客运专线无碴轨道设计理论与方法研究
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摘要
随着我国客运专线的大量兴建,无碴轨道得到了快速发展与广泛应用,但各型无碴轨道的设计不尽相同,没有形成统一的无碴轨道设计理论。本文在吸收国内外无碴轨道及相关工程研究成果的基础上,通过理论与试验研究,初步建立了统一的无碴轨道设计理论,并成功应用于遂渝线无碴轨道综合试验段、武广客运专线无碴轨道试验段及250km/h双块式轨道、板式轨道设计参考图的设计中。本文的主要研究工作和结论分为以下几个方面:
(1)发展了无碴轨道列车荷载应力计算方法
针对无碴轨道的结构特点,建立弹性地基上的梁板模型计算列车荷载应力,其中钢轨以Euler梁模拟,承载层以弹性薄板模拟,扣件、中间层及地基的弹性支承均以弹簧模拟,采用有限单元法实现。素混凝土或水硬性支承层宜采用折减弹性模量进行计算,以反映开裂对其抗弯刚度的影响。支承层弹性模量越高、厚度越厚、层间连接越强、裂缝间距越密,开裂后的弹性模量折减程度越高。对不同计算模型的计算结果和遂渝线实测资料进行了对比,验证了计算模型和参数的正确性。
应用模型对板式轨道、双块式轨道进行了参数分析,结果表明:轨道板、底座板厚度对板式轨道承载层荷载应力影响较大,结构优化时,应着重在降低轨道板厚度、增加底座板厚度方面进行;底座板宽度宜按照45°荷载扩散角确定;尽量延长底座板长度,并在端部设置传力杆,以改善基床的受力条件;双块式轨道中结合式双层结构的应力水平较分离式双层结构低,在满足双块式轨枕埋置宽度的基础上应采用较窄的道床板宽度。
(2)建立了无碴轨道温度应力计算方法
根据连续式无碴轨道的裂缝发展特点,推导了连续式无碴轨道的温度应力、裂缝间距和裂缝宽度的计算公式,并进行了参数分析。为控制连续式无碴轨道的裂缝宽度在容许范围内应将裂缝控制为不稳定裂缝型式。此时钢筋最大应力由混凝土抗拉强度和配筋率控制,最大裂缝宽度则与钢筋和混凝土之间的粘结强度、混凝土抗拉强度以及配筋率有关,均与降温幅度无关。采用C40混凝土时,为满足0.5mm的裂缝宽度要求,配筋率应达到0.73%以上,钢筋直径宜在18～25mm间选择。采用高标号混凝土道床板、低标号混凝土支承层以及滑模施工或涂层钢筋时,应对应提高道床板配筋率。
综合考虑国外无碴轨道、路面工程温度梯度取值以及遂渝线实测无碴轨道温度场,提出了我国无碴轨道温度梯度建议值。以板式轨道为例,研究了不同约束条件和CA砂浆弹性模量情况下的轨道板翘曲应力,得出无碴轨道翘曲应力可按无限大板进行计算的结论。
(3)研究了基础变形对无碴轨道的受力影响
将路基不均匀沉降和桥梁挠曲变形假设为正弦和半波正弦曲线,利用考虑基础变形的梁板有限元模型和简化的刚性基础、弹性基础模型对比分析了无碴轨道承载层附加弯矩,研究认为对于正弦型基础变形引起的无碴轨道附加弯矩的计算可采用刚性基础法进行。对于刚度较大的单元式道床板,不均匀沉降限值应适当提高,以保证自重作用下不产生空吊。
梁端位移对无碴轨道扣件系统的受力影响较大,特别是错台高度、梁端转角和胶垫刚度。综合考虑列车荷载、错台等因素,从保护扣件受力的角度提出了不同胶垫刚度时的梁端转角限值。梁端位移对无碴轨道上抬稳定性有一定的影响,特别是在采用大抗拔力扣件系统时,需在梁端部位加强无碴轨道与桥梁的联结。
(4)初步建立了我国无碴轨道设计理论与方法
将无碴轨道设计分为功能设计与结构设计两部分。功能设计主要用于确定轨道的结构组成和施工方法等,使之满足高稳定和高平顺要求;结构设计则主要根据列车荷载、温度变化及基础变形及其共同作用确定承载层结构配筋等,使之满足强度与耐久性要求。
在对国内外无碴轨道总结分类的基础上,对无碴轨道及主要部件进行了功能分析,提出功能设计的概念以保证无碴轨道的高平顺和高稳定性。对于使用寿命要求60年的无碴轨道结构,应保证在荷载作用下结构始终处于弹性工作阶段,宜采用以容许应力法为基础的结构设计方法。普通钢筋混凝土结构在荷载作用下可能会开裂,开裂之后抗弯刚度的降低将引起荷载作用下弯矩的改变,引入结构系数以反映此影响。以双块式轨道为例进行了路基和桥梁上单元式、连续式无碴轨道的结构设计。结构设计算例表明,对于单元式无碴轨道,配筋受列车荷载弯矩控制,而连续式无碴轨道配筋则受降温和混凝土收缩控制。
(5)建立了无碴轨道落轴试验模拟模型,对无碴轨道动力特性进行评价
以弹性地基上梁板模型为基础,建立了无碴轨道落轴试验模拟模型,对板式轨道动力特性进行了研究,结果表明扣件刚度对各部件加速度影响显著,为降低系统的振动水平,应采用较低的扣件刚度。CA砂浆弹性模量对轨道板和底座板加速度影响较大,底座板加速度明显低于双块式轨道支承层,且频率较低,说明CA砂浆具有一定的隔振作用,为降低下部基础的加速度水平,应采用弹性模量较低的CA砂浆。路基面支承刚度主要影响底座板的加速度,但影响程度较小。为降低系统振动水平,轨道板厚度宜取为0.2m左右,底座板厚度宜取为0.3m。
With the large scale construction of Passenger Dedicated Lines(PDLs), the ballastless track has got rapid development and extensive application. However, the design methods of different ballastless tracks were different, a uniform design theory for ballastless track did not exist. Based on the systematical summarization of ballastless track and corresponding projects home and aboard, a uniform ballastless track theoretical system is established through academic and experimental research in this thesis. The theory was successfully used in several projects, such as the ballastless track synthetically test section on Suining-Chongqing line(Suiyu line), the ballastless track test section on Wuhan-Guangzhou PDL, as well as the design of bi-block ballastless track and slab track for 250km/h reference blueprint design. The research work and main conclusion were divided into following areas:
(1)Develop the stress calculation method of ballastless track under train load
Considering the structure character of ballastless track, the stress under the train load should be calculated using the beam-shell model on elastic foundation. Rails are simulated by Euler beam. Bearing layers are simulated by elastic thin shell. The elasticity of the fastener, CA motar and subgrade are simulated by spring combination. The model is actualized using Finite Element Method. The plain concrete or hydraulic bounded layer should be modeled by using their reduced elastic modulus to reflect the influence to their bending stiffness when cracked. The greater the elastic modulus, or the larger the thickness of the supporting layer, or the stronger the interlaminar connection status, or the less the interval between cracks, the smaller the reduced elastic modulus of the cracked support layer will be resulted in. The calculation model and parameters were verified by the comparison between different models and field test data on Suiyu line.
A parameter study about slab track and bi-block ballastless track was carried out using the beam-shell model. The results show the thickness of the track slab and base slab have great influence to the stress in bearing layer. The thickness of the track slab should be reduced and that of the base slab should be increased in structural optimization. The width of the base slab should be ascertained according to the 45°load dispersion angle. The length of the base slab should be extended and dowels should be set at the base slab ends to improve the subgrade mechanical condition. In bi-block ballastless track, the stress level in combined structure is less than that in separated structure. A smaller track slab width should be used when the embedded width constraint of the bi-block sleeper is satisfied.
(2)Establish the thermal stress calculation method of ballastless track
The thermal stress, cracks interval and crack width calculation formula were derivated according to the crack develop character of continuous ballastless track. A parameter study was carried out using these formulas. The crack type should be controlled to unstable cracks to limit the crack width in continuous ballastless track. The maximum stress in rebar is controlled by concrete tensile strength and reinforcement ratio. The maximum crack width is related to the bond strength between rebar and concrete, the concrete tensile strength and reinforcement ratio. The maximum rebar stress and crack width have no relation to the temperature drop range. The reinforcement ratio should be larger than 0.73% to limit the crack width within 0.5mm when using C40 concrete. The diameter of the rebar should be selected between 18mm and 25mm. The reinforcement ratio should be enhanced when using high-grade concrete in track slab or low-grade concrete in support layer or coated rebar or slip form construction method.
Considering the temperature gradient value in ballastless track aboard, pavement and the test data on Suiyu Line comprehensively, the maximum temperature gradient value of our ballastless track was proposed. Taking slab track for example, the warp stress was analyzed under different constraint conditions and elastic modulus of CA motar. As a conclusion the warp stress of the ballastless track can be calculated using the infinite plate formula.
(3)Study the foundation deformation influence to the ballastless track
The subgrade uneven deformation and the deflection of the bridge are assumed to a sine or half-wave sine curve. The additional moment of the ballastless track bearing layer was calculated using the beam-shell finite element model considering the foundation deformation, a simplified rigid foundation and an elastic foundation model separately. As a conclusion the additional moment due to sine type foundation deformation can be calculated using rigid foundation method. The uneven deformation limit should be raised to guarantee no suspending under self-weight in short high stiffness track slab.
The displacements at bridge end have great influence to the fastening system, especially for step height, bridge end rotation and pad stiffness. Considering the influence of the train load and step, a limit for bridge end rotation was proposed from the viewpoint of fastening system protection. The bridge end displacements have a certain effect to the uplift stability of the ballastless track, especially when using large uplift resistance fastening system. The interlaminar connection between ballastless track and bridge should be strengthened at bridge end.
(4) Establish the design theory and method of ballastless track preliminarily
The ballastless track design is divided into two parts: the function design and structure design. The track components and construction method are determined in the function design to satisfy the high evenness and stability requirements. The reinforcement in the bearing layer is determined to satisfy the strength and durability requirements in the structure design according to external loads and their interaction. The external loads include train loads, influences of temperature and the foundation deformations.
A function analysis about ballastless track and their main components was carried out based on the summarization and classification of ballastless tracks home and aboard. The high evenness and stability of the ballastless track on PDLs is guaranteed by the function design conception. The ballastless track structure should always be in elastic stage because of its 60 years life span requirement, so the structure design method should be based on allowable stress method. The reinforcement concrete structure will crack due to load action and the bending stiffness will decrease which result in the change of the moment. A structure coefficient was introduced to reflect its influence. Taking bi-block ballastless track for example, the structure designs of ballastless track with single slabs and continuous slab on subgrade and bridge were carried out. The structure design examples show that the reinforcement for ballastless track with single slabs is controlled by the moment under train load, the reinforcement for ballastless track with continuous slab is controlled by the temperature drop and concrete shrinkage.
(5)Establish the simulation model of the ballastless track falling wheelset experiment to estimate and evaluate the dynamic character of the ballastless track
Based on the beam-shell model on elastic foundation, a ballastless track falling wheelset experiment simulation model was established. The dynamic character of the slab track was analyzed. The results show the fastener stiffness has great influence to the acceleration of each component. Lower fastener stiffness should be used to reduce the system vibration level. The elastic modulus of the CA motar has great influence to the track slab and base slab acceleration. The acceleration and the frequency of the base slab are significant lower than that of the support layer in bi-block ballastless track, which reflect that CA motar can isolate vibration to a certain degree. The subgrade stiffness mainly influences the acceleration of the base slab, but the degree is relatively small. The thickness of the track slab and the base slab should be about 0.2m and 0.3m to reduce the system vibration level.
(1)发展了无碴轨道列车荷载应力计算方法
针对无碴轨道的结构特点,建立弹性地基上的梁板模型计算列车荷载应力,其中钢轨以Euler梁模拟,承载层以弹性薄板模拟,扣件、中间层及地基的弹性支承均以弹簧模拟,采用有限单元法实现。素混凝土或水硬性支承层宜采用折减弹性模量进行计算,以反映开裂对其抗弯刚度的影响。支承层弹性模量越高、厚度越厚、层间连接越强、裂缝间距越密,开裂后的弹性模量折减程度越高。对不同计算模型的计算结果和遂渝线实测资料进行了对比,验证了计算模型和参数的正确性。
应用模型对板式轨道、双块式轨道进行了参数分析,结果表明:轨道板、底座板厚度对板式轨道承载层荷载应力影响较大,结构优化时,应着重在降低轨道板厚度、增加底座板厚度方面进行;底座板宽度宜按照45°荷载扩散角确定;尽量延长底座板长度,并在端部设置传力杆,以改善基床的受力条件;双块式轨道中结合式双层结构的应力水平较分离式双层结构低,在满足双块式轨枕埋置宽度的基础上应采用较窄的道床板宽度。
(2)建立了无碴轨道温度应力计算方法
根据连续式无碴轨道的裂缝发展特点,推导了连续式无碴轨道的温度应力、裂缝间距和裂缝宽度的计算公式,并进行了参数分析。为控制连续式无碴轨道的裂缝宽度在容许范围内应将裂缝控制为不稳定裂缝型式。此时钢筋最大应力由混凝土抗拉强度和配筋率控制,最大裂缝宽度则与钢筋和混凝土之间的粘结强度、混凝土抗拉强度以及配筋率有关,均与降温幅度无关。采用C40混凝土时,为满足0.5mm的裂缝宽度要求,配筋率应达到0.73%以上,钢筋直径宜在18～25mm间选择。采用高标号混凝土道床板、低标号混凝土支承层以及滑模施工或涂层钢筋时,应对应提高道床板配筋率。
综合考虑国外无碴轨道、路面工程温度梯度取值以及遂渝线实测无碴轨道温度场,提出了我国无碴轨道温度梯度建议值。以板式轨道为例,研究了不同约束条件和CA砂浆弹性模量情况下的轨道板翘曲应力,得出无碴轨道翘曲应力可按无限大板进行计算的结论。
(3)研究了基础变形对无碴轨道的受力影响
将路基不均匀沉降和桥梁挠曲变形假设为正弦和半波正弦曲线,利用考虑基础变形的梁板有限元模型和简化的刚性基础、弹性基础模型对比分析了无碴轨道承载层附加弯矩,研究认为对于正弦型基础变形引起的无碴轨道附加弯矩的计算可采用刚性基础法进行。对于刚度较大的单元式道床板,不均匀沉降限值应适当提高,以保证自重作用下不产生空吊。
梁端位移对无碴轨道扣件系统的受力影响较大,特别是错台高度、梁端转角和胶垫刚度。综合考虑列车荷载、错台等因素,从保护扣件受力的角度提出了不同胶垫刚度时的梁端转角限值。梁端位移对无碴轨道上抬稳定性有一定的影响,特别是在采用大抗拔力扣件系统时,需在梁端部位加强无碴轨道与桥梁的联结。
(4)初步建立了我国无碴轨道设计理论与方法
将无碴轨道设计分为功能设计与结构设计两部分。功能设计主要用于确定轨道的结构组成和施工方法等,使之满足高稳定和高平顺要求;结构设计则主要根据列车荷载、温度变化及基础变形及其共同作用确定承载层结构配筋等,使之满足强度与耐久性要求。
在对国内外无碴轨道总结分类的基础上,对无碴轨道及主要部件进行了功能分析,提出功能设计的概念以保证无碴轨道的高平顺和高稳定性。对于使用寿命要求60年的无碴轨道结构,应保证在荷载作用下结构始终处于弹性工作阶段,宜采用以容许应力法为基础的结构设计方法。普通钢筋混凝土结构在荷载作用下可能会开裂,开裂之后抗弯刚度的降低将引起荷载作用下弯矩的改变,引入结构系数以反映此影响。以双块式轨道为例进行了路基和桥梁上单元式、连续式无碴轨道的结构设计。结构设计算例表明,对于单元式无碴轨道,配筋受列车荷载弯矩控制,而连续式无碴轨道配筋则受降温和混凝土收缩控制。
(5)建立了无碴轨道落轴试验模拟模型,对无碴轨道动力特性进行评价
以弹性地基上梁板模型为基础,建立了无碴轨道落轴试验模拟模型,对板式轨道动力特性进行了研究,结果表明扣件刚度对各部件加速度影响显著,为降低系统的振动水平,应采用较低的扣件刚度。CA砂浆弹性模量对轨道板和底座板加速度影响较大,底座板加速度明显低于双块式轨道支承层,且频率较低,说明CA砂浆具有一定的隔振作用,为降低下部基础的加速度水平,应采用弹性模量较低的CA砂浆。路基面支承刚度主要影响底座板的加速度,但影响程度较小。为降低系统振动水平,轨道板厚度宜取为0.2m左右,底座板厚度宜取为0.3m。
With the large scale construction of Passenger Dedicated Lines(PDLs), the ballastless track has got rapid development and extensive application. However, the design methods of different ballastless tracks were different, a uniform design theory for ballastless track did not exist. Based on the systematical summarization of ballastless track and corresponding projects home and aboard, a uniform ballastless track theoretical system is established through academic and experimental research in this thesis. The theory was successfully used in several projects, such as the ballastless track synthetically test section on Suining-Chongqing line(Suiyu line), the ballastless track test section on Wuhan-Guangzhou PDL, as well as the design of bi-block ballastless track and slab track for 250km/h reference blueprint design. The research work and main conclusion were divided into following areas:
(1)Develop the stress calculation method of ballastless track under train load
Considering the structure character of ballastless track, the stress under the train load should be calculated using the beam-shell model on elastic foundation. Rails are simulated by Euler beam. Bearing layers are simulated by elastic thin shell. The elasticity of the fastener, CA motar and subgrade are simulated by spring combination. The model is actualized using Finite Element Method. The plain concrete or hydraulic bounded layer should be modeled by using their reduced elastic modulus to reflect the influence to their bending stiffness when cracked. The greater the elastic modulus, or the larger the thickness of the supporting layer, or the stronger the interlaminar connection status, or the less the interval between cracks, the smaller the reduced elastic modulus of the cracked support layer will be resulted in. The calculation model and parameters were verified by the comparison between different models and field test data on Suiyu line.
A parameter study about slab track and bi-block ballastless track was carried out using the beam-shell model. The results show the thickness of the track slab and base slab have great influence to the stress in bearing layer. The thickness of the track slab should be reduced and that of the base slab should be increased in structural optimization. The width of the base slab should be ascertained according to the 45°load dispersion angle. The length of the base slab should be extended and dowels should be set at the base slab ends to improve the subgrade mechanical condition. In bi-block ballastless track, the stress level in combined structure is less than that in separated structure. A smaller track slab width should be used when the embedded width constraint of the bi-block sleeper is satisfied.
(2)Establish the thermal stress calculation method of ballastless track
The thermal stress, cracks interval and crack width calculation formula were derivated according to the crack develop character of continuous ballastless track. A parameter study was carried out using these formulas. The crack type should be controlled to unstable cracks to limit the crack width in continuous ballastless track. The maximum stress in rebar is controlled by concrete tensile strength and reinforcement ratio. The maximum crack width is related to the bond strength between rebar and concrete, the concrete tensile strength and reinforcement ratio. The maximum rebar stress and crack width have no relation to the temperature drop range. The reinforcement ratio should be larger than 0.73% to limit the crack width within 0.5mm when using C40 concrete. The diameter of the rebar should be selected between 18mm and 25mm. The reinforcement ratio should be enhanced when using high-grade concrete in track slab or low-grade concrete in support layer or coated rebar or slip form construction method.
Considering the temperature gradient value in ballastless track aboard, pavement and the test data on Suiyu Line comprehensively, the maximum temperature gradient value of our ballastless track was proposed. Taking slab track for example, the warp stress was analyzed under different constraint conditions and elastic modulus of CA motar. As a conclusion the warp stress of the ballastless track can be calculated using the infinite plate formula.
(3)Study the foundation deformation influence to the ballastless track
The subgrade uneven deformation and the deflection of the bridge are assumed to a sine or half-wave sine curve. The additional moment of the ballastless track bearing layer was calculated using the beam-shell finite element model considering the foundation deformation, a simplified rigid foundation and an elastic foundation model separately. As a conclusion the additional moment due to sine type foundation deformation can be calculated using rigid foundation method. The uneven deformation limit should be raised to guarantee no suspending under self-weight in short high stiffness track slab.
The displacements at bridge end have great influence to the fastening system, especially for step height, bridge end rotation and pad stiffness. Considering the influence of the train load and step, a limit for bridge end rotation was proposed from the viewpoint of fastening system protection. The bridge end displacements have a certain effect to the uplift stability of the ballastless track, especially when using large uplift resistance fastening system. The interlaminar connection between ballastless track and bridge should be strengthened at bridge end.
(4) Establish the design theory and method of ballastless track preliminarily
The ballastless track design is divided into two parts: the function design and structure design. The track components and construction method are determined in the function design to satisfy the high evenness and stability requirements. The reinforcement in the bearing layer is determined to satisfy the strength and durability requirements in the structure design according to external loads and their interaction. The external loads include train loads, influences of temperature and the foundation deformations.
A function analysis about ballastless track and their main components was carried out based on the summarization and classification of ballastless tracks home and aboard. The high evenness and stability of the ballastless track on PDLs is guaranteed by the function design conception. The ballastless track structure should always be in elastic stage because of its 60 years life span requirement, so the structure design method should be based on allowable stress method. The reinforcement concrete structure will crack due to load action and the bending stiffness will decrease which result in the change of the moment. A structure coefficient was introduced to reflect its influence. Taking bi-block ballastless track for example, the structure designs of ballastless track with single slabs and continuous slab on subgrade and bridge were carried out. The structure design examples show that the reinforcement for ballastless track with single slabs is controlled by the moment under train load, the reinforcement for ballastless track with continuous slab is controlled by the temperature drop and concrete shrinkage.
(5)Establish the simulation model of the ballastless track falling wheelset experiment to estimate and evaluate the dynamic character of the ballastless track
Based on the beam-shell model on elastic foundation, a ballastless track falling wheelset experiment simulation model was established. The dynamic character of the slab track was analyzed. The results show the fastener stiffness has great influence to the acceleration of each component. Lower fastener stiffness should be used to reduce the system vibration level. The elastic modulus of the CA motar has great influence to the track slab and base slab acceleration. The acceleration and the frequency of the base slab are significant lower than that of the support layer in bi-block ballastless track, which reflect that CA motar can isolate vibration to a certain degree. The subgrade stiffness mainly influences the acceleration of the base slab, but the degree is relatively small. The thickness of the track slab and the base slab should be about 0.2m and 0.3m to reduce the system vibration level.
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