Vibration prediction of immersed tube tunnels under vehicle loads based on Timoshenko beam theory

Considering the influences of vehicle loads, the element of immersed tunnels is equivalent to the Timoshenko's beam, and the traditional model for flexible joints is improved, which can bring their damping into play. According to the above improvement, this research presents a theoretical model for the analysis of the dynamic response of immersed tunnel elements under vehicle loads. On the basis of the Timoshenko's beam theory, the differential equation for the vertical vibration of the element is established, and the numerical method is used to derive the displacement response of the element. Based on the Yongjiang Immersed Tunnel in Ningbo, the responses of vertical displacement in the middle and at the ends of elements under vehicle loads are analyzed, the difference of the vertical displacement at the two ends of joint is calculated, and the influences of changing any single factor are analyzed. The results show that the vertical displacement of the element near the middle of the river is larger than that near the bank sides, and the vertical displacement in the middle of the element is larger than that at the ends of the element. The maximum vertical displacement is 3.7 mm. Under the same joint parameters, the difference of vertical displacement of side joints is larger than that of middle joints. The difference of the maximum vertical displacement is 1 mm. The spring coefficient of foundation, joint stiffness and vehicle speed have a large effect on the vertical displacement of the element, while the density of traffic flow has little effect on the vertical displacement of the element if the safety space between two vehicles is enough.