Advanced Gyro-Lumped Parameter Model and its Application to Pile Groups Supporting Multistory Buildings

Advanced Gyro-Lumped Parameter Model and its Application to Pile Groups Supporting Multistory Buildings

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A simplified and efficient soil structure interaction (SSI) method has been proposed for structures supported by pile foundation system using recently proposed lumped parameter model with gyro-element (GLMP) which shows efficient and accurate representation of frequency dependent impedance function (IFs) of the soil-foundation systems. The original GLPM has been transformed to make the gyro-element compatible with the conventional software framework. The transformed GLPM has been verified with the IFs of a pile group supporting a single degree of freedom system and implemented in multi-story building supported by a pile group. The effects of frequency dependent characteristics have been studied for the multi-story building by comparing the results with conventional Kelvin-Voigt model and rigid foundation system. OpenSees software framework has been used in the modelling of superstructure and foundation system with GLPM. The results show significant effects of the frequency dependent IFs on the response of the foundation.


In general, the impedance functions (IFs) of the soil-foundation system show frequency dependent characteristics and thus frequency domain analysis is compulsory to incorporate them. However, time history analysis is mandatory to integrate the inelastic behavior of materials and structural members which strongly depends on the stress path being integrated stepwise 1). Although varieties of methods are available to consider the frequency dependent IFs in a time history analysis, they are either very complex for practical use having many numbers of elements and degrees of freedom or they do not represent the frequency dependent IFs with sufficient accuracy.
Recently, Saitoh 1) proposed a ...

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...g. 4 Inter-story drift for magnified FIM with different assumptions of the foundation.

Fig. 5 Maximum displacement at the foundation with magnified FIM with different assumptions of the foundation.


Multi-story buildings supported by the pile groups show frequency dependent characteristics. The sophisticated GLPMs can be used efficiently to incorporate those frequency dependent properties using the conventional software platform.

1. Saitoh M. Simple model of frequency-dependent impedance functions in soil-structure interaction using frequency-independent elements. J Eng Mech. 2007;133(10):1101–14.
2. Saitoh M. On the performance of lumped parameter models with gyro-mass elements for the impedance function of a pile-group supporting a single-degree-of-freedom system. Earthq Eng Struct Dyn. 2012;41(4):623–41.

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