عنوان مقاله [English]
Nowadays, it is highly conspicuous that the problems of urban transportation are failed to be resolved on the ground, thus the best and quickest remedy is using underground facilities in metropolises. Especially, in congested urban areas, shallow depth underground structures (tunnels, subways and metro stations) are frequently built. Besides, the geometrical aspects, these box-shaped structures have some characteristics that are different from those of the mined circular tunnels. For example, the dimension of the box-type tunnels is, in general, greater than those of circular tunnels. This characteristic along with the potential of large seismic ground deformations that are typical for shallow soil deposits increase interaction effects of these shallow tunnels with their surrounding medium and adjacent structures . Therefore, investigating the effect of these shallow underground structures on the seismic response of surface structures is of great importance [2-5]. In the current study, the effects of single and twin box-shaped underground structures on the amplification patterns and seismic response of ground surface are parametrically examined.
In this research, using a finite difference approach, the effects of parameters such as; depth, horizontal space, lining stiffness of tunnels and input excitation frequency on the seismic response of the ground surface have been parametrically studied. Numerical analyses are performed through using the FLAC 2D software. Moreover, analytical results of Luco and De Barros  and numerical result of Yiouta-Mitra et al.  are chosen for the validation of the numerical approach.
To investigate the variations of frequency-dependent ground surface response, first, Ricker wavelets have been utilized as seismic excitations. Then the model subjected to seven real earthquake records and accordingly accelerations response spectra (spectral accelerations) have been presented.
Results and Discussion
This section exhibits the important results obtained from the parametric study. The results demonstrate that in the presence of twin tunnels, the maximum value of amplification always occur in center of the ground surface (x/a=0) while for case of single tunnel it occurs in the sides. Moreover, it can be deduced that the presence of the twin tunnels creates more serious condition with respect to the single tunnel. Furthermore, several real earthquake excitations were selected for further investigation about the effect of box-shaped tunnels on the ground surface acceleration. The results show that the presence of box-shaped underground structures has considerable influence on the seismic amplification patterns of the ground surface and characteristics of acceleration response spectrum. This issue is particularly evident in the case of shallow and twin underground tunnels. The main reasons of this occurrence may be related to significant wave sweeping effects due to the waves scattering by the shallow structures, which increase interaction effects of the shallow tunnels with their surrounding medium and adjacent structures.
Summary and Conclusion
In the current study, the effects of single and twin box-shaped underground structures on the amplification patterns and seismic response of ground surface are parametrically examined. For this purpose, using a verified numerical approach, the effects of crucial parameters, such as depth, horizontal spacing, lining stiffness of tunnels and frequency content of wave excitations on the ground surface response are evaluated. In the next stage, seven real earthquake excitations are selected for further investigation about the effect of box-shaped tunnels on the seismic response spectra of ground surface and the results are compared with the free-field condition. The main important conclusions drawn from the present study are as follows:
1. The box-shaped underground structures have considerable influence on the seismic amplification of the ground surface and characteristics of acceleration response spectrum.
2. The presence of twin tunnels creates more serious condition with respect to single tunnel.
3. The presence of the tunnel resulted in deamplification in short periods (high frequencies) and amplification in long periods with respect to the free-field model.
4. The significant wave sweeping effects due to the waves scattering by shallow structures, increase interaction effects of the shallow tunnels with their surrounding medium and adjacent structures.
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