考虑列车轴载时序的有砟轨道路基动应力频响特性

Frequency response of dynamic stress in subgrade of ballasted track considering axle load sequence

列车移动轴列荷载经轨道结构传递扩散至路基,引起的动应力受车辆几何参数影响具有周期性。以单位脉冲函数描述轴载时序的周期特征,引入颗粒介质随机应力扩散理论建立单轴载沿深度扩散分布模型,运用卷积定理推导路基动应力时程及频谱表达式,分析高速铁路有砟轨道路基动应力主频过渡、幅度抑制、快速衰减特性及随列车编组、路基深度的演化规律,并通过现场实测进行验证。研究表明:随列车编组n增加,路基动应力频谱主频由车辆定距频率f_(b)整数倍逐步过渡到车长频率f_(c)整数倍,中国标准动车组条件下存在基频f_(1)=(1+0.398/n^(1.546))·f_(c)拟合关系;车长频率f_(c)部分整数倍N_(r)所对应频率f_(r)=N_(r)·f_(c)出现幅度抑制为零现象,由车长L_(c)和轴距L_(a)决定,产生周期性幅度抑制条件需满足0.5L_(c)/L_(a)为整数;路基动应力频谱谱峰值随主频增加呈快速衰减趋势,并沿路基深度大幅降低,幅度衰减90%所对应截止频率由基床顶面的11倍f_(c)减至基床底部的2倍。研究成果对深入分析高速铁路路基动力响应特性具有参考价值。

The axle loads of moving trains transfer and spread to the subgrade via the track structure,resulting in periodic dynamic stress response affected by the geometrical configuration of the trains.The unit impulse function is used to describe the sequence periodicity of axle loads,the theory of stochastic diffusion for stress applied on the granular media is introduced to establish a model for load dispersion and distribution of a single axle load with depth,and the convolution theorem is employed to derive the expressions for the time history and frequency spectrum of subgrade dynamic stress.The characteristics of dominant frequency transition,magnitude suppression,rapid attenuation of dynamic stress in subgrade and their variations with train formation and depth were analyzed and then verified by field tests.The research results indicated that:with the increase of train formation n,the dominant frequency of the dynamic stress spectrum gradually transits from the integer multiple of bogie passage frequency(f_(b))to the integer multiple of carriage passage frequency(f_(c)).For the Chinese standard electric multiple units,there exists a relationship between fundamental frequency f_(1) and n fitted by the function of f_(1)=(1+0.398/n^(1.546))·f_(c).Some dominant frequencies with zero magnitude,defined by f_(r)=N_(r)·f_(c),may occur in the subgrade dynamic stress spectrum,and the suppression frequency factor Nr is determined by the carriage length L_(c) and wheel set spacing L_(a).When 0.5L_(c)/L_(a) is an integer,the magnitude suppression can be characterized by periodicity.The peaks of spectrum magnitude not only decay rapidly with the increase of the dominant frequency,but also decrease significantly with the depth.The cutoff frequency corresponding to magnitude attenuation of 90% is reduced from 11f_(c) at the subgrade surface to 2f_(c) at the bottom of subgrade.The results may serve as reference for in-depth analysis of the dynamic response of high-speed railway subgrades.