地铁列车进出站时土层空间振动特性分析

地铁列车进、出站引起的土层振动是一种振源特性丰富且复杂的特殊振动。为了研究地铁进、出站时引起土层振动差异性和空间振动特性，首先将地铁进、出站过程中变速移动的振源简化成振动频率、车离站相对位置及行驶位置不断变化的柱面振源。基于波动原理，采用波函数展开法建立空间振源在土层内的波动场表达式；利用反射定律推导不同波型反射波的传播方向，再根据Graf加法公式以及贝塞尔函数的变换特性将波场表达式转换到统一坐标系下，利用大圆弧地表的边界条件求解不同振源位置下的待定波场系数；最后根据频域内振动叠加原理，确立在整个列车进、出站过程中变速移动振源的总波动场。通过比较计算得到的列车进、出站时地表振动频谱和实测地表频谱特性，验证柱面振源的有效性，发现进、出站引起的地表振动低频特性更明显。参数分析表明，启动最大加速度和制动初速度的增加都将使地表竖向振动响应增大。

Space vibration of subsoil during metro train arriving at or leaving station

Subsoil vibration induced by metro train arriving at or leaving station is a special vibration with vast vibration sources. In this study, the train vibration source is simplified to the cylindrical vibration source to study vibration characteristics and different vibrations caused by metro train arriving at and leaving station. On the basis of wave theory, the wave field expression in soil space is obtained by wave function expansion method. Secondly, the reflection law is used to deduce the propagation direction of different types of reflection waves. Thirdly, according to Graf addition formula and the Bessel function transformation, the wave field expression is converted into a uniform coordinate system, and undetermined coefficients are solved by boundary conditions of large circular arc surface. Finally, according to vibration superposition in frequency domain, the wave field expression of the moving vibration source is established during the whole train arriving at or leaving the station. The validity of cylindrical vibration source calculation method is verified by comparing the theoretical calculation results of ground vibration frequency spectrum with its actual monitoring results. In addition, low-frequency vibration characteristics are more obvious when the train arriving at or leaving station. Parameteric analysis shows that both the maximum starting acceleration and initial braking speed increase with increasing the vertical vibration response.