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


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

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    Natural Period of System considering Soil–Structure Interaction.


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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).

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