Keywords: train-bridge interaction, numerical modelling, experimental study, modal analysis.

The study of train-bridge interaction is important for the design of a bridge, especially when verifying its serviceability state. Interaction models will also provide information about the comfort of the passengers and the safety of the train vehicles during the passage of bridges. The bridge structure, the rail support, the train speed, the train itself, including the linking and suspension system, can influence the interaction between bridges and trains.

The results of a dynamic experiment on the Antoing bridge are reported. The U-shaped bridge is constructed for the high speed connection between Paris and Brussels. The bridge is situated near the Belgian village Antoing, close to the Belgian-French border. Displacements, accelerations and strains were measured during several passages of Thalys trains with articulated vehicles. There are no data available about the stiffness and damping features of the ballast. The rail pads have a static stiffness of 120 kN/mm in the load interval between 15 and 90 kN. Their dynamic stiffness is about 250 kN/mm for frequencies lower than 5 Hz. The rails are UIC60 profiles and concrete bi-blocks are used as sleepers. From the measured rail irregularities, it can be concluded that the rail quality is very good when using the criteria of reference [3].

The vibration measurements are used to update a Finite Element model of the bridge and afterwards to validate train-bridge interaction models. A first model developed by Xia He is described in [2]. The bridge structure is modelled by its lowest modes. Each carriage of the train is modelled as a three-dimensional rigid body with 5 DOFs connected to, supported by the wheels by springs and dampers. Each wheel has 3 DOFs. In this way a 6-axle locomotive has in total 23 DOFs. The movement of the wheel-sets can be expressed by a linear composition of the generalized bridge modal coordinates. Analogous models are described in [4,5,6]. In [8] a specific model is developed for the Thalys train. The lack of data about the track system and the vehicle response is the main reason to focus on the comparison between measurements and simulations of the bridge response: in this case, a more simple model can be adapted. First of all a FE model, which incorporates the railway track as a supplementary mass, is tuned to the results obtained from applying system identification to the measured accelerations. This FE model is used to calculate by modal superposition the bridge response for a moving unit load on one of the two tracks. Afterwards this result is used to calculate the total response for a convoy of loads, corresponding to the Thalys composition. The influence of train speed on the bridge response has been studied.

The time behaviour of the displacements in the mid section, at either side of the bridge, is compared with the measurements. There is a very good correspondence between measured and calculated bridge response. It is clear that the Antoing bridge is very stiff: for a double Thalys passage the maximum dynamic displacement is less then 2 mm for a span of about 50 m! This high stiffness explains why a FE model which considers only a moving convoy of constant loads gives already excellent results.

1

Maeck, J., Teughels, A., De Roeck, G., "Experimental and numerical modal analysis of a concrete high speed train railway bridge", MCCI'2000 International Symposium on Modern Concrete Composites & Infrastructures, Beijing, China, November 30- December 2, 61-68, 2000.

2

Xia, H., De Roeck, G., Zhang, H.R., Zhang, N., "Dynamic analysis of a train-bridge system and its application in steel girder reinforcement", Computers & Structures, Vol. 79, 1851-1869, 2001. doi:10.1016/S0045-7949(01)00115-8

3

Braun, H., Hellenbroich, T., "Meßergebnisse von Straßenunebenheiten", VDI Berichte (877), 47-80, 1991.

4

Zhang, Q.L., Vrouwenvelder, A., Wardenier, J., "Numerical simulation of train-bridge interactive dynamics", Computers & Structures, Vol. 79, 1059-1075, 2001. doi:10.1016/S0045-7949(00)00181-4

5

Cheng, Y.S., Au, F.T.K., Cheung, Y.K., "Vibration of railway bridges under a moving train by using bridge-track-vehicle element", Engineering Structures, Vol. 23, 1597-1606, 2001. doi:10.1016/S0141-0296(01)00058-X

6

Yang, Y.B., Wu, Y.S., "A versatile element for analyzing vehicle-bridge interaction response", Engineering Structures, Vol. 23, 452-469, 2001. doi:10.1016/S0141-0296(00)00065-1

7

ANSYS Version 5.6, ANSYS Inc., 275 Technology Drive, Canonsburg, PA 15317.

8

Xia, H., Zhang, N., De Roeck, G., "Dynamic Analysis of a High-Speed Railway Bridge Under Articulated Trains, accepted for publication in Computers & Structures, 2003. doi:10.1016/S0045-7949(03)00309-2

9

Claes, E., "Train-Bridge Interaction: Parameter Study", Master Thesis, Department of Civil Engineering, K.U.Leuven, 2003.

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