Assessment of the lateral vibration serviceability limit state of slender footbridges including the postlock-in behaviour

Resumen

The lateral vibrations of slender footbridges caused by walking pedestrians have been the subject of many studies over the last few decades. However, despite the large amount of research, a common design guidance has not been set yet. The phenomenon of experiencing excessive lateral accelerations (generally known as the lock-in effect) occurs in low-damped structures with natural frequencies in the range 0.4–1.3 Hz when the number of pedestrians on the footbridge is above a certain “critical number”. The lock-in behaviour is characterised by a sudden increase in the amplitude of vibrations, usually associated with resonant loads but that can also be explained by the phenomenon of interaction between pedestrians and the structure. Pedestrians are biomechanical systems that generate ground reaction forces while walking, due to the acceleration or deceleration of their centre of mass. The lateral force is the consequence of the action of keeping the body balance during walking and can be affected by the ground stability. As people perceive the floor vibration, they modify their gait in order to avoid losing balance. People interact with the structure, generating the auto-induced force in the natural frequency of the footbridge, with independence of the pedestrian frequency. This phenomenon, known as human-structure interaction (HSI), is widely accepted as the main cause of the sudden onset of high amplitudes of vibration. However, the current design recommendations do not include an expression for the auto-induced component of the pedestrian action and, as a consequence, it is not possible to evaluate the footbridge comfort once the lock-in effect has developed. Hence, the main purpose of this Thesis is to propose an easy-to-apply but general formulation, useful for practical engineering applications, to evaluate the lateral vibration serviceability limit state (VSLS) of slender footbridges, even when the crowd density exceeds the “critical number” (postlock-in behaviour). The key finding of the study is that the proposed method, based on the frequency domain analysis, allows expressing the response due to the auto-induced component of the pedestrian load in terms of amplification ratio of the response with no interaction. The ratio only depends on the dynamic properties of the structure, making it very simple to estimate the dynamic response and the structural damping required for any possible pedestrian traffic scenario, as well as to analyse the footbridge sensitivity to the HSI phenomenon. The performance of the method is successfully verified by simulations of the numerical response of real footbridges, as its predictions are in good agreement with the experimental data recorded. Furthermore, the method predicts well the lock-in point and estimates the response after HSI develops. Additionally, the lateral response of the structures is also verified by using the methodologies found in the current state-of-art. Moreover, as mentioned earlier, the structural dynamic response depends on the modal parameters of the structure, the natural frequency and the damping ratio. Since footbridges are subject to environmental and operational changes, these parameters may not have a fixed value during the footbridge overall life cycle; they are stochastic variables, and it is not possible to assign them a value without a level of uncertainty and variability. Hence, the lateral response is also evaluated under uncertain conditions by using the proposed method. These uncertainties are considered with a probabilistic approach and a fuzzy approach (possibility theory). In both cases, the proposed method, turns out to be very useful for highlighting the impact of environmental and operational changes on the lateral response of footbridges, which represents an important advantage over most current design guidelines. Finally, in order to provide further confirmation of the proposed method, the Thesis includes the experimental lateral vibration assessment of two in-service footbridges: La Paz footbridge (Madrid) and Zuheros footbridge (Córdoba). The results of the full-scale crowd pedestrian test performed in Zuheros footbridge (June 2021), are used for the experimental validation of the proposed method and, in addition, to verify the HSI phenomenon.