任意动载作用下长隧道纵向响应解析解

Analytical Solutions for Long Tunnels Under Arbitrary Dynamic Loadings

摘要:

将长隧道简化为作用在Pasternak双参数地基上的无限长均质直梁，基于EulerBernoulli梁理论给出动力问题的控制方程，运用积分变换以及卷积定理对该偏微分方程进行求解，推导出长隧道在任意动载作用下竖向位移、竖向速度、竖向加速度、弯矩、剪力等响应的解析表达式.讨论了简谐线荷载、移动线荷载和行波荷载三种典型动力荷载下长隧道响应的退化解析表达，并与已有文献对比，验证了所推导解析解的正确性.以行波荷载为例，通过参数化分析，研究了行波波速、频率以及不同地基反力系数对隧道动力响应的影响规律.研究结论对长隧道抗震设计具有一定的参考价值.

关键词:长隧道; 动力荷载; 纵向响应; 积分变换; 解析解

Abstract:

Assuming the long lined tunnel as an infinite homogeneous beam resting on a Pasternak foundation, the governing equation of the dynamic problem can be established based on EulerBernoulli beam theory. Integration transform and Residue theorem are applied to solve the differential equation, thus the analytical solutions of displacement, velocity, acceleration, bending moment, shear force for long lined tunnels subjected to arbitrary dynamic loads are obtained. The specified solutions for harmonic line loads, moving line loads and travelling loads are discussed and compared with the exiting solutions, and therefore, the validation of the presented generic form of solutions is verified. Taking travelling loads as an example, parametric analyses are performed to investigate the influence of the velocity and frequency of travelling loads and the shear modulus of foundation on the tunnel dynamic responses. The proposed solution is of value for seismic design of long line tunnel.

Key words:long lined tunnel; dynamic loads; longitudinal response; integration transform; analytical solution