Benjamin Hirzinger

Contributions to modeling and reliability assessment strategies in railway bridge dynamics

The detailed consideration of the dynamic response characteristics of railway bridges has become an increasingly important design issue of railway bridges in recent years due to the encouraged expansion and construction of high-speed lines. Bridges located on high-speed railway lines can be vulnerable to resonant excitation when crossed by high-speed trains. In a state of resonance, the bridge is excited to excessive structural vibrations, leading to ballast instability, impaired rail quality, and an increased risk of train derailment. These aspects demand a detailed assessment of the reliability of railway bridges for high-speed trains, for which in this doctoral thesis stochastic methods based on a fully stochastic approach are used in the reliability evaluation process. For the reliability assessment, suitable mechanical models are required to determine the structural responses accurately and efficiently. Semi-analytical bridge models allow for an efficient evaluation of the structural responses of the bridge-train interaction problem and also of the soil-structure-vehicle interaction problem.

In this doctoral thesis the performance and computational efficiency of various stochastic simulation methods for a stochastic based reliability assessment of railway bridges subjected to high-speed trains are evaluated and contrasted. Depending on the degree of sophistication, application of crude Monte Carlo simulation to a realistic mechanical model of the uncertain bridge-train interacting dynamical system can be prohibitively expensive. Thus, three alternative stochastic methods, i.e. line sampling, subset simulation, and asymptotic sampling, are tested on two example problems. These examples represent two classes of bridges with random properties characterized by significant different dynamic response behavior. While in the one class of bridges distinctive resonance peaks govern the dynamic peak response, the random response amplification of the second group of bridges is primarily induced by track irregularities. Main sources of uncertainty, i.e. damping, track irregularities, and the environmental impact are taken into account. The studies are conducted on a simplified mechanical model, composed of a plane beam representing the bridge and a planar mass-spring-damper system representing the train. In this approach that considers explicitly dynamic bridge-train interaction, random irregularity profiles describe the effect of track irregularities. This modeling strategy captures the fundamental characteristics of dynamic bridge-train interaction, and thus, facilitates the desired assessment of the stochastic methods with reasonable computational effort. It is shown that both line sampling and subset simulation reduce significantly the computational expense for the first class of bridges, while maintaining the accuracy of the predicted bridge reliability. To ensure accuracy and efficiency, these methods need to be modified when applied to systems where track irregularities dominate the random response. For the latter class of bridges, subset simulation proved to be a suitable method for assessing the reliability of this dynamic interacting system when appropriately modified.

Next, in this doctoral thesis, several more sophisticated measures of the probability of failure of the bridge-train interaction problem are proposed, considering the peak acceleration as a function of the speed in a certain interval and the distribution of the actual train speed. The peak bridge deck acceleration, which is commonly the governing response quantity for dynamic bridge design and failure, depends strongly on the type of train and the train speed. Since in many cases the critical speeds related to response maxima are below the design speed and failure, and during operation the speed varies up to the design speed, the assessment of the probability of failure is not straightforward. These measures are tested on the two considered test bridges. It is shown that in certain speed intervals the predicted probability of failure strongly depends on the underlying measure of the probability of failure. In the first example bridge, whose response is governed by a pronounced resonance peak, exceedance of the serviceability limit state is predicted by all measures at virtually the same speed. The second example problem, where track irregularities lead to considerable response amplifications, only some of the measures predict failure.

The subsequent chapter presents a formalism to efficiently determine the dynamic responses of high-speed railway bridges taking into account both bridge-train interaction as well as soil-structure interaction effects. A viscoelastically supported Euler-Bernoulli beam with general end conditions, which is crossed by a mass-spring-damper system, is utilized as a simplified model of the high-speed railway bridge and the high-speed train, respectively. Due to its viscoelastic supports, the bridge model is non-classically damped. Complex modal analysis provides the complex mode shapes and the complex modal equations of motion of the bridge model to which inherent structural damping is added modally. Based on a dynamic substructuring technique, the beam subsystem in modal state space representation is coupled with the interacting degrees of freedom of the mass-spring-damper system by applying a generalized corresponding assumption, which implies equal displacement of the bridge model and the wheels of the mass-spring-damper system at the contact points. Special attention is paid to the appropriate formulation of the mass-spring-damper system's arrival and departure conditions on the bridge model. In an application example, the dynamic response of a viscoelastically supported bridge model with a lumped mass at both ends crossed by a mass-spring-damper system is analyzed. In particular, the effect of the speed and various parameters of the viscoelastic bearings on the maximum acceleration of the bridge model is examined. The results of the coupled beam-mass-spring-damper system show on the one hand the significant influence of the subsoil on the structural responses and on the other hand by a comparison with the results of a less expensive approach, where the train is represented simplified by its static axle loads, how important explicit consideration of the interaction between the beam and the mass-spring-damper system is for accurate prediction of system behavior.



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