Analytical solution for vertical site response analysis and its validation

  • Junwei Liu
  • Xiao Zhang
  • Zewei Cao
  • Bo HanEmail author
  • Shizeng Yang


Existing studies for site response analysis in geotechnical earthquake engineering have widely concentrated on the horizontal component of the ground motion. However, strong vertical ground motions have been repeatedly observed, resulting in significant vertical compression damage of engineering structures. Furthermore, for the seismic design of critical structures (e.g. large-scale dams and nuclear power plants), the ground motions in all three directions should be considered. Therefore, there is a need to investigate the site response subjected to the vertical component of the ground motion, especially for the seismic design of critical structures. Consequently, in this study, a numerical program for vertical site response analysis is proposed based on the commonly used analytical transfer function method. The proposed program is then validated against well-documented case studies obtained from the Japanese KiK-net (Kiban Kyoshin network) downhole array monitoring system. Results show that the response spectra at the ground surface are well predicted in the low frequency range (<5 Hz), while discrepancies are observed in the high frequency range. However, the high frequency discrepancies do not significantly affect the overall prediction accuracy, as the overall seismic response of geotechnical structures are usually dominated by low frequency vibrations. Furthermore, the limitations in the analysis are also discussed.


site response analysis vertical ground motions transfer function analytical solution 


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This work was supported by the National Natural Science Foundation of China (Grant No. 51579154) and the Natural Science Foundation of Shandong Province (Grant No. ZR2018QEE008).


  1. Amorosi A, Boldini D and Elia G (2010), “Parametric Study on Seismic Ground Response by Finite Element Modelling,” Computers and Geotechnics, 37: 515–528.CrossRefGoogle Scholar
  2. Borja RI, Chao HY, Montans FJ and Lin CH (1999), “Nonlinear Ground Response at Lotung LSST Site,” Journal of Geotechnical and Geoenvironmental Engineering, 125(3): 187–197.CrossRefGoogle Scholar
  3. Bradley BA (2011), “Near-Source Strong Ground Motions Observed in the 22 February 2011 Christchurch Earthquake,” Seismological Research Letters, 82(6): 853–865.CrossRefGoogle Scholar
  4. Chenari RJ and Taleshani SAB (2016), “Site Response of Heterogeneous Natural Deposits to Harmonic Excitation Applied to More than 100 Case Histories,” Earthquake Engineering and Engineering Vibration, 15(2): 341–356.CrossRefGoogle Scholar
  5. Han B, Yang Z, Zdravković L and Kontoe S (2015), “Non-Linearity of Gravelly Soils under Seismic Compressional Deformation Based on KiK-Net Downhole Array Observations”, Geotechnique Letters, 5(4): 287–293.CrossRefGoogle Scholar
  6. Han B, Zdravković L and Kontoe S (2018), “Analytical and Numerical Investigation of Site Response Due to Vertical Ground Motion,” Geotechnique, DOI: 10.1680/jgeot.15.P.191.Google Scholar
  7. Han B, Zdravković L, Kontoe S and Taborda DMG (2016), “Numerical Investigation of the Response of the Yele Rockfill Dam during the 2008 Wenchuan Earthquake,” Soil Dynamics and Earthquake Engineering, 88: 124–142.CrossRefGoogle Scholar
  8. Han B, Zdravković L, Kontoe S and Taborda DMG (2017), “Numerical Investigation of Multi-Directional Site Response Based on KiK-Net Downhole Array Monitoring Data,” Computers and Geotechnics, 89: 55–70.CrossRefGoogle Scholar
  9. Kramer SL (1996), Geotechnical Earthquake Engineering. New Jersey: Prentice Hall.Google Scholar
  10. Lee CP, Tsai YB and Wen KL (2006), “Analysis of Nonlinear Site Response Using the LSST Downhole Accelerometer Array Data,” Soil Dynamics and Earthquake Engineering, 26: 435–460.CrossRefGoogle Scholar
  11. Liu H, Bo J, Li P, Qi W and Zhang Y (2016), “Site Amplification Effects as an Explanation for the Intensity Anomaly in the Hanyuan Town during the Wenchuan Mw 7.9 Earthquake,” Earthquake Engineering and Engineering Vibration, 15(3): 435–444.CrossRefGoogle Scholar
  12. Ministry of Housing and Urban-Rural Development of the People’s Republic of China (2010), China Earthquake-resistant Design Standard for Civil Engineering Structures.Google Scholar
  13. Papazoglou AJ and Elnashai AS (1996), “Analytical and Field Evidence of the Damaging Effect of Vertical Earthquake Ground Motion,” Earthquake Engineering and Structural Dynamics, 25(2): 1109–1137.CrossRefGoogle Scholar
  14. Sato K, Kokusho T, Matsumoto M and Yamada E (1996), “Nonlinear Seismic Response and Soil Property During Strong Motion,” Soils and Foundations, 36(Special issue): 41–52.Google Scholar
  15. Kaklamanos J, Bradley BA, Thompson EM and Baise LG (2013), “Critical Parameters Affecting Bias and Variability in Site-Response Analyses Using KiK-Net Downhole Array Data,” Bulletin of the Seismological Society of America, 103(3): 1733–1749.CrossRefGoogle Scholar
  16. UBC (1997), Uniform Building Code. International Conference of Building Officials, California.Google Scholar
  17. Wang H, Xie L, Wang S and Ye P (2013), “Site Response in the Qionghai Basin in the Wenchuan earthquake,” Earthquake Engineering and Engineering Vibration, 12(2): 195–199.CrossRefGoogle Scholar
  18. Yang J and Sato T (2000), “Interpretation of Seismic Vertical Amplification Observed at an Array Site,” Bulletin of the Seismological Society of America, 90(2): 275–285.CrossRefGoogle Scholar

Copyright information

© Institute of Engineering Mechanics, China Earthquake Administration and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Junwei Liu
    • 1
  • Xiao Zhang
    • 2
  • Zewei Cao
    • 3
  • Bo Han
    • 2
    Email author
  • Shizeng Yang
    • 4
  1. 1.School of Civil EngineeringQingdao University of TechnologyQingdaoChina
  2. 2.School of Civil EngineeringShandong UniversityJinanChina
  3. 3.Nantong Municipal Engineering Design Institute Co. Ltd.NantongChina
  4. 4.Huangdao Municipal Water Resources BureauQingdaoChina

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