基于土层振动频响函数预测地铁环境振动的频域解析方法

Frequency Domain Analytical Method for Predicting Metro Environmental Vibration Based on Soil Frequency Response Function

根据土层振动频响函数反映土层固有特性的原理,提出基于土层振动频响函数预测地铁环境振动的频域解析方法。首先采用车轨解析模型计算得到作用于隧道基底的系列频域力;然后采用土体解析模型计算得到系列频域力作用点处到地面预测点处的系列土层振动频响函数;再根据土层固有特性不随输入荷载大小而改变的性质,将单个频域力与其对应的土层振动频响函数进行复数相乘,得到单个频域力作用下地面预测点处的振动响应;最后将各作用点处振动响应累加得到地面预测点处的振动响应。采用此方法预测北京地铁1号线东单站至建国门站区间由地铁列车运行引起的地面振动响应,并利用现场地面振动测试数据进行验证。结果表明:预测的地面振动加速度时程波形及频谱波形、地面振动1/3倍频程加速度级曲线和Z振级均与现场实测结果基本一致;该预测方法具有计算速度快、预测精度高、预测频带宽等特点,可以有效地预测地铁运行引起的环境振动响应。

According to the principle that soil frequency response functions can reflect the inherent characteristics of soil layer, an analytical method in frequency domain based on soil frequency response functions was presented to predict the environmental vibration induced by metro train. Firstly, train-track analytical model was used to calculate the frequency domain force acting on tunnel base. Secondly, the analytical model of soil mass was used to calculate the frequency response functions of soil layer from the acting points of frequency domain force to ground prediction points. Thirdly, according to the inherent character- istics of soil layer invariable with input load, a single force and its corresponding frequency response func- tion were multiplied to obtain the vibration response of ground prediction point under single frequency do- main force. Finally, the vibration response of each acting point was added up to obtain the vibration re- sponse of ground prediction point. The method was used to predict the ground vibration response induced by metro train at the section between Dongdan Station and Jianguomen Station of Beijing Metro Line 1. In- situ ground vibration measurements were used to validate the calculated results. It shows that the predic- ted time history waveform and frequency spectrum waveform of ground vibration acceleration as well as the 1/3 octave acceleration level curve and Z vibration level of ground vibration are consistent with field measured results. The prediction method is of fast calculation speed, high prediction accuracy and wide prediction frequency band, which can effectively predict the environmental vibration response induced by metro train.