Abstract
Zigui Basin is a major landslide-prone region in the Three Gorges Reservoir region of China, and the stabilizing pile is an effective and widely employed countermeasure to reinforce landslides in this region. However, stabilizing piles are mostly designed using deterministic and stability-oriented methods, which generally ignore the system performance and cost-effectiveness. Using the Majiagou landslide reinforced with stabilizing piles as a case study, a probabilistic multi-objective optimization framework for the design of stabilizing piles is proposed and illustrated. Specifically, performance objectives related to failure probability, system robustness and life-cycle cost of the landslide-stabilizing pile system with feasible designs are evaluated, then the best compromised design is obtained by means of Pareto optimality. Expert knowledge and professional judgment are required to set necessary restrictions and finally determine the optimal design. The results show that there is a better design of stabilizing piles than the existing one, with which acceptable reinforcement effectiveness, compromised life-cycle cost and robust system performance can be realized. The optimal design will also vary with the concerned performance objectives and knowledge-based judgment. Further relationships and interpretations between design parameters and system responses are discussed through parametric analyses.
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Abbreviations
- σ c :
-
Uniaxial compression strength of rock
- h :
-
Pile length
- b :
-
Width of rectangular pile cross-section
- a :
-
Height of rectangular pile cross-section
- L :
-
Pile spacing
- h 1 :
-
Cantilever sectional length of the pile
- h 2 :
-
Embedded sectional length of the plie
- R i :
-
Resistant force of the ith slice
- T i :
-
Sliding force of the ith slice
- W i :
-
Gravity of the ith slice
- k h :
-
Pseudo-static horizontal seismic coefficient
- α i :
-
Angle between the slip surface of the ith slice and the horizontal plane
- c i :
-
Cohesion of soil on the slip surface of the ith slice
- φ i :
-
Friction angle of soil on the slip surface of the ith slice
- l i :
-
Length of the slip surface of the ith slice
- P i :
-
Imbalance thrust of the ith slice
- F S :
-
Factor of safety
- Pi′:
-
Effective imbalance thrust of the ith slice
- F su :
-
Upper limit value of factor of safety
- F sl :
-
Lower limit value of factor of safety
- F TS :
-
Target factor of safety
- P ti :
-
Target imbalance thrust of the ith slice
- P di :
-
Design imbalance thrust of the ith slice
- P :
-
Design resistant stress of the pile
- K :
-
Foundation coefficient
- E :
-
Young’s modulus of the pile
- I :
-
Inertia moment of the pile
- d :
-
Diameter of circular pile cross-section
- B p :
-
Calculative width of the pile
- β :
-
Deformation coefficient of the laterally loaded pile
- x :
-
Deflection of the pile (x0, deflection of the pile head; xs, deflection of the pile part with x and y coordinates of 0; xb, deflection of the pile tip)
- θ :
-
Rotation of the pile (θ0, rotation of pile head; θs, deflection of the pile part with x and y coordinates of 0;θb, rotation of the pile tip)
- M :
-
Bending moment of the pile (M0, bending moment of the pile head; Ms, deflection of the pile part with x and y coordinates of 0; Mb, bending moment of the pile tip)
- Q :
-
Shearing force of the pile (Q0, shearing force of the pile head; Qs, deflection of the pile part with x and y coordinates of 0; Qb, shearing force of the pile tip)
- S i :
-
Horizontal compressive stress that pile applies on the ith bedrock stratum
- S imax :
-
Maximal horizontal compressive stress that pile applies on the ith bedrock stratum
- x imax :
-
Maximal deflection of the pile segment embedded in the i-th bedrock stratum
- [σhi]:
-
Allowable horizontal bearing capacity of the i-th bedrock stratum
- C hi :
-
Horizontal conversion ratio related to the structure of the ith bedrock stratum
- η i :
-
Coefficient related to the geotechnical properties of the ith bedrock stratum
- [xh]:
-
Allowable deflection of the pile head
- σ cm :
-
Uniaxial compression strength of rock mass
- s :
-
A constant of rock mass
- a :
-
A constant of rock mass
- GSI:
-
Geological strength index
- D :
-
Foctor of disturbance of rock mass subjected to blast damage and stress relaxation
- P f :
-
Failure probability
- E[x0]:
-
Mean value of deflection of the pile head
- σ[x0]:
-
Standard deviation of deflection of the pile head
- C T :
-
Expected cost of a landslide-stabilizing pile system during its lifetime
- C INI :
-
Initial construction cost
- C INS :
-
Cost of inspections
- C REP :
-
Cost of repair measures
- C F :
-
Expected failure cost
- c ini :
-
Initial construction cost of unit cubic meter of the pile
- c ins :
-
Inspection cost of each pile per year
- c rep :
-
Cost of repair related to a unit cubic meter of the landslide during the designed lifetime of piles
- n :
-
Counts of piles
- V p :
-
Volume of each pile
- T :
-
Designed lifetime of piles
- V :
-
Volume of the landslide
- L F :
-
Failure loss of landslide global failure
- V bj :
-
Vulnerability of the j-th disaster-bearing body
- E bj :
-
Economic value of the j-th disaster-bearing body
- n db :
-
Counts of disaster-bearing bodies
- C S :
-
Expected engineering cost
- L S :
-
Expected failure loss
- P T :
-
Target failure probability
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Acknowledgements
This research is supported by the National Key R&D Program of China (2017YFC1501304, 2018YFC1507200), the National Science Fund for Excellent Young Scholars of China (41922055), the Key Program of National Natural Science Foundation of China (41931295, 41630643), and the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (CUGCJ1701). We thank the Editors and two anonymous reviewers for their constructive comments which help us substantially improve the quality of the manuscript.
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Yao, W., Li, C., Zhan, H. et al. Probabilistic multi-objective optimization for landslide reinforcement with stabilizing piles in Zigui Basin of Three Gorges Reservoir region, China. Stoch Environ Res Risk Assess 34, 807–824 (2020). https://doi.org/10.1007/s00477-020-01800-5
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DOI: https://doi.org/10.1007/s00477-020-01800-5