Vibration Characteristics Analysis of Immersed Tunnel Structures Based on a Viscoelastic Beam Model Embedded in a Fluid-Saturated Soil System Due to a Moving Load  
[PERSON]  
1 Department of Civil Engineering, Nanchang Institute of Technology, Nanchang 330029, China; [EMAIL_ADDRESS] (H.  
For example, the 1646 m long Fort McHenry Tunnel in the United States has a maximum settlement of 162 mm, and the Shanghai Outer Ring immersed tunnel has a maximum settlement of 310 mm. As a special type of underground building, the prediction of the stress, deformation, and riverbed settlement of an immersed tunnel caused by train operation has become a hot topic in civil engineering. Currently, the main methods for analyzing the structural dynamic response and foundation settlement of underwater immersed tunnels during operation are indoor experiments, on-site monitoring, theoretical calculations, and numerical analysis. Such as [PERSON] [1; 3] The multiple causes of the settlement of the immersed tunnel were summarized, and the theory was verified by multiple tunnel monitoring data sets. [PERSON] et al. [4] monitored the settlement of the Second Hampton Roads Tunnel from the construction period to the operation period, and the results showed that the immersed tunnel on the soft soil foundation had a large settlement. Based on the long-term health monitoring of the large diameter tunnel in Hangzhou, [PERSON] et al. [5] summarized the rules of the reinforcement internal force, the interface pressure, and the settlement of the tunnel and analyzed the reasons when the long-term upper load changes and the short-term tide level were large. Considering the underwater immersed tunnel was greatly influenced by the surrounding medium, the dynamic characteristic analysis process was more complex; simplification is generally performed. The underwater immersed tunnel structure is supported by a continuous beam on an elastic foundation or joint using spring simulation, and soil-structure interaction is simulated using spring and damping to simulate multiple particle systems, such as wei gang, etc. [6] introduced the Kelvin viscoelastic simple-supported Euler beam model into the dynamic analysis of the submarine immersed tunnel and obtained the dynamic analytical solution of the displacement, bending moment, and ground reaction force of the immersed tunnel under the action of a vehicle load. [PERSON] et al. [7] obtained the maximum reaction value of the train load to the foundation of the immersed tunnel by the influence line method. [PERSON] et al. [8] modified the elastic foundation beam method for calculating the vertical settlement of an immersed tunnel, proposed a method of calculating the foundation soil settlement using the rebound modulus of the soil body, and calculated the vertical settlement of an immersed tunnel in normal and limiting conditions, respectively. In recent years, numerical analysis has been widely applied in related fields. [PERSON] et al. [9] used a combination of model tests and numerical simulations, based on time-domain and frequency-domain analysis, to study the response of excess pore water pressure and the vertical acceleration response of shield tunnel structures under train vibration loads. [PERSON] et al. [10] used numerical simulation to study the dynamic response of tunnel structures as well as the attenuation characteristics of vibration waves in the stratum based on time-frequency analysis. In documents [11; 12; 13] the seismic design analysis of immersed tunnels was carried out using the response displacement method of a multi-particle system and the mass-spring model method. The structure of submerged tube tunnels is typically composed of concrete and polymer composites. Under external loads, it exhibits not only elastic deformation, which demonstrates the characteristics of an elastic solid, but also viscous deformation, which demonstrates the characteristics of a viscous material. This means that it can generate damping during the energy dissipation process.