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

This study aims to investigate the vibration responses on underwater immersed tunnels caused by moving loads, taking into account factors such as the viscoelastic characteristics of riverbed water, foundation soil, and the immersed tunnel itself. An ideal fluid medium is adopted to simulate the water, while a saturated porous medium is used to simulate the riverbed soil layer. The immersed tunnel structure is simplified as an infinitely long viscoelastic Euler beam, and the vibration effects are described by the theory of the standard linear solid model, taking into account structural damping. The coupled dynamic control equations were established by utilizing the displacement and stress conditions at the interface between the ideal fluid medium, the saturated porous medium, and the immersed tunnel structure. The equivalent stiffness of the riverbed water and site foundation was obtained. Furthermore, the numerical solutions of the tunnel displacement, internal forces, and pore pressure in the riverbed site were obtained in the time-space domain using the IFFT (Inverse Fast Fourier Transform) algorithm. The correctness of the model was validated by comparing the results with existing studies. The numerical results show that the riverbed water significantly reduces the Rayleigh wave velocity of the immersed tunnel structure in the riverbed-foundation system. Therefore, it is necessary to control the driving speed during high water levels. As the permeability of the saturated riverbed foundation increases, the vertical displacement, bending moment, and shear force of the beam in the immersed tunnel structure will increase. As the viscosity coefficient of the viscoelastic beam in the immersed tunnel structure increases, the vertical vibration amplitude of the beam will decrease, but further increasing the viscosity coefficient of the beam will have little effect on its vibration amplitude. Therefore, the standard solid model of the viscoelastic beam can effectively describe the creep and relaxation phenomena of materials and can objectively reflect the working conditions of the concrete structure of the immersed tunnel.