Frequency-dependent equivalent linearization method based on strain interval reduction theory

In order to overcome the problem of underestimating the high-frequency Fourier spectrum amplification ratio obtained by the original equivalent linearization method, a frequency-dependent equivalent linearization method considering the effective strain interval reduction is proposed. Based on the traditional equivalent linearization analysis theory, various frequency-dependent equivalent linear methods are combined. The standardized strain spectrum is utilized to characterize the relationship between the equivalent strain and the frequency. The concept of shear strain elastic threshold is introduced to modify the standardized strain spectrum amplitude at the frequency within the elastic strain range. The standardized strain spectrum is fitted by the Gaussian smoothing method, then the piecewise function for the effective strain interval reduction coefficient is established. The ground motion measurement records at vertical stations are utilized to investigate the reliability and applicability of the proposed method. The analysis results of various sites show that the method fully considers the actual situation of the larger shear modulus and smaller damping ratio. Those factors are corresponding to the high-frequency component of the ground motion. The proposed method gives the optimization results of the site seismic response in the high frequency band and provides a basis for the seismic design of the actual projects.