Half-space response to trains moving along curved paths by 2.5D finite/infinite element approach

Abstract

For a train moving along a curved path, centrifugal forces are induced in addition to gravitational loads. In this paper, the 2.5D approach for loads moving along a straight path is extended to treating both the vertical and horizontal loads moving along a curved path. Firstly, closed-form solutions for the problem are derived for the cases of vertical and horizontal loads. Then, the 2.5D approach with finite/infinite elements in the Cartesian coordinates are summarized. By approximating a curved path by a number of small chordwise segments and by using the 2.5D approach to simulate each segment, the displacements in the global polar coordinates are obtained by summing up those of each segment in the local Cartesian coordinates, considering the time lags and direction changes. For linear systems, the responses due to vertical and radial loads can be computed separately. In the numerical simulation, the theory presented will be verified by two typical cases. The frequency-splitting phenomenon is found to exist for the horizontal loads, as well as for the vertical loads, moving over a curved path. The radial response induced by the centrifugal force cannot be ignored, and the displacement outside the railway track is larger than that inside. Such an effect should be considered in the design of curved paths for highspeed railways. The method presented herein can be adopted to solve problems with varying radius of curvature.