Journal of Engineering Geology

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Introduction
Study on the main characteristics of strong ground motions, has relatively long history. The observations and investigations on the structural damages after strong earthquakes such as Northridge 1994 in California, Kobe 1995 in Japan, Tabas 1978 and Bam 2003 in Iran, are representatives of the destructive effects of strong near-field records. The most important specification of the near-field records which distinguish them from far-field records, is their ability to generate energized and relatively short-duration acceleration spikes as well as high amplitude and long-domain velocity pulses. Moreover, according to the lack of accurate statistical profiles as well as many deficiencies, processing the spectral existent data is not able enough to fully explain the seismic tremors. Based on the fact that the great earthquakes have long recurrence interval and also many high seismic zones of Iran do not possess strong tremors, hence generating and simulating feasible great events is required by applying closed form models and analysis of available data. In this study, in order to simulate the existent pulses in the time history of near-field records, the developed mathematical configuration is presented by analytical comprehensive attitude on the closed form model by Mavroeidis and Papageorgiou (2003).
Material and methods
Simulation of strong ground shakings, especially in areas where there is limited recorded data, plays a key role in assessing dynamic behavior of structures. Owing to unique characteristics of strong near-field ground motions, it is not possible to determine exact effects of these strong records on structures using simplified mathematical models. It is feasible to develop more complicated models which represent much more characteristics of near-field ground motions. Mavroeidis and Papageorgiou (2003) studied the parameters affecting near-fault ground motions. Their studies resulted in introducing a mathematical model capable of interpolating velocity pulses of near-field earthquake records (MP model). This closed-form MP model interpolates long duration pulses using a set of input spectral parameters.
 The pulse period, the pulse amplitude, the number and phase of half cycles are the key parameters that define the shape of velocity pulse. Thus, a four-parameter model has been developed to describe velocity pulses which contain forward directivity effects. In this research, it was observed that by using a combination of cubic and exponential terms, an enhanced model for interpolating the pulses presented in near-field earthquake records could be achieved (EMP model). Figure 1 shows the analytical interpolation of acceleration and velocity time histories using MP and EMP models.
 
Figure 1. Fitting of acceleration time histories with MP and EMP models
 
Results and discussion
Based on the obtained results, it is observed that there is a striking similarity between analytical characteristics obtained by actual earthquake records and mathematical pulses. Moreover, using the enhanced closed-form model (EMP model) reduces discrepancy between the results obtained under actual and the synthetic earthquake records.
Conclusion
Findings of this research reveal that equivalent pulses could be a good representative of actual earthquake records analytically, in order to assess the seismological characteristics of these tremors. It is worth mentioning that modelization of forward directivity pulses displayed in time history of strong ground shakings, is an efficient measure in evaluating seismic response of structures. In addition, due to stochastic nature of earthquakes, computational uncertainties and descriptive limitations of analytical parameters, using closed-form models require a high level of accuracy../files/site1/files/124/8nazari%DA%86%DA%A9%DB%8C%D8%AF%D9%87.pdf
 

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Introduction
The nature of near-field earthquake records is very complicated and uncertain. Due to this complexity, the prediction of the real structural responses has become very difficult. Based on the analysis of the physical characteristics of near-field records, it is possible to use the simplified mathematical models. Near-field ground motions which are often associated with a progressive directional phenomenon due to their particular type of the causative fault, have much more destructive effects on the structures than the other quake tremors. The related research results show that under the influence of a strong near-field ground motion which contains forward directivity effects, the structural responses would be entered to a great nonlinear domain. On the other hand, due to the limited number of available near-field records, it is needed to prepare artificial acclerograms which can simulate the characteristics of the strong ground motions. Thus, it is possible to achieve a vast data base corresponding to wide range of powerful ground motions using mathematical wavelets. As a result, it provides a general overview of these types of artificial quake tremors and prepares an extended knowledge on the performance of structures in confronting these destructive movements.
Material and methods
The results obtained from the seismological studies on strong near-field records indicate that the most of these tremors contain large amounts of kinetic energy corresponding to the content of low frequency band. Additionally, by ignoring the high-frequency band the coherent velocity pulses can be detected with acceptable accuracy. In order to separate the high and low frequency bands, the empirical mode decomposition (EMD) method is used based on programming in MATLAB software. Various methods have been proposed for simulation of near-field records which most of them is based on using harmonic functions and the spectral assessment of the low frequency band of earthquake records.
In this regards, one of the best closed form evaluation has been performed by Mavroeidis and Papageorgiou (2003) which is to be formulated by making parametric changes to the so-called Gabor wavelet and replacing a simpler function instead of the Gaussian curve with a more efficient algebraic statement. Ghodrati Amiri et al. (2012) proposed another efficient formulation matched either of the benefits of Mavroeidis’s and Gabor wavelets. Both of the aforementioned models are based on the preparing of an efficient multi-statement parametric configuration of harmonic wavelets as noted above. In this study, in addition to calibrate the desired closed-formulations on the velocity pulses of the selected strong records, the accuracy of the notified simulation has also been investigated from the spectral and energy point of views.

Results and discussion
The band of high frequencies corresponding to the spectral content of strong near-field records can be ignored appropriately. This is because the major amount of the related kinetic energy is usually transmitted in the form of a low frequency pulse along with a number of high frequency spikes. Generally, these features are displayed over a relatively short time domain. In this study, the analytical attention to this subject is concentrated on the simulation of coherent multiple pulses via EMD method. The purpose of such simulation is to create a wide range of powerful and high-energy artificial motions. Moreover, due to the limited availability of natural near-field earthquake records, the proposed pulses can be used to evaluate the structural seismic performance.
Conclusion
Generally, strong near-field records contain a few consecutive pulses with different periods and spectral configurations. The essential effects of these pulses must not be ignored in conducting of nonlinear dynamic time history analyses. Obviously, the effects of these type of earthquake records on the seismic response of mid-to-high rise structures (with a large periodic range) will be significant. Furthermore, the probable occurrence of the resonant mode, may cause destructive effects on the seismic response of structural skeletons. The proposed pulses in this study were formulated through the EMD method as well as performing an analytical calibration process related to both bands of high and low frequencies. The spectral evaluations of the fitted mathematical closed-form pulses were accomplished for the selected earthquake records. The obtained results indicate a good analytical convergence and correlation with the physical parameters of the natural ground motions.


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