高速铁路无砟轨道路基动力特性及参数研究
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摘要
随着高速铁路的发展,无砟轨道结构在我国应用越来越普遍。但目前无砟轨道路基结构的设计大多借鉴国外经验以及大型模拟试验结果,在高速列车荷载作用下路基的动力特性及其影响参数的研究还远不够。本文在总结和吸取前人研究的基础上,结合原铁道部专项科研基金项目,采用理论分析、数值模拟和模型试验对无砟轨道路基的动力特性进行了研究,采用大型动三轴试验对高速铁路路基粗粒土B组填料的动弹模和阻尼比进行了研究,主要取得了以下成果：
(1)将钢轨和无砟轨道结构视为Euler梁,扣件和CA砂浆视为有阻尼的弹簧,路基视为各向同性粘弹性半空间体,建立了无砟轨道-路基系统动力分析模型。通过移动坐标和Fourier积分变换得到了系统的稳态响应在波数域内的积分表达式。利用自适应数值积分算法和IFFT算法对积分表达式进行了数值计算,分析了列车荷载频率、速度以及路基弹性模量对板式无砟轨道路基表面竖向位移的影响,结果表明当速度小于200km/h时,路基表面的竖向动位移主要发生在轨道结构宽度范围内,且位移幅值随频率增加而减小；当速度大于250km/h时,路基的表面的竖向位移振动逐渐扩大至轨道结构范围以外,且位移幅值随频率增加而增大。列车速度接近路基瑞利波速时,路基表面竖向位移急剧增加。
(2)大型动三轴试验结果表明动应变是影响粗粒土B组填料动弹模和阻尼比的最主要因素。当动应变小于0.075%时,动弹模随动应变的增加而急剧减小；当动应变大于0.075%时,动弹模随动应变的增加而缓慢减小。当动应变小于0.015%时,阻尼比随动应变的增加而急剧增加；当动应变大于0.015%时,阻尼比随动应变的增加而缓慢增加并逐渐趋于稳定。随着固结围压或加载频率的增加,动弹模和阻尼比均增大。随着振动次数的增加,动弹模减小,且应力水平越高衰减越快。
(3)利用无砟轨道-路基系统的三维有限元模型研究了路基动力特性的时空分布规律,分析了轨道结构型式、材料特性、列车速度、轴重、轨道不平顺等因素对系统动力特性的影响,并在此基础上对这些参数进行了评价。此外,利用有限元模型探讨了路基局部(长宽高约为1.3mm×1.6m×0.6m)填料不密实、不均匀沉降等路基病害对系统动力特性的影响,分析表明局部填料不密实导致无砟轨道-路基系统的动力响应幅值变化率在10%以下；当不均匀沉降导致路基与轨道局部脱空时,路基内的动应力幅值增加达3倍以上。
(4)建立了无砟轨道路基模型试验系统,该系统由无砟轨道路基实尺模型、反力及动力加载系统、数据测试及采集系统三部分组成。根据试验模型和列车载荷的传递路径,设计了列车荷载的分配体系和加载方案,并在此基础上采用有限元法建立了能考虑转向架荷载叠加效应的加载时程曲线；根据模型路基在填筑阶段和静置期的沉降观测结果,探讨了无砟轨道路基沉降的发展规律,采用开尔文流变模型对路基各结构层在静置期内的变形进行了预测。
With the development of high speed railway, ballastless track is widely applied in our country. But at this moment, the design of ballastless track-subgrade is usually based on experience and model-test result abroad. Research on the dynamic response of subgrade under high-speed train load and its influencing factors are still far from enough. In this thesis, based on the achievements of previous literatures, supported by scientific research fund of the ministry of railways, the dynamic characteristics of ballastless track/subgrade in high-speed railway is investigated by theoretical study, numerical simulation and model test, and large-scale dynamic triaxial tests were used to study the dynamic properties of coarse-grained soil fillings. The main research work and conclusions are listed as below:
1. A dynamic analytical model of ballastless track-subgrade was established, in which the rail and ballastless track was modeled as Euler beam, fastener and CA layer were simplified to the spring-damping structure and the subgrade was regarded as homogeneous viscoelatic half-space. By mean of moving coordinate and Fourier Transform, the equations of track system and subgrade structure were established respectively and solved in the wave number domain. According to deformation compatibility conditions and IFFT algorithm, the integral expressions were calculated by numerical method. Then the influence of frequency, velocity of train, and the elastic modulus of subgrade on the displacement on the surface of subgrade were analyzed. Results show that, when velocity is less than200km/h, the vertical vibration on the surface of subgrade distributes right below the track structure, and its amplitude decreases with the increment of frequency. When velocity is larger than250km/h, the distribution of vertical vibration is not limited to the region under the track structure, and its amplitude increases with the increment of frequency. Resonance will emerge while the speed of train approaches Rayleigh wave speed.
2.The results of large-scale dynamic triaxial tests indicate that dynamic strain is the most important factor affecting the dynamic modulus and damping ratio of group-B fillings. With the increase of dynamic strain, dynamic modulus decreases rapidly when dynamic strain is less than0.075%, and damping ratio increases rapidly when dynamic strain is less than0.015%. Both dynamic modulus and damping ratio increase with the enlargement of loading frequency and confining pressure. Dynamic modulus decreases with the increment of vibration number, and the reduction is more obvious under higher stress level.
3.Three-dimensional dynamic finite element model of ballastless track/subgrade system was developed and validated to discuss spatio-temporal distribution law of the dynamic characteristics of subgrade. Using3D finite element model of ballastless track-subgrade, the time/space distribution of dynamic response in subgrade, and the influence of material parameters, train axle load and speed, irregularity of rail on the dynamic response of the whole system are studied. And an overall evaluation about the parameters was conducted. The influence of filling defects (insufficient compaction) and submergence were also analyzed using this model. Results show that. Filling defects have limited effect on the dynamic response of subgrade. If submergence leads to the separation between track structure and subgrade, the dynamic stress in subgrade will enlarge more than3times.
4.A ballastless track-subgrade model test system was built. This system contains full scale ballastless track-subgrade model, reaction frames, dynamic loading system and data acquisition system. Depending on the test model and the diffusion path of train load, a load distribution system and corresponding loading scheme were designed. Then finite element method was employed to calculate the load-time curve of actuators which can take the additive effect of adjacent bogies into consideration. Based on the long-term observational data of subgrade settlement during different construction processes, the main rules were analyzed, and then the post-construction deformation of each subgrade layer was predicted using Kelvin model.
(1)将钢轨和无砟轨道结构视为Euler梁,扣件和CA砂浆视为有阻尼的弹簧,路基视为各向同性粘弹性半空间体,建立了无砟轨道-路基系统动力分析模型。通过移动坐标和Fourier积分变换得到了系统的稳态响应在波数域内的积分表达式。利用自适应数值积分算法和IFFT算法对积分表达式进行了数值计算,分析了列车荷载频率、速度以及路基弹性模量对板式无砟轨道路基表面竖向位移的影响,结果表明当速度小于200km/h时,路基表面的竖向动位移主要发生在轨道结构宽度范围内,且位移幅值随频率增加而减小；当速度大于250km/h时,路基的表面的竖向位移振动逐渐扩大至轨道结构范围以外,且位移幅值随频率增加而增大。列车速度接近路基瑞利波速时,路基表面竖向位移急剧增加。
(2)大型动三轴试验结果表明动应变是影响粗粒土B组填料动弹模和阻尼比的最主要因素。当动应变小于0.075%时,动弹模随动应变的增加而急剧减小；当动应变大于0.075%时,动弹模随动应变的增加而缓慢减小。当动应变小于0.015%时,阻尼比随动应变的增加而急剧增加；当动应变大于0.015%时,阻尼比随动应变的增加而缓慢增加并逐渐趋于稳定。随着固结围压或加载频率的增加,动弹模和阻尼比均增大。随着振动次数的增加,动弹模减小,且应力水平越高衰减越快。
(3)利用无砟轨道-路基系统的三维有限元模型研究了路基动力特性的时空分布规律,分析了轨道结构型式、材料特性、列车速度、轴重、轨道不平顺等因素对系统动力特性的影响,并在此基础上对这些参数进行了评价。此外,利用有限元模型探讨了路基局部(长宽高约为1.3mm×1.6m×0.6m)填料不密实、不均匀沉降等路基病害对系统动力特性的影响,分析表明局部填料不密实导致无砟轨道-路基系统的动力响应幅值变化率在10%以下；当不均匀沉降导致路基与轨道局部脱空时,路基内的动应力幅值增加达3倍以上。
(4)建立了无砟轨道路基模型试验系统,该系统由无砟轨道路基实尺模型、反力及动力加载系统、数据测试及采集系统三部分组成。根据试验模型和列车载荷的传递路径,设计了列车荷载的分配体系和加载方案,并在此基础上采用有限元法建立了能考虑转向架荷载叠加效应的加载时程曲线；根据模型路基在填筑阶段和静置期的沉降观测结果,探讨了无砟轨道路基沉降的发展规律,采用开尔文流变模型对路基各结构层在静置期内的变形进行了预测。
With the development of high speed railway, ballastless track is widely applied in our country. But at this moment, the design of ballastless track-subgrade is usually based on experience and model-test result abroad. Research on the dynamic response of subgrade under high-speed train load and its influencing factors are still far from enough. In this thesis, based on the achievements of previous literatures, supported by scientific research fund of the ministry of railways, the dynamic characteristics of ballastless track/subgrade in high-speed railway is investigated by theoretical study, numerical simulation and model test, and large-scale dynamic triaxial tests were used to study the dynamic properties of coarse-grained soil fillings. The main research work and conclusions are listed as below:
1. A dynamic analytical model of ballastless track-subgrade was established, in which the rail and ballastless track was modeled as Euler beam, fastener and CA layer were simplified to the spring-damping structure and the subgrade was regarded as homogeneous viscoelatic half-space. By mean of moving coordinate and Fourier Transform, the equations of track system and subgrade structure were established respectively and solved in the wave number domain. According to deformation compatibility conditions and IFFT algorithm, the integral expressions were calculated by numerical method. Then the influence of frequency, velocity of train, and the elastic modulus of subgrade on the displacement on the surface of subgrade were analyzed. Results show that, when velocity is less than200km/h, the vertical vibration on the surface of subgrade distributes right below the track structure, and its amplitude decreases with the increment of frequency. When velocity is larger than250km/h, the distribution of vertical vibration is not limited to the region under the track structure, and its amplitude increases with the increment of frequency. Resonance will emerge while the speed of train approaches Rayleigh wave speed.
2.The results of large-scale dynamic triaxial tests indicate that dynamic strain is the most important factor affecting the dynamic modulus and damping ratio of group-B fillings. With the increase of dynamic strain, dynamic modulus decreases rapidly when dynamic strain is less than0.075%, and damping ratio increases rapidly when dynamic strain is less than0.015%. Both dynamic modulus and damping ratio increase with the enlargement of loading frequency and confining pressure. Dynamic modulus decreases with the increment of vibration number, and the reduction is more obvious under higher stress level.
3.Three-dimensional dynamic finite element model of ballastless track/subgrade system was developed and validated to discuss spatio-temporal distribution law of the dynamic characteristics of subgrade. Using3D finite element model of ballastless track-subgrade, the time/space distribution of dynamic response in subgrade, and the influence of material parameters, train axle load and speed, irregularity of rail on the dynamic response of the whole system are studied. And an overall evaluation about the parameters was conducted. The influence of filling defects (insufficient compaction) and submergence were also analyzed using this model. Results show that. Filling defects have limited effect on the dynamic response of subgrade. If submergence leads to the separation between track structure and subgrade, the dynamic stress in subgrade will enlarge more than3times.
4.A ballastless track-subgrade model test system was built. This system contains full scale ballastless track-subgrade model, reaction frames, dynamic loading system and data acquisition system. Depending on the test model and the diffusion path of train load, a load distribution system and corresponding loading scheme were designed. Then finite element method was employed to calculate the load-time curve of actuators which can take the additive effect of adjacent bogies into consideration. Based on the long-term observational data of subgrade settlement during different construction processes, the main rules were analyzed, and then the post-construction deformation of each subgrade layer was predicted using Kelvin model.
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