Abstract
Gravity dam reliability analysis is inherently complex considering the parameters randomness caused by the spatial variability of dam foundation, the coupled influence of seepage and high nonlinearity of dam safety evaluation. Taking the seepage randomness and dam foundation spatial variability into account, a fluid structure interaction (FSI) stochastic finite element approach and a weighted dynamic response surface method (WD-RSM) are proposed based on the integrated 3D engineering geological model. When applying the methods to gravity dam reliability analysis, three technical issues are considered: (1) the influence of dam foundation spatial variability on the gravity safety, (2) the key effect that the FSI makes on the gravity analysis and (3) the available safety evaluation method for the highly nonlinearity problem. The FSI stochastic finite element approach and the WD-RSM are validated using a real case of a gravity dam in operation with karst foundation. The results show the evident negative effect that seepage militated on the dam stability and the consistency and discreteness that spatial variability of dam foundation incarnated, which facilitates understanding the role of seepage and spatial variability.
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Abbreviations
- \(M_{\varOmega }\) :
-
The whole geological model in \(\varOmega\)
- n :
-
Entire number of geological bodies
- \(M_{i}\) :
-
Geological body
- \(S_{i1}\) :
-
Main structural surfaces
- \({\text{Sl}}_{ik}\) :
-
Peripheral surfaces
- m :
-
Entire number of peripheral surfaces
- \(Y_{i1}\) :
-
Point sets for \(S_{i1}\)
- \(\partial S_{ij}\) :
-
Set of all bounding vertexes
- \(\mu\) :
-
Mean value of random variable
- \(\delta\) :
-
The correlation distance
- \(T\) :
-
Length of the local average unit
- \(\rho_{\text{l}}\) :
-
Density of the fluid
- \(\rho_{\text{s}}\) :
-
Density of the solid
- \(\phi\) :
-
Porosity
- \(v\) :
-
Velocity
- \(\varepsilon_{\text{v}}\) :
-
Solid volumetric strain
- K :
-
Permeability coefficient
- \(c_{\rho }\) :
-
Compressibility coefficient of fluid
- \(E_{\text{m}}\) :
-
Elasticity modulus of solid frame
- \(P_{\text{f}}^{k}\) :
-
Probability of failure
- \(R^{2}\) :
-
Determination coefficient
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Acknowledgements
The research was supported by the Natural Science Foundation of China (Grant No. 51439005), the National Basic Research Program of China (973 Program) (No. 2013CB035906) and the Groups of the National Natural Science Foundation of China (No. 51621092).
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Zhu, X., Wang, X., Li, X. et al. A New Dam Reliability Analysis Considering Fluid Structure Interaction. Rock Mech Rock Eng 51, 2505–2516 (2018). https://doi.org/10.1007/s00603-017-1369-x
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DOI: https://doi.org/10.1007/s00603-017-1369-x