Discussion on the Multi-Solution of Three-Dimensional Slope Safety Factor

Abstract

The limit equilibrium method cannot yield a unique value of safety factor in three-dimensional (3D) analysis of slope. However, the calculated value of safety factor according to limit equilibrium method directly determines the design of slope engineering. So, the study of multi-solution of three-dimensional slope safety factor may help people to judge further the reasonableness of the computation results and select the range of safety factor’s possible values. In this paper, the initial distribution of normal stresses over the sliding surface is assumed, which is then modified by a function involving four parameters to satisfy force and moment equilibrium conditions of the sliding body. Then, according to a series of assumed safety factors, the corresponding minimum value of the normal stress of sliding surface is calculated by force and moment equilibrium conditions of the sliding body. Then the reasonable range of slope safety factor is justified according to the reasonableness of the normal stress distribution over the sliding surface. The calculation results of engineering examples show that the reasonable range of safety factor for symmetric slopes is between 8 and 12% and that the reasonable range of safety factor for asymmetric slope is over 30%. Therefore, it is necessary to further verify the rationality of normal stress for the safety factor of three-dimensional asymmetric slope in order to further apply it to engineering.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

References

  1. Baligh MM, Azzouz AS (1975) End effects on stability of cohesive slopes. J Geotech Eng Div 101(11):1105–1117

    Google Scholar 

  2. Bishop AW (1955) The use of the slip circle in the stability analysis of earth slopes. Géotechnique 5(1):7–17

    Article  Google Scholar 

  3. Duncan JM (1996) State of the art: limit equilibrium and finite-element analysis of slopes. J Geotech Engrg ASCE 122(7):577–596

    Article  Google Scholar 

  4. Fellenius W (1936) Calculation of the stability of earth dams. In: proceedings of transactions of the 2nd congress on large dams, international commission on large dams of the world power conference 4: 445–462

  5. Gens A, Hutchision JN, Cavounidis S (1988) Three dimensional analysis of slides in cohesive soils. Geotechnique 38(1):1–23

    Article  Google Scholar 

  6. Hovland HJ (1977) Three-dimensional slope stability analysis method. J Geotech Eng Div Proc Am Soc Civ Eng 1103(GT9):971–986

    Google Scholar 

  7. Huali L, Dayong Z (2007) Discussion on multiple solution of safety factor of a slope. Rock Soil Mech 28(8):1661–1664

    Google Scholar 

  8. Hungr O (1987) An extension of Bishop’s simplified method of slope stability analysis to three dimension. Geotechnique 37:113–117

    Article  Google Scholar 

  9. Leshchinsky D, Baker R, Silver ML (1985) Three-dimensional analysis of slope stability. Int J Numer Anal Meth Geomech 9:199–223

    Article  Google Scholar 

  10. Liu H (2006) 2D and 3D slope stability analysis methods based on the assumption regarding the distribution of normal stresses over the sliding surface [Ph.D.Thesis]. Nanjing. PLA University of Science and Technology

  11. Liu H (2019) The influence of initial normal stress assumption of slip surface on safety factor of symmetrical three-dimensional slopes. Adv Mater Sci Eng. https://doi.org/10.1155/2019/4216179

    Article  Google Scholar 

  12. Ugai K, Leshchinsky D (1995) Three-dimensional limit equilibrium and finite element analyses: a comparison of results. Soils Found 35(4):1–7

    Article  Google Scholar 

  13. Zhang X (1988) Three-dimensional stability analysis of concave slopes in plan view. ASCE J Geotech Eng 114(6):658–671

    Article  Google Scholar 

  14. Zhu DY, Ding XL, Deng JH (2008) Explicit solution to 3D safety factor of slope based on force equilibrium and its application to engineering. Rock Soil Mech 29(8):2011–2015

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Huali Liu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Liu, H., XU, D. & Min, Y. Discussion on the Multi-Solution of Three-Dimensional Slope Safety Factor. Geotech Geol Eng (2021). https://doi.org/10.1007/s10706-021-01697-z

Download citation

Keywords

  • Three-dimensional (3D)
  • Slope
  • Stability
  • Safety factor
  • Limit equilibrium method