province, China (Grant No. 2019JJ50772).

References

  1. Atkinson, J.H. (1981), Foundations and Slopes: An Introduction to Applications of Critical State Soil Mechanics, McGraw-Hill, London, U.K.
  2. Bai, T., Qiu, T., Huang, X.M. and Li, C. (2014), "Locating global critical slip surface using the Morgenstern-Price method and optimization technique", Int. J. Geomech., 14(2), 319-325. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000312.
  3. Bishop, A.W. (1955), "The use of the slip circle in the stability analysis of slopes", Geotechnique, 5(1), 7-17. https://doi.org/10.1680/geot.1955.5.1.7.
  4. Chen, Z.Y. and Morgenstern, N.R. (1983), "Extensions to the generalized method of slices for stability analysis", Can. Geotech. J., 20(1), 104-119. https://doi.org/10.1139/t83-010.
  5. Cheng, H. and Zhou, X.P. (2015), "A novel displacement-based rigorous limit equilibrium method for three-dimensional landslide stability analysis", Can. Geotech. J., 52(12), 2055-2066. https://doi.org/10.1139/cgj-2015-0050.
  6. Deng, D.P., Lu, K. and Li, L. (2019), "LE analysis on unsaturated slope stability with introduction of nonlinearity of soil strength", Geomech. Eng., 19(2), 179-191. http://doi.org/10.12989/gae.2019.19.2.179.
  7. Duncan, J.M. and Chang, C.Y. (1970), "Nonlinear analysis of stress and strain in soils", J. Soil Mech. Found. Div., 96(5), 1629-1653. https://doi.org/10.1061/JSFEAQ.0001458
  8. Enoki, M., Yagi, N. and Yatabe, R. (1990), "Generalized slice method for slope stability analysis", Jap. Soc. Soils Mech. Found., 30, 1-13. http://doi.org/10.3208/sandf1972.30.2.1.
  9. Fredlund, D.G., Krahn, J. and Pufahl, D.E. (1981). "Relationship between limit equilibrium slope stability methods", Proceedings of 10th International Conference on Soil Mechanics and Foundation Engineering, Stockholm, Sweden, June.
  10. GeoStudio (2012), Geo-Slope International Ltd., Calgary, Alberta, Canada.
  11. Ghanbari, A., Khalilpasha, A., Sabermahani, M. and Heydari, B. (2013), "An analytical technique for estimation of seismic displacements in reinforced slopes based on horizontal slices method (HSM)", Geomech. Eng., 5(2), 143-164. http://doi.org/10.12989/gae.2013.5.2.143.
  12. Gong, B. and Tang C.A. (2016), "Slope-slide simulation with discontinuous deformation and displacement analysis", Int. J. Geomech., 17(5), E4016017. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000746.
  13. Guo, M.W., Liu, S.J., Wang, S.L. and Yin, S.D. (2020), "Determination of residual thrust force of landslide using vector sum method", J. Eng. Mech., 146(7), 04020063. https://doi.org/ 10.1061/(ASCE)EM.1943-7889.0001791.
  14. Himanshu, N., Kumar, V., Burman, A., Maity, D. and Gordan, B. (2019), "Grey wolf optimization approach for searching critical failure surface in soil slopes", Eng. Comput., 1-14. https://doi.org/10.1007/s00366-019-00927-6.
  15. Huang, C.C. (2013), "Developing a new slice method for slope displacement analyses", Eng. Geol., 157(5), 39-47. https://doi.org/10.1016/j.enggeo.2013.01.018.
  16. Huang, C.C. (2014), "Force equilibrium-based finite displacement analyses for reinforced slopes: Formulation and verification", Geotext. Geomembranes, 42(4), 394-404. https://doi.org/10.1016/j.geotexmem.2014.06.004.
  17. Itasca Consulting Group. (2012), FLAC3D 5.0 Manual, Itasca Consulting Group, Minneapolis, Minnesota, U.S.A.
  18. Janbu, N. (1973), Slope Stability Computations, in Embankment Dam Engineering: Casagrande Memorial Volume, John Wiley, New York, U.S.A., 47-86.
  19. Kondner, R.L. (1963), "Hyperbolic stress-strain response: Cohesive soils", J. Soil Mech. Found. Div., 89(1), 115-143. https://doi.org/10.1061/JSFEAQ.0000479
  20. Mandal, A.K., Li, X.P. and Shrestha, R. (2019), "Influence of water level rise on the bank of reservoir on slope stability: A case study of Dagangshan Hydropower Project", Geotech. Geol. Eng., 37(6), 5187-5198. https://doi.org/10.1007/s10706-019-00972-4.
  21. McCombie, P.F. (2009), "Displacement based multiple wedge slope stability analysis", Comput. Geotech., 36(1), 332-341. https://doi.org/10.1016/j.compgeo.2008.02.008.
  22. Mohtarami, E., JafariM, A. and Amini, M. (2014), "Stability analysis of slopes against combined circular-toppling failure", Int. J. Rock Mech. Min. Sci., 67(4), 43-56. https://doi.org/10.1016/j.ijrmms.2013.12.020.
  23. Morgenstern, N.R. and Price, V.E. (1965), "The analysis of the stability of general slip surfaces", Geotechnique, 15(1), 79-93. https://doi.org/10.1680/geot.1968.18.1.92.
  24. Pei, H.F., Zhang, S.Q., Borana, L., Zhao, Y. and Yin, J.H. (2019), "Slope stability analysis based on real-time displacement measurements", Measurement, 131(1), 686-693. https://doi.org/10.1016/j.measurement.2018.09.019.
  25. Rocscience Inc. (2003), Slide Verification Manual, Rocscience Inc., Toronto, Canada, 8-118.
  26. Siacara, A.T., Napa-Garcia, G.F., Beck, A.T. and Futai, M.M. (2020), "Reliability analysis of earth dams using direct coupling", J. Rock Mech. Geotech. Eng., 12(2), 366-380. https://doi.org/10.1016/j.jrmge.2019.07.012.
  27. Spencer, E. (1973), "Thrust line criterion in embankment stability analysis", Geotechnique, 23(1), 85-100. https://doi.org/10.1680/geot.1973.23.1.85.
  28. Sun, G.H., Cheng, S.G., Jiang, W. and Zheng, H. (2016), "A global procedure for stability analysis of slopes based on the Morgenstern-Price assumption and its applications", Comput. Geotech., 80(12), 97-106. https://doi.org/10.1016/j.compgeo.2016.06.014.
  29. Tran, A.T.P., Kim, A.R. and Cho, G.C. (2019), "Numerical modeling on the stability of slope with foundation during rainfall", Geomech. Eng., 17(1), 109-118. http://doi.org/10.12989/gae.2019.17.1.109.
  30. Vanneschi, C., Eyre, M., Burda, J., Zizka, L., Francioni, M. and Coggan, J.S. (2018), "Investigation of landslide failure mechanisms adjacent to lignite mining operations in North Bohemia (Czech Republic) through a limit equilibrium/finite element modelling approach", Geomorphology, 320, 142-153. http://doi.org/10.1016/j.geomorph.2018.08.006.
  31. Wang, L., Wu, C.Z., Li, Y.Q., Liu, H.L., Zhang, W.G. and Chen, X. (2019), "Probabilistic risk assessment of unsaturated slope failure considering spatial variability of hydraulic parameters", KSCE J. Civ. Eng., 23(12), 5032-5040. http://doi.org/10.1007/s12205-019-0884-6.
  32. Yamaguchi, K., Takeuchi, N. and Hamasaki, E. (2018), "Three-dimensional simplified slope stability analysis by hybrid-type penalty method", Geomech. Eng., 15(4), 947-955. http://doi.org/10.12989/gae.2018.15.4.947.
  33. Zhou, X.P., Cheng, H. and Wong, L.N.Y. (2019), "Three-dimensional stability analysis of seismically induced landslides using the displacement-based rigorous limit equilibrium method", B. Eng. Geol. Environ., 78(7), 4743-4756. https://doi.org/10.1007/s10064-018-01444-4.
  34. Zhu, D.Y., Lee, C.F., Qian, Q.H. and Chen, G.R. (2005). "A concise algorithm for computing the factor of safety using the Morgenstern-Price method", Can. Geotech. J., 42(1), 272-278. https://doi.org/10.1139/t04-072.