高速铁路无碴轨道过渡段路基的动力特性研究
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摘要
武广客运专线要求全线铺设无碴轨道，与普通线路的有碴轨道相比，对路基的变形要求更严、更高，工后沉降不能超过30mm，甚至要求地基为“零沉降”，任意路基地段20m长度范围的不均匀沉降不得大于20mm／20m，路桥(涵、隧)过渡段或任意两段路基沉降造成的折角不得大于1／1000，沉降差异造成的错台不大于5mm。因此，无碴轨道过渡段的刚度值平稳变化以及减少差异沉降和控制轨面弯折变形等措施，是保证线路平顺性的关键。由于线路过渡段刚度值不连续、差异沉降、轨面弯折的存在，将使路面在台背回填土处发生沉陷或开裂，从而会破坏线路的平顺、危害行车安全，并影响到旅客乘车的舒适度。随着我国高速铁路无碴轨道的建设，对过渡段问题的重视就显得比以前更为重要，本文基于国内外过渡段的研究现状，结合博士点基金项目和铁道部科技攻关课题，通过理论分析、室内试验、现场测试和数值模拟等方法，对无碴轨道路-桥-隧过渡段结构系统的动力计算模型进行了深入的探讨，取得了以下几方面的主要研究成果和结论：
(1)基于D’Alembert原理的弱变分和整体Lagrange格式，建立了无碴轨道路-桥-隧过渡段半无限三维空间动力有限元计算模型。该模型视路-桥-隧过渡段结构为一个相互作用的整体，不同的结构采用不同的单元离散，其中，地基层采用无限元，以消除边界效应的影响。不同材料接触面之间相互耦合，无相对位移。该模型充分地考虑了系统的空间、时变、耦合特性及路-桥-隧过渡段的设计断面和设计参数，可提供无碴轨道路-桥-隧过渡段系统的动态响应时程及动态响应场分布等，具有合理选择无碴轨道过渡段设计参数、优化设计及预测动力性能等功能，从而为高速铁路无碴轨道过渡段系统的设计提供了理论分析依据。
(2)基于Timoshenko梁假设和刚体力学理论，建立了各种不同性质的单元耦合约束方程，并使用Lagrange增广法，对其进行了有效的处理，很好地解决了无碴轨道路-桥-隧过渡段结构系统因相互衔接而引起的建模问题。
(3)材料变形特性的计算模型采用了线性、非线性弹性、Drucker-Prager、混凝土弹塑性等本构模型；车辆系统与无碴轨道路-桥-隧过渡段系统之间的耦合作用，是通过垂向平面内对外力输入来进行的。整体刚度矩阵方程的求解采用Newmark隐式积分法进行，因计算模型中包含有大量的耦合约束方程，采用了波前求解器和缩减法求解器。
(4)利用道床荷载“锥体分布”和“质量-弹簧-阻尼”理论，获得了过渡段结构等效刚度及刚度变异阈值的一般列式，并对过渡段两侧等效刚度进行了仔细讨论，进而指出过渡段刚度小的一侧刚度取值不仅与过渡段刚性大一侧的材料属性有关，而且还与其自身的材料属性有关，除此之外，还与其两侧不平顺波的振幅、波长和车速有关。
(5)引入小波分析和现场大量实测数据的时频分析，获取了路基面动应力、振动加速度、动应力速度动力系数变化特征，进而提出了各类过渡段都存在相应“临界速度”，并指出过渡段路基合适的“超高”填筑可以减小过渡段的动态响应。
(6)通过对水泥稳定碎石层各种性能的试验分析，得出级配碎石掺入5％～5.5％水泥剂量是合适的，能满足过渡段各类功能的要求。试验还发现不同级配碎石都存在一个动应力的临界值，此时动弹模量最大。
(7)运用无碴轨道路-桥-隧过渡段耦合动力学理论，建立了高速铁路路-桥-隧过渡段与无碴轨道相互作用的动力学模型，研究了轮重、车速、不平顺和材料特性与无碴轨道过渡段结构系统相互作用的动态响应特征，并指明了在车辆移动荷载作用下，确定过渡段轨下结构型式、不平顺、材料特性、基床表层厚度和动态响应分布、传递特征、路堤本体工后沉降以及刚度值差异、轨面弯折的控制参数等，是高速铁路过渡段路基结构设计的必然要求和技术保证。
It is requested to paved by ballastless tracks on the whole line ofWu-Guang express railway engineering, compared with common railwayof ballast tracks, it is stricter in deformation of the subgrade. Thesettlement of post construction on high-speed railway is required less than30 mm, even of road foundation no settlement. The subsidence differencemust not exceed 20 mm with any 20 m in length section of the subgrade.Making an angle must not exceed 1/1000 within a railway-bridge(ortunnel, or culvert) transition section or the settlement of any two sectionssubgrades. Stagger for subsidence difference must not exceed 5mm. Thus,it's the key of subgrade design to control the stiffness discrepancy and thesubsidence difference and the bending of the track, which reduces greatlythe safety and ride comfort of the train in motion. With the rapiddevelopment of the high-speed railway in our country, the question oftransition zone come into view obviously than before. The dissertationcombines the research projects supported by National Doctor ScienceFund and railway ministry, it generalizes the previous achievements, andreviews the advanced development of the transitional sections, thedynamic analysis model of the railway-bridge-tunnel transition under theballastless tracks, with theory analysis and indoor test and site test andnumerical simulation, was studied thoroughly, and some originalconclusions are obtained as following:
(1) A analysis model of semi-infinite tri-dimensional spatial finiteelements has been founded for the ballasfless track-bridge-tunneltransition system, based on weak variational form of the equilibriumequations for the transitional section in D'Alembert method and wholeLagrangian form. In the model, the track structure and the transitionsystem are dispersed to different elements and infinite element method isapplied to eradicate boundary effects. There is relative restricted couplingbetween contact interfaces of various materials of the system. It canprovide dynamic responses of the system with changes of wheel load,vehicle velocity, frequency and irregularities of the track, and distribution of dynamic responses in the subgrade can be given, also beused to select parameters, optimize designs and forecast dynamicproperties of the system, etc.
(2) Based on Timoshenko beam and geostatic theory, couplingrestricted equations of various finite elements are founded. The restrictedequations have been dealt with by Lagrangian enlarging multipliers. Bythis way, the difficult problem of the coupling between the contactinterfaces of various materials of the ballastless track-bridge-tnnneltransition has been solved effectively.
(3) Based on deformation characteristics of materials, the dissertationadopts analysis models, such as linear, nonlinear elasticity,Drucker-Prager, reinforced concrete elastic-plasticity constitutive model,etc. The coupling between vehicles system and the ballastless track-bridge-tunnel transition is affected by putting external simplified force onthe plane of the track vertically. The matrices equations as a whole havebeen solved, using implicit time integration of Newmark. Because thereare many restricted equations in the dynamic model, frontal solution isadopted to the modal analyses, and reduced solution is adopted totransient dynamic analysis.
(4) Based on cone-shaped distributing of railway bed load and amass-spring-damper model, the equivalent stiffness and variogramstiffness thresholds of the system are acquired, which have something todo with the material properties of its oneself, besides the effects of thevertical amplitude and wavelength and irregularities of the track and thevehicle moving velocity on the system.
(5) Based on wavelet theory and analysis of the time domain andfrequency domain with a great deal of field test data, and study oncharacteristics of the roadbed surface dynamic stress, vibrationacceleration, dynamic coefficient of the dynamic-stress speed, a "criticalspeed"conception is advanced, and it will influence the change trend onthe dynamic response of railway roadbed. At one time, a design idea isadvanced that "appropriate excess height"of roadbed can reduce thedifferential settlement and the dynamic response of transition sectionroadbed.
(6) Test analyses on various function of stable graded crushed stoneslayer of cement additives have been accomplished, it is fit with thegraded crushed stones doped in adaptive 5%～5.5% cement additivesamount, can satisfy to transfer an each kind of function of the transition.It is advanced that critical value of dynamic stress exists in gradedcrushed stones. At one time, it is biggest for dynamic modulus ofelasticity in the graded crushed stones.
(7) Applying the system dynamic model above-mentioned, theinfluences of wheel load, vehicle velocity, irregularity, materialparameter, stiffness and subsidence discrepancy on the dynamicresponses of the system were studied systematically. As for the furtherresearch on the same work and on the optimizing design of thetransition system, such a work may provide a helpful reference.
(1)基于D’Alembert原理的弱变分和整体Lagrange格式，建立了无碴轨道路-桥-隧过渡段半无限三维空间动力有限元计算模型。该模型视路-桥-隧过渡段结构为一个相互作用的整体，不同的结构采用不同的单元离散，其中，地基层采用无限元，以消除边界效应的影响。不同材料接触面之间相互耦合，无相对位移。该模型充分地考虑了系统的空间、时变、耦合特性及路-桥-隧过渡段的设计断面和设计参数，可提供无碴轨道路-桥-隧过渡段系统的动态响应时程及动态响应场分布等，具有合理选择无碴轨道过渡段设计参数、优化设计及预测动力性能等功能，从而为高速铁路无碴轨道过渡段系统的设计提供了理论分析依据。
(2)基于Timoshenko梁假设和刚体力学理论，建立了各种不同性质的单元耦合约束方程，并使用Lagrange增广法，对其进行了有效的处理，很好地解决了无碴轨道路-桥-隧过渡段结构系统因相互衔接而引起的建模问题。
(3)材料变形特性的计算模型采用了线性、非线性弹性、Drucker-Prager、混凝土弹塑性等本构模型；车辆系统与无碴轨道路-桥-隧过渡段系统之间的耦合作用，是通过垂向平面内对外力输入来进行的。整体刚度矩阵方程的求解采用Newmark隐式积分法进行，因计算模型中包含有大量的耦合约束方程，采用了波前求解器和缩减法求解器。
(4)利用道床荷载“锥体分布”和“质量-弹簧-阻尼”理论，获得了过渡段结构等效刚度及刚度变异阈值的一般列式，并对过渡段两侧等效刚度进行了仔细讨论，进而指出过渡段刚度小的一侧刚度取值不仅与过渡段刚性大一侧的材料属性有关，而且还与其自身的材料属性有关，除此之外，还与其两侧不平顺波的振幅、波长和车速有关。
(5)引入小波分析和现场大量实测数据的时频分析，获取了路基面动应力、振动加速度、动应力速度动力系数变化特征，进而提出了各类过渡段都存在相应“临界速度”，并指出过渡段路基合适的“超高”填筑可以减小过渡段的动态响应。
(6)通过对水泥稳定碎石层各种性能的试验分析，得出级配碎石掺入5％～5.5％水泥剂量是合适的，能满足过渡段各类功能的要求。试验还发现不同级配碎石都存在一个动应力的临界值，此时动弹模量最大。
(7)运用无碴轨道路-桥-隧过渡段耦合动力学理论，建立了高速铁路路-桥-隧过渡段与无碴轨道相互作用的动力学模型，研究了轮重、车速、不平顺和材料特性与无碴轨道过渡段结构系统相互作用的动态响应特征，并指明了在车辆移动荷载作用下，确定过渡段轨下结构型式、不平顺、材料特性、基床表层厚度和动态响应分布、传递特征、路堤本体工后沉降以及刚度值差异、轨面弯折的控制参数等，是高速铁路过渡段路基结构设计的必然要求和技术保证。
It is requested to paved by ballastless tracks on the whole line ofWu-Guang express railway engineering, compared with common railwayof ballast tracks, it is stricter in deformation of the subgrade. Thesettlement of post construction on high-speed railway is required less than30 mm, even of road foundation no settlement. The subsidence differencemust not exceed 20 mm with any 20 m in length section of the subgrade.Making an angle must not exceed 1/1000 within a railway-bridge(ortunnel, or culvert) transition section or the settlement of any two sectionssubgrades. Stagger for subsidence difference must not exceed 5mm. Thus,it's the key of subgrade design to control the stiffness discrepancy and thesubsidence difference and the bending of the track, which reduces greatlythe safety and ride comfort of the train in motion. With the rapiddevelopment of the high-speed railway in our country, the question oftransition zone come into view obviously than before. The dissertationcombines the research projects supported by National Doctor ScienceFund and railway ministry, it generalizes the previous achievements, andreviews the advanced development of the transitional sections, thedynamic analysis model of the railway-bridge-tunnel transition under theballastless tracks, with theory analysis and indoor test and site test andnumerical simulation, was studied thoroughly, and some originalconclusions are obtained as following:
(1) A analysis model of semi-infinite tri-dimensional spatial finiteelements has been founded for the ballasfless track-bridge-tunneltransition system, based on weak variational form of the equilibriumequations for the transitional section in D'Alembert method and wholeLagrangian form. In the model, the track structure and the transitionsystem are dispersed to different elements and infinite element method isapplied to eradicate boundary effects. There is relative restricted couplingbetween contact interfaces of various materials of the system. It canprovide dynamic responses of the system with changes of wheel load,vehicle velocity, frequency and irregularities of the track, and distribution of dynamic responses in the subgrade can be given, also beused to select parameters, optimize designs and forecast dynamicproperties of the system, etc.
(2) Based on Timoshenko beam and geostatic theory, couplingrestricted equations of various finite elements are founded. The restrictedequations have been dealt with by Lagrangian enlarging multipliers. Bythis way, the difficult problem of the coupling between the contactinterfaces of various materials of the ballastless track-bridge-tnnneltransition has been solved effectively.
(3) Based on deformation characteristics of materials, the dissertationadopts analysis models, such as linear, nonlinear elasticity,Drucker-Prager, reinforced concrete elastic-plasticity constitutive model,etc. The coupling between vehicles system and the ballastless track-bridge-tunnel transition is affected by putting external simplified force onthe plane of the track vertically. The matrices equations as a whole havebeen solved, using implicit time integration of Newmark. Because thereare many restricted equations in the dynamic model, frontal solution isadopted to the modal analyses, and reduced solution is adopted totransient dynamic analysis.
(4) Based on cone-shaped distributing of railway bed load and amass-spring-damper model, the equivalent stiffness and variogramstiffness thresholds of the system are acquired, which have something todo with the material properties of its oneself, besides the effects of thevertical amplitude and wavelength and irregularities of the track and thevehicle moving velocity on the system.
(5) Based on wavelet theory and analysis of the time domain andfrequency domain with a great deal of field test data, and study oncharacteristics of the roadbed surface dynamic stress, vibrationacceleration, dynamic coefficient of the dynamic-stress speed, a "criticalspeed"conception is advanced, and it will influence the change trend onthe dynamic response of railway roadbed. At one time, a design idea isadvanced that "appropriate excess height"of roadbed can reduce thedifferential settlement and the dynamic response of transition sectionroadbed.
(6) Test analyses on various function of stable graded crushed stoneslayer of cement additives have been accomplished, it is fit with thegraded crushed stones doped in adaptive 5%～5.5% cement additivesamount, can satisfy to transfer an each kind of function of the transition.It is advanced that critical value of dynamic stress exists in gradedcrushed stones. At one time, it is biggest for dynamic modulus ofelasticity in the graded crushed stones.
(7) Applying the system dynamic model above-mentioned, theinfluences of wheel load, vehicle velocity, irregularity, materialparameter, stiffness and subsidence discrepancy on the dynamicresponses of the system were studied systematically. As for the furtherresearch on the same work and on the optimizing design of thetransition system, such a work may provide a helpful reference.
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