Luca Bruno

Crowd-structure interaction in lively footbridges under synchronous lateral excitation: A literature review

This paper aims to provide a review and critical analysis of the state of the art concerning crowd-structure interaction phenomena on footbridges. The problem of lateral vibrations induced by synchronised pedestrians, namely the Synchronous Lateral Excitation, is specifically addressed. Due to the multi-physic and multi-scale nature of the complex phenomenon, several research fields can contribute to its study, from structural engineering to biomechanics, from transportation engineering to physics and applied mathematics. The different components of the overall coupled dynamical system - the structure, the crowd and their interactions - are separately analysed from both a phenomenological and modelling point of view. A special attention is devoted to those models, which explicitly account for the interaction between mechanical and living systems.

Crowd dynamics on a moving platform: Mathematical modelling and application to lively footbridges

This paper proposes a mathematical model and a computational approach to study the complex multiphysical non-linear coupled system that results from the interaction between a moving platform and the pedestrians who walk on it. The described method is based on the mathematical and numerical decomposition of the coupled system into two subsystems and on the two-way interaction between them. In particular, the dynamics of the crowd is modelled referring to a macroscopic description in analogy to that of a compressible flow. The proposed approach is applied to the lateral vibrations of footbridge decks under human-induced excitation. First, the computational parameters of the model are optimized. Then, the effects of the crowd initial density and of the runnability conditions are evaluated on a motionless platform. Finally, the results obtained from the simulations of the crowd-structure interaction are commented on.

Non-local first-order modelling of crowd dynamics: A multidimensional framework with applications

Abstract In 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 two-dimensional 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 validity of 2D numerical simulations of vortical structures around a bridge deck

This paper deals with a computational study for evaluating the capability of 2D numerical simulation for predicting the vortical structure around a quasibluff bridge deck. The laminar form, a number of BANS equation models, and the LES approach are evaluated. The study was applied to the deck section of the Great Belt East Bridge. The results are compared with wind-tunnel data and previously conducted computational simulations. Sensitivity of the results with regard to the computational approaches applied for each model is discussed. Finally, the study confirms the importance of safety-barrier modelling in the analysis of bridge aerodynamics.

Importance of Deck Details in Bridge Aerodynamics

This paper focuses on the effects of the deck equipment – such as median dividers, edge safety barriers or parapets – on the aerodynamic response of long-span suspension and cable-stayed bridges. The importance of modelling such members in the analysis of bridge aerodynamics is demonstrated using numerical simulations both with and without barriers. The numerical technique is applied to two famous long-span bridge decks (the Normandy cable-stayed bridge and the Great Belt suspension bridge), presented by different cross section geometries and various aerodynamic characteristics. The obtained results are compared with each other and with wind-tunnel data. In particular, the numerical modelling of the barriers provides a closer insight into the mechanisms responsible for the vortex-induced oscillations of the Great Belt East bridge in 1998.

High Statistics Measurements of Pedestrian Dynamics

Aiming at a quantitative understanding of basic aspects of pedestrian dynamics, extensive and high-accuracy measurements of real-life pedestrian trajectories have been performed. A measurement strategy based on Microsoft Kinect™ has been used. Specifically, more than 100,000 pedestrians have been tracked while walking along a trafficked corridor at the Eindhoven University of Technology, The Netherlands. The obtained trajectories have been analyzed as ensemble data. The main result consists of a statistical descriptions of pedestrian characteristic kinematic quantities such as positions and fundamental diagrams, possibly conditioned to the local crowd flow (e.g. co-flow or counter-flow).

Determination of the aeroelastic transfer functions for streamlined bodies by means of a Navier-Stokes solver

This paper proposes a method to determine the flutter derivatives of two-dimensional streamlined cylinders by means of a modified indicial approach adapted to a Navier-Stokes solver using an Arbitrary Lagrangian Eulerian formulation. The method relies on heave or pitch motion imposed onto the section according to smoothed-ramp time-histories and on the computational evaluation of the transient forces arising on the obstacle. Hence, the indicial transfer function relating the plate motion to the induced force in the frequency domain is obtained. Application to a flat plate of finite thickness and length is proposed. The steady viscous flow simulated around the motionless plate is compared with the well-known Blasius solution. The computed flutter derivatives are compared both with those obtained from the Theodorsen function in the frame of the thin airfoil theory and with those resulting from previous methods in the frame of the computational approach.

Pedestrian lateral action on lively footbridges: A new load model

This paper proposes a new load model to predict the lateral force exerted by pedestrians walking on lively footbridges. The aim of the model is to take into account some important features of the synchronous lateral excitation phenomenon, which so far has not been fully understood or modelled, e.g. the distinction between synchronization among pedestrians, due to crowd density, and between the pedestrians and the structure, caused by deck oscillations; the triggering of the lock-in phenomenon and its self-limited nature. The proposed load model has been tested with reference to two crowd events that were recorded on the T-bridge in Japan (1993) and on the Millennium Bridge in London (2001). The results obtained with the present model are compared to results predicted by other load models found in literature and are then further discussed.

Effects of the Equivalent Geometric Nodal Imperfections on the stability of single layer grid shells

Abstract The present paper discusses the sensitivity of the global and local stability of a hybrid single layer grid shell to a set of Equivalent Geometric Nodal Imperfections representative of the actual structural and construction imperfections. Since imperfections are hard to be measured and controlled in experimental facilities, the stability of the structure is extensively investigated in numerical experiments. The imperfections are set by means of the so-called Eigenmode Imperfection Method. The method parameter space is densely sampled, and different structural models are adopted. The results are given in terms of two bulk parameters: the well established Load Factor and the proposed Buckling Shape Length, the latter being introduced to provide a continuous measure of the degree of “globalness” of the instability. Significant and non monotonic changes in both the Load Factor and Buckling Shape Length are observed versus the growth of the imperfection amplitude. Further, a local metrics of the grid shell geometry, named nodal apex, is introduced for each structural node. Special emphasis is given to the analysis of the correlation between the apex of the initial imperfect geometry and the apex of the deformed shape at collapse. The observed high correlation suggests that the mechanical behavior of the imperfect grid shell is significantly influenced by this local geometrical feature.

From individual behaviour to an evaluation of the collective evolution of crowds along footbridges

This paper proposes a crowd dynamic macroscopic model grounded on microscopic phenomenological observations which are upscaled by means of a formal mathematical procedure. The actual applicability of the model to real-world problems is tested by considering the pedestrian traffic along footbridges, of interest for Structural and Transportation Engineering. The genuinely macroscopic quantitative description of the crowd flow directly matches the engineering need of bulk results. However, three issues beyond the sole modelling are of primary importance: the pedestrian inflow conditions, the numerical approximation of the equations for non trivial footbridge geometries and the calibration of the free parameters of the model on the basis of in situ measurements currently available. These issues are discussed, and a solution strategy is proposed.