Introduction
The present study investigates the effect of a three-dimensional (3D) underground space on the seismic response at the ground surface. FLAC 3D finite difference code was used and verified against the previous studies. Harmonic SV waves with different frequencies were used in the analyses. The seismic response at the ground surface in the presence of the 3D space was compared to the free field response and the results were presented in the form of amplification ratio pattern. From the parametric studies, it was concluded that the amplification pattern at the ground surface is strongly influenced by the dimensions of the underground space, or length ratio (L/W) parameter, where L and W are length and width of the underground space. The amplifications pattern and their values are quite different for the models with different L/W . The results show that two-dimensional consideration of the 3D underground spaces causes more or less estimation of the amplifications at the ground surface. The amplification pattern for the three-dimensional geometry is quite different with two-dimensional geometry. Therefore, it is necessary to consider the three-dimensional geometry in investigating the effect of underground spaces or structures on the ground surface during earthquakes.
Keywords: Three-dimensional, Underground Space, Seismic Response of Ground Surface, Amplification Ratio, Amplification Pattern, Numerical Analysis.
Methodology
This study examines the effect of 3D underground spaces on the seismic response of the ground surface. While previous research primarily focused on 2D models, this study validates the results of earlier work by Alielahi and Ramezani (2016) through both FLAC 2D and FLAC 3D simulations. The comparison confirms that the 3D model accurately predicts the 2D results. A comprehensive parametric analysis was then performed to investigate the influence of 3D underground box-shaped spaces, considering varying depths, on surface seismic response. The findings highlight the importance of accounting for 3D effects in seismic studies.
Results and Discussion
A three-dimensional numerical model was developed to investigate the effect of a three-dimensional box-shaped underground space on ground surface seismic responses under vertical SV waves. To account for the geometry of the underground space, a dimensionless parameter, L/W, was introduced, and its variations were examined in the seismic site amplification pattern. The seismic response at the ground surface in the presence of the three-dimensional space was compared with the free-field response, and the results were presented as an amplification pattern.
Summary and Conclusion
A 3D numerical model was developed to investigate the effect of a box-shaped underground space on the seismic response of the ground surface under vertical SV waves. A dimensionless parameter, L/W, was introduced to examine its impact on seismic amplification patterns. Key findings include:
1. The dimensions of the underground space directly affect surface seismic response, with varying amplification patterns for different L/W values.
2. Complex amplification patterns reflect the influence of underground space geometry.
3. λ/D (dimensionless wavelength) and L/W are critical parameters. Maximum amplification occurs at L/W=1 for λ/D=3 and L/W=10 for λ/D=8. Larger λ/D shifts amplification peaks to higher L/W values.
4. Larger underground structures affect broader regions.
5. Amplification distribution is radial for small L/W values and becomes linear as L/W increases.
6. Simplified 2D models cannot fully capture the effects of 3D underground spaces during earthquakes.
These conclusions apply to an unlined box-shaped cavity in an elastic rock medium under harmonic SV waves and are specific to the studied conditions.