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Analytical Model for Natural Frequency of SDOF System Considering Soil–Pile–Structure Interaction

Abstract

Exact estimation of vibration fundamental period of structures plays a vital role in their designing procedure. The proposition of a relatively exact expression which considers the effects of a pile group on the fundamental period of the structures was of less interest to the previous researchers. This study aims to propose an analytical model and expression so as to estimate the free vibration period of the structures located on a pile group. To reach the objectives of this study, several numerical analyses have been carried out using the method of equivalent spring which takes into account the effects of soil–pile–structure interaction on the fundamental period of the structures and an approximate expression based on the obtained data from the numerical studies has been proposed. In the next step of the study, the effects of a pile group on the fundamental period of the structures have been analyzed analytically. To this end, a five degrees-of-freedom analytical model and its corresponding expression have been proposed considering the soil–pile–structure system. The numerical modeling has been performed using the direct method due to the neglect of the soil in analytical expression and the necessity of considering the participation of the soil around piles, and the results have been compared with those of the proposed analytical expression. The soil mass participation coefficient (λ) has been obtained to modify the analytical expression using the discrepancy between the results of the two different methods. The comparison between the results of the proposed expression and those of case and numerical studies confirms that the proposed expressions benefit from a relative accuracy and can be used as an initial criterion in designing procedure.

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Notes

  1. 1.

    Natural Period of System considering Soil–Pile–Structure Interaction.

  2. 2.

    Natural Period of System considering Soil–Structure Interaction.

References

  1. 1.

    FEMA-440 (2005) Improvement of Nonlinear Static Seismic Analysis Procedures. Applied Technology Council (ATC-55 Project), Federal Emergency Management Agency, Washington, DC

  2. 2.

    Jaya V, Dodagoudar GR, Boominathan A (2012) Seismic soil–foundation–structure interaction analysis of deeply embedded ventilation stack. J Earthq Tsunami 6:1

    Google Scholar 

  3. 3.

    Elsabee F, Morray JP (1977) Dynamic behavior of embedded foundations. Report no. R77-33, department of civil engineering. MIT, Cambridge

    Google Scholar 

  4. 4.

    Veletsos AS (1977) Dynamic of structure-foundation systems. In: Hal WJ (ed) Structural and geotechnical mechanics. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  5. 5.

    Veletsos AS, Prasad AM (1989) Seismic interaction of structures and soils: stochastic approach. J Struct Eng ASCE 115:935–956

    Article  Google Scholar 

  6. 6.

    Kim S, Stewart JP (2003) Kinematic soil-structure interaction from strong motion recordings. J. Geotech Geoenviron Eng ASCE 129 (4), 323–335

    Article  Google Scholar 

  7. 7.

    Iguchi M, Luco JE (1982) Vibration of flexible plate on viscoelastic medium. J Eng Mech ASCE 108(6):1103–1120

    Google Scholar 

  8. 8.

    Riggs HR, Waas G (1985) Influence of foundation flexibility on soil-structure interaction. J Earthq Eng Struct Dyn 13(5):597–615

    Article  Google Scholar 

  9. 9.

    Liou GS, Huang PH (1994) Effects of foundation flexibility on impedance functions for circular foundations. J Eng Mech ASCE 120(7):1429–1446

    Article  Google Scholar 

  10. 10.

    Khalili N, Yazdchi M, Vallipan S (1999) Wave propagation analysis of two-phase saturated porous media using coupled finite-element method. Soil Dyn Earthq Eng 18:533–553

    Article  Google Scholar 

  11. 11.

    Yazdchi M, Khalili N, Vallipan S (1999) Dynamic soil-structure interaction analysis via coupled finite-element-boundary-element method. Soil Dyn Earthq Eng Vol 18:499–517

    Article  Google Scholar 

  12. 12.

    Chang DW, Cheng SH, Wang YL (2014) One-dimensional wave equation analyses for pile responses subjected to seismic horizontal ground motions. Soils Found 54:313–328

    Article  Google Scholar 

  13. 13.

    Ghanbari E, Ghanbari A (2016) A new criterion for considering soil-structure interaction on analysis of moment frames. Int J Struct Eng 7(1):31–47

    Article  Google Scholar 

  14. 14.

    Hokmabadi AS, Fatahi B, Samali B (2014) Seismic response of mid-rise buildings on shallow and end-bearing pile foundations in soft soil. Soils Found 54(3):345–363

  15. 15.

    Shirgir V, Ghanbari A, Sharuzi M (2015) Natural frequency of single pier bridges considering soil-structure interaction. J Earthq Eng 209(4):611–632

    Article  Google Scholar 

  16. 16.

    Fattah MY, Mustafa FS (2017) Development of excess pore water pressure around piles excited by pure vertical vibration. Int J Civ Eng 15(6):907–920

    Article  Google Scholar 

  17. 17.

    Li X, Cai G, Liu S, Puppala AJ, Zheng J, Jiang T (2017) Undrained shear strength and pore pressure changes due to prestress concrete pile installation in soft clay. Int J Civ Eng 2017:1–11

    Google Scholar 

  18. 18.

    Sharafi H, Sojoudi Y (2017) Experimental and numerical study of pile-stabilized slopes under surface load conditions. Int J Civ Eng 14(4):221–232

    Article  Google Scholar 

  19. 19.

    Minasidis G, Hatzigeorgiou G, Beskos D (2014) SSI in steel frames subjected to near-fault eearthquakes. Soil Dyn Earthq Eng 66:56–68

    Article  Google Scholar 

  20. 20.

    ASCE 7–10 (2010) Minimum design loads for buildings and other structures. American Society of Civil Engineers, Reston

    Google Scholar 

  21. 21.

    Pacheco G, Pando M (2008) Dynamic lateral response of single piles considering soil inertia contributions. Beijing, China

  22. 22.

    Novak M (1974) Dynamic stiffness and damping of piles. Can Geotech J 11:574–598

    Article  Google Scholar 

  23. 23.

    Wolf JP (1985) Dynamic soil structure interaction. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  24. 24.

    Mendoza M, Romo M (1989) Behavior of building foundations in mexico city during the 1985 earthquake: the second stage in: Bertero V (ed) Lessons learned from the mexico earthquake. Publication 89 – 02, Earthquake Engineering Research Institute, pp 66–70

  25. 25.

    Nikolaou S, Mylonakis G, Gazetas G, Tazoh T (2001) Kinematic pile bending during earthquakes: analysis and field measurements. Geotechnique 51(5):425–440

    Article  Google Scholar 

  26. 26.

    Kumar S, Prakash S (2004) Estimation of fundamental period for structures supported on pile foundations. Geotech Geol Eng 22:375–389

    Article  Google Scholar 

  27. 27.

    Maravas A, Mylonakis G, Karabalis DL (2007) Dynamic characteristics of structures on piles and footing. Thessaloiki-Greece, s.n., pp 25–28

  28. 28.

    Srbulov M (2011) Practical soil dynamics case studies in earthquake and geotechnical engineering. Springer, Dordrecht Heidelbrg, London

    Google Scholar 

  29. 29.

    Fenves GL, Filippou FC, Sze DT (1992) Response of the Dumbarton bridge in the Loma Prieta earthquake (No. UCB/EERC-92/02)

  30. 30.

    Fenves GL, DesRoches R (1994) Response of the northwest connector in the Landers and Big Bear earthquakes(No. UCB/EERC-94/12). Earthquake Engineering Research Center, University of California

  31. 31.

    Makris N, Badoni D, Delis E, Gazetas G (1994) Prediction of observed bridge response with soil-pile-structure interaction. J Struct Eng 120(10):2992–3011

    Article  Google Scholar 

  32. 32.

    Werner SD, Beck JL, Levine MB (1987) Seismic response evaluation of Meloland Road Overpass using 1979 Imperial Valley earthquake records. Earthq Eng Struct Dyn 15(2):249–274

    Article  Google Scholar 

  33. 33.

    Ohira A, Tazoh T, Dewa K, Shimizu K, Shimada M (1984) Observations of earthquake response behaviours of foundation piles for road bridge. In: Proceedings of the 8th world conference on earthquake engineering, vol III, San Francisco, CA, pp 577–584

  34. 34.

    Berrill JB, Christensen SA, Keenan RP, Okada W, Pettinga JR (2001) Case study of lateral spreading forces on a piled foundation. Geotechnique 51(6):501–517

    Article  Google Scholar 

  35. 35.

    Hamada M (1992) Large ground deformations and their effects on lifelines: 1964 Niigata earthquake. In: Hamada M, O’Rourke T (eds) Case studies of liquefaction and lifeline performance during past earthquakes—volume 1: Japanese case studies. Technical report NCEER-92-0001, National Centre for Earthquake Engineering Research, State University of New York at Buffalo

  36. 36.

    Mylonakis G, Syngros C, Gazetas G, Tazoh T (2006) The role of soil in the collapse of 18 piers of Hanshin Expressway in the Kobe earthquake. Earthq Eng Struct Dyn 35(5):547–575

    Article  Google Scholar 

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Correspondence to Ali Ghanbari.

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Amiri, A., Ghanbari, A. & Derakhshandi, M. Analytical Model for Natural Frequency of SDOF System Considering Soil–Pile–Structure Interaction. Int J Civ Eng 16, 1399–1411 (2018). https://doi.org/10.1007/s40999-018-0284-1

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Keywords

  • Soil–pile–structure interaction
  • Free vibration
  • Analytical formula
  • Steel frame
  • Numerical study