MS9.7 - Dynamics of Railway infrastructures

Vibration-based damage detection commonly relies on a monitoring of the modal characteristics of a structure over time. It is assumed that damage will result in a change of the structural stiffness, which will in turn lead to a change of the natural frequencies and the displacement/strain mode shapes. The monitoring of the modal characteristics generally consists of two consecutive steps. First, the modal characteristics are identified by application of operational modal analysis (OMA) on a time series of response measurements, typically accelerations. This is for example repeated on an hourly basis. In a second crucial step, which is referred to as the mode tracking, the modes obtained from the OMA are grouped, resulting in a limited set of physical modes that occur in multiple time frames. The mode tracking typically relies on the assumption that the natural frequency and mode shape of a given mode do not alter significantly between two consecutive time frames. In this paper, we consider the case of a bowstring railway bridge in Halle, Belgium, where the structural dynamic behavior is characterized by two clearly separate states. This is observed from the identified natural frequencies which are characterized by sudden shifts between consecutive time frames. It is explained how these transitions are explicitly accounted for in the mode tracking, leading to a significant improvement of the mode tracking accuracy. Displacement measurements at the bearings show that the transition is due to a change in support conditions under thermal action.

With increasing axle loads and train speeds, predicting the dynamic behavior of railway bridges under high-speed traffic plays an increasingly important role in assessing bridge structures. However, the discrepancy between vibrations measured on structures and those predicted by calculations reveals the insufficient modeling depth of simple calculation models, which are primarily applied when there is a lack of reliable information about the structures and the passing trains. In particular, the computational acceleration results often significantly overestimate reality, which can be attributed to the fact that beneficial influences are often omitted in favor of straightforward calculation models. More realistic results can be obtained by considering the interaction dynamics between the train masses, superstructure, and supporting structure. With this, precise knowledge of coupling properties has a central role as they significantly influence the calculated vibrations. When taking vehicle bridge interaction into account by multi-body modeling of the train, the access to information on train properties is often kept secret by manufacturers due to economic interests. Therefore, the present contribution focuses on the influence of modeling the bridge structures as coupling beams, i.e., by considering them as two vertically coupled beams representing the track (rails and sleepers) and the supporting structure. Both beams are interconnected vertically by Kelvin Voigt elements, whose stiffness and damping properties reflect those of the ballasted superstructure. The equation of motion of the proposed model is approximated using trigonometric shape functions and solved by numerical time step integration, whereby the system can be dynamically exerted by moving load models as well as multi-body models of the train. A computational parameter study is carried out with a locomotive-hauled Railjet over a wide range of realistic combinations of single-span girder bridge characteristics: span, natural frequency, mass distribution, and assumed coupling stiffness representing the load distribution capacity of the ballast bed. The calculation results are subsequently compared with the ones of a reference simple beam model. The vertical structural acceleration at midspan is used as a comparative criterion. The evaluation of results enables identifying the structural properties for which applying coupling beam models has a particularly significant influence on the maximum accelerations and quantifying that influence. Additionally, it is examined to what extent the influence of the coupling beam modeling depends on the chosen train model. The analyses demonstrate the potential for obtaining lower acceleration results by considering the load-distributing impact of the ballasted superstructure in coupling beam models (facilitating verification of compliance with normative acceleration limits). They indicate that the influence of multi-body models of the train, which consider vehicle bridge interaction, is particularly pronounced for different structures than that of the coupling beam modeling. These findings open up the possibility of formulating structure-dependent recommendations concerning the targeted application of more complex modeling of the structure (coupling beam model) on the one hand and train (multi-body model) on the other. Thus, they enable a realistic calculational prediction of the structural vibrations independent of vehicle information for the greatest possible share of structures.

This contribution presents the structure of a developed software for static and transient linear-elastic coupled Finite Element (FE) – Boundary Element (BE) analyses and demonstrates its application for the analysis of soil-structure interaction of portal frame bridges in two and three dimensions shown. Particular attention is given to the formulation and implementation of the elastodynamic boundary element method in two and three dimensions, with a separate discussion of its dimension-dependent properties. Major part of the Finite-Element formulation is outsourced to commercial software, with the import of FE models from ABAQUS realized in the current implementation. For the transient analyses, the system matrices of the FE and BE model are assembled using a direct coupling strategy at the interface nodes of the two subdomains. To ensure the reliability and stability of the numerical computations, special attention is paid to the subdivision of boundary elements and the implementation of a time-weighted method. This general-purpose computer program is subsequently used to model and analyze portal frame bridges. Herein, the bridge structure is modeled by FE, while the half-space is discretized by BE, which allows an adequate description of wave propagation in the subsoil toward infinity. With this modeling strategy, the natural frequencies and geometric damping of the portal frame structure are determined, based on the free vibration response of the frame structure due to impulse loading. By parameter variation and comparison of analyses in 2D and 3D, different modeling variants for determining geometric damping are assessed and differences, as well as limitations, are shown.