分层及饱和分层地基列车运行引起的地面振动特性分析
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摘要
随着铁路尤其是高速铁路运输的发展，引起的振动日益频繁，对邻近振动敏感的精密仪器、设备和建筑物等有不可忽视的影响。一方面，随着高速铁路的发展，振动对人们生活环境和工作环境的影响愈显突出；另一方面，随着人们生活水平的提高，人们对生活环境和工作环境的质量要求也越来越高。铁路交通振动产生的环境影响与治理已成为亟需解决的重要课题之一。本文对铁路交通引起的地面振动的传播与衰减进行了研究，主要内容如下：
(1) 把轨道作为弹性地基上的梁，考虑轨枕的离散作用，得到轨枕与道床之间的动反力，根据薄层法原理，推导了柱坐标系下的二次形函数薄层法模拟分层地基，得到了半空间分层土体的稳态响应，建立了运行车辆-轨道-地基的振动模型，得到频域内地基的振动响应，对频域内解答进行傅立叶逆变换得到时域振动反应；对分层地基上列车运行引起的地面振动进行分析，详细讨论了列车轴重、运行速度、列车长度等因素对地表振动的影响规律。结果表明：当列车速度小于场地的瑞利波速时，列车运行速度的提高对振动幅值的影响不大，而列车速度一旦接近场地的瑞利波速，场地的振动会显著增大；列车的固定轴距作用率对振动的频谱曲线影响比较明显，在移动轴重作用率附近出现加速度峰值；距轨道中心线越近，列车引起的地面振动越大，随着距离的增加而有较大的衰减，超过一定距离衰减变缓；振动加速度峰值受轮轴荷载的影响较大，基本上呈线性增加趋势；而列车长度对振动加速度的影响较小。
(2) 从饱和土的Biot波动方程出发，根据薄层法的原理，将圆柱坐标系下饱和土的Biot轴对称波动方程在竖向进行离散，沿切向坐标及轴向分别进行Fourier级数分解和Hankel变换，得到饱和层状介质中频域波数域中的位移表达式，对此位移表达式进行Hankel逆变换和Fourier综合，求得频域柱坐标系内的位移表达式；结合运行列车-轨道-地基振动模型，对饱和分层地基上列车运行引起的地面振动进行分析，详细讨论了渗透系数、孔隙率、流体粘滞系数、剪切波速等主要土层参数对振动的传播及衰减的影响规律。结果表明：地基的第一层土体参数(表层参数)对列车运行引起的地面振动有较大的影响，随着表层土厚度的增加，下覆土层土体参数对地表振动的影响越来越小；地面振动随距
With the railway development, especially for high-speed train, the ground-borne vibration due to railway traffic has an increasing effect on precision instruments, equipment, buildings and the living environment of human beings as well. On the other hand, the increasing improvement of living standard makes the requirement to the environment of living and working more strictly than before. As a result, the project on the ground-borne vibration due to railway traffic is becoming a special concern in the civil and environmental engineering field. In this paper, the propagation and attenuation of the ground vibration due to high-speed train are studied. The main contents of the paper are as follows.
The force between the sleeper and the ground is derived from the deflection curved of track, modeled as a beam on an elastic foundation. The basic solution of layered half space is obtained by the TLM (Thin Layer Method) using the second shape function and the vibration model of moving train-track-ground is constructed. The vibration amplitudes of the ground in the frequency domain can be calculated. By using IFFT, the vibration amplitudes in frequency domain are translated into time domain. The effects on the ground vibration by the factors such as the length, the load and the speed of the train are analyzed. The results indicated that the acceleration spectrum has a maximum at the fundamental axle passage frequency; the acceleration has a rather weak dependence on train speed when the speed below the Ralyeigh wave velocity of the upper layer, while a vibration boom may be expected when the train speed reaches this Ralyeigh wave velocity. A common character is that vibration generated by traveling trains attenuates much quickly in the near distance and decreases slowly in the far distance. The ground vibration is effected largely by the load of the axis and less by the train length.
Based on Biot's dynamic equation, the TLM is adopted to derive the solution of Lamb's problem for layered saturated foundation under the action of dynamic load. The displacement expression in the frequency-wave number domain for layered
(1) 把轨道作为弹性地基上的梁，考虑轨枕的离散作用，得到轨枕与道床之间的动反力，根据薄层法原理，推导了柱坐标系下的二次形函数薄层法模拟分层地基，得到了半空间分层土体的稳态响应，建立了运行车辆-轨道-地基的振动模型，得到频域内地基的振动响应，对频域内解答进行傅立叶逆变换得到时域振动反应；对分层地基上列车运行引起的地面振动进行分析，详细讨论了列车轴重、运行速度、列车长度等因素对地表振动的影响规律。结果表明：当列车速度小于场地的瑞利波速时，列车运行速度的提高对振动幅值的影响不大，而列车速度一旦接近场地的瑞利波速，场地的振动会显著增大；列车的固定轴距作用率对振动的频谱曲线影响比较明显，在移动轴重作用率附近出现加速度峰值；距轨道中心线越近，列车引起的地面振动越大，随着距离的增加而有较大的衰减，超过一定距离衰减变缓；振动加速度峰值受轮轴荷载的影响较大，基本上呈线性增加趋势；而列车长度对振动加速度的影响较小。
(2) 从饱和土的Biot波动方程出发，根据薄层法的原理，将圆柱坐标系下饱和土的Biot轴对称波动方程在竖向进行离散，沿切向坐标及轴向分别进行Fourier级数分解和Hankel变换，得到饱和层状介质中频域波数域中的位移表达式，对此位移表达式进行Hankel逆变换和Fourier综合，求得频域柱坐标系内的位移表达式；结合运行列车-轨道-地基振动模型，对饱和分层地基上列车运行引起的地面振动进行分析，详细讨论了渗透系数、孔隙率、流体粘滞系数、剪切波速等主要土层参数对振动的传播及衰减的影响规律。结果表明：地基的第一层土体参数(表层参数)对列车运行引起的地面振动有较大的影响，随着表层土厚度的增加，下覆土层土体参数对地表振动的影响越来越小；地面振动随距
With the railway development, especially for high-speed train, the ground-borne vibration due to railway traffic has an increasing effect on precision instruments, equipment, buildings and the living environment of human beings as well. On the other hand, the increasing improvement of living standard makes the requirement to the environment of living and working more strictly than before. As a result, the project on the ground-borne vibration due to railway traffic is becoming a special concern in the civil and environmental engineering field. In this paper, the propagation and attenuation of the ground vibration due to high-speed train are studied. The main contents of the paper are as follows.
The force between the sleeper and the ground is derived from the deflection curved of track, modeled as a beam on an elastic foundation. The basic solution of layered half space is obtained by the TLM (Thin Layer Method) using the second shape function and the vibration model of moving train-track-ground is constructed. The vibration amplitudes of the ground in the frequency domain can be calculated. By using IFFT, the vibration amplitudes in frequency domain are translated into time domain. The effects on the ground vibration by the factors such as the length, the load and the speed of the train are analyzed. The results indicated that the acceleration spectrum has a maximum at the fundamental axle passage frequency; the acceleration has a rather weak dependence on train speed when the speed below the Ralyeigh wave velocity of the upper layer, while a vibration boom may be expected when the train speed reaches this Ralyeigh wave velocity. A common character is that vibration generated by traveling trains attenuates much quickly in the near distance and decreases slowly in the far distance. The ground vibration is effected largely by the load of the axis and less by the train length.
Based on Biot's dynamic equation, the TLM is adopted to derive the solution of Lamb's problem for layered saturated foundation under the action of dynamic load. The displacement expression in the frequency-wave number domain for layered
引文
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