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CivilComp Proceedings
ISSN 17593433 CCP: 83
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 53
HighSpeed Train Induced Vibrations: A Comprehensive BE Model P. Galvín and J. Domínguez
Department of Continuum Mechanics, University of Seville, Spain P. Galvín, J. Domínguez, "HighSpeed Train Induced Vibrations: A Comprehensive BE Model", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 53, 2006. doi:10.4203/ccp.83.53
Keywords: boundary elements, high speed train, wave propagation, transient vibrations, experimental validation.
Summary
High speed trains are becoming a usual mean of
transportation for intermediate distances in many countries. New
lines have been constructed in recent years. Factors such as:
vibrations in the train, wave propagation in the soil next to the
track and dynamic effects in nearby construction, are much more
important in high speed trains than in conventional ones. These
effects require analysis in order to maintain security and
comfort in the trains and to avoid problems in nearby
construction as a result of vibrations induced by waves transmitted
through the soil. Particularly serious would be situations in
which the train speed may be higher than that of the surface waves
in the underneath soil. This possibility was completely
unthinkable in conventional trains but it is now something that
should be taken into account when high speed trains operate at
locations with particularly soft soils or underground
discontinuities that may result in a relatively low surface wave
speed.
The study of these problems requires comprehensive models that take into account many factors related to the characteristics of the train, the track, and the particular soil properties. Nearby structures should also be modeled in case the effects on these structures are being analyzed. Different analytical, semianalytical or numerical methods have been developed in recent years. Numerical methods are intended to reproduce more precisely the particular conditions of the problem taking into account the important dynamic interaction effects. The finite element method (FEM) and the boundary element method (BEM) have been used to study the problem of high speed trains passing taking into account the propagation of waves in the soil and dynamic soilstructure interaction [1,2]. The main differences between these models are based on the way in which excitation and interaction effects are considered. It is known that boundary elements are very well suited for dynamic soilstructure interaction problems. They are able to represent unbounded regions in a natural way as a result of the fact that the fundamental solution and, therefore the solution of the problem at hand, satisfies the radiation conditions. A three dimensional time domain formulation of the BEM with a fullspace fundamental solution is used in this paper. Nine node quadrilateral and six node triangular quadratic elements are used. Piecewise linear and piecewise constant time interpolation are used for displacements and tractions, respectively. Special attention is paid to stabilizing algorithms and element subdivision to improve efficiency, stability and accuracy of the procedure. A decaying law for wave amplitude is introduced in order to represent internal damping in the soil. The soil is assumed to be a uniform viscoelastic halfspace and is discretized into quadratic elements in a zone of the soil surface around the points of interest. The passing of a high speed Thalys train is assumed. Two symmetry axes of the problem were considered in order to reduce the number of degrees of freedom of the problem. A track length of 86.4 m was discretized. The discretized surface has a width of 25m. During 1997 the Structural Mechanics Group of the Catholic University of Leuven obtained a series of experimental results of soil induced vibrations due to the passing of a Thalys train at different speeds. In the present paper, results for the type of train and soil conditions of those experiments are computed using the time domain BEM. The soil properties are as proposed by Degrande and Schillemans [3] taking into account the measured values of P and Swave speeds and the internal damping. Those values are: , (top layer) and an internal damping higher than 3% (we consider ). Krylov's loading distribution has been used to represent the constant load transmitted by each train wheel. The coefficient controlling stability of the time domain BEM is set equal to 0.3 in relation to the smallest elements of the mesh. It can be seen that there is a rather good agreement between the numerical results obtained by the model proposed and the experimental results obtained by Degrande and Schillemans [3]. Both sets of results have rather close values of amplitude and the main frequency and show a similar decaying law with the distance to the track. More results corresponding to different train velocities and other locations will be presented in a forthcoming paper. References
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