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An investigation of accuracy of inertial interaction analyses with frequency-independent impedance coefficients

Yılmazok, Özgün
The inertial interaction between the soil and structure alters dynamic response characteristics of a structure due to foundation deformability, such that the flexibility and energy dissipation capability of surrounding soil may lead to a significant increase in period and damping of structural oscillations. The inertial interaction analyses can be accomplished through utilisation of frequency dependent foundation impedance coefficients that are reported in literature for various soil conditions and foundation types. However, such analyses should be performed in frequency domain, and applicable to only cases that linear structural response is considered. Alternatively, equivalent frequencyindependent foundation impedance coefficients can be employed, such that a constant excitation frequency is assumed in calculation of these coefficients. In this study, it is assumed that the fundamental frequency of a fixed-base structure, which can be obtained through employing available empirical relationships or a modal analysis, can be substituted for excitation terms in impedance expressions. The error induced in calculation of peak structural distortions is investigated through comparisons of structural response due to frequency-dependent and frequency-independent foundation impedance coefficients. For analyses, a linear single-degree of freedom oscillator is considered for modeling the structure. The frequency-dependent impedance of a rigid disk foundation resting on elastic halfspace is simulated by a limited number of discrete elements. The response calculations are performed in frequency domain, through employing 72 acceleration records. It is concluded that, the natural frequency of fixed-base building can be considered as effective excitation frequency for calculation of foundation impedance coefficients, when the effect of inertial interaction on structural response is moderate. Through employing equivalent-linear approximation for the structural response, it is shown that the conclusion is also valid in cases that nonlinear structural response is considered. However, when the inertial interaction has more profound effects on the structural response, the use of natural frequency of flexible-base structure, which is calculated iteratively due to its dependence on foundation-impedance factors is recommended.