基于断裂和损伤力学的无砟轨道静动力特性研究
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摘要
无砟轨道以其高平顺、高稳定和少维修等一系列优点成为高速铁路的主要轨道结构型式。由钢筋混凝土组成的无砟轨道主体结构受列车荷载及温度等因素的影响,开裂难以避免,而采用理想弹性梁或板来模拟轨道主体结构不能完全反映其实际受力状态。本文在国内外无砟轨道静、动力学研究的基础上,将断裂力学、轮轨系统动力学、损伤力学和有限单元法相结合,对含裂纹的无砟轨道静、动力特性进行探索性研究。主要研究工作如下:
(1)无砟轨道主体结构损伤类型分析
对我国首条无砟轨道试验段进行了现场跟踪调查,分别对单元板式、双块式和纵连板式轨道主体结构损伤进行了分类,总结了无砟轨道主体结构损伤的主要特征和规律,并对裂纹损伤产生的原因进行分析。
(2)初步建立基于断裂力学的无砟轨道空间有限元分析方法
根据无砟轨道的结构特征,基于线弹性断裂力学理论,采用有限单元法建立了含裂纹的无砟轨道空间有限元模型。其中钢轨以Euler梁模拟,道床混凝土以20节点六面体等参元模拟,道床钢筋以杆单元模拟,同时考虑了钢筋对道床裂纹张开的约束,构造20节点六面体奇异等参单元反映裂纹尖端奇异。给出了模型的实现方法,编制了计算程序,并结合已有的结果对计算方法进行了验证。
(3)列车荷载下含裂纹无砟轨道受力
首先给出了列车荷载下无裂纹无砟轨道的受力,然后计算了相同条件下道床底面20mm等深裂纹尖端的应力场、应力强度因子、裂纹张开量、裂纹处钢筋应力;分析了裂纹深度、裂纹位置和列车荷载位置对裂纹特征参数的影响;最后,根据混凝土断裂韧度,对常规列车荷载下道床裂纹稳定度进行评价。结果表明,道床裂纹对无砟轨道整体受力与变形影响不大,钢筋对裂纹扩展有明显限制作用,道床裂纹因常规列车荷载明显扩展的可能性不大,裂纹处道床下层纵向钢筋应力发生突变且随裂纹深度的增大快速增加,道床中部裂纹对其受力最为不利,列车荷载作用下的道床底面等深裂纹基本属于张开型裂纹。
(4)温度梯度下含裂纹无砟轨道受力
对具有道床顶面等深裂纹的双块式轨道在温度梯度作用下的受力进行了分析,给出了裂纹尖端的应力强度因子、裂纹张开量、裂纹处钢筋应力;分析了裂纹深度、裂纹位置及温度梯度大小等因素对裂纹特征参数的影响;最后,对负温度梯度作用下道床顶面裂纹稳定度进行了评价。结果表明,温度梯度作用下道床钢筋对裂纹扩展的限制作用不明显,道床裂纹因温度梯度影响存在明显扩展的可能性,裂纹处道床上层钢筋应力出现突变,且随温度梯度和裂纹深度的增大而快速增加,裂纹出现在道床中部时对其受力最为不利。
(5)考虑裂纹的无砟轨道动力分析
根据双块式轨道道床裂纹特点,引入损伤函数描述道床裂纹,基于轮轨系统动力学理论,建立考虑道床裂纹的“车辆-无砟轨道”耦合振动分析方法,给出了考虑道床裂纹的无砟轨道振动响应,分析了车辆速度及裂纹位置对无砟轨道振动响应的影响。结果表明,道床裂纹对车辆和钢轨的动力响应影响很小,而对道床本身及其下部结构有一定影响;道床动弯应力和路基面动应力随车辆速度的增大而增大,道床中部裂纹对道床动弯应力和路基面动应力的影响更为明显。
Ballastless track has become the main type of high-speed railway infrastructure due to its advantages such as high smoothness, high stability and low maintenance. However, damaged cracks of the main concrete structure of the ballastless track was unavoidable taking into account a variety of factors such as the vehicular load or temperature influences, and using elastic beam or slab to simulate the track could not reflect its actural state. In this thesis, on the basis of study at home and abroad, static and dynamic property of ballastless track with damaged cracks was researched by the theory of fracture mechanics, wheel-rail system dynamics, damage mechanics and finite element method. The research work and main conclusion were divided into following areas:
(1) Classify the damage of ballastless track main stucture
The damage of track main structure of China's first ballastless track experimental section was investigated; the damage of slab, bi-block and continuous ballastless track were classified respectively. The characteristics and rules of the damage of track main structure were summarized, and the reason of the damaged cracks was analyzed.
(2) Establish the spatial finite element method of ballastless track preliminarily based on fracture mechanics
According to the structural characters of ballastless track, a spatial finite element method of ballastless track with damaged cracks was established with finite element method based on the theory of elastic fracture mechanics. Rail was simulated by Euler beam. Concrete and longitudinal bars of track bed were simulated as 20-node hexahedron isoparameteric element and truss element, respectively. Constraint of the crack's opening by bars was also considered. The singularity of crack tip was simulated by 20-node hexahedron isoparameteric singular element. A calculating program of the method was coded and verified by some known results.
(3) The mechanical analysis of ballastless track with damaged cracks under vehicular load
Firstly, the mechanics of ballastless track without crack under vehicular load was given, and then for the same track but with full-depth crack of 20mm at the track bed bottom face, some cracking parameters at the crack tip such as the concrete stress, stress intensity factor (SIF), crack opening displacement (COD) and bar stress were calculated. The effects of crack depth, crack location and vehicular location on the cracking parameters were studied. Finally, the crack stability was evaluated according to the fracture toughness of concrete. The results show that the crack has little effect on the global stress and deformation of the track, and the constraint of the crack's opening by bars is significant. The crack is not likely to propagate by general vehicular load. The bar stress at the crack has a sudden increase, and increase with crack length increasing. The most unfavorable crack for the track mechanics is that at the middle of the track bed, and the crack belongs to opening mode crack.
(4) The mechanical analysis of ballastless track with damaged cracks under temperature gradient
The mechanics of bi-block track with full-depth crack at the track bed top face under minus temperature gradient were calculated, and SIF, COD and bar stress at the crack tip were also given. The effects of crack depth, crack location and temperature gradient magnitude on the cracking parameters were studied, and the crack stability was also evaluated. The results show that the constraint of the crack's opening by bars under temperature gradient is not significant. The crack is likely to propagate cause of temperature gradient. The bar stress at the crack has a sudden increase, and it increase with crack length and temperature gradient magnitude increasing. The most unfavorable crack for the track mechanics is that at the middle of the track bed.
(5) Dynamic analysis of ballastless track with damaged cracks
According to the crack characters of the bi-block track bed, a damagefunction was introduced to simulate deterioration of the bending stiffness, the dynamic coupling analysis method of vehicle and bi-block ballastless track with cracks was established. The dynamic responses of track were given, and the effects of vehicle velocity and crack location on the track dynamic responses were also studied. The results show that crack has little influence on the vehicle and rail vibration responses, while more on the track bed and substructure. Dynamic bending stress of track bed and dynamic stress of subgrade increase obviously with the increase of vehicle velocity. The crack at the middle of the track bed has more effect on dynamic bending stress of track bed and dynamic stress of subgrade than crack at other location.
(1)无砟轨道主体结构损伤类型分析
对我国首条无砟轨道试验段进行了现场跟踪调查,分别对单元板式、双块式和纵连板式轨道主体结构损伤进行了分类,总结了无砟轨道主体结构损伤的主要特征和规律,并对裂纹损伤产生的原因进行分析。
(2)初步建立基于断裂力学的无砟轨道空间有限元分析方法
根据无砟轨道的结构特征,基于线弹性断裂力学理论,采用有限单元法建立了含裂纹的无砟轨道空间有限元模型。其中钢轨以Euler梁模拟,道床混凝土以20节点六面体等参元模拟,道床钢筋以杆单元模拟,同时考虑了钢筋对道床裂纹张开的约束,构造20节点六面体奇异等参单元反映裂纹尖端奇异。给出了模型的实现方法,编制了计算程序,并结合已有的结果对计算方法进行了验证。
(3)列车荷载下含裂纹无砟轨道受力
首先给出了列车荷载下无裂纹无砟轨道的受力,然后计算了相同条件下道床底面20mm等深裂纹尖端的应力场、应力强度因子、裂纹张开量、裂纹处钢筋应力;分析了裂纹深度、裂纹位置和列车荷载位置对裂纹特征参数的影响;最后,根据混凝土断裂韧度,对常规列车荷载下道床裂纹稳定度进行评价。结果表明,道床裂纹对无砟轨道整体受力与变形影响不大,钢筋对裂纹扩展有明显限制作用,道床裂纹因常规列车荷载明显扩展的可能性不大,裂纹处道床下层纵向钢筋应力发生突变且随裂纹深度的增大快速增加,道床中部裂纹对其受力最为不利,列车荷载作用下的道床底面等深裂纹基本属于张开型裂纹。
(4)温度梯度下含裂纹无砟轨道受力
对具有道床顶面等深裂纹的双块式轨道在温度梯度作用下的受力进行了分析,给出了裂纹尖端的应力强度因子、裂纹张开量、裂纹处钢筋应力;分析了裂纹深度、裂纹位置及温度梯度大小等因素对裂纹特征参数的影响;最后,对负温度梯度作用下道床顶面裂纹稳定度进行了评价。结果表明,温度梯度作用下道床钢筋对裂纹扩展的限制作用不明显,道床裂纹因温度梯度影响存在明显扩展的可能性,裂纹处道床上层钢筋应力出现突变,且随温度梯度和裂纹深度的增大而快速增加,裂纹出现在道床中部时对其受力最为不利。
(5)考虑裂纹的无砟轨道动力分析
根据双块式轨道道床裂纹特点,引入损伤函数描述道床裂纹,基于轮轨系统动力学理论,建立考虑道床裂纹的“车辆-无砟轨道”耦合振动分析方法,给出了考虑道床裂纹的无砟轨道振动响应,分析了车辆速度及裂纹位置对无砟轨道振动响应的影响。结果表明,道床裂纹对车辆和钢轨的动力响应影响很小,而对道床本身及其下部结构有一定影响;道床动弯应力和路基面动应力随车辆速度的增大而增大,道床中部裂纹对道床动弯应力和路基面动应力的影响更为明显。
Ballastless track has become the main type of high-speed railway infrastructure due to its advantages such as high smoothness, high stability and low maintenance. However, damaged cracks of the main concrete structure of the ballastless track was unavoidable taking into account a variety of factors such as the vehicular load or temperature influences, and using elastic beam or slab to simulate the track could not reflect its actural state. In this thesis, on the basis of study at home and abroad, static and dynamic property of ballastless track with damaged cracks was researched by the theory of fracture mechanics, wheel-rail system dynamics, damage mechanics and finite element method. The research work and main conclusion were divided into following areas:
(1) Classify the damage of ballastless track main stucture
The damage of track main structure of China's first ballastless track experimental section was investigated; the damage of slab, bi-block and continuous ballastless track were classified respectively. The characteristics and rules of the damage of track main structure were summarized, and the reason of the damaged cracks was analyzed.
(2) Establish the spatial finite element method of ballastless track preliminarily based on fracture mechanics
According to the structural characters of ballastless track, a spatial finite element method of ballastless track with damaged cracks was established with finite element method based on the theory of elastic fracture mechanics. Rail was simulated by Euler beam. Concrete and longitudinal bars of track bed were simulated as 20-node hexahedron isoparameteric element and truss element, respectively. Constraint of the crack's opening by bars was also considered. The singularity of crack tip was simulated by 20-node hexahedron isoparameteric singular element. A calculating program of the method was coded and verified by some known results.
(3) The mechanical analysis of ballastless track with damaged cracks under vehicular load
Firstly, the mechanics of ballastless track without crack under vehicular load was given, and then for the same track but with full-depth crack of 20mm at the track bed bottom face, some cracking parameters at the crack tip such as the concrete stress, stress intensity factor (SIF), crack opening displacement (COD) and bar stress were calculated. The effects of crack depth, crack location and vehicular location on the cracking parameters were studied. Finally, the crack stability was evaluated according to the fracture toughness of concrete. The results show that the crack has little effect on the global stress and deformation of the track, and the constraint of the crack's opening by bars is significant. The crack is not likely to propagate by general vehicular load. The bar stress at the crack has a sudden increase, and increase with crack length increasing. The most unfavorable crack for the track mechanics is that at the middle of the track bed, and the crack belongs to opening mode crack.
(4) The mechanical analysis of ballastless track with damaged cracks under temperature gradient
The mechanics of bi-block track with full-depth crack at the track bed top face under minus temperature gradient were calculated, and SIF, COD and bar stress at the crack tip were also given. The effects of crack depth, crack location and temperature gradient magnitude on the cracking parameters were studied, and the crack stability was also evaluated. The results show that the constraint of the crack's opening by bars under temperature gradient is not significant. The crack is likely to propagate cause of temperature gradient. The bar stress at the crack has a sudden increase, and it increase with crack length and temperature gradient magnitude increasing. The most unfavorable crack for the track mechanics is that at the middle of the track bed.
(5) Dynamic analysis of ballastless track with damaged cracks
According to the crack characters of the bi-block track bed, a damagefunction was introduced to simulate deterioration of the bending stiffness, the dynamic coupling analysis method of vehicle and bi-block ballastless track with cracks was established. The dynamic responses of track were given, and the effects of vehicle velocity and crack location on the track dynamic responses were also studied. The results show that crack has little influence on the vehicle and rail vibration responses, while more on the track bed and substructure. Dynamic bending stress of track bed and dynamic stress of subgrade increase obviously with the increase of vehicle velocity. The crack at the middle of the track bed has more effect on dynamic bending stress of track bed and dynamic stress of subgrade than crack at other location.
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