Abstract
Slope stability assessment is one of the most important issues for geotechnical engineers. In the framework of a nonlinear failure criterion, four different types of safety factors are presented and their relationships are investigated for soil slope in this study. The variational method is incorporated into the kinematic approach of limit analysis to assess the stability of soil slope with known geometric boundary, and seismic effects are considered. The seismic loads are simplified as external forces acting on the slope. A rotational failure mechanism is used to describe the sliding mode of slopes. The differential equations for the sliding surface and corresponding stress distribution are derived using the variational method and then are employed to generate the sliding surface via the fourth-order Runge-Kutta approach. To avoid the computational complexity, the energy-work balance equation of the kinematic approach, instead of the static equilibrium equation, is used to judge whether the state of the slope is critical. The safety factor is designed as the minimum factor that brings the slope in the limit state. Computational schemes are proposed to calculate the values of safety factors. The validity of the proposed approach is demonstrated through comparison with previous works. Finally, parametric study is conducted to further reveal the relationships among the four types of safety factors.
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Abbreviations
- c 0 :
-
Initial cohesion
- c t :
-
Equivalent cohesion
- c F :
-
Reduced cohesion
- D :
-
Internal work rate
- F s1 :
-
Safety factor defined by D/W
- F S2 :
-
Safety factor defined by gravity increase method
- F S3 :
-
Safety factor defined by reducing c0 and σt
- F s4 :
-
Safety factor defined by reducing c0
- H :
-
Slope height
- H q :
-
Resultant force in horizontal direction in Eq. (13)
- I :
-
Total virtual work
- k h :
-
Horizontal seismic coefficient
- m :
-
Nonlinear coefficient
- M q :
-
Resultant moment about rotational point
- r :
-
Polar radius of the sliding surface
- V q :
-
Resultant force in vertical direction
- W :
-
External work rate
- W γ :
-
External work rate done by gravity
- W kh :
-
External work rate done by seismic force
- x 0 :
-
x-coordinate of the beginning point of sliding surface
- x c :
-
x-coordinate of the origin of polar coordinates
- x n :
-
x-coordinate of the terminal point of sliding surface
- X :
-
Defined variable in Eq. (22)
- Y 0 :
-
y-coordinate of the beginning point of sliding surface
- y n :
-
y-coordinate of the terminal point of sliding surface
- y c :
-
y-coordinate of the origin of polar coordinates
- y1 :
-
Function for the slope geometry
- y′:
-
dy/dx
- Y :
-
Defined variable in Eq. (23)
- γ :
-
Unit weight of soil
- \(\dot{\gamma}^{P}\) :
-
Rate of the plastic shear strain
- Δu :
-
Virtual displacement in horizontal direction
- Δv :
-
Virtual displacement in vertical direction
- ΔΩ:
-
Virtual rotation angle
- \(\dot{\varepsilon}^{P}\) :
-
Rate of the plastic normal strain
- σ n :
-
Normal stress in the failure surface
- σ t :
-
Uniaxial tensile strength
- τ :
-
Shear stress in the failure surface
- τ F :
-
Shear strength after reduction
- φ t :
-
Equivalent frictional angle
- φ F :
-
Reduced frictional angle
- ω :
-
Angular velocity
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Acknowledgments
The preparation of the paper has received financial supports from the Fundamental Research Funds for the Central Universities (No. JZ2020HGTB0042 and No. JZ2020HGQA0212) and National Natural Science Foundation of China (No. 52004088). Their financial supports are greatly appreciated.
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Hou, C., Zhang, R., Li, Y. et al. Comparisons of Safety Factors for Slope in Nonlinear Soils. KSCE J Civ Eng 25, 3737–3749 (2021). https://doi.org/10.1007/s12205-021-0298-0
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DOI: https://doi.org/10.1007/s12205-021-0298-0