高速列车运行于无砟轨道引起的地面振动数值模拟
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摘要
近年来,中国铁路实现了跨越式的发展,高速铁路也初具规模,由此引发的环境振动势必影响到铁路沿线居民的正常生活。因此有必要开展高速铁路引起的地面振动的研究,掌握其振动特性和传播规律。本文以软土地区高速铁路无砟轨道为例展开研究。在总结了轨道交通引起的环境振动问题研究方法、基本研究内容以及国内外高速铁路引起的环境振动问题的基础上,本文利用车辆轨道耦合理论建立了列车-轨道垂向耦合模型,采用有限元方法利用ANSYS有限元软件建立了路堤-地基二维有限元模型和轨道-路堤-地基三维有限元模型,结合上述模型分别从二维和三维角度进行了研究。
首先,利用简化的路堤-地基二维有限元模型,研究了0-90Hz范围内简谐载荷作用下的均匀弹性半空间土体和分层土体地面振动衰减规律。结果表明：简谐载荷作用下的均匀弹性半空间土体的竖向地面振动呈波动衰减,频率越高衰减越快,在距离线路一定的范围内地面振动的中高频部分不容忽视；对于分层土体,地面振动随距离衰减的波动更加剧烈,而且存在较为明显的反弹现象。
接着,在谐响应分析的基础上,利用列车-轨道垂向耦合模型获取沿线路纵向各个位置的路基表面上作用力作用于二维有限元模型中,研究高速列车运行于无砟轨道线路时引起的竖向地面振动加速度的时域、频域特征以及传播规律。利用平面应变问题等效思想,得到作用在有限元模型路基表面的等效载荷,并发现其中高频成分较为突出。仿真结果表明：虽然时域特征与实际差距较大,但是主频在中频范围内,而且与轴距引起的特征频率较为接近；竖向地面振动加速度幅值在近轨道处非常明显,20m以后已很小且衰减缓慢；计权竖向地面振动加速度级的衰减在30m之前较为迅速,30m以后衰减较慢。
最后,利用列车-轨道垂向耦合模型获取沿线路纵向钢轨扣件载荷,输入到三维有限元模型中,进行高速铁路引起的地面振动规律研究。通过竖向地面振动位移时程曲线发现,至少50m范围内竖向地面振动能够明显反映列车的经过。沿垂直线路方向的振动位移能够较为明显反映土体特性和桩基加固对地面振动的影响。振动速度和加速度是振动位移的一阶、二阶偏导,其中轴距引起频率所在范围20-50Hz的振动特征更加明显。竖向地面振动加速度幅值和计权竖向地面振动加速度级沿垂直线路方向的衰减趋势与二维模型较为接近,但受三维模型尺寸的限制整体偏大,而二维模型结果跟实测更为接近。受轨道不平顺的影响,竖向地面振动位移、速度和加速度沿平行线路方向的变化并不均匀,竖向地面振动加速度幅值和计权竖向地面振动加速度级总体上存在较小差距,在一定程度上可以采用二维模型预测列车以350km/h及以上速度运行于无砟轨道线路引起的地面振动加速度,并用于对人体影响的评价。
Chinese railway realizes a tremendous development nowadays with high-speed railway taking shape, and environmental problem induced by high-speed railway will without doubt affect the normal life of residents nearby. Therefore, it is necessary to carry out research about ground vibration caused by high-speed railway and grasp vibration characteristics and propagation regularity. This paper discusses about ground vibration of non-ballasted high-speed railway in soft soil region. After three parts of summary which is about research method in rail-transit-induced environmental problems, basic problems and environmental problems caused by high-speed railway, a vertical train-track coupled model is established according to vehicle-track coupled dynamics, and two FEM models, containing a2D embankment-foundation FEM model and a3D track-embankment-foundation FEM model, are also established by means of FEM method in ANSYS software. By combining these models above, the investigation is carried out in both2D and3D aspect.
First of all, by using the simplified2D embankment-foundation FEM model, ground vibration attenuations of homogeneous elastic half space and layered ground with the harmonic load between0and90Hz are discussed. Results show that vertical ground vibration of homogeneous elastic half space reveals a fluctuating decay under the harmonic load, and the higher the frequency is, the faster the attenuation is. Within a certain distance from the track centerline, ground vibration induced by mid and high frequencies should not be neglected. For layered ground, the fluctuation of the decaying of ground vibration is more severe, and there occurs obvious rebound.
On the basis of harmonic response analysis, forces on the surface of subgrade along the track are obtained from the vertical train-track coupled model, and applied onto the2D FEM model to investigate time-domain characteristics, frequency-domain characteristics and propagation behavior of vertical ground vibration acceleration, when the high-speed train is running on non-ballasted track in soft region. The forces are converted to an equivalent force loading on subgrade surface of the2D model according to the plain-strain equivalent methodology, and the equivalent force contains mid-frequencies and high-frequencies. Simulation results show, despite of the differences in time-domain characteristics, the domain frequency is in the mid-frequencies, close to wheelbase-induced characteristic frequency. The time-domain peak values of vertical ground vibration are apparent near the railway, and then become very small with slow attenuation after20m away. Frequency-weighted vertical acceleration level of ground vibration presents a dramatic decrease within30meters, and then gets slower after that.
At last, rail fastener loads along the track are achieved using the vertical train-track coupled model, and are applied onto the3D FEM model to investigate the regulation of vertical ground vibration when the high-speed train is running on non-ballasted track. It shows vertical ground vibration displacement can reflect the passage of train at least within50m from track centerline. Vibration displacement along transverse direction can reflect soil characteristics and the effect of pile foundation reinforcement clearly. Vibration velocity and acceleration are respectively the first derivative and second derivative of vibration displacement, thus vibration characteristics is more obvious in the frequency band which contains the wheelbase-induced frequency. Compared with the2D case, both time-domain peaks of vertical vibration acceleration and frequency-weighted vertical acceleration level of ground vibration have the consistent tendency but larger values because of the limitation of model size. Due to the track irregularity, variation of vertical ground vibration displacement, velocity and acceleration along longitudinal direction of the trackline is not homogeneous, but for time-domain peaks of vertical vibration acceleration and frequency-weighted vertical acceleration level of ground vibration, there is a little difference in general. The2D FEM model can somewhat forecast vertical ground vibration acceleration with train passages at speed of350km/h on non-ballasted track, and it also can be used for evaluating human perception.
首先,利用简化的路堤-地基二维有限元模型,研究了0-90Hz范围内简谐载荷作用下的均匀弹性半空间土体和分层土体地面振动衰减规律。结果表明：简谐载荷作用下的均匀弹性半空间土体的竖向地面振动呈波动衰减,频率越高衰减越快,在距离线路一定的范围内地面振动的中高频部分不容忽视；对于分层土体,地面振动随距离衰减的波动更加剧烈,而且存在较为明显的反弹现象。
接着,在谐响应分析的基础上,利用列车-轨道垂向耦合模型获取沿线路纵向各个位置的路基表面上作用力作用于二维有限元模型中,研究高速列车运行于无砟轨道线路时引起的竖向地面振动加速度的时域、频域特征以及传播规律。利用平面应变问题等效思想,得到作用在有限元模型路基表面的等效载荷,并发现其中高频成分较为突出。仿真结果表明：虽然时域特征与实际差距较大,但是主频在中频范围内,而且与轴距引起的特征频率较为接近；竖向地面振动加速度幅值在近轨道处非常明显,20m以后已很小且衰减缓慢；计权竖向地面振动加速度级的衰减在30m之前较为迅速,30m以后衰减较慢。
最后,利用列车-轨道垂向耦合模型获取沿线路纵向钢轨扣件载荷,输入到三维有限元模型中,进行高速铁路引起的地面振动规律研究。通过竖向地面振动位移时程曲线发现,至少50m范围内竖向地面振动能够明显反映列车的经过。沿垂直线路方向的振动位移能够较为明显反映土体特性和桩基加固对地面振动的影响。振动速度和加速度是振动位移的一阶、二阶偏导,其中轴距引起频率所在范围20-50Hz的振动特征更加明显。竖向地面振动加速度幅值和计权竖向地面振动加速度级沿垂直线路方向的衰减趋势与二维模型较为接近,但受三维模型尺寸的限制整体偏大,而二维模型结果跟实测更为接近。受轨道不平顺的影响,竖向地面振动位移、速度和加速度沿平行线路方向的变化并不均匀,竖向地面振动加速度幅值和计权竖向地面振动加速度级总体上存在较小差距,在一定程度上可以采用二维模型预测列车以350km/h及以上速度运行于无砟轨道线路引起的地面振动加速度,并用于对人体影响的评价。
Chinese railway realizes a tremendous development nowadays with high-speed railway taking shape, and environmental problem induced by high-speed railway will without doubt affect the normal life of residents nearby. Therefore, it is necessary to carry out research about ground vibration caused by high-speed railway and grasp vibration characteristics and propagation regularity. This paper discusses about ground vibration of non-ballasted high-speed railway in soft soil region. After three parts of summary which is about research method in rail-transit-induced environmental problems, basic problems and environmental problems caused by high-speed railway, a vertical train-track coupled model is established according to vehicle-track coupled dynamics, and two FEM models, containing a2D embankment-foundation FEM model and a3D track-embankment-foundation FEM model, are also established by means of FEM method in ANSYS software. By combining these models above, the investigation is carried out in both2D and3D aspect.
First of all, by using the simplified2D embankment-foundation FEM model, ground vibration attenuations of homogeneous elastic half space and layered ground with the harmonic load between0and90Hz are discussed. Results show that vertical ground vibration of homogeneous elastic half space reveals a fluctuating decay under the harmonic load, and the higher the frequency is, the faster the attenuation is. Within a certain distance from the track centerline, ground vibration induced by mid and high frequencies should not be neglected. For layered ground, the fluctuation of the decaying of ground vibration is more severe, and there occurs obvious rebound.
On the basis of harmonic response analysis, forces on the surface of subgrade along the track are obtained from the vertical train-track coupled model, and applied onto the2D FEM model to investigate time-domain characteristics, frequency-domain characteristics and propagation behavior of vertical ground vibration acceleration, when the high-speed train is running on non-ballasted track in soft region. The forces are converted to an equivalent force loading on subgrade surface of the2D model according to the plain-strain equivalent methodology, and the equivalent force contains mid-frequencies and high-frequencies. Simulation results show, despite of the differences in time-domain characteristics, the domain frequency is in the mid-frequencies, close to wheelbase-induced characteristic frequency. The time-domain peak values of vertical ground vibration are apparent near the railway, and then become very small with slow attenuation after20m away. Frequency-weighted vertical acceleration level of ground vibration presents a dramatic decrease within30meters, and then gets slower after that.
At last, rail fastener loads along the track are achieved using the vertical train-track coupled model, and are applied onto the3D FEM model to investigate the regulation of vertical ground vibration when the high-speed train is running on non-ballasted track. It shows vertical ground vibration displacement can reflect the passage of train at least within50m from track centerline. Vibration displacement along transverse direction can reflect soil characteristics and the effect of pile foundation reinforcement clearly. Vibration velocity and acceleration are respectively the first derivative and second derivative of vibration displacement, thus vibration characteristics is more obvious in the frequency band which contains the wheelbase-induced frequency. Compared with the2D case, both time-domain peaks of vertical vibration acceleration and frequency-weighted vertical acceleration level of ground vibration have the consistent tendency but larger values because of the limitation of model size. Due to the track irregularity, variation of vertical ground vibration displacement, velocity and acceleration along longitudinal direction of the trackline is not homogeneous, but for time-domain peaks of vertical vibration acceleration and frequency-weighted vertical acceleration level of ground vibration, there is a little difference in general. The2D FEM model can somewhat forecast vertical ground vibration acceleration with train passages at speed of350km/h on non-ballasted track, and it also can be used for evaluating human perception.
引文
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