基于Timoshenko梁理论的车辆荷载下沉管隧道振动预测

考虑车辆荷载影响,将沉管隧道管节等效为置于黏弹性地基上的Timoshenko梁,改进传统柔性接头等效模型,考虑接头阻尼作用,建立沉管隧道管节动力响应计算模型。依据Timoshenko梁理论,推导管节竖向振动微分方程,采用数值方法对管节位移响应进行求解。依托宁波甬江沉管隧道工程,分析车辆荷载下沉管隧道管节中点和端部的竖向位移响应情况,计算接头两端最大竖向位移差,并进行单因素影响分析。研究结果表明:江中段管节竖向位移较岸边段大,管节中点竖向位移较管节端部大,最大竖向位移达到3.7 mm;各接头参数相同的情况下,岸边接头的竖向位移差较中间接头大,最大竖向位移差达到1 mm;地基分布弹簧系数、接头刚度和车速对管节竖向位移幅值影响较大,而在安全车距范围内,车流密度对管节竖向位移幅值影响不大。

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.