Abstract Summary
Dynamic soil-structure interaction (SSI) should be considered when modeling railway bridges on soft soil, as it results in (1) more accurate prediction of the bridge response, and hence, a safer and possibly more cost-effective design; (2) better estimation of the modal characteristics; and (3) improved prediction of ground-induced vibration due to train passages, which is relevant for bridges built in urban areas. The use of 3D element-based models is restricted to a few spans due to computational limits. Therefore, periodic structure theory is employed in this paper to take advantage of the repetitive geometry of the bridge. For very long periodic multi-span bridges, the computational domain can be restricted to a reference cell by application of the Floquet transform. Alternatively, in a wave finite element method (WFEM), free wave characteristics of the reference cell are used to describe the structural response; this method can also be used to model periodic structures of finite length. As, in most cases, a single bridge span is relatively long, the size of the reference cell (including bridge deck, piers, piled foundations and soil) remains large, and the solution of the corresponding system of equations is challenging. We therefore propose a formulation that also takes advantage of the periodicity of the bridge deck and the soil in between piers. Dynamic SSI can be accounted for in two ways: (1) by fully incorporating through-soil coupling between neighboring foundations, or (2) by using pre-computed impedance functions for a single piled foundation, which are subsequently added as spring-damper connections to the bridge footings (and, hence, neglecting through-soil coupling). When, in the first approach, the soil is modeled with finite elements in combination with perfectly matched layers (PMLs), we presently encounter stability problems when computing the dynamic stiffness matrix of the reference cell. The second approach results in a smaller system of equations and corresponding computational effort. For these reasons, we mainly present results obtained with the second approach, and with the first approach whenever available. The focus in this paper is on the response of continuous periodic concrete box girder bridges subjected to moving loads. The bridge is modeled with shell elements, while the piled foundation and the soil are modeled with solid elements surrounded by PMLs. The response of bridges with gradually increasing number of spans is compared to the response of an infinitely long bridge with equal span length. Results are presented for a soft, medium and stiff soil. It is shown that, if dynamic SSI is taken into account, the response of relatively short bridges can be well represented by infinitely long bridge models.
