Train bridge interaction: problems and models

In this paper, a procedure for the numerical simulation of train-bridge interaction is described. This is based on a finite element schematisation of the bridge (and possibly of the track) and on a multi-body schematisation of the railway vehicles. Wheel-rail contact forces are defined using a non-linear contact model which accounts for the main non-linear effects related to wheel-rail contact forces. The numerical procedure considers train-bridge interaction in both the vertical and horizontal plane. With reference to train ride safety and passenger comfort, the dynamic interaction model allows the analysis of the effect of global and local structure deformations on vehicle dynamics. When dealing with long span suspension bridges, in addition to the limits regarding global deformations during train passage, the structure must satisfy restrictive requirements concerning the effect on rail vehicle dynamics produced by structure deformations under wind loads. An example of numerical simulation for the case of an ETR500 train crossing the Messina bridge at the maximum design speed, in the presence of extreme transversal wind conditions was reported. Another interesting example of global interaction analysis is that involving the identification of critical velocity phenomena. The train transit over a bridge generates a periodic excitation whose fundamental frequency depends on the speed and on the distance end-to-end between the coaches; as a consequence, resonance occurs if one of the excitation frequencies approaches one of the bridge's natural frequencies. While this phenomenon is generally negligible in long span bridges, it is particularly interesting for smaller bridges, like the bow-arch bridge considered in the paper as the second case study. Local interaction phenomena involve bridge and track deformations having a scale much smaller than that of the complete bridge. Although being of small entity, local deformations play a key role with respect to the cyclic dynamic stresses induced in the bridge structural elements by repeated train passages and the generation of structural noise and vibrations. One key issue is the design of the track system. An example is presented referring to the comparison of two design alternatives for the Messina bridge track system: a conventional design with rails resting on timber sleepers and an innovative embedded rail system. The analysis was performed by comparing the two design solutions in terms of forces and vibrations locally transmitted to the deck. A numerical-experimental comparison is reported at the end of the paper, which refers to the measurements taken on a bow-arch bridge on the Milano-Torino high speed line, crossed by a test train at the maximum speed of 280km/h. The comparison demonstrates the reliability of the developed train-bridge interaction model in reproducing both bridge accelerations and stresses.