Abstract
Slope stability has been the research focus in the field of geotechnical engineering. Both the asynchronous decay speeds and distinct stability contributions of cohesion c and friction φ during slope instability have been evidenced. In this study, based on linear softening model and weighted average hypothesis, a modified double-reduction method is established. The research includes: 1) the asynchronism between decay speeds of c and φ are described by adopting different slopes in linear softening model for c and tanφ, in which case the respective reduction factors in strength reduction method Fc and Fφ are solved. 2) The distinct slope stability contributions of c and φ is readily linked with the different influences to safety factor, and therefore, introducing the equivalent influence angle θe (defined as the slope angle at which c and φ share identical contributions to stability), as well as its determination method. 3) According to weighted average hypothesis that the overall safety factor Fs is the weighted average of Fc and Fφ, the contribution scaling factor μ (defined as the weighted ratio of Fc and Fφ is proposed, which promotes the solution of respective weighted coefficients wc and wφ of two reduction factors by combining θe, achieving a new double-reduction method. 4) The validity of this method is verified via comprehensive comparison with existing double-reduction methods of practical slope examples.
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Abbreviations
- c :
-
Cohesion
- c cr :
-
Critical cohesion of slope
- c ini :
-
Initial cohesion of slope
- F c :
-
The reduction factor of cohesion
- F s :
-
The overall safety factor of slope
- F φ :
-
The reduction factor of friction
- w c :
-
Weighted coefficients of the reduction factor of cohesion
- w φ :
-
Weighted coefficients of the reduction factor of internal friction angle
- Δx :
-
Translation distance in x-direction
- Δy :
-
Translation distance in y-direction
- η :
-
Scaling coefficient
- θ e :
-
Equivalent influence angle of slope
- ϑ :
-
Rotation angle
- μ :
-
Contribution scaling factor
- φ :
-
Friction
- φ cr :
-
Critical internal friction angle of slope
- φ ini :
-
Initial internal friction angle of slope
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Acknowledgements
This paper gets its funding from project (51774107, 51774322, 51774131) supported by National Natural Science Foundation of China; Project (2018JJ2500) supported by Hunan Provincial Natural Science Foundation of China; Scientific research innovation project for graduate students of Central South University (2019zzts303). The authors wish to acknowledge these supports.
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Chen, Y., Lin, H., Wang, Y. et al. Modified Double-Reduction Method considering Strain Softening and Equivalent Influence Angle. KSCE J Civ Eng 24, 3257–3266 (2020). https://doi.org/10.1007/s12205-020-0547-7
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DOI: https://doi.org/10.1007/s12205-020-0547-7