Robust vibration serviceability assessment of footbridges for crowd walking excitation

For slender footbridges, the dynamic response to human-induced loading needs to be verified in a vibration serviceability assessment. The assessment is commonly based on a simplified load model and relying on the nominal values of the modal parameters of the structure as predicted by a finite element model. Often, resonance with a single mode is considered and a reduction factor rates the risk for resonance with that mode. For a reliable response prediction, uncertainties in the modal parameters of the structure must be dealt with, however. If the vibration levels exceed a predefined comfort criterion, a Tuned Mass Damper (TMD) can be installed. In this contribution, a robust vibration serviceability assessment is proposed. Different levels of uncertainty are introduced to account for the effect of uncertainties in the modal parameters resulting in a multi-interval assessment. Realistic loading scenarios are implemented using detailed simulations considering variability of the pedestrian walking characteristics. The contribution of multiple modes is considered and the instantaneous peak acceleration is retained and tested to criteria for vibration comfort. The procedure is illustrated for a slender footbridge. First, the response is evaluated for different levels of uncertainty. Second, the procedure is applied in the design of a TMD by tuning its mass, stiffness and damping constants such that an effective reduction of the vibration levels is ensured. The advantage of the robust interval-based approach is that it allows understanding how the uncertainties in the modal parameters of the structure affect the response prediction. Besides, the method investigates the trade-off between the TMD parameters and its robustness against uncertainties in the modal parameters. The level of uncertainty can be determined based on a monitored or assumed range of variations of the modal parameters of the structure.