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为了对地铁列车运营引起的环境振动进行高效、高精度的预测,全面考虑列车真实行进过程对环境产生的效应,并假想隧道–地层系统为线路纵向无限个完全相同的薄片结构两两相接所组成的周期结构,其中各薄片结构均由围绕隧道近场的有限单元及可提供良好边界条件的远场无限单元构成。在将环境振动激励力分解为各激励频率轮轨力对应的成分基础上,利用叠加原理及线路纵向任意一薄片结构在单一频率轮轨力激励下存有的周期性边界条件,在频域内将列车引起三维隧道–地层系统振动响应问题的求解转化到在线路纵向一个薄片范围内进行。研究结果表明,提出的模型能有效地对列车运营引起隧道–地层系统在任意方向上的任意振动物理量进行预测,其不仅预测精度高,而且计算速度快、计算能力强;地铁列车运营引起地表在横向、垂向及纵向3个方向上的振动速度及加速度响应具有相似的频率成分及同一量级的时域最大振幅。
In order to predict the environmental vibration caused by the subway train operation efficiently and accurately, the environmental effects of the train’s true travel process are fully considered. The hypothetical tunnel-formation system is composed of an infinite number of identical sheet structures in the longitudinal direction of the line. The periodic structure consists of finite elements around the tunnel near the field and can provide good boundary conditions far-field infinite elements. On the basis of decomposing the environmental vibration excitation force into the components corresponding to the wheel-rail force of each excitation frequency, by using the principle of superposition and the periodic boundary conditions of any one slice structure in the longitudinal direction of the line under single-frequency wheel-rail force excitation, The solution to the problem of the vibration response of the three-dimensional tunnel-formation system caused by the train is transformed into a slice in the longitudinal direction of the line. The results show that the proposed model can effectively predict the arbitrary vibration of the tunnel-formation system in any direction caused by train operation, which not only has high prediction accuracy, but also has high calculation speed and high computational ability. Vibration velocity and acceleration responses in three directions of horizontal, vertical and vertical directions have similar frequency components and maximum amplitude in time domain of the same magnitude.