Numerical Study of the Effect of Geometry on the Seismic Behavior of Symmetric and Asymmetric Two-Dimensional Semi-Sin Topographic Features

In recent years, many reports of damages caused by earthquakes have been observed in different parts of the world, especially after observing the severity of damage in the Mexico City earthquake in 1985, special attention was paid to the discussion of site effect, and many researchers have investigated this issue in Mexico City and also investigated the site effect on the seismic response in other regions. The effects of topography have been stated as an important factor in the amplification of earthquake waves. Due to the great importance of the effect of these features, including valleys and hills, on the seismic response, many researchers investigated this field, while most research on the effect of topography on seismic behavior has been focused on symmetric topographic features.
In this research, the seismic behavior of topographic features, including symmetrical and asymmetrical semi-sine valleys and hills with different shape ratios, has been studied. The reason for choosing semi-sine features is that they are the most common form of topographic features in nature, and this is very important in applying the results of the studies. The most important reason for the current study is that in nature, topographic features are rarely seen symmetrically, and studying asymmetric features in seismic studies is necessary.
The results in this research have been obtained by using numerical modeling, in order to carry out numerical modeling, the Boundary Element Method (BEM) has been used, which has shown very high accuracy in modeling the distribution of seismic waves among the existing numerical methods.
The main goal of this research is to investigate the seismic behavior of symmetric and asymmetric homogeneous two-dimensional semi-sine topographic features. According to the literature review, different studies have investigated the seismic response in different parts of the topographic features, and have pointed out the importance of the topographic shape in the seismic response. In this regard, two symmetric and asymmetric semi-sine topographic features have been studied and their effects on seismic waves with frequency domains of 3 and 5 Hz have been investigated. The symmetrical features consist of eight valleys and semi-sine hills with a half-width of 500 meters and different heights of 125, 250, 375, and 500 meters, which have shape ratios of 0.25, 0.5, 0.75, and 1 respectively. The seismic response has been examined at three points at the top, middle, and bottom of the features. The second part of the study is investigating the seismic behavior of homogeneous and asymmetric topographic features. For this purpose, 10 asymmetric valleys and hills with the same height of 500 meters and different half-widths of 125, 250, 500, 1000, and 2000 meters, have symmetry ratios of 0.25, 0.5, 1, 2, and 4, respectively.
In this research, the amplification obtained for features with different shape ratios has been compared with the values suggested by the building codes and the results prove that the effect of features dimensions and asymmetry on the seismic response of topographic features is significantly more than the suggested coefficients in these codes.
In the following, the most important results of this study are briefly discussed:

In symmetrical hills, the effect of the shape ratio on the spectral amplification increases from the foot to the top of the hills. In addition, the period of the maximum spectral amplification increases with the increase of the aspect ratio.
In symmetrical valleys, increasing the shape ratio causes a decrease in the minimum spectral amplification inside the valleys. By moving away from the valleys, a fluctuation of amplification and de-amplification is seen in the seismic wave, which increases the number of these fluctuations with the increase of the shape ratio.
The study of the seismic behavior of asymmetric hills shows that as the symmetry ratio increases, the effect of topography on the seismic behavior decreases, especially at the top of the hill, this is clearly visible. In addition, the highest spectral amplification in each symmetry ratio is in the asymmetric part of the hill (the slope with different symmetry ratios).
Asymmetric valleys show the effect of asymmetry in the form of intensification in the fluctuation of amplification and de-amplification at the edge that has a greater slope. In addition, in the valley, decreasing in de-amplification is seen with the increase in the symmetry ratio (the symmetry ratio and de-amplification show an opposite relationship).
In asymmetric valleys, a side of the valley that has a constant symmetry ratio shows the same behavior in all valleys (valleys with different symmetry ratios), while in asymmetric hills, it can be seen that the asymmetry affects the seismic behavior of the side of the hill that has a constant symmetry ratio.