Introduction

Past research studies have demonstrated that seismic ground motion can vary significantly over distances comparable to the dimensions of long span engineering structures. The accurate determination of earthquake ground motion at the base of long span structures such as dams and bridges whose piers are located on the valleys surface is one of the most important issues in earthquake engineering. In this paper, the spatially variable earthquake ground motions are generated at stations located on the valley slopes, considering the topography effect of a triangular valley. To this end, the simplified geometry of the valley of Masjed Soleyman embankment dam has been used for numerical modeling. The spatially varying ground motions are simulated by using spectral representation method. According to this methodology, the generated time histories are compatible with prescribed response spectra reflecting the wave passage and loss of coherence effects. This method assumes that the response spectrum is identical for all stations i.e., they have the same amplitudes and frequency content. This assumption is not valid for stations located on valley surface in which the amplitude and frequency content of the seismic waves are changed considerably by topography features. It is concluded that the proposed method in this study can lead to artificial spatially variable earthquake ground motions which can be readily reflect the amplification pattern of 2D triangular valleys.

Material and methods

In the first part of this paper, seismic response of a triangular valley is investigated through time history analysis conducted by using FLAC2D computer program. The geometry of the valley analyzed in this paper is chosen close to the valley of the Masjed Soleyman embankment dam. Dynamic analysis is conducted using an artificial earthquake generated by spectral representation method. The material properties are obtained based on the results of a comprehensive study carried out to identify the dynamic characteristics of two large embankment dams in Iran. Spectral amplification functions of seismic waves are calculated by dividing the response spectra of stations located on the slope of the valley to that in base of the valley. These functions are then used as target quantity for generation of spatially variable ground motions at points located on the valley. In this study, spectral representation method, the most widely accepted method for generation of spatially variable ground motions, is developed to take into account the topography effect. According to this methodology, the generated time histories are compatible with prescribed spectral amplification functions reflecting the wave passage and loss of coherence effects. The Harichandran-Vanmarcke coherency model is used to simulate spatially variable seismic ground motions.

Results and discussion

Based on the obtained results the maximum and minimum values of peak acceleration are yielded at the base and at the edge of the valley, respectively. The results indicate considerable increase of the acceleration RMS at points near the edge of the valley. Maximum spectral amplification is also observed at the edge of the valley. For all points located on the valley, the first peak spectral amplification occurred at frequency of 1.15Hz, which can be readily interpreted as the natural frequency of the valley. In order to evaluate the accuracy of the proposed method, the RMS and spectral amplification functions of artificial earthquakes are compared to target quantities. A very good consistency between the spectral amplification of artificial earthquakes and target spectral amplifications was observed in terms of both amplitude and frequency content.

Conclusion

The following conclusions were drawn from this paper.

- Artificial earthquakes generated using proposed method of this paper are in a very good agreement with the amplification pattern of the valley.

- The results of this study can be readily used to investigate the influence of spatial variability of earthquake ground motion on structures like bridges and dams whose supports are located inside the valley and are subjected to multi-support earthquake excitation.

- The proposed method of this paper is not limited only to the valley topography, but it can be effectively used in the generation process of non - uniform artificial earthquakes for stations located on other topography features. The latter can be carried out by establishing the spectral amplification functions of other topography features such as slopes and hills resulted from field or numerical studies.