高速列车荷载作用下轨道系统与饱和地基动力分析
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摘要
随着我国高速铁路的发展,以及既有线路的提速改造,列车荷载作用下地基和轨道系统的振动响应,以及对周边环境的影响得到了广泛的重视。高速列车运行时会在轨道系统和下卧土体中引起很大的动力响应,影响列车运营的安全性和轨道结构的耐久性,同时高速列车引起的环境振动将影响线路周边人民群众的生产和生活。因此,分析研究列车荷载作用下轨道系统和地基的振动响应问题是十分必要的。
本文首先采用半解析法研究了列车荷载作用下板式轨道-下卧饱和土体系统的动力响应问题。采用双层弹性Euler梁来模拟板式轨道中的钢轨和轨道板,采用弹簧-阻尼器来模拟轨下垫圈。列车荷载采用一系列移动的点荷载来模拟,下卧土体采用多孔饱和半空间模型,并假定半空间土体表面与轨道板接触面完全透水。利用Fourier变换方法在变换域内求解轨道和土体的控制方程,并通过快速Fourier变换得到了饱和土体动力响应在时域内的结果。文章中主要研究了轨道板刚度和土体渗透系数对土体位移和加速度响应的影响。研究表明,土体中液相介质的存在会对土体的振动响应产生很大影响,且适当增大轨道板刚度可有效控制高速列车引起的土体动力响应。
接着,本文研究了列车荷载作用下列车-轨道-饱和地基系统的耦合振动问题。研究模型共分为三部分：车体简化为一个多刚体系统,在车轮与钢轨之间引入线性Hertizian弹簧接触模型模拟轮轨动力相互作用；采用离散轨枕支承的弹性Euler梁来模拟轨道系统；下卧土体采用多孔饱和半空间模型。列车荷载分为列车轴重和由轨道不平顺引起的轮轨动力相互作用力。采用Fourier变换分别求解各子系统的控制方程,并通过动力子结构法对各子系统进行耦合。土体在时域内的动力响应通过快速Fourier变换求得。在分析了轮轨动力相互作用力的基础上,文章中研究了轮轨动力作用力和列车轴重作用下饱和地基的动力响应,并分析了轨枕间距和土体渗透系数对饱和地基振动响应的影响。
最后,本文将下卧土体考虑为成层土,其中上层为横观各向同性弹性介质,下层为Biot波动方程描述的饱和半空间；采用弹性离散点支承的Euler梁模型模拟轨道系统,将轨枕与横观各向同性弹性层之间的作用力简化为均匀分布的矩形荷载；采用考虑车体、前后转向架、轮对以及一、二系悬挂系统的整车模型,在轮对与钢轨之间引入线性Hertizian弹簧接触模型模拟轮轨动力相互作用。采用Fourier变换和待定系数法分别求解各子系统的控制方程,并通过动力子结构法对各子系统进行耦合。土体在时域内的动力响应通过快速Fourier变换求得。本章中分析了由钢轨表面连续不平顺引起的轮轨动力作用力和列车轴重荷载对线路系统周边环境的影响。
With the development of high speed railways, dynamic responses of track-ground system and vibration alongside tracks under moving trains are becoming of paramount importance. The excessive vibrations of the track and ground induced by the high speed trains could impact the security of the railway operation, the durability of the structures and the built-up residential and industrial areas. Studies of the dynamic responses subjected to moving trains are important in viewpoints of track stability and environmental protection.
First, the dynamic responses of a slab track on the poroelastic half-space subjected to moving train loads are investigated by a semi-analytical approach. The track model is described as an upper Euler beam to simulate rails and a lower Euler beam to model the slab. Rail pads between the rails and slab are represented by a continuous layer of springs and dashpots. It is assumed that the interface of the slab and the poroelastic half-space soil medium is permeable. A series of point loads are formulated to describe the moving train loads. The governing equations of track-ground system are solved using the Fourier transform. The dynamic responses in time domain are obtained through the fast Fourier transform (FFT). Effects of the soil intrinsic permeability and the stiffness of slab on soil displacement and acceleration have been carefully analyzed. Numerical results show that the vibration responses of the ground are significantly affected by the fluid phase in the soil medium and soil dynamic responses decrease with increasing stiffness of the slab.
Second, the vibrations of vehicle-track-poroelastic ground coupling system subjected to moving train loads are investigated. The theoretical model is divided into three components:The vehicle is described as a multi-rigid-body system and a linear Hertizian contact spring between each wheel and the rail is used to simulate the dynamic wheel-rail interaction forces; a periodically supported Euler beam is introduced to simulate the track system; neglecting the body force and the compressibility of solid grain, Biot's fully poroelastic dynamic theory is applied to formulate the poroelastic half-space. Train loads are divided into two parts:the axle loads and the dynamic wheel-rail loads assumed to be generated from the rail surface roughness. The governing equations of each component are solved using the Fourier transform, and these components of the whole system are integrated to meet the displacement compatibility and force equilibrium by the substructure method. The time domain responses of the ground are obtained through the fast Fourier transform. On the basis of the analysis of the dynamic wheel-rail loads, the dynamic responses of the ground subjected to the axle loads and the dynamic wheel-rail loads are investigated. Influences of the sleeper spacing and the soil intrinsic permeability on the soil dynamic responses are also analyzed.
Last, the track system foundation is divided into two parts:the upper layer modeled by transversely isotropic elastic medium and the lower by the poroelastic half-space governed by Biot's theory. The track system is described as a discretely supported Euler beam. The interaction between the sleepers and the transversely isotropic elastic layer is simplified as uniformly distributed vertical loads. Taken car body, bogies, a primary and a secondary suspension into account, the vehicle is modeled as a multi-rigid-body system. A linear Hertizian contact spring between each wheel and the rail is used to simulate the dynamic wheel-rail interaction forces. The governing equations of each component are solved combined with the Fourier transform and the undetermined coefficient method. These components of the whole system are coupled by the substructure method. The dynamic response of the ground is solved in the time domain by applying fast Fourier transform computation. The influence of the train axle loads and the dynamic wheel-rail interaction forces generated from the rail irregularities on the entironmental vibration is carefully analyzed.
本文首先采用半解析法研究了列车荷载作用下板式轨道-下卧饱和土体系统的动力响应问题。采用双层弹性Euler梁来模拟板式轨道中的钢轨和轨道板,采用弹簧-阻尼器来模拟轨下垫圈。列车荷载采用一系列移动的点荷载来模拟,下卧土体采用多孔饱和半空间模型,并假定半空间土体表面与轨道板接触面完全透水。利用Fourier变换方法在变换域内求解轨道和土体的控制方程,并通过快速Fourier变换得到了饱和土体动力响应在时域内的结果。文章中主要研究了轨道板刚度和土体渗透系数对土体位移和加速度响应的影响。研究表明,土体中液相介质的存在会对土体的振动响应产生很大影响,且适当增大轨道板刚度可有效控制高速列车引起的土体动力响应。
接着,本文研究了列车荷载作用下列车-轨道-饱和地基系统的耦合振动问题。研究模型共分为三部分：车体简化为一个多刚体系统,在车轮与钢轨之间引入线性Hertizian弹簧接触模型模拟轮轨动力相互作用；采用离散轨枕支承的弹性Euler梁来模拟轨道系统；下卧土体采用多孔饱和半空间模型。列车荷载分为列车轴重和由轨道不平顺引起的轮轨动力相互作用力。采用Fourier变换分别求解各子系统的控制方程,并通过动力子结构法对各子系统进行耦合。土体在时域内的动力响应通过快速Fourier变换求得。在分析了轮轨动力相互作用力的基础上,文章中研究了轮轨动力作用力和列车轴重作用下饱和地基的动力响应,并分析了轨枕间距和土体渗透系数对饱和地基振动响应的影响。
最后,本文将下卧土体考虑为成层土,其中上层为横观各向同性弹性介质,下层为Biot波动方程描述的饱和半空间；采用弹性离散点支承的Euler梁模型模拟轨道系统,将轨枕与横观各向同性弹性层之间的作用力简化为均匀分布的矩形荷载；采用考虑车体、前后转向架、轮对以及一、二系悬挂系统的整车模型,在轮对与钢轨之间引入线性Hertizian弹簧接触模型模拟轮轨动力相互作用。采用Fourier变换和待定系数法分别求解各子系统的控制方程,并通过动力子结构法对各子系统进行耦合。土体在时域内的动力响应通过快速Fourier变换求得。本章中分析了由钢轨表面连续不平顺引起的轮轨动力作用力和列车轴重荷载对线路系统周边环境的影响。
With the development of high speed railways, dynamic responses of track-ground system and vibration alongside tracks under moving trains are becoming of paramount importance. The excessive vibrations of the track and ground induced by the high speed trains could impact the security of the railway operation, the durability of the structures and the built-up residential and industrial areas. Studies of the dynamic responses subjected to moving trains are important in viewpoints of track stability and environmental protection.
First, the dynamic responses of a slab track on the poroelastic half-space subjected to moving train loads are investigated by a semi-analytical approach. The track model is described as an upper Euler beam to simulate rails and a lower Euler beam to model the slab. Rail pads between the rails and slab are represented by a continuous layer of springs and dashpots. It is assumed that the interface of the slab and the poroelastic half-space soil medium is permeable. A series of point loads are formulated to describe the moving train loads. The governing equations of track-ground system are solved using the Fourier transform. The dynamic responses in time domain are obtained through the fast Fourier transform (FFT). Effects of the soil intrinsic permeability and the stiffness of slab on soil displacement and acceleration have been carefully analyzed. Numerical results show that the vibration responses of the ground are significantly affected by the fluid phase in the soil medium and soil dynamic responses decrease with increasing stiffness of the slab.
Second, the vibrations of vehicle-track-poroelastic ground coupling system subjected to moving train loads are investigated. The theoretical model is divided into three components:The vehicle is described as a multi-rigid-body system and a linear Hertizian contact spring between each wheel and the rail is used to simulate the dynamic wheel-rail interaction forces; a periodically supported Euler beam is introduced to simulate the track system; neglecting the body force and the compressibility of solid grain, Biot's fully poroelastic dynamic theory is applied to formulate the poroelastic half-space. Train loads are divided into two parts:the axle loads and the dynamic wheel-rail loads assumed to be generated from the rail surface roughness. The governing equations of each component are solved using the Fourier transform, and these components of the whole system are integrated to meet the displacement compatibility and force equilibrium by the substructure method. The time domain responses of the ground are obtained through the fast Fourier transform. On the basis of the analysis of the dynamic wheel-rail loads, the dynamic responses of the ground subjected to the axle loads and the dynamic wheel-rail loads are investigated. Influences of the sleeper spacing and the soil intrinsic permeability on the soil dynamic responses are also analyzed.
Last, the track system foundation is divided into two parts:the upper layer modeled by transversely isotropic elastic medium and the lower by the poroelastic half-space governed by Biot's theory. The track system is described as a discretely supported Euler beam. The interaction between the sleepers and the transversely isotropic elastic layer is simplified as uniformly distributed vertical loads. Taken car body, bogies, a primary and a secondary suspension into account, the vehicle is modeled as a multi-rigid-body system. A linear Hertizian contact spring between each wheel and the rail is used to simulate the dynamic wheel-rail interaction forces. The governing equations of each component are solved combined with the Fourier transform and the undetermined coefficient method. These components of the whole system are coupled by the substructure method. The dynamic response of the ground is solved in the time domain by applying fast Fourier transform computation. The influence of the train axle loads and the dynamic wheel-rail interaction forces generated from the rail irregularities on the entironmental vibration is carefully analyzed.
引文
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