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Advances in Design Theories of High-Speed Railway Ballastless Tracks

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Advances in Design Theories of High-Speed Railway Ballastless Tracks Journal of Modern Transportation Volume 19, Number 3, September 2011, Page 154-162 Journal homepage: jmt.swjtu.edu.cn DOI: 10.1007/BF03325753 Advances in design theories of high-speed railway ballastless tracks Xueyi LIU*, Pingrui ZHAO, Feng DAI MOE Key Laboratory of High-Speed Railway Engineering, Southwest Jiaotong University, Chengdu 610031, China Abstract: The design theories of the ballastless track in the world are reviewed in comparison with the innovative re- search achievements of high-speed railway ballastless track in China. The calculation methods and parameters concern- ing train load, thermal effect, and foundation deformation of high-speed railway ballastless track, together with the structural design methods are summarized. Finally, some suggestions on the future work are provided. Key words: high-speed railway; ballastless track; design theory © 2011 JMT. All rights reserved. 1. Introduction 2. Overview of ballastless track design theories tructure forms and design theories of ballastless S tracks vary across the world due to the different In the design of Japanese slab track, the train load effect development backgrounds. In Japan, the slab track was is a primary concern. Using the elastic design method, the typically laid on the solid foundation such as a bridge or security during the manufacturing, hoisting, and construct- tunnel at first, and then gradually developed to the soil ing of the slab track is maximized. As seriously damaged subgrade afterwards. It adopts the unit design that takes CA mortar at the slab corner and the slab warping caused into account the effect of train load. The German ballas- by temperature gradients emerged, the uneven support tless track was first laid on the soil subgrade and then on caused by warping is considered in the analysis [1]. In the the foundation of bridges and tunnels. Its continuous baseplate design, in accordance with the limit state method, structure involves the consideration of thermal effects. the train load and the subgrade’s uneven settlement are The early ballastless track in China was mainly laid in considered together with the influence of weather condi- tunnels with the chief concern being the influence of tions, concrete contraction, and construction. train load. With the increasing application of ballastless German developed its ballastless track by borrowing track, a relatively general design theory and a structural the design concept and method of pavement engineer- system have been gradually formed after the innovative ing [2]. Most has longitudinally continuous structure, and research with high-speed railway ballastless track. temperature load and concrete contraction are the main This paper reviews the calculation methods and pa- factors to be considered in the design. The reinforcement rameters as well as the structure design procedures, and is located near the neutral axis and does not bear the train briefly introduces the advance in the design theories, of load. The effect of train load and temperature gradient is ballastless track based on the innovative research resisted by the rupture strength of the concrete. achievements in China.Finally, some suggestions on the In China, the early monolithic roadbed track, whose future work are provided, including fatigue properties structure design mainly considers the train load, was under the coupling action of train and temperature load, applied in the tunnels with good foundation condition durability, long-term dynamic properties, and mainte- and little temperature variation. The structural design nance mechanics of the ballastless track. of the Suining-Chongqing railway took into account the effect of uneven foundation deformation and tem- perature load [3-4]. Following systematic research on the ballastless track, the design theory based on the al- Received Jul. 17, 2011; revision accepted Aug. 29, 2011 *Corresponding author. Tel.:+86-28-87600243 lowable stress method was created with full considera- E-mail: [email protected] (X.Y. LIU) tion of train load, temperature, and foundation defor- © 2011 JMT. All rights reserved mation effect. doi: 10.3969/j.issn.2095-087X.2011.03.002 Journal of Modern Transportation 2011 19(3): 154-162 155 In general, the design theory of ballastless track in and the generality of analysis method. In Germany, different country was relevant to its own construction however, the design theory and parameters selection of environment and structure evolution. The design theory ballastless track were developed from the experience of proposed in different periods could meet the construc- highway concrete pavement design; thus, its structural tion requirements for different types of ballastless track. difference in ballastless track can also be attributed to heritance of the traditional design theory. 3. Calculation of train load stress In accordance with the structural characteristics that the rail and the sleeper are cross-supported on the elastic The track supports the train load and guides the vehi- foundation in the ballast track, the cross beam model on cle operation. The calculation of train load stress must the elastic foundation [14-15] was developed on the ba- be considered in the ballastless track design. The elastic sis of the elastic foundation beam model, and can also foundation beam model [5-6] is mainly used for calcula- be used for the stress calculation of the ballastless track tion of the load stress in the traditional track structure. [16] once the values of the model parameters are deter- The model can be solved using the multilayer composite mined. Thanks to the development of the computing beam theory on the elastic foundation [7-10] according technology, the solid finite element model [17-19] can to the complexity and analysis requirement of the track be employed to obtain the particular stress state inside structure. In Germany, however, the Eisenmann theory the ballastless track structure. [11-13] was adopted to calculate the stress of the rail As the major supporting structure of the ballastless structure under the train load. In this theory, rail is re- track, the track slab (or bed slab) and baseplate (or sup- garded as an infinite beam on the elastic foundation to porting layer), whose deflections under the train load are calculate the support reaction of the fastener; the multi- far smaller than their thicknesses, have a far smaller size layer structure is translated into a monolayer one ac- in the vertical direction than in the longitudinal or lateral cording to the connection status of the structural layer, direction. This feature conforms to the structural charac- and then the internal force and displacement of the con- teristics of the elastic plate. Consequently, the elastic verted monolayer structure under the action of fastener plate [20] is generally adopted for simulation and analy- force is calculated using the infinite beam on the elastic sis of the supporting structure of ballastless track. The foundation and Westgaard’s stress function. rail, a slender structure, is reasonably simulated by the To sum up, the main components are treated as flex- beam model, while the fastener and the intermediate ural members in the train load design of ballastless track elastic layer, as well as the foundation below, are simu- in China and Japan. This is because the ballastless track lated with different kinds of springs. As a result, a design was originally developed based on the traditional beam-plate model of ballastless track on elastic founda- design methods for ballast track that put an emphasis on tion [21-23] is built as shown in Fig. 1. simulation of the force properties of main components ERJR Es, hs Kf Eb, hb P kRD P Ki Notes: ERJR is the flexural rigidity of rail, where ER is the modulus of elasticity of rail, and JR the moment of inertia of rail; Es and hs are the modulus of elasticity and thickness of track slab, respectively; Eb and hb are the modulus of elastic- ity and thickness of baseplate, respectively; Kf is the rigidity of fastener; Ki is the rigidity of intermediate elastic layer; kRD is the rigidity of foundation below; and, P is the train load. Fig. 1 The elastic foundation beam-plate model of ballastless track 156 Xueyi LIU et al. / Advances in design theories of high-speed railway ballastless tracks The load stress of the track slab (or bed slab) and the ferred at the crack location, resulting in a reduction in baseplate (or supporting layer) in the longitudinal and the entire rigidity and the modulus of elasticity. There- lateral directions can be obtained by exerting a vertical fore, the reduced elastic modulus is used for calculation train load on the rail. This avoids the calculation in the [26]. As for the reinforced concrete structure, the rein- longitudinal and lateral directions separately in the mul- forcement is helpful to improve the flexural rigidity of tilayer elastic foundation beam model. Moreover, the the structural layers. However, due to the possible computational accuracy [7] is higher than that via the cracking, the transmission of the bending moment at the composite beam model or the cross beam model, and cracked location may be weakened. Consequently, only the computing workload is less than that via the solid the concrete elastic modulus is used for calculation, finite element model. without consideration of the influence of the reinforce- The design wheel load of the Japanese slab track ment and crack. takes into consideration the wheel load variation due to wheel tread damage and tolerates three times the static 4. Calculation of temperature stress wheel load. In fatigue checking, the allowable wheel load is 1.45 times the static wheel load. On the basis of The ballastless track is exposed to the atmosphere. the allowable value of the derailment coefficient, the de- With changes in external temperature, the temperature sign lateral force was determined, and the lateral force in every structural layer will vary. Once the deformation for fatigue checking takes half of the design lateral force.
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