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 b s t r a c tIn this work a physical modelling framework is presented, describing the intelligent, non-local, and anisotropic behaviour of pedestrians. Its phenomenological basics and constitutive elements are detailed, and a qualitative analysis is provided. Within this common framework, two first-order mathematical models, along with related numerical solution techniques, are derived. The models are oriented to specific real world applications: a one-dimensional model of crowd-structure interaction in footbridges and a twodimensional model of pedestrian flow in an underground station with several obstacles and exits. The noticeable heterogeneity of the applications demonstrates the significance of the physical framework and its versatility in addressing different engineering problems. The results of the simulations point out the key role played by the physiological and psychological features of human perception on the overall crowd dynamics.
The relation between density and velocity of pedestrian movement has so far mainly been analysed using an empirical approach and fundamental relations found from the fitting of experimental measurements of the main quantities. The present study proposes a phenomenological model that is able to distinguish and take into account various factors that can affect the density-velocity relation by means of the induced microscopic walking phenomena. In particular, the effect of the lateral vibrations of the platform on which pedestrians walk is considered in the light of the use of the fundamental diagrams within a crowd-structure interaction model applied to lively footbridges. A comparison with some of the empirical fundamental laws shows an excellent agreement, demonstrating that the main walking phenomena are correctly assumed in the present model.
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