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Review and Comparative Analysis of Factor of Safety Definitions in Slope Stability

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Abstract

There are several definitions of the factor of safety used to quantitatively characterize slope or landslide stability, which can yield varying results. A comprehensive comparison of the differences among various definitions is necessary for practitioners. In this study, the characteristics of the existing definitions are comprehensively summarized. They can essentially be classified into five categories, including the rotation moment ratio defined by Fellenius, the shear strength-stress ratio defined by Bishop same as the shear strength reduction coefficient, the amplification coefficient of driving forces defined in the China code, the work rate ratio alternatively suitable for the analytical kinematical limit method, and the square root of deformation energy ratio with rigorous physical meaning. Some examples show that the safety factor based on the Fellenius definition is the smallest, while that by the Kulhawy definition is the largest, and relatively increasing by (6.6–13.4)%. The difference among the safety factors defined by Fellenius, Bishop, and Kulhawy is mainly due to distinct assumptions on the interslice forces using different slice methods rather than the different definitions. The shear strength reduction via numerical simulation method is the most complicated approach for slope stability in terms of execution and computation time. The two definitions using the work rate ratio and strength reduction in the limit analysis method are close only for slopes initially approaching the limit state. The square root of the work rate ratio is consequently proposed for comparability. The definitions of the shear strength-stress ratio and square root of deformation energy ratio are generally recommended.

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Data Availability

All data generated or analyzed during this study are included within the article. All data used are available from the corresponding author by request.

Abbreviations

c :

Soil cohesion

D :

External work rate on the slide body in the limit state of a soil slope, where subscript a stands for the actual state or the non-limit state

E :

Internal energy dissipation on the slip surface in the limit state of a soil slope

E m :

Elastic modulus

F s :

Factor of safety, where superscript W and S stand for the work rate ratio and shear strength reduction in AKLM, respectively

h :

Slope height

H i :

Tangential interslice force on vertically divided slice i

N i :

Normal force on the local slip surface of soil slice i

P i :

Normal interslice force on vertically divided slice i

R i :

Tangent force on the local slip surface of soil slice i

W :

Self-weight of soil mass

α :

Dip angle of the local slip surface in each slice

γ :

Soil unit weight

τ xy :

Shear stress on the boundaries of a square element on the slip surface

τ u :

Ultimate shear strength of a point on the slip surface

τ :

Shear stress of a point on the slip surface

σ x :

Horizontal stress

σ y :

Vertical stress

σ n :

Normal stress of a point on the slip surface

φ :

Soil internal friction angle

β :

Slope angle

μ :

Poisson’s ratio

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Acknowledgements

This research was supported by the Construction S&T Project of Department of Transportation of Sichuan Province (Grant no. 2024A04), Construction S&T Project of China Railway Construction Corporation Limited (Grant no. 2023-B15), and National Natural Science Foundation of China (Grant no. 51578466).

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Authors and Affiliations

  1. Key Laboratory of High-Speed Railway Engineering, Ministry of Education, Southwest Jiaotong University, Chengdu, 610031, China

    Shiguo Xiao

  2. School of Civil Engineering, Southwest Jiaotong University, Chengdu, 610031, China

    Tianyi Dai

  3. Department of Geological Engineering, Southwest Jiaotong University, Chengdu, 610031, China

    Shaohong Li

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  1. Shiguo Xiao
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by SX, TD and SL. The first draft of the manuscript was written by SX, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Shiguo Xiao.

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Xiao, S., Dai, T. & Li, S. Review and Comparative Analysis of Factor of Safety Definitions in Slope Stability. Geotech Geol Eng (2024). https://doi.org/10.1007/s10706-024-02793-6

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