Keywords: high-speed trains, induced vibration, finite element modelling, commercial software, decoupling of vibrations, negative stiffness, composite materials, Reuss bound, Rayleigh damping, numerical analysis.

The passage of high-speed trains may cause environmental problems, as they induce high ground and track vibrations, which, besides increasing wheel, rail and track deterioration, propagates through the soil, interacts with nearby buildings and causes discomfort of the habitants. As the train velocity increases, noise and soil vibrations are getting more important, especially when trains reach the critical speed corresponding to the natural wave velocity of the ground-track system [1].

Detailed information on surrounding soil vibrations can only be gathered from full three-dimensional models. Finite element analyses are able to predict many kinds of ground vibrations. However, close to the train critical speed, very fine meshes are required to capture accurately the generated waves. Commercial software is usually adopted for this purpose, but there is still lack of unified approaches and clearly stated reliable analyses.

In order to perform an accurate analysis, the model size and boundary conditions must be dealt with carefully. Particular attention must be put on the representation of dynamic loads and on the specification of material behaviour, especially damping properties. Adoption of inappropriate damping coefficients can drastically distort the output. There are basically two levels of damping, one is inherent to the interface material implemented in the rail-sleeper fixing system, the other one is a consequence of hysteretic soil properties. Full understanding and correct modelling of the latter feature is inevitable for soil improvement. Interface damping can be controlled directly, and might be improved by introduction of new and more efficient materials.

In this paper, full three-dimensional model for a case study is constructed in a parametric way. The viability of two-dimensional models is discussed, either as a longitudinal cut or as a transverse cut of the thee-dimensional model. For this purpose, full transient analyses are performed. It is concluded that interface damping can be studied and analysed in longitudinal cut analysis and that only qualitative comparison of soils damping modelling can be performed in a transverse cut analysis.

Two types of damping, as specified above, are examined. Negative stiffness materials and composite materials saturating lower Reuss bound in dynamic correspondence principle of the theory of linear viscoelasticity [2] are suggested in order to decouple efficiently rail and soil vibrations. Regarding the soil damping modelling, it is concluded that as Rayleigh damping does not seem to be the correct approach for two reasons: (i) calculation of damping constants alpha and beta is ambiguous; (ii) experience shows that energy is dissipated in soils by internal friction in hysteretic loops with no dependence on frequency. Preliminary results implementing hysteretic energy loss are obtained exploiting software ANSYS.

1

A.M. Kaynia, C. Madshus and P. Zackrisson, "Ground Vibration from High-Speed Trains: Prediction and Countermeasure", Journal of Geotechnical and Geoenvironmental Engineering, 126, 531-537, 2000. doi:10.1061/(ASCE)1090-0241(2000)126:6(531)

2

R.S. Lakes, "Extreme Damping in Composite Materials with a Negative Stiffness Phase", Physical Review Letters, 86(13), 2897-2900, 2001. doi:10.1103/PhysRevLett.86.2897

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