Smoothed response spectra including soil-structure interaction effects

  • 3 Accesses


Elastic response spectra that take into account the effects of soil-structure interaction on soft soils are developed. The response spectra are calculated utilizing a 3DOF system including deformations of the superstructure and foundation. The equations of motion of the system are solved using direct integration under normalized earthquake records. Statistical processing of the results is implemented resulting in response spectra for “short and dense buildings with low interaction”, “short and dense buildings with high interaction”, “tall and light buildings with low interaction” and “tall and light buildings with high interaction”. The resulting response spectra are smoothed and discussed.

This is a preview of subscription content, log in to check access.

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA


  1. ASCE 7 (2010), Minimum Design Loads for Buildings and Other Structures, American Society of Civil Engineers, Virginia, USA.

  2. ASCE 41 (2013), Seismic Rehabilitation of Existing Buildings, American Society of Civil Engineers, Virginia, USA.

  3. Aydemir ME and Aydemir C (2016), “Overstrength Factors for SDOF and MDOF Systems with Soil Structure Interaction,” Earthquakes and Structures, 10(6): 1273–1289.

  4. Babaei AH (2006), Providing Linear & Nonlinear Spectra Containing Soil-Structure Interaction Effects, Islamic Azad University, Tehran Brunch, Tehran, Iran. (in Farsi)

  5. Chen X, Liu B, Wang HW and Zhang HL (2007), “Earthquake Response Spectrum of Considering Soil-Structure Interaction,” Journal of Tianjin Institute of Urban Construction, 1: 002.

  6. Chopra AK (2000), Dynamics of Structures, Second Edition, Prentice Hall.

  7. Fanaei N (2002), Elastic & Non-Elastic Seismic Spectra for Iran Earthquakes, Sharif University of Technology, Tehran, Iran. (in Farsi)

  8. Gu Q, Liu Y, Li Y and Lin C (2018), “Finite Element Response Sensitivity Analysis of Three-Dimensional Soil-Foundation-Structure Interaction (SFSI) Systems,” Earthquake Engineering and Engineering Vibration, 17(3): 555–566.

  9. Guddati M and Savadatti S (2012), “Effi cient and Accurate Domain-Truncation Techniques for Seismic Soil-Structure Interaction,” Earthquakes and Structures, 3(3-4): 563–580.

  10. Gupta ID and Trifunac MD (1990), “Probabilistic Spectrum Superposition for Response Analysis Including the Effects of Soil-Structure Interaction,” Probabilistic Engineering Mechanics, 5(1): 9–18.

  11. Hokmabadi AS, Fatahi B and Samali B (2015), “Physical Modeling of Seismic Soil-Pile-Structure Interaction for Buildings on Soft Soils,” International Journal of Geomechanics, 15(2): 1–10.

  12. Hokmabadi AS and Fatahi B (2016), “Influence of Foundation Type on Seismic Performance of Buildings Considering Soil-Structure Interaction,” International Journal of Structural Stability and Dynamics, 16(8): 1550043.

  13. Jayalekshmi BR, Thomas A and Shivashankar R (2014), “Dynamic Soil-Structure Interaction Studies on 275 m Tall Industrial Chimney with Openings,” Earthquakes and Structures, 7(2): 233–250.

  14. Krishnamoorthy A (2013), “Effect of Soil-Structure Interaction for a Building Isolated with FPS,” Earthquakes and Structures, 4(3): 285–297.

  15. Li W, Liu W, Wang S and Du D (2012), “Response Spectrum Analysis of Pile-Soil-Structure Interaction Based on Simulink,” World Earthquake Engineering, 1: 015.

  16. Malhotra PK (2006), “Smooth Spectra of Horizontal and Vertical Ground Motions,” Bulletin of the Seismological Society of America, 96(2): 506–518.

  17. Mir-Ahsani V (1990), Method for Determining the Design Earthquake and Spectrum, and Producing and Using Artificial Ground Motions for Analysis and Design of Important Structures, University of Tehran, Iran. (in Farsi)

  18. Mortezaei A (2013), “Plastic Hinge Length of RC Columns Considering Soil-Structure Interaction,” Earthquakes and Structures, 5(6): 679–702.

  19. Mulliken JS and Karabalis DL (1998), “Discrete Model for Dynamic Through-the-Soil Coupling of 3-D Foundations and Structures,” Earthquake Engineering & Structural Dynamics, 27(7): 687–710.

  20. Mylonakis G and Gazetas G (2000), “Seismic Soil-Structure Interaction: Benefi cial or Detrimental?” Journal of Earthquake Engineering, 4(3): 277–301.

  21. NEHRP (2015), NEHRP Recommended Seismic Provisions for New Buildings and Other Structures, Federal Emergency Management Agency, USA.

  22. Newmark NM, Rosenblueth E (1971), Fundamentals of Earthquake Engineering, Prentice-Hall, Englewood Cliffs, NJ.

  23. Nguyen QV, Fatahi B and Hokmabadi AS (2016), “The Effects of Foundation Size on the Seismic Performance of Buildings Considering the Soil-Foundation-Structure Interaction,” Structural Engineering and Mechanics, 58(6): 1045–1075.

  24. Nguyen QV, Fatahi B and Hokmabadi AS (2017), “Infl uence of Size and Load-Bearing Mechanism of Piles on Seismic Performance of Buildings Considering Soil-Piles-Structure Interaction,” International Journal of Geomechanics, 17(7): 1–15.

  25. NIST (2012), Soil-Structure Interaction for Building Structures, National Institute of Standards and Technology, U.S. Department of Commerce.

  26. Ramazi HR (1998), Basic Accelerograms Data of the Iranian Accelerographs Network, BHRC, Tehran, Iran. (in Farsi)

  27. Richart FE and Whitman RV (1967), “Comparison of Footing Vibrations Tests with Theory,” Journal of the Soil Mechanics and Foundations Division, ACSE, 93(6): 143–168.

  28. Rong F, Wang JC, He SY, and Dong ZF (2006), “Analysis of Soil-Structure Interaction and Floor Response Spectrum of Reactor Building for China Advanced Research Reactor,” Nuclear Power Engineering, 27(5): 19–23.

  29. Standard 2800 (2005), Iranian Code of Practice for Seismic Resistant Design of Buildings, 3rd Edition, BHRC, Tehran, Iran. (in Farsi)

  30. Stewart JP, Comartin C and Moehle JP (2004), “Implementation of Soil-Structure Interaction Models in Performance Based Design Procedures,” Proceedings of the 3rd UJNR Workshop on Soil-Structure Interaction, Menlo Park, California.

  31. Tehranizadeh M and Hamedi F (2003), “Infl uence of Iran’s Earthquake Ground Motion Parameters on Design Spectra Using Deterministic and Probabilistic Approaches,” Journal of Earthquake Engineering, 7(2): 275–295.

  32. Weiming LJY (1987), “Nonclassical Modal Analysis Response Spectrum Method for Seismic Response of Soil-Structure Interaction,” Earthquake Engineering & Engineering Vibration, 2: 002.

  33. Wolf JP (1985), Dynamic Soil-Structure Interaction, Englewood Cliffs, Prentice Hall.

  34. Zhao X, Wang S, Du D and Liu W (2017), “Simplified Analysis of Frame Structures with Viscoelastic Dampers Considering the Effect of Soil-Structure Interaction,” Earthquake Engineering and Engineering Vibration, 16(1): 199–217.

Download references

Author information

Correspondence to Farhad Behnamfar.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Behnamfar, F., Babaei, A.H. & Ghandil, M. Smoothed response spectra including soil-structure interaction effects. Earthq. Eng. Eng. Vib. 19, 37–51 (2020) doi:10.1007/s11803-020-0546-1

Download citation


  • response spectrum
  • soil-structure interaction
  • soft soil