The Analysis of Earthquake Waves Based on Nonlinear Responses of RC Structures

Abstract

The calculation of the nonlinear time-response of structures such as RC (reinforced concrete) frames to base excitation such as earthquake waves is vital to ensure the safety of structures. Of course the response changes significantly with the applied base excitation. The usual approaches to compare the different earthquake waves are based on non-localized spectra, such as response spectra and power spectra, which do not contain any time information. However these non-localized spectra often do not explain the large difference between structural responses, and are not able to reflect all of the characteristics of the earthquake waves. Local spectra, which can be easily obtained by the wavelet transform, calculate the energy distribution of the waves in the time-frequency domain. Using the wavelet transform it is easy to see the differences in the energy distribution via the local spectra of each wave, and therefore to understand the very different structural responses. Hence the time-frequency distribution of the wave energy should be taken into account during the selection of earthquake waves to apply to structural models to determine the nonlinear time response.

Improvement of and Parameter Identification for the Bimodal Time-Varying Modified Kanai-Tajimi Power Spectral Model

“…Research by Vlachos et al [11] suggested that, in the bimodal modified Kanai-Tajimi model, the spectrum strength factors, (1) 0 ( ) and (2) 0 ( ), have no direct relationship with the spectral energy of each mode; their values only represent linear combinations of the modes. Therefore, the following ratio is defined to replace the absolute values:…”

“…Among the identified parameters, (1) , (2) are defined as damping ratios of the top soil layer on the bedrock, which are normally constants. To simplify the analysis, the values of parameters (1) , (2) are set to the mean value of { (1) ( ), (2) ( )} identified at each time :…”

“…Therefore, based on characteristics of the actual parameters identified for the ground motion time-varying power spectral model, this paper employs a Gaussian distribution function to fit the identified (1) ( ) and (2) ( ), whereas (2) 0 ( ) is fitted using smooth splines. The resulting expressions for (1) ( ) and (2) ( ) are as follows: Figure 1 is a diagram of the parameter identification process for the bimodal modified Kanai-Tajimi model.…”

“…, (2) , which are determined by (12) and (14), and are treated as known parameters, and a genetic algorithm is employed to perform quadratic optimization of 1 to identify the values of the remaining parameters in the model at each time point ; they are recorded as…”

“…Among the known seismic characteristics that have significant impacts on the seismic response of a structure, in addition to its nonstationary strength characteristics, the impact of nonstationary seismic frequency characteristics on a structure's nonlinear seismic response has become a focus in recent years. Research by Yeh and Wen [1] showed that nonstationary seismic frequencies have substantial impacts on rigid structures as their strength degrades; Cao et al [2]. believed that concentrated seismic energy in the time domain had a considerably unfavorable effect on a structure.…”