Keywords: high-speed railway, arch bridge, train, interaction, dynamic response.

The Beijing-Shanghai High-speed Railway is one of the most important construction engineering in China for recent years. The railway is design for trains whose speed is up to 350km/h. More than half the length of the Beijing-Shanghai High-speed Railway is designed as bridges, among them the bridge across the Yangtze River near Nanjing in Jiangsu Province is one of the most important ones.

In general concept, the passage of trains on the bridge at high speed may induce the vibration of the bridge structure [1,2,3,4,5]. It is a new challenge for the designer to ensure the safety of the bridge and the comfort of passenger trains when it passes the bridge. It is necessary for the designers to control the vibration of the long span arch bridge with relative low stiffness in the design phase.

The dynamic model of the vehicle-bridge system is composed of three sub-systems: the vehicle system, the bridge system and the wheel-rail interaction system.

The vehicle system of a train can be modeled by several independent vehicle elements. Each element represents a locomotive or a passenger carriage. A vehicle element is composed of 1 car body, 2 bogies and 4 or 6 wheel sets, which are linked by the longitudinal, lateral and vertical springs and dampers. Each car body or bogie has 5 DOFs: Y, Z, R_X, R_Y, R_Z. Each wheel has 4 DOFs: Y, Z, R_X, R_Z. Therefore, there are 31 DOFs for a 4-wheel-set locomotive or passenger-carriage element and 39 DOFs for a 6-wheel-set locomotive element.

The bridge system is adopted by its overall mass matrix and stiffness matrix, which can be obtained by the finite element method. The damping matrix of bridge system is defined as Rayleigh damping by use of the first two frequencies of the bridge structure and a given damping ratio.

The wheel-rail interaction system is established, from which the wheel-rail forces are determined by the Hertz contact theory in the normal direction and Kalker creep theory in the tangent direction [6].

Four types of high-speed trains, the ICE3 train made in Germany, the TGV articulated train made in France, the 500 Series train made in Japan and a high speed train made in China, are simulated passing the Nanjing Yangtze River Bridge.

The Nanjing Yangtze River Bridge is a continuous arch bridge with spans of 108+ 192+336+336+192+108m. The arch is 68.68m in height, including the main truss height 16m. The main truss, the 2 spans of the 3 parallel arches, and the cross-bracing systems at each joint section of the bridge, with intervals of 12m or 15m, are steel frame structures. The bridge deck is composed of steel longitudinal and lateral beams and concrete deck slab.

All the members in the main truss, arches and cross-link systems are regarded as spatial beam elements in the FEM model. The steel main arch and cross link system is simplified into spatial beam elements, while the deck system, are simplified into 4 longitudinal beam elements, by keeping their lateral and vertical stiffness and masses equivalent to the original structures, in which the concrete deck slab contributes only mass to the model. There are 80 orders of natural frequencies and modes for the bridge to be calculated.

The whole histories of the trains passing through the bridge are simulated, from which the dynamic responses of the bridge and the train vehicles are obtained.

The results show that the four types of trains have similar dynamic characteristics and all the safety and comfort factors increase with train speed. The results show that the derail factors, offload factors, vertical and lateral accelerations of car bodies increase with train speed. The dynamic responses of ICE3, TGV, J500 and CHN trains satisfy the standards for safety and comfort of running vehicles within the train speed range 250-420km/h.

The maximum vertical deflection of the bridge at the arch top is about 80% of and in phase with the deck. The maximum lateral displacement at the arch top is about 2.5 times of and with a phase delay behind the deck. The dynamic responses of the bridge girder at mid-span under the train speed of 250-420km/h are quite small: The maximum vertical deflection and lateral displacement are less than 20mm and 3mm, respectively; Both the vertical and lateral accelerations are less than 0.2m/s, much smaller than the related limitations in the Chinese Code.

1

Diana G., Cheli F., "Dynamic interaction of railway systems with large bridges", Vehicle System Dynamics, 18(1-3), 71-106, 1989. doi:10.1080/00423118908968915

2

Frýba L., "Vibration of Solids and Structures Under Moving Loads", Thomas Telford, London, 1999.

3

Xia H., Xu Y.L., "Dynamic Interaction of Long Suspension Bridges with Running Trains", J Sound & Vibration, 237(2), 263-280, 2000. doi:10.1006/jsvi.2000.3027

4

Yang, Y.B., Yau J.D., "Vehicle-bridge interaction element for dynamic analysis", J Structural Engineering ASCE, 123(11), 1512-1518, 1997. doi:10.1061/(ASCE)0733-9445(1997)123:11(1512)

5

Xia H., et al, "Dynamic analysis of high speed railway bridge under articulated trains", Computer & Structure, 81, 2467-2478, 2003. doi:10.1016/S0045-7949(03)00309-2

6

Zhai W., True H., "Vehicle-track dynamics on a ramp and on the bridges: simulation and measurements", Vehicle System Dynamics, 33(Supplement), 604-615, 1999.

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