Modelling framework for dynamic interaction between multiple pedestrians and vertical vibrations of footbridges

Abstract

After 15 years of active research on the interaction between moving people and civil engineering structures, there is still a lack of reliable models and adequate design guidelines pertinent to vibration serviceability of footbridges due to multiple pedestrians. There are three key issues that a new generation of models should urgently address: pedestrian “intelligent” interaction with the surrounding people and environment, effect of human bodies on dynamic properties of unoccupied structure and inter-subject and intra-subject variability of pedestrian walking loads. This paper presents a modelling framework of human–structure interaction in the vertical direction which addresses all three issues. The framework comprises two main models: (1) a microscopic model of multiple pedestrian traffic that simulates time varying position and velocity of each individual pedestrian on the footbridge deck, and (2) a coupled dynamic model of a footbridge and multiple walking pedestrians. The footbridge is modelled as a SDOF system having the dynamic properties of the unoccupied structure. Each walking pedestrian in a group or crowd is modelled as a SDOF system with an adjacent stochastic vertical force that moves along the footbridge following the trajectory and the gait pattern simulated by the microscopic model of pedestrian traffic. Performance of the suggested modelling framework is illustrated by a series of simulated vibration responses of a virtual footbridge due to light, medium and dense pedestrian traffic. Moreover, the Weibull distribution is shown to fit well the probability density function of the local peaks in the acceleration response. Considering the inherent randomness of the crowd, this makes it possible to determine the probability of exceeding any given acceleration value of the occupied bridge

A Robust Methodology for the Reconstruction of the Vertical Pedestrian-Induced Load from the Registered Body Motion

“…Next, the identified time-variant pacing rates are applied to reconstruct the GRFs according to Equations (4) and (5). It is important to note that neither the time of double-stance peaks nor those of the single-step dips coincide with the actual onset of each step.…”

“…This section investigates the impact of the applied generalised single-step load model in Equations (4) and (5). To this end, the comparison is made between the original GRFs, simulated using the single-step load model introduced by Li et al [23], and the GRFs reconstructed the single-step load model introduced by Butz [24].…”

“…Although the dynamic performance under high crowd densities is often imperative for the design, these loading conditions have virtually never been verified [4]. Concerns about these load models are strengthened by the fact that recent studies indicate the significant impact of human-structure interaction (HSI) phenomena [5][6][7][8][9]. However, large-scale experimental evidence corroborating these results is absent.…”

Nonlinear Stochastic Analysis of Footbridge Lateral Vibration Based on Probability Density Evolution Method

“…erefore, it is necessary to investigate the serviceability of pedestrians when they walk on the footbridge. At present, most of the vibration serviceability assessment on the pedestrian structure are concentrated on the subjects of floor vertical vibration [24][25][26] and the footbridge vertical vibration [27][28][29], most of which belong to the linear vibration system. However, there are few reports about the serviceability of pedestrian impacting by the lateral vibration of the footbridge.…”

Coupled Systems in Mechanics: Fluid Structure Interactions

“…As said before, the principal source of these instabilities are generally the fluid-structure interactions, but in some cases, the instability can be reached with other sources of excitation, for instance the case of the Millennium Bridge in London (excited by pedestrians through a coupling between the force generated by their steps and the dynamic of the bridge, as it shown in [1], [48] or [57]). As seen in the first chapters, fluid-structure interactions can act in different ways on the dynamic of the structure and large oscillations of the bridge may be expected due to negative damping effect or even due to the couple mode flutter effect for instance.…”