Short Communication
Sensitivity analysis of free vibration characteristics of an in situ railway concrete sleeper to variations of rail pad parameters

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Abstract

The vibration of in situ concrete sleepers in a railway track structure is a major factor causing cracking of prestressed concrete sleepers and excessive railway track maintenance cost. Not only does the ballast interact with the sleepers, but the rail pads also take part in affecting their free vibration characteristics. This paper presents a sensitivity analysis of free vibration behaviors of an in situ railway concrete sleeper (standard gauge sleeper), incorporating sleeper/ballast interaction, subjected to the variations of rail pad properties. Through finite element analysis, Timoshenko-beam and spring elements were used in the in situ railway concrete sleeper modeling. This model highlights the influence of rail pad parameters on the free vibration characteristics of in situ sleepers. In addition, information on the first five flexural vibration modes indicates the dynamic performance of railway track when using different types of rail pads, as it plays a vital role in the cracking deterioration of concrete sleepers.

Introduction

Due to the nature of undergoing numerous dynamic loadings on railway track, the vibration characteristics of in situ railway concrete sleepers are essential in analysis and design procedures. Clearly, the sleeper damage occurs mostly at resonant frequencies of the sleepers, especially for the dominance in the first five modes of vibration. There have been a number of studies shown that the resonant vibrations of sleepers affect not only the sleepers themselves, but also the wheel–rail interaction forces [1], [2], [3]. Grassie and Cox [2] presented the responses of railway track to high-frequency excitation. They also found that the higher pad stiffness tends to increase the contact forces. It is very important to note that the typical corrugation-passing frequencies (e.g. 750 Hz for a corrugation of 60 mm wavelength and train speed of 45 m/s) are most likely to cause much damage on concrete sleepers at their second and third dynamic mode shapes. Esveld [4] also described that the normal train operation causes the dynamic forces at the frequency range from 0 to 20 Hz for sprung mass and from 20 to 125 for unsprung mass. In particular, corrugations, bad welds, and wheel flats would create the forces varying from 0 to 2000 Hz, depending on the train speeds. An analytical model for analyzing dynamic behaviors of concrete sleepers in both free–free and in situ conditions was later developed by Dahlberg and Nielsen [5]. Subsequently, based on a number of experimental results, Grassie [6] developed a simplified two-dimensional dynamic modeling for vibration analysis of concrete sleepers in free–free condition. It has been found from the last two works that the Timoshenko beam element is the best approximation of the concrete sleepers, even though the elastic properties of prestressed concrete sleepers may not be exact. Those analytical models were treated through sophisticated numerical procedures, e.g. the modified Wittrick–Williams bisection algorithm. Ilias [7] investigated the effect of rail pad stiffness on wheelset/track interaction and corrugation growth. It was found that the stiffer the rail pad, the higher the global track resonance. However, it has been found that the effect of rail pad parameters on the dynamic responses of in situ railway concrete sleepers has not been studied, although the modern rail pads play a vital role on the track dynamics nowadays [8], [9]. In practice, the rail pads are replaced with new synthetic ones during the track maintenance, while their influence on dynamic changes within the concrete sleepers themselves is yet unknown. The structural behaviors of the railway concrete sleepers in the track structure system or so-called ‘the in situ railway concrete sleepers’ can be found in a recent work [10].

This paper presents the results of a sensitivity analysis of free vibration characteristics of the in situ railway concrete sleepers to variations of rail pad properties. The concrete sleeper modelled herein is the modified Australian standard gauge sleeper type, whose similar results (Swedish sleeper) can be found in literature [5], [6]. The emphasis was placed on only the in situ mono-block sleepers fitted in ballasted railway tracks. The aim was to examine the effect of rail pad parameters on the dynamic behavior of in situ sleepers while the sleeper/ballast interaction was also taken into account. The in situ sleepers were considered as beams on elastic foundation of the Winker type. The in situ sleeper model was analyzed based on the finite elements using a computer package, STRAND7. Two-dimensional beam element, considering shearing effects, was employed as the concrete sleeper to embrace the shear deformation and rotational inertia, whereas the ballast-support system and rail pad were modelled using elastic support feature and spring elements, respectively. Changes in natural frequencies and dynamic mode shapes of the sleepers are presented to describe the effect of rail pads with various types. Information on dynamic changes is of significant benefit to the research on non-destructive testing and health monitoring of on-track concrete sleepers.

Section snippets

In situ railway concrete sleeper modeling

Considering the system of an in situ sleeper model in Fig. 1, the Timoshenko beam elements were adopted for modeling the sleeper, in order to obtain better agreement at higher frequencies because the rotatory inertia and shear deformation have been taken into account in the dynamic simulation. The free–free condition exists when the sleeper is virtually in space without any constraints, whilst the in situ one represents the condition of assembled sleepers resting on ballast in the actual track.

Sensitivity analysis

Free vibration characteristics of concrete sleepers with several types of rail pads assembled in the in situ sleeper model were investigated using two-dimensional finite element modeling. The pad stiffness used in this study was varied from 0 to 5000 MN/m. These stiffness values cover the range of all modern rail pads, from very soft rubber, to polymeric, to high-density-polyethelene, or EVA pads (see Table 1). In contrast, the rail stiffness is usually limited depending on different rail

Conclusions

Free vibration characteristics of the in situ railway concrete sleepers in a track structure system with different types of rail pads are examined using the finite element approach. The two-dimensional simulation based on the Timoshenko beam and spring elements has been verified and found in very good agreements with previous investigations. The results show that the rail pad parameters have the nonlinear effect on the effective stiffness significantly influencing the first three modes of the

Acknowledgements

The authors are grateful to acknowledge the Cooperative Research Centre (CRC) for Railway Engineering and Technologies, Australia, for the financial support as part of Project #5/23. The authors also would like to thank Dr. Jens Nielsen of Chalmers University of Technology for providing some supporting information.

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    The tendency of stiff rail pads to increase the probability of concrete sleepers cracking could be demonstrated by the analysis of free vibration characteristics of sleepers. As Kaewunruen and Remennikov [101] indicated based on the FE model of an in-situ concrete sleeper, the first three modes of vibration of concrete sleepers are remarkably influenced by rail pad stiffness, and the flexural modes take place of translation and rotation modes as the stiffness is increased, expediting cracks on the in-situ sleepers in normal train operations, which cause frequencies in the range of 0–125 Hz [1]. Grassie and Cox [102] used a mathematical model to analyse the influence of rail pad resilience on the dynamic wheel-rail contact force, deflection of the fastening, and rail seat strain under the condition of voided (unsupported) sleepers (discussed in section 5.4).

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