A Mathematical Model to Consider the Pulse-Like Earthquake Effects in Seismic Design Spectrums Based on Strong Motions of Iran

The purpose of this research is to generate a pulse-like acceleration spectrum from the horizontal component of a non-pulse-like acceleration spectrum. Three different methods have been used for this purpose. Therefore, 63 accelerograms were selected from 450 recorded accelerograms in the near-field and according to the pulse-like and near-
fault acceleroram criteria. The geological location of the stations is based on the data published by BHRC (Building and Housing Research Center). Required corrections have been applied in the frequency and time range of the used accelerograms, their values have been scaled to 1 g, and the spectrum of each of the accelerograms is calculated. Computing and modeling of pulse-like coefficients of the accelerograms have been done using three statistical methods as follows:1) Representing the average for ratios of acceleration spectrum of horizontal components, which are perpendicular along the fault, to the non-pulse-like acceleration spectrum of horizontal components for the same accelerogram, for all of the rock and soil type data, individually. 2) Representing the average for the ratios of acceleration spectrum for horizontal components of non-pulse-like accelerograms, which are perpendicular along the fault, to the acceleration spectrum horizontal components of non-pulse-like accelerogram that is recorded in another station. 3) The average for the ratio of acceleration spectrum for vertical component, to the acceleration spectrum of the horizontal component perpendicular along the fault, for the same pulse-like accelerogram.
Due to the scattering of data and their shortage, especially in sites of groups 3 and 4, the outputs of these two groups are combined and represented as the group of soil, and the outputs recorded in the sites of groups 1 and 2 are also combined and represented as a rock group representative. Then, a comparison was made between the correction coefficients of the obtained spectra and the coefficient N introduced in the 2800 buildings standard in Iran. Errors in each method have been determined and appropriate mathematical models are presented for the 50% balance in each of the three methods. Then, the coefficients obtained from the methods are applied to the non-pulse-like spectrums and are compared with the recorded pulse-like spectrums. The following results have been obtained from these studies:- The proposed mathematical models for modification of the design spectrum in each of the methods have a fairly high accuracy and reliability; however, these methods have considerable differences compared to the Iran's 2800 standard of buildings.
- The basis and criterion for obtaining the N coefficient in Iran's 2800 standard is not known, whereas by applying this coefficient it can be said that the effects of the near-field have been applied. It is suggested that this issue is addressed in revision of Iran's 2800 standard.
- The natural period of the structures designed by the regulations (short and medium order construction structures) is usually less than 2 seconds. In this interval, the proposed coefficient of the regulations and the proposed coefficient models presented in this study have the largest differences in relation to each other.
- The N coefficient always increases after a period of 0.5 seconds for up to 4 seconds, after which it remains constant, which is very conservative and irrational. While in the first and second methods suggested in this study, the slope of the curve is descending from a certain periodic range. This part confirms the justification of the applied procedures too.
- Error values are presented separately for each method. In the model provided for the soil, the error value is slightly higher than the rock model.
- The magnitude of the error is mostly positive in many periods, which means that the domains of the proposed models of the N coefficient are less.
- The absolute and relative errors in the first method are about 0.33 and 5%, and for the second method, it is equal to 0.05% and 15% respectively.
- Among the results of the three methods carried out at 50% level, the first and second methods have a much better and more reliable consistency than the third method, and also compared to the 2800 standard.
- As one of the most important results of this research, it can be stated that the results of the third method presented in these studies has no logical connection with the pulse-like accelerograms to be used to understand the N coefficient.
- According to the comparisons, from the first and second methods, the results of the first method are found more countable. The reason for this is the insignificant difference between the pulse-like modeled spectrum by the application of this coefficient (N) in the proposed model and the pulse-like spectrum of the real records obtained from the earthquakes.