# The Vibration Response Characteristics of Neighboring Tunnels Induced by Shield Construction
###### Abstract  
With the increasing complexity of engineering environments in tunnel construction, the vibrations generated by shield tunneling in hard rock strata pose significant challenges to the operation and maintenance of adjacent tunnels. This study investigates the vibration characteristics induced by shield tunneling and provides an in-depth analysis of the propagation behavior of these vibrations within tunnel segments and surrounding soil layers. Through a combination of theoretical derivations, on-site monitoring, and numerical simulations, the research examines the distribution of vibration energy and its attenuation patterns with increasing propagation distance. The findings reveal that vibration energy is primarily concentrated in the low-frequency range (3-4 Hz) and follows an exponential decay trend as distance increases. Furthermore, the vibration response of neighboring tunnels is heavily influenced by the construction vibration source, with rapid energy attenuation observed over short distances. Numerical simulations conducted using PFC3D6.0 (Particle Flow Code) software validate the theoretical model and emphasize the critical roles of soil-damping properties and tunnel segment material characteristics in vibration attenuation. This study offers a robust theoretical framework and valuable data to support the control of tunnel vibrations and the optimization of construction practices. m +
Footnote †: journal: applied sciences  
article  
[color=gray!20, linecolor=gray! in the ground through pendulum impact tests. They proposed a method for calculating the energy source, offering valuable theoretical insights into the transmission of vibration waves through soil layers. [PERSON] et al. (2018) presented the development and testing of the Smart 4 controller for monitoring vibration loads in drill strings during deep well drilling, aimed at improving operational efficiency and providing an evidence base for maintenance and warranty issues. In theoretical studies, [PERSON] et al. (2019) assumed no interference between elastic wave energies within structures and derived differential control equations using structural vibration energy density as the core variable. [PERSON] and [PERSON] (2019) identified limitations of the statistical energy method for high-frequency analysis and introduced energy density as a more effective approach for describing high-frequency structural vibrations. [PERSON] and [PERSON] (2019, 2020) established relationships between energy flow and energy density, outlining energy transmission for rods and beams. Building on this, [PERSON] and [PERSON] (2019, 2020, 2021) expanded the energy flow model to higher-dimensional systems, deriving motion equations for membranes, acoustic cavities, and fields. [PERSON] et al. (2019) examined vibration attenuation over distance and damping effects in ground layers, proposing a practical method to estimate vibration impacts on the surrounding environment. [PERSON] et al. (2017) conducted parametric analyses of tunnel-rock interactions, investigating the influence of tunnel dimensions, depth, and other factors on subway vibration transmission. [PERSON] and [PERSON] (2018) employed a Gaussian formula to model settlement curves for tunnels excavated via the shield method. By combining these curves, they calculated the total settlement trough for twin tunnels and, using data from a Bangkok metro tunneling project, observed that maximum settlement typically occurred off-center, with the settlement trough often being asymmetric. [PERSON] et al. (2019) proposed a new design for a dry friction shell shock absorber with excellent damping characteristics, capable of operating under high loads. The design also includes a mechanical model that predicts its behavior under cyclic loading, with potential applications in the mining, oil and gas, and construction industries.