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


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.


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


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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).


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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

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