Advertisement

Earthquake Engineering and Engineering Vibration

, Volume 16, Issue 4, pp 841–857 | Cite as

Probabilistic analysis for the response of nonlinear base isolation system under the ground excitation induced by high dam flood discharge

  • Chao Liang
  • Jinliang Zhang
  • Jijian Lian
  • Fang Liu
  • Xinyao Li
Technical Papers
  • 68 Downloads

Abstract

According to theoretical analysis, a general characteristic of the ground vibration induced by high dam flood discharge is that the dominant frequency ranges over several narrow frequency bands, which is verified by observations from the Xiangjiaba Hydropower Station. Nonlinear base isolation is used to reduce the structure vibration under ground excitation and the advantage of the isolation application is that the low-frequency resonance problem does not need to be considered due to its excitation characteristics, which significantly facilitate the isolation design. In order to obtain the response probabilistic distribution of a nonlinear system, the state space split technique is modified. As only a few degrees of freedom are subjected to the random noise, the probabilistic distribution of the response without involving stochastic excitation is represented by the δ function. Then, the sampling property of the δ function is employed to reduce the dimension of the Fokker-Planck- Kolmogorov (FPK) equation and the low-dimensional FPK equation is solvable with existing methods. Numerical results indicate that the proposed approach is effective and accurate. Moreover, the response probabilistic distributions are more reasonable and scientific than the peak responses calculated by conventional time and frequency domain methods.

Keywords

ground vibration high dam flood discharge structural response nonlinear base isolation system probabilistic analysis 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgement

This work was supported by the National Key R & D Program of China (No. 2016YFC0401705), Science Fund for Creative Research Groups of the National Natural Science Foundation of China (51621092), the National Natural Science Foundation of China (No. 51579173, No. 51379140, No. 51309177 and No. 51509180), the Fund for Key Research Area Innovation Groups of China Ministry of Science and Technology (No. 2014RA4031), the Program of Introducing Talents of Discipline to Universities (No. B14012) and the Tianjin Innovation Team Foundation of Key Research Areas (No. 2014TDA001).

References

  1. Chen BJ, Tsai CS, Chung LL and Chiang TC (2006), “Seismic Behavior of Structures Isolated with a Hybrid System of Rubber Bearings,” Structural Engineering & Mechanics, 22(6): 761–783.CrossRefGoogle Scholar
  2. Chopra AK (2001), Dynamics of Structures: Theory and Applications to Earthquake Engineering, 2nd Edition, Prentice Hall, Englewood Cliffs, New Jersey.Google Scholar
  3. Clough RW and Penzien J (1993), Dynamics of Structure, 2nd Edition, McGraw-Hill, Inc., New York.Google Scholar
  4. Darbre GR, Smet CAMD and Kraemer C (2000), “Natural Frequencies Measured from Ambient Vibration Response of the Arch Dam of Mauvoisin,” Earthquake Engineering & Structural Dynamics, 29(5): 577–586.CrossRefGoogle Scholar
  5. Dezfuli FH and Alam MS (2014), “Sensitivity Analysis of Carbon Fiber-Reinforced Elastomeric Isolators Based on Experimental Tests and Finite Element Simulations,” Bulletin of Earthquake Engineering, 12(2): 1025–1043.CrossRefGoogle Scholar
  6. Dezfuli FH and Alam MS (2016), “Effect of Different Steel-Reinforced Elastomeric Isolators on the Seismic Fragility of a Highway Bridge,” Structural Control and Health Monitoring, Published online, DOI: 10.1002/stc.1866.Google Scholar
  7. Er G (2000), “Exponential Clos ure Method for Some Randomly Excited Non-Linear Systems,” International Journal of Non-Linear Mechanics, 35(1): 69–78.CrossRefGoogle Scholar
  8. Er G and Lu V (2012), “State-S pace-Split Method for Some Generalized Fokker-Planck-Kolmogorov Equations in High Dimensions,” Physical Review E Statistical Physics Plasmas Fluids & Related Interdisciplinary Topics, 85(6): 3112–3113.Google Scholar
  9. He L, Lian J, Ma B and Wang H (2014), “Optimal Multiaxial Sensor Placement for Modal Identification of Large Structures,” Structural Control & Health Monitoring, 21(1): 61–79.CrossRefGoogle Scholar
  10. He L, Lian JJ and Ma B (2014), “Intelligent Damage Identification Method for Large Structures Based on Strain Modal Parameters,” Journal of Vibration and Control, 20: 1783–1795.CrossRefGoogle Scholar
  11. Heredia-Zavoni E and Santa-Cruz S (2015), “Modal Response Analysis of Multi-Support Structures Using a Random Vibration Approach,” Earthquake Engineering & Structural Dynamics, 44: 2241–2260.CrossRefGoogle Scholar
  12. Hwang JS and Ku SW (1997), “An alytical Modeling of High Damping Rubber Bearings,” Journal of Structural Engineering, ASCE, 123(8): 1029–1036.CrossRefGoogle Scholar
  13. Hwang JS, Wu JD, Pan TC and Yang G (2002), “A Mathematical Hysteretic Model for Elastomeric Isolation Bearings,” Earthquake Engineering & Structural Dynamics, 31(4): 771–789.CrossRefGoogle Scholar
  14. Kalman RE (1959), “On the Gene ral Theory of Control Systems,” Automatic Control Ire Transactions on, 4(3): 110.CrossRefGoogle Scholar
  15. Kawashima K (1994), “Developme nt of Seismic Isolation Systems for Bridges,” Report, Ministry of Construction, Earthquake Engineering Division, Japan.Google Scholar
  16. Kotlyakov AV, Shumakova EM and Artem’Ev SA (2007), “Dynamics of the Coastal Zone of the Kuibyshev and Saratov Reservoirs in the Tolyatti Area and Its Correlation with the Operation Regime of the Zhigulevskaya HPP,” Water Resources, 34(6): 657–662.CrossRefGoogle Scholar
  17. Li S, Lian J and Ouyang Q (2014), “Study on Source of High Dam Discharge-induced Vibration in Dam Region and Site,” Water Resources and Hydropower Engineering, 45: 47–51. (in Chinese)Google Scholar
  18. Lian J (2009), “Safety Evaluat ion and Dynamic Coupling Analysis of Counter-arched Slab in Plunge Pool,” Science in China, 52(5): 1397–1412.CrossRefGoogle Scholar
  19. Lian J, Li C, Liu F and Wu S (2014), “A Prediction Method of Flood Discharge Atomization for High Dams,” Journal of Hydraulic Research, 52(2): 274–282.CrossRefGoogle Scholar
  20. Lian J, Zhang Y, Liu F and Zhao Q (2015), “Analysis of the Ground Vibration Induced by High Dam Flood Discharge Using the Cross Wavelet Transform Method,” Journal of Renewable & Sustainable Energy, 7(4): 043146.CrossRefGoogle Scholar
  21. Liu F, Lian J and Gu J (2009), “Spectral Analysis of Pressure Fluctuation Signals of Flow Using AR Method,” Journal of Hydraulic Engineering, 40(11): 1397–1402. (in Chinese)Google Scholar
  22. Liu F, Lian J, Zhang X and Li C (2010), “Experimental Study of Atomization and Splashing Caused by a Ski-Jump Jet into Scour Pool,” Journal of Hydroelectric Engineering, 29(4): 113–117. (in Chinese)Google Scholar
  23. Liu G, Lian J, Liang C, Li G a nd Hu J (2015), “An Improved Complex Multiple-support Response Spectrum Method for the Non-classically Damped Linear System with Coupled Damping,” Bulletin of Earthquake Engineering, 14(1): 161–184.CrossRefGoogle Scholar
  24. Liu G, Lian J and Liang C (2016), “Completeness Verification of Complex Response Spectrum Method for Underdamped and Overdamped Systems Regarding the Decoupled Damping as Mathematical Parameter without Physical Meaning,” Journal of Earthquake Engineering, 20(7): 1104–1125.CrossRefGoogle Scholar
  25. Proulx J, Paultre P, Rheault J and Robert Y (2001), “An Experimental Investigation of Water Level Effects on the Dynamic Behaviour of a Large Arch Dam,” Earthquake Engineering & Structural Dynamics, 30(30): 1147–1166.CrossRefGoogle Scholar
  26. Rachael RB, Brian DB and Juan AGC (2016), “Experimental Demonstration of a New Extension Plate Scour Countermeasure Downstream of Stilling Basins,” Journal of Hydraulic Engineering, ASCE, pp: 06016013.Google Scholar
  27. Shumakova EM, Kotlyakov AV and Shumakov GV (2010), “The Effect of Vibrations in the Zhigulevskii Hydropower Structure on Soils in the Nearby Territories of Tolyatti City,” Water Resources, 37(37): 306–310.CrossRefGoogle Scholar
  28. Souza M and Ferguson NS (2016), “Variability in the Dynamic Response of Connected Atructures–A Mobility Approach for Point Connections,” 3rd International Symposium on Uncertainty Quantification and Stochastic Modeling, Maresias, Brazil, 25pp.Google Scholar
  29. Yu R and Zhou X (2007), “Respo nse Spectrum Analysis for Non-Classically Damped Linear System with Multiple-Support Excitations,” Bulletin of Earthquake Engineering, 6(2): 261–284.CrossRefGoogle Scholar
  30. Yu R, Zhou X and Yuan M (2012), “Dynamic Response Analysis of Generally Damped Linear System with Repeated Eigenvalues,” Structural Engineering & Mechanics, 42(4): 449–469.CrossRefGoogle Scholar
  31. Zhang Y, Lian J, Liu F and Yu X (2015), “Vibration Characteristics of Powerhouse Structure of Roof Overflow Hydropower Station Based on Prototype Observation,” Journal of Tianjin University, 2015(7): 584–590. (in Chinese)Google Scholar

Copyright information

© Institute of Engineering Mechanics, China Earthquake Administration and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Chao Liang
    • 1
    • 2
  • Jinliang Zhang
    • 1
    • 2
    • 3
  • Jijian Lian
    • 1
    • 2
  • Fang Liu
    • 1
    • 2
  • Xinyao Li
    • 1
    • 2
  1. 1.State Key Laboratory of Hydraulic Engineering Simulation and SafetyTianjin UniversityTianjinChina
  2. 2.School of Civil EngineeringTianjin UniversityTianjinChina
  3. 3.Yellow River Engineering Consulting Co., Ltd.Henan ProvinceChina

Personalised recommendations