Bulletin of Engineering Geology and the Environment

, Volume 78, Issue 6, pp 4187–4200 | Cite as

Stability analysis of the Zhangmu multi-layer landslide using the vector sum method in Tibet, China

  • Mingwei GuoEmail author
  • Sujin Liu
  • Shunde Yin
  • Shuilin Wang
Original Paper


The Zhangmu landslide is located on the China–Nepal border in Tibet, China, which has recently become a serious threat to the lives and properties of local people. In order to efficiently quantify the stability of the Zhangmu landslide, a new method named the vector sum method (VSM) is proposed. Differing from conventional slope-stability analysis methods, the VSM considers both the magnitude, the direction of force and the strength-reserving definition of the safety factor based on the actual stress field of slope achieved from finite element analysis. Moreover, the global sliding direction of potential landslides was theoretically deduced by the principle of minimum potential energy, while the safety factor can be directly computed by not only the force limit equilibrium of the whole sliding body in the global sliding direction but also the moment limit equilibrium at the moment center. Finally, stability analysis of the Zhangmu landslide was performed by the proposed method, and verified against the rigorous Morgenstern–Price method.


Vector sum method Slope stability Limit equilibrium method Strength reduction method Zhangmu landslide 



This research was supported by the Regional Collaboration and Innovation Project between the Chinese Academy of Sciences and Tibet, titled the ‘Geologic exploration, risk assessment and comprehensive prevention and control of Zhangmu Landslide’, as well as by the general program from the National Natural Science Foundation of China (Grants no.51674239). We deeply appreciate their support for this research.


  1. Basudhar PK, Lakshminarayana AMR (2017) Three-dimensional limit-equilibrium stability analyses ofSlopes and effect of inclusion of soil nails. Int J Geomech 17(9):04017067CrossRefGoogle Scholar
  2. Bishop AW (1955) The use of the slip circle in the stability analysis of slopes. Geotechnique 5(1):7–17CrossRefGoogle Scholar
  3. Chakraborty A, Goswami D (2016) State of the art: three dimensional (3D) slope-stability analysis. Int J Geotech Eng 10(5):493–498CrossRefGoogle Scholar
  4. Chen J, Yin JH, Lee CF (2003) Upper bound limit analysis ofslope stability using rigid finite elements and nonlinear programming. Can Geotech J 40(4):742–752CrossRefGoogle Scholar
  5. Chen ZY, Yin JH, Wang YJ (2006) The three-dimensional slopstability analysis: recent advances and a forward look. ASCEgeotechnical special publication, no. 151. Adv Earthstruct: Res Pract: 1–42Google Scholar
  6. Cheng YM, Yip CJ (2007) Three-dimensional asymmetrical slopestability analysis extension of Bishop’s, Janbu’s, and Morgenstern–Price’s techniques. J Geotech Geoenviron Eng 133(12):1544–1555CrossRefGoogle Scholar
  7. Cheng YM, Lansivaara T, Wei WB (2007) Two-dimensional slope stability analysis by limit equilibrium and strength reduction methods. Comput Geotech 34:137–150CrossRefGoogle Scholar
  8. Duncan JM (1996) State of the art: limit equilibrium and finite-element analysis of slopes. J Geotech Geoenviron Eng 122(7):577–596CrossRefGoogle Scholar
  9. Fredlund DG, Krahn J (1977) Comparison of slope stability methods of analysis. Can Geotech J 14:429–439CrossRefGoogle Scholar
  10. Fu X, Sheng Q, Zhang Y, Chen J, Zhang S, Zhang Z (2017) Computation of the safety factor for slope stability using discontinuousdeformation analysis and the vector sum method. Comput Geotech 92:68–76CrossRefGoogle Scholar
  11. Ge XR (2008) Deformation control law of rock fatigue failure, real-time X-ray CT scan of geotechnical testing and new method of stability analysis of slopes and dam foundations. Chin J Geotech Eng 30(1):1–20 (in Chinese)Google Scholar
  12. Ge XR (2010) The vector sum method: a new approach to calculating the safety factorof stability against sliding for slope engineering and dam foundation problems. Chen Y, Zhan L, Tang X, editors. Advances in environmental geotechnics: Proceedings of the international symposium on geoenvironmental engineering in Hangzhou, China; p. 99–110Google Scholar
  13. Griffiths DV, Lane PA (1999) Slope stability analysis by finite elements. Geotechnique 49(3):387–403CrossRefGoogle Scholar
  14. Guo M, Wang S, Ge X, Li C, Zheng H (2013) A new practical method for two-dimensional slope stability analysis. Disast Adv 6(S4):258–269Google Scholar
  15. Hamdhan IN, Schweiger HF (2013) Finite element method–based analysis of an unsaturated soil slope subjected to rainfall infiltration. Int J Geomech 13(5):653–658CrossRefGoogle Scholar
  16. Hu RL, Zhang XY, Gao W et al (2015) Structure and stability of Zhangmu deposit in Tibet. 10th Asian Reg Conf IAEGGoogle Scholar
  17. Huang CC, Tsai CC (2000) New method for 3D and asymmetricalslope stability analysis. J Geotech Geoenviron Eng 126(10):917–927CrossRefGoogle Scholar
  18. Isakov A, Moryachkov Y (2014) Estimation of slope stability using two-Parameter Criterion of stability. Int J Geomech 14(3):06014004CrossRefGoogle Scholar
  19. Jia ZY, Liu YP, Lei Y et al (2006) Overall investigation and evaluation of geological disaster in Zhangmu Port, Nielamu county, Tibet. China Highway Geotechnical Engeneering Co., Ltd. (Technical report in Chinese), Xi’anGoogle Scholar
  20. Kelesoglu MK (2016) The evaluation of three-dimensional effects on slope Stabilityby the strength reduction method. KSCE J Civ Eng 20:229–242CrossRefGoogle Scholar
  21. Kim JY, Lee SR (1997) An improved search strategy for the critical slip surface using finite element stress fields. Comput Geotech 21(4):295–313CrossRefGoogle Scholar
  22. Lam L, Fredlund DG (1993) A general limit equilibrium model forthree-dimensional slope stability analysis. Can Geotech J 30:905–919CrossRefGoogle Scholar
  23. Lim K, Li AJ, Schmid A, Lyamin AV (2017) Slope-stability assessments using finite-element limit-analysis methods. Int J Geomech 17(2):06016017CrossRefGoogle Scholar
  24. Liu G, Xiaoying Z, Zhouquan C (2017) Three-dimensional slope stability analysis using independent cover based numerical menifold and vector method. Eng Geol 225:83–95CrossRefGoogle Scholar
  25. Lu KL, Zhu DY (2016) A three-dimensional rigorous method for stability analysisand its application. Bull Eng Geol Environ 75:1445–1457CrossRefGoogle Scholar
  26. Luo G, Xiewen H, Bowman ET, Jingxuan L (2017) Stability evaluation and prediction of the Donglareactivated ancient landslide as well as emergencymitigation for the Dongla Bridge. Landslides 14:1403–1418CrossRefGoogle Scholar
  27. Ma F, Li Z, Jie W, Kuo D (2017) Monitoring and engineering geology analysis of the Zhangmu landslide in Tibet, China. Bull Eng Geol Environ 76:855–873CrossRefGoogle Scholar
  28. Mao C (2008) Analyzing and evaluating the stability of welfare institute landslide in Zhangmu town of Tibet. Dissertation, Xian University of Science and TechnologyGoogle Scholar
  29. Pham HTV, Fredlund DG (2003) The application of dynamic programming to slope stability analysis. Can Geotech J 40(4):830–847CrossRefGoogle Scholar
  30. Shen J, Karakus M (2014) Three-dimensional numerical analysis for rock slope stability using shear strength reduction method. Can Geotech J 51:164–172CrossRefGoogle Scholar
  31. Sloan SW (2013) Geotechnical stability analysis. Geotechnique 63(7):531–572CrossRefGoogle Scholar
  32. Stianson JR, Fredlund DG, Chan D (2011) There-dimensional slope stability based on stresses from a stress-deformation analysis. Can Geotech J 48(6):891–904CrossRefGoogle Scholar
  33. Tang H, Xiao L, Chengren X et al (2016) Proof of nondeterministic polynomial-time completeproblem for soil slopestability evaluation. Int J Geomech 16(5):C4015004CrossRefGoogle Scholar
  34. Tang G, Zhao L, Liang L, Zuo S, Zhang R (2017) Stability design charts for homogeneous slopes under typical conditions based on the double shear strength reduction technique. Arab J Geosci 10:280CrossRefGoogle Scholar
  35. Tu Y, Xinrong L, Zuliang Z, Yayong L (2016) New criteria for defining slope failure using the strengthreduction method. Eng Geol 212:63–71CrossRefGoogle Scholar
  36. Viratjandr C, Michalowski RL (2006) Limit analysis of submergedslopes subjected to water drawdown. Can Geotech J 43(8):802–814CrossRefGoogle Scholar
  37. Wu Z (2013) New analysis method for slope stability considering force-vector characteristics. J Geotech Geoenviron Eng 139(10):1813–1816CrossRefGoogle Scholar
  38. Xie LP, Li DH, Qiao G et al (2003) The added engineering geological investigation report on Zhangmu landslide prevention project Phase II, Tibet. Sichun Huadi Building Engineering Co., Ltd. (in Chinese)Google Scholar
  39. Yi SM, Tang HM (1996) The fractal feature of Zhangmu landslides group in Tibet and its significance. J Changchun Univ Earth Sci 26(4):392–397 (in Chinese)Google Scholar
  40. Zheng H, Tham LG (2009) Improved Bell’s method for the stabilityanalysis of slopes. Int J Num Anal Methods Geomech 33(14):1673–1689CrossRefGoogle Scholar
  41. Zheng H, Liu DF, Li CG (2005) Slope stability analysis based on elasto-plastic finite element method. Int J Numer Methods Eng 64(14):1871–1888CrossRefGoogle Scholar
  42. Zheng H, Tham LG, Liu DF (2006) On two definitions of the factor of safety commonly used in the finite element slope stability analysis. Comput Geotech 33:188–195CrossRefGoogle Scholar
  43. Zhou XP, Chen H (2013) Analysis of stability of three-dimensionalslopes using the rigorous limit equilibrium method. Eng Geol 160(6):21–33CrossRefGoogle Scholar
  44. Zhou XP, Cheng H (2014) Stability analysis of three-dimensional seismic landslides using therigorous limit equilibrium method. Eng Geol 174:87–102CrossRefGoogle Scholar
  45. Zhu DY, Lee CF, Jiang HD (2003) Generalised framework of limit equilibrium methods for slope stabilityanalysis. Geotechnique 53(4):377–395CrossRefGoogle Scholar
  46. Zhu J, Cai QE, Jiang HB (2010) Deformation monitoring and analysis of ancient landslide at Zhangmu Port in Tibet. J Eng Geol 18(1):66–70 (in Chinese)Google Scholar
  47. Zienkiewicz OC, Humpheson C et al (1975) Associated and non-associated visco-plasticity in soil mechanics. Geotechnique 25(4):671–689CrossRefGoogle Scholar
  48. Zou JZ, Williams DJ, Xiong WL (1995) Search for critical slope surfaces based on finite element method. Geotechnique 32(2):233–246Google Scholar
  49. Zou Y, Mingwei G, Shuilin W, Ge X (2017) Dynamic stability analysis of three dimensional slopes under seismic loads. Chin J Rock Mech Eng 36(5):1174–1184 (in Chinese)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Mingwei Guo
    • 1
    Email author
  • Sujin Liu
    • 1
    • 2
  • Shunde Yin
    • 3
  • Shuilin Wang
    • 1
  1. 1.State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil MechanicsChinese Academy of SciencesWuhanChina
  2. 2.University of Chinese Academy of SciencesBeijingChina
  3. 3.Department of Civil and Environmental EngineeringUniversity of WaterlooWaterlooCanada

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