## 4 Vibration Characteristics during Various Building Construction Stages
### Transfer Function of Soil and Pile Foundation  
To investigate the vibration characteristics during various stages of construction, the transfer function \(R(\omega)\) is used to represent the coupling loss between the soil of the free field and structure, which can be denoted as  
\[R(\omega)=\frac{A(\omega)}{A_{0}(\omega)} \tag{3}\]  
where \(A(\omega)\) and \(A_{0}(\omega)\) are the vertical vibration accelerations of the structures and soil in the frequency domain, respectively.  
Figure 14 shows the vibration transfer function of the soil and pile when the simulated train operates on track #2. These observed locations are equipped with group pile foundations, characterized by a depth of 1 m, a pile length of 53 m, a pile diameter of 0.8 m, and an inter-pile spacing of 9 m in the direction perpendicular to the track. The presence of the structures is observed to moderately dampen vibrations and induce kinematic effects when compared to the free field soil, with attenuation generally increasing as the frequency rises.  
The transmission of soil vibration to the pile resulted in an amplification effect within the frequency range of 8-15 Hz, particularly evident at a distance of 8.3 m from the source at the building construction, exhibiting a clear inertia effect. This phenomenon can be attributed to the formation of a novel soil-structure integrated system during pile foundation construction and subsequent stages, characterized by a resonant frequency within the range of 8-15 Hz, resulting in enhanced vibration amplification within this frequency band. In the frequency range of 20-50 Hz, the transfer coefficient exhibits a decreasing trend with increasing distance from the vibration source. This can be attributed to the dominance of surface waves in the far field, while body waves play a relatively minor role, and there is a weakened interaction between body waves and piles within the  
Figure 14: The transfer function of soil and pile foundation. (**a**) Pile foundation construction; (**b**) platform construction; (**c**) building construction.  
soil. The transfer coefficient in the 50-80 Hz frequency range at the far field surpasses that observed near the vibration source under all the construction stages, which was attributed to the decrease in the effective interaction area between the soil and the structure with increasing distance, resulting in a decrease in the structure's suppression of vibration, especially in some high-frequency bands. This implies that the presence of the building plays a significant role in attenuating high-frequency vibration propagation.  
Hence, the construction of pile foundations effectively mitigates soil vibration to a significant extent, with a minimal impact on the transfer function of soil and piles compared to platform construction and building construction. After the completion of pile foundation construction, the timely measurement of pile vibration acceleration can be conducted. By utilizing the measured vibration acceleration as input for the building model, the calculation of the building vibration response becomes feasible, thereby enabling prompt adjustments to be made to the building's vibration reduction measures.