地铁车致隧道与土体振动的高效时⁃频混合预测方法

Efficient time-frequency hybrid method for predicting the subway train induced vibrations of tunnel and ground

提出了一种地铁列车引起的隧道与土体振动的高效时⁃频混合预测方法。该方法基于两步法开展。通过建立车辆⁃轨道⁃隧道⁃土体2D多体动力学/有限元模型,在时域中获取轨⁃隧相互作用力;将转化后的作用力施加在2.5D有限元⁃最佳匹配层模型上,在频域⁃波数域中求解隧道⁃土体系统的动力响应。同时,为提高频域⁃波数域计算效率,提出了波数范围随激励频率变化的高效波数采样方案。数值算例中,依次通过与时域3D有限元方法和传统固定波数域采样方案对比,对所提方法的准确性和高效性进行了验证。结果表明,采用时⁃频混合方法计算的观测点竖向振动速度时程曲线在波形和幅值上与时域3D有限元方法计算结果吻合较好。就振动速度级而言,时⁃频混合方法的计算结果略小于时域方法,但两种方法计算结果的相对误差小于3%。同时,所提出的高效波数采样方案能较好地预测不同频率荷载下的有效波数范围。除2 Hz以下低频振动外,高效波数采样方案与传统采样方案计算的观测点竖向振动速度1/3倍频曲线几乎吻合。就计算效率而言,高效波数采样方案计算时间为固定波数域采样方案计算时间的3/5。

This paper presents an efficient time-frequency hybrid method for predicting the tunnel and ground vibrations caused by subway trains.This method contains two steps.Firstly,a 2D multibody system/finite element model of subway train-track-tunnel-soil is established to obtain the track-tunnel interaction forces in the time domain.Secondly,the transformed forces are applied to the 2.5D finite element method-perfectly matched layers model to solve the dynamic response of the tunnel-soil system in the fre-quency-wavenumber domain.Moreover,to improve the efficiency of frequency-wavenumber domain computation,an efficient wavenumber sampling scheme is proposed.In numerical examples,the accuracy and efficiency of the proposed method are verified by comparing with the time-domain 3D finite element method and the traditional fixed wavenumber domain sampling scheme,re-spectively.The results show that the time histories of vertical velocity of the observation points calculated by the time-frequency hy-brid method are in good agreement with the 3D finite element method.The vertical velocity levels of the observation points calculat-ed by the time-frequency hybrid method are slightly smaller than those by the time-domain 3D finite element method,but the rela-tive error of the two methods is less than 3%.Furthermore,the proposed wavenumber sampling scheme can well predict the effec-tive wavenumber ranges of different frequency loads.In addition to the low-frequency vibration below 2 Hz,the 1/3 octave curves of the vertical velocity calculated by the proposed wavenumber sampling scheme is almost consistent with those by the traditional sampling scheme.In terms of computational efficiency,the CPU time of the proposed wavenumber sampling scheme is 3/5 of that of the fixed wavenumber domain sampling scheme.