Response of a train moving on multi-span railway bridges undergoing ground settlement

This paper presents an incremental-iterative procedure to investigate the influence of ground settlement on dynamic interactions of train–bridge system. The train is simulated as a sequence of identical sprung mass units with equal intervals and the bridge system as a series of simple beams with identical properties. To resolve the train-induced vibrations of a beam structure undergoing support settlement, this study decomposes the total beam response into two parts: the static response due to vertical support settlement and the dynamic component caused by inertia effect of beam vibration. An exact solution for static displacement is presented by exerting the support displacements on the beam statically. Thus the remaining dynamic response of the vehicle/bridge coupling system is solved by Galerkin’s method and computed using an iterative approach with Newmark’s finite difference formulas. Numerical studies indicate that for the dynamic interactions of train–bridge system, the inclusion of ground settlement is generally small on the bridge response, but it can amplify drastically the vertical response of the moving train, especially for the concave-up settlement profile. This conclusion is of significance in aligning a rail route that has to cross a region with local land subsidence.