1 Section for Structural Engineering, Department of Civil Engineering, Technical University of Denmark2 Department of Civil Engineering, Technical University of Denmark
Experimental studies and probabilistic modelling
The dissertation investigates the phenomenon of excessive pedestrian-induced lateral vibrations as observed on several high-profile footbridges. In particular, the temporary closures of both Paris’ Solferino Bridge (1999) and the London Millennium Bridge (2000) have led to an understanding on the part of engineers and architects of the need to evaluate the potential for footbridge vibrations that can be attributed to pedestrians. Within the scientific community, the closures have also led to the initiation of a new tract of research, focused on the understanding of pedestrian loading, bridge response and their interaction. In the last decade, a significant amount of research has been carried out in this field. As a consequence, numerous other bridges of different length and type have been found prone to similar excessive lateral vibrations when exposed to large pedestrian crowds. However, only few national and international codes of practice and official design guidelines currently exist to help the designer address this issue. Most of these are based on the main hypothesis, that pedestrian-induced lateral loads can be modelled as velocity proportional or as negative dampers, resulting from the synchronised lateral movement of pedestrians. This excitation mechanism is often characterised as Synchronous Lateral Excitation (SLE). Reports from a limited number of controlled pedestrian crowd tests have verified the existence of a transition point at which a rapid increase in the lateral bridge response is triggered. This disproportionate increase in the lateral vibration response is caused by a dynamic interaction between the pedestrian and the laterally moving structure, although the governing mechanism which generates the load is still disputed. In this thesis, a comprehensive literature review is presented, solely focused on pedestrianinduced lateral forces, their effect on footbridges and existing theoretical models of humanstructure interaction. It is shown that different hypotheses exist about the nature of this interaction, many of which are only supported by theoretical modelling and lack sufficient experimental evidence to support their applicability. Especially, the importance of human-structure synchronisation for the development of large footbridge vibrations is questionable. Therefore, an extensive experimental campaign has been carried out to determine the lateral forces generated by pedestrians during walking on a laterally moving treadmill. Two different conditions are investigated; initially the treadmill is fixed and then it is laterally driven in a sinusoidal motion at varying combinations of frequencies (0.33 – 1.07 Hz) and amplitudes (4.5 – 48mm). The experimental campaign involved 71 test subjects who covered approximately 55 km of walking distributed on almost 5000 individual tests. An in-depth analysis of the movement of the pedestrians that participated in the experimental campaign reveal that synchronisation is not a pre-condition for the ix development of large amplitude lateral vibrations on footbridges, as walking frequencies remain largely unaffected by the lateral motion. Instead, large amplitude vibrations are the result of correlated pedestrian forces in the form of negative damping that can be generated irrespective of the relationship between the walking frequency and the frequency of the lateral movement. These forces are self-excited in the sense that they are generated by the movement of the body’s centre of mass, which in turn is caused by the lateral acceleration of the underlying pavement. Due to the random nature of the human-induced loadings and a large scatter in the experimental data, a novel stochastic load model for the frequency and amplitude dependent lateral forces is presented. The parameters in the model are based directly on the measured lateral forces from the experimental campaign. Thereby, the model is currently the most statistically reliable analytical tool for modelling of pedestrian-induced lateral vibrations. It is shown that the modal response of a footbridge subject to a pedestrian crowd is sensitive to the selection of the pacing rate distribution within the group, the magnitude of ambient loads and the total duration of the load event. The selection of these parameters ultimately affects the critical number of pedestrians needed to trigger excessive vibrations in a particular simulation. Finally, a simplified frequency dependent stability criterion is presented, for which the critical number of pedestrians needed to cancel the inherent modal damping of a footbridge can be obtained.