# The Vibration Response Characteristics of Neighboring Tunnels Induced by Shield Construction
## 3 Monitoring Data Validation Analysis
### Monitoring Results
#### 3.3.1 Analysis of Vibration Monitoring Results on the Construction Tunnel Side
The thrust force generated by the shield machine jacks primarily propagates along the tunnel axis, resulting in significant energy concentration in this direction. Radial and vertical vibrations, while present, are secondary and typically exhibit lower amplitudes due to energy dispersion and damping effects. The axial dominance underscores the critical role of shield machine parameters--such as uniformity of thrust force and the alignment of jacking operations--in controlling vibration intensity. Additionally, the directional distribution of vibration responses highlights the need for differentiated control strategies. For the construction-side tunnel, mitigating axial vibration requires optimizing shield machine operations, including thrust force control, cutterhead rotation speed, and soil conditioning. Enhancing the stability of the tunnel lining segmentsthrough improved segment reinforcement and material selection can further reduce the transmission of vibration energy along the axial direction. These findings emphasize the importance of tailoring vibration mitigation measures to the specific characteristics of the construction-side tunnel, thereby improving the overall effectiveness of vibration control strategies in shield tunneling construction. Due to significant variations in vibration data at the cutterhead, the first segment, the fourth segment, and the tenth segment, the displacement data at these four locations were subjected to Fourier transform to calculate their displacement power density. However, since the displacement spectrum data did not exhibit clear patterns, the original vibration displacement data were converted back to obtain the vibration acceleration, which was then processed through Fourier transform to calculate the acceleration power density. Notably, the power density of the cutterhead differs from that of the segments by a factor of 1000. The power density spectrum is shown in Figure 7.  
Figure 7: Power density spectrogram of the construction side tunnel. (**A**) Displacement power density comparison chart (2D: two-dimensional view); (**B**) displacement power density comparison chart (3D: three-dimensional view); (**C**) acceleration power density comparison chart. From Figure 7,B, it can be observed that the displacement power density attenuates to 0.28% from the cutterhead to the first ring segment. However, its pattern in the frequency domain is not evident, and no phenomenon of concentrated power density in specific frequency domains is observed. Figure 7 demonstrates the results of back-calculating the displacement time-history data to obtain the acceleration time-history data and then performing a Fourier transform. The peak power densities of the lined pipe sheets were concentrated in the range of 3.6-3.7 Hz, with peaks of 0.00378 ((mm/s\({}^{2}\))/Hz) for the first section of lining, 0.000464 ((mm/s\({}^{2}\))/Hz) for the fourth section, and 0.00063 ((mm/s\({}^{2}\))/Hz) for the tenth section. Therefore, in the subsequent frequency domain analysis, the power density of the acceleration is selected for analysis to identify its regularity. This result indicates that, although all lined pipe sheets exhibited a significant concentration of vibration energy at 3.64 Hz, there was a notable difference in the intensity of vibration at this frequency across different locations. The highest peak power density was observed in the first section of the lining, suggesting that it was most strongly affected by vibration. As the distance from the shield cutter increased, the vibration energy gradually decayed, and the intensity was significantly reduced by the fourth and tenth sections of the lining. This phenomenon may be related to the axial thrust generated during the advancement of the shield machine, the rotational frequency of the cutter disk, and the soil-structure interaction--particularly the resonance effect around 3.6-3.7 Hz, which made this frequency the primary source of vibration.