Dynamic analysis of rail track for high speed trains. 2D approach.
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1 Dynamic analysis of rail track for high speed trains. 2D approach. A. Gomes Correia & J. Cunha University of Minho, Department of Civil Engineering, Civil Engineering Centre, Guimarães, Portugal J. Marcelino & L. Caldeira Laboratório Nacional de Engenharia Civil, Lisbon, Portugal J. Varandas, Z. Dimitrovová, A. Antão & M. Gonçalves da Silva New University of Lisbon, Lisbon, Portugal
2 Summary Introduction Objective Background Case study Simulation of Thalys HST Diana, Plaxis Dynamic and Models Results Conclusions Acknowledgements
3 Introduction The behavior of the railway track and infrastructure under the combination of high speed and repetitive axle loadings is affected as a result of a complex soilstructure interaction problem that constitutes a motivation for geotechnical and structural R&D. High speed trains bring some new problems: (1) demand tighter tolerances and track alignment for the purpose of safe and passenger comfort; (2) after a critical speed drastic dynamic amplification appears on the deformation of the track, embankment and supporting soft soil. Proper modelling of the dynamic behaviour of the railway track system, the soil and embankment materials and of the loading is essential to obtain realistic results.
4 Objective This work was done as part of an ongoing national research project involving the University of Minho, the National Laboratory of Civil Engineering and the New University of Lisbon. The objective of this work is to model the dynamic performance of a high speed train track using different FEM commercial software. Each institution was assigned to develop models with a defined software and as such University of Minho used DIANA, the National Laboratory of Civil Engineering used Plaxis and the New University of Lisbon used. The initial part here presented, consists in the development of 2D linear plane strain models. The verification of the results was made by comparison with measured data.
5 Background Winkler model Not possible to distinguish between the contribution of the sleeper and underlying layers. Springdashpot, a moving load and also an axial beam force (Koft and Adam, 25). Only steady state solutions can be provided. FEM and hybrid methods. Modeling the ballast with DEM. Need validation by field monitoring (M. Lu and G. R. McDowell)
6 Case study This study is related to a railway track between Brussels and Paris where vibration measurements were made for a site near Ath, 55 km south of Brussels. The vibrations were obtained at several distances ranging from 4m to 72 m of the track, during the passage of a Thalys HST (high speed train), at speeds between 16km/h and 33km/h. The experimental data is obtained from the literature (Degrande & Schillemans, 21)
7 The Thalys HST consists of 2 locomotives and 8 carriages with a total length of 2.18 m. The total number of bogies equals 13 and, consequently, the number of axles on the train is 26. The carriage length Lt, the distance Lb between bogies, the axle distance La and the total axle mass Mt of all carriages are summarized (Degrande & Lombaert, 2).
8 Simulation of Thalys HST The loads to be considered in the calculations are those that derive from the passing of the train. The loading history depends, naturally, on the train speed. In this study the simulation is made for the train speed of 314km/h. Assuming a distribution adjusted to the sleeper spacing as is considered in the Japanese regulations, was defined that 4% of the load is distributed to the adjacent sleepers. Combining this with the solution of the Winkler beam for the movement of a load, results in the following unitary distribution:
9 Combining the diverse axles in accordance with the geometry and load distribution of the train and applying the previous distribution, it is possible to establish the loading plan to apply. Time (s) Load (kn)
10 DIANA, Plaxis Dynamic and Models. The models created with DIANA are comprised of 2775 elements of 8 and 6 nodes. The Plaxis model is composed of 135 finite elements of 15 nodes. The model is composed of 321 finite elements of 4 nodes. All models consider Rayleigh damping. DIANA and Plaxis Dynamic models feature bounding elements used at the limits of the model to take into account the propagation of waves to outer regions. Non reflecting boundary conditions are not available in the code. For that reason, a sensitivity analysis was performed in order to fix a correct depth and width.
11 Results Calculations were made through linear dynamic analysis for the different models used. Comparison between numerical and measured accelerations was made for points A4, A5 and A7
12 a c c e le ra tio n (m /s 2 ) Results A Measurements DIANA acceleration (m /s2) Results A Measurements Plaxis Results A4 5 4 Rates A4 a c c e le ra tio n (m /s 2 ) Measurements DIANA Values m/s DIANA.1 Plaxis Plaxis , Measurements 4.96
13 Results A5 Results A5 acceleration (m/s2) Measurements DIANA acceleration (m/s2) Measurements Plaxis Results A5 4 3 Rates A5 acceleration (m/s2) Measurements DIANA Plaxis Values m/s DIANA 2.4 Plaxis , Measurements 2.84
14 Results A7 Results A7 acceleration (m/s2) Measurements DIANA acceleration (m/s2) Measurements Plaxis Results A Rates A7 acceleration (m/s2) Measurements DIANA Plaxis Values m/s DIANA 3.1 Plaxis Measurements 1.11
15 A new dynamic load was calculated through a method proposed by Hall (22). In this method the dynamic loading is defined through the static deflection of an equivalent Winkler model subject to a unitary load. acceleration (m/s2) load (kn) Results A Measurements New Dynamic loading
16 Conclusions The peak accelerations estimated are rather close. However, the estimated values have rates very different from unity related with the measured values, particularly for the acceleration on the sleeper. Several reasons can contribute to this discrepancy, the major being: a) simplifying assumptions made (dynamic loading, interface between sleeper and ballast rail rail pad); b) differences between material values; c) simplifying dynamic material behavior. The ongoing research work in the project involving cooperation between specialists in soil dynamics and structural dynamics is a guarantee of the further improvements in modelling. Some significant aspects considered for further developments include: (a) simulation of dynamic loading, (b) vibrations characteristics and dynamic interaction of concrete sleepers and ballast support system and (c) frequency and strain dependence of the materials stiffness and damping.
17 Acknowledgement The authors acknowledge the financial support for this research from the Foundation for Science and Technology (FCT) (project POCI/ECM/61114/24 Interaction soilrailway track for high speed trains).
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