Abstract
Based on the limit analysis upper bound method, a new mechanism of soil slope failure has been proposed which was consisted of plastic shear zone and rigid block zone. The different zones interface were regarded as discontinuity lines. Two sliding blocks of the slope were also incorporated horizontal seismic force and vertical gravity force. The velocities and forces were analyzed in two blocks, and the expression of velocity discontinuities was derived according to the principle of incompressibility. The external force done work for the blocks and the internal energy dissipated of the plastic shear zone and the velocity discontinuous were solved. The stability ratios were derived for the height of two-level slope with different rates to involve seismic and no seismic. The present stability ratios were compared to the previous study, which showed the superiority of the mechanism and the rationality of the analysis. The critical height of the slope can provide a theoretical basis for slope support and design.
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Abbreviations
- c :
-
Soil cohesion, N
- C u :
-
Undrained shear strength, kPa
- H :
-
Total height of the slope, m
- H c :
-
Critical height of the soil slope, m
- H i :
-
Height of different levels, i =1, 2, m
- K c :
-
Critical acceleration factor
- K c W 1 :
-
Seismic force in the horizontal direction of block AMOB, N
- K c W 2 :
-
Seismic force in the horizontal direction of block BOC, N
- N :
-
Stability ratio
- N v :
-
Change rate of stability ratio
- r 0 :
-
Width of block BCO base, m
- r 1 :
-
Horizontal distance of slope top A to slope top C, m
- u(r):
-
Horizontal velocity at horizontal distance r, m/s
- u 1(r):
-
Uniform horizontal velocity across BO, m/s
- v 0 :
-
Initial vertical velocity, m/s
- v 1 :
-
Vertical velocity of the block zone, m/s
- v h :
-
Horizontal velocity of the shearing zone, m/s
- v v :
-
Vertical velocity of the shearing zone, m/s
- V :
-
Volume of the zone, m3
- W 1 :
-
Gravity force of block AMOB, N
- W 2 :
-
Gravity force of the block BOC, N
- α i :
-
Slope angle, i = 1, 2, °
- β :
-
Geometric parameter of the shearing zone
- βr 0 :
-
Width of the slope base, m
- γ :
-
Bulk unit weight of the soil, kN/m3
- ε :
-
Largest principal plastic strain rate
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Acknowledgements
The author(s) would like to thank Dr. XIE Jun for valuable discussion in this research.
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Foundation item: the National Natural Science Foundation of China (No. 51478444, 51574115 and 51774121)
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Yin, X., Wang, L. Block Limit Analysis Method for Stability of Slopes During Earthquakes. J. Shanghai Jiaotong Univ. (Sci.) 23, 764–769 (2018). https://doi.org/10.1007/s12204-018-1997-7
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DOI: https://doi.org/10.1007/s12204-018-1997-7