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A novel numerical methodology is presented to solve the dynamic response of railway bridges under the passage of running trains, considering soil–structure interaction. It is advantageous compared to alternative approaches because it permits, (i) consideration of complex geometries for the bridge and foundations, (ii) simulation of stratified soils, and, (iii) solving the train-bridge dynamic problem at minimal computational cost. The approach uses sub-structuring to split the problem into two coupled interaction problems: the soil–foundation, and the soil–foundation–bridge systems. In the former, the foundation and surrounding soil are discretized with Finite Elements (FE), and padded with Perfectly Match Layers to avoid boundary reflections. Considering this domain, the equivalent frequency dependent dynamic stiffness and damping characteristics of the soil–foundation system are computed. For the second sub-system, the dynamic response of the structure under railway traffic is computed using a FE model with spring and dashpot elements at the support locations, which have the equivalent properties determined using the first sub-system. This soil–foundation–bridge model is solved using complex modal superposition, considering the equivalent dynamic stiffness and damping of the soil–foundation corresponding to each natural frequency. The proposed approach is then validated using both experimental measurements and an alternative Finite Element–Boundary Element (FE–BE) methodology. A strong match is found and the results discussed.

Fast simulation of railway bridge dynamics accounting for soil–structure interaction