Pedestrian Loads and Dynamic Performances of Lively Footbridges: an Overview

1 CSHM 2 Workshop, 28 th September 1 st October 2008, Taormina Pedestrian Loads and Dynamic Performances of Lively Footbridges: an Overview Fiammetta Venuti Luca Bruno Politecnico di Torino (Italy) Department of Structural Engineering and Geotechnics

2 Introduction PEDESTRIAN BRIDGES Increasing strength of materials Increase of slenderness Critical performances of new structures reduced serviceability high costs for dynamic assessment after construction ROAD BRIDGES Increase of traffic Increase of vehicles weight Critical performances of existing structures reduced safety and stability The dynamic behaviour should be considered in a very early design stage Need for comfort criteria Need for suitable and predictive load models Need for practical design rules

3 Introduction Human-induced vibration problems on footbridges were discovered in the 19 th century collapse of a footbridge in Broughton due to marching soldiers Attention focused on vertical vibrations in the 20 th century From 2000, with the closure of the London Millennium Bridge, the attention is focused on lateral vibrations due to synchronisation phenomena (a few episodes had been already reported from the Seventies) Auckland Harbour bridge, 1975 London Millennium Bridge opening day, July 2000

4 Introduction In the last decade, increasing attention to human-induced vibrations on footbridges testified by: Specific international conference International reseach projects and guidelines FIB Federation International du Beton. Guidelines for the design of footbridges, fib Bulletin No. 32, Lausanne, 2006. SETRA/AFGC. Passerelles piétonnes Evaluation du comportement vibratoire sous l action de piétons. Guide méthodologique. Paris, 2006 European Project SINPEX BUTZ C. et al., Advanced load models for synchronous pedestrian excitation and optimised design guidelines for steel footbridges (SYNPEX), Final report, RFS-CR 03019, Research Fund for Coal and Steel, 2007

5 Introduction Objective state-of-the-art about human-induced vibrations on footbridges Summary Phenomenological analysis of pedestrian loading pedestrian on a rigid surface pedestrian on a vibrating surface human-structure interaction Comfort criteria Pedestrian load models single pedestrian groups of pedestrians crowds Experimental tests laboratory tests field tests

6 PHENOMENOLOGICAL ANALYSIS

7 Pedestrian walking on a rigid surface 100 50 Exp. Theor. Number of people F L l p F H F V F V F V F H 1.2 1.6 2.0 2.4 f V Matsumoto et al. (1978) Walking frequency V = v / l p 2 Hz = V f H f Walking frequency ranges F for L different activities after Bachmann (2002) F L f / 2 1Hz Andriacchi et al. (1997)

8 Pedestrians walking on a vibrating surface Human-structure interaction Modification of the footbridge dynamic properties Change in natural frequencies due to pedestrians mass Change in damping (the effect of moving people is still unexplored) Synchronisation between the pedestrians and the structure The phenomenon is much more probable in the horizontal direction Auckland Harbour New Zealand 1975 Synchronous Lateral Excitation (SLE) Groves Bridge Chester (UK) 1977 T-bridge Japan 1993 Passerelle Solferino Paris 2000 Millennium Bridge London 2000 [..] the phenomenom could occour on any bridge with a lateral frequency below about 1.3 Hz loaded with a sufficient number of pedestrians. (Dallard et al., 2001)

9 Synchronous Lateral Excitation KEY FEATURES OF THE PHENOMENON 2 kinds of synchronisation: The deck lateral motion triggers the synchronisation between the pedestrians and the structure LOCK-IN The probability of lock-in grows for increasing amplitude of the deck motion Dallard et al. (2001), Bachmann (2002), Nakamura (2003) High crowd density causes synchronisation among pedestrians Venuti et al. (2005), Ricciardelli (2005)

10 Synchronous Lateral Excitation Self-excitation: Self-limitation: The lateral force grows for increasing amplitude of the deck motion Dallard et al. (2001) Pizzimenti (2003) Pedestrians detune or stop walking when vibrations exceed a threshold value Nakamura (2003)

11 COMFORT CRITERIA

12 Comfort requirements The reaction of pedestrians to vibration is very complex: different people react differently to the same vibration condition an individual reacts differently to the same vibrations on different days a pedestrian alone is more sensitive to vibration than in a crowd a pedestrian who expects vibrations is less sensitive Comfort requirements: Limit values for structural frequencies Limit values of accelerations the bridge natural frequencies should fall outside the pedestrian loading frequencies Code/Standard Vertical [Hz] Horizontal [Hz] Eurocode 2 Eurocode 5 Eurocode 1 (UK NA) 1.6 2.4 < 5 Seldom fulfilled in new footbridges < 8 (unloaded bridge) 0.8 1.2 0.5 2.5 < 1.5 (loaded bridge) If the limit on frequencies is not satisfied, a dynamic calculation with suitable load models is required

13 ISO 10137 Eurocode 5 ISO 10137 (2007): Bases for design of structures Serviceability of buildings and walkways against vibrations. The limit values are obtained by multiplying the base curves of rms accelerations by a factor 60 (pedestrians) or 30 (standing persons) vertical horizontal av - RMS [m/s 2 ] ah - RMS [m/s 2 ] Limit values for pedestrians a v,rms a v,rms = 0.6/ = 0.3 4 f 8 a h,rms = 0.2 1 f 2 f 1 f 4 f [Hz] f [Hz] Eurocode 5: a v,max = 0.7 m/s 2 a h,max = 0.2 m/s 2

14 SETRA Guideline Comfort requirements are not absolute but depend on the comfort level specified by the Owner. Stage 1: determination of the footbridge class Traffic Class I II III IV Density d (P=person) d=1.0 P/m 2 d=0.8 P/m 2 d=0.5 P/m 2 Stage 2: choice of the comfort level Stage 3: determination of frequencies (risk of resonance) Description urban footbridge linking up high pedestrian density areas or that is frequently used by dense crowds, subjected to very heavy traffic urban footbridge linking up populated areas, subjected to heavy traffic and that may occasionally be loaded throughout its bearing area footbridge for standard use, occasionally crossed by large groups of people but that will never be loaded throughout its bearing area seldom used footbridge, built to link sparsely populated areas Comfort level 1 2 3 Degree of comfort maximum average minimum Acceleration level Vertical [m/s 2 ] < 0.5 0.5 1.0 1.0 2.5 4 discomfort > 2.5 Stage 4: dynamic calculation (if necessary) Acceleration level Horizontal [m/s 2 ] < 0.1 0.15 0.3 0.3 0.8 > 0.8 Lock-in

15 SYNPEX Guideline Acceleration checks should be performed if: vertical 1.3 f 2.3 Hz v horizontal 0.5 f 1.2 Hz Definition of design scenarios, characterised by a traffic class and a comfort level Traffic Class TC 1 TC 2 TC 3 TC 4 TC 5 Comfort level CL 1 CL 2 CL 3 Density d (P=person) 15 P d=0.2 P/m 2 d=0.5 P/m 2 d=1.0 P/m 2 d=1.5 P/m 2 Degree of comfort maximum medium minimum Description Very weak traffic: 15 single persons Weak traffic: comfortable and free walking Dense traffic: unresctricted walking, overtaking can inhibit Very dense traffic: uncomfortable situation, obstructed walking Exceptional dense traffic: crowding begins Acceleration level Vertical [m/s 2 ] < 0.5 0.5 1.0 1.0 2.5 CL 4 discomfort > 2.5 Acceleration level Horizontal [m/s 2 ] < 0.1 0.1 0.3 0.3 0.8 > 0.8 h Lock-in

16 UK National Annex to EN 1991-2 Limit on the vertical acceleration: Comfort criterion on synchronous lateral excitation: Pedestrian excitation mass damping parameter D = m m lim 1.0 k 1 k 2 k 3 k 4 m/s 2 a = 2 0.5 a lim 2.0 m/s bridge ξ pedestrian k 4 =1 exposure factor

17 Comments Standard codes and new guidelines has different approaches Absolute values of comfort requirements Comfort requirements decided by the owner as a function of the footbridge traffic class and required level of comfort UK National Annex has a different approach towards the avoidance of SLE mass damping parameter instead of limit on the lateral acceleration

18 LOAD MODELS

19 Classification of load models TIME DOMAIN FORCE MODELS Assumption: both feet produce exactly the same periodic force Deterministic Probabilistic FREQUENCY DOMAIN FORCE MODELS general force model for each type of human activity take into account that some parameters which influence human force (e.g. frequency, person s weight) are random variables whose statistical nature should be considered in terms of their probability distribution functions. pedestrian loads modelled as random processes walking forces represented by power spectral densities (PSD)

20 Single pedestrian load model Framework: Fourier decomposition of the three force components G = 700 N pedestrian weight α i = Dynamic Load Factor (DLF) of the ith harmonic F n = + G α 2 π f vert = G i vert sin( p t ϕ i F F i 1,, vert ) n = = G α π f sin( ϕ lat i, lat p t i, lat ) i 1 n = = G 2 π f long i, long p t i, long ) i 1 vertical lateral α sin( ϕ longitudinal Bachmann & Ammann (1987) Load models in codes and guidelines usually considers only the first harmonic and the resulting sinusoidal force is applied in resonance to the footbridge natural mode of interest vertical lateral longitudinal

21 Crowd load models: framework Assumption: the action of a group of pedestrians or a crowd is generally modelled by multiplying the action of a single pedestrian by an effective number of pedestrians n eff action of a single pedestrian F0 = G F 0 [N] SETRA - SYNPEX UK N.A. EN1991-2 F ( t ) = F sin(2 π ft ) n ψ ( = 0 eff DLF effective number of pedestrians reduction coefficient Vertical Longitudinal Lateral 280 140 35 280 (walk) 910 (jogging) - - The action should be applied in resonance with the footbridge natural frequency

22 Effective number of pedestrians It can be interpreted as a synchronisation factor it represents the percentage of people in the crowd that, by chance, walk in step Matsumoto et al. (1978) ISO 10137 SETRA SYNPEX n eff = n Uncorrelated pedestrians arriving on the bridge with a Poisson distribution, with resonant frequencies and random phases This model is not suitable to model SLE n eff = 10. 8 nξ for d<=1 P/m 2 n eff = 1. 85 n for d>=1.0 P/m 2 from probabilistic assumptions: account for synchronisation due to high density number of pedestrians who, walking in step with the footbridge natural frequency and equally distributed along the deck, produce the 95% fractile of the peak acceleration due to random pedestrian streams.

23 Reduction coefficient Reduction factors to account for the probability of occurrence of step frequencies SETRA SYNPEX ψ vert,long ψ lat First harm. Second harm. UK N.A. EN1991-2 Population factor k ( f v ) f v Only for vertical vibration

24 Load distribution along the deck Single pedestrian or group: Pulsating force F[N] moving across the span at constant speed v Crowd: The distributed oscillating loading should be applied in order to obtain the most unfavourable effect the amplitude of the load has the same sign as the mode shape configuration Setra (2006)

25 EXPERIMENTAL TESTS

26 Objectives of tests Measurement of: the intensity of the force exerted by a pedestrian on a rigid surface the intensity of the force exerted by a pedestrian on a moving surface the probability that a pedestrian synchronises to the motion of the walking surface the frequency and velocity of people walking the crowd characteristic quantities (e.g. density, velocity) the probability of synchronisation among pedestrians done partially done to be done

27 Force on a rigid surface: laboratory tests FORCE PLATE four tri-axial force sensors that measure the force acting between the foot and the ground in 3 axes: transverse (X), anteroposterior (Y) and vertical (Z). Z X Y INSTRUMENTED SHOES Sole with force transducers, allows to measure vertical forces during gait over a great number of steps TREADMILL

28 Force on a moving surface and lock-in: laboratory tests Treadmill laterally moving with different frequencies and amplitudes measure the force on a moving platform and estimate the degree of synchronisation Pizzimenti, 2005 University of Reggio Calabria SETRA, 2006 7m-long platform to recreate the same condition of a footbridge

29 Pedestrian-structure synchronisation: field tests measure the footbridge dynamic response to different crowd conditions and the triggering of the lock-in measure the pedestrian lateral motion London Millennium Bridge 2001 Nakamura & Kawasaki, 2003 M-bridge, Japan Passerelle Simone de Beauvoire, 2006, Paris

30 Crowd characteristic quantities Available techniques: Counting: flow measured by counting the number of persons at a specific cross-section in a certain time interval; speed and frequency measured by noting down the number of steps and time taken by randomly selected pedestrians to cross a given length. GPS: Infrared: Videos: measure velocity, step frequency, step length count people moving across a line, extract complete pedestrian trajectories. observation to measure crowd density and velocity.

31 Synchronisation among pedestrians Observation of videos recorded during crowd events measure the motion of pedestrians heads and the motion of the deck allow the percentage of synchronised pedestrians to be estimated T-bridge, Fujino et al. 1993

32 What has to be done Measure the probability of synchronisation among pedestrians as a function of the crowd density Measure the way in which walking velocity (and frequency) are modified by the motion of the walking surface Measure the forces exerted on real footbridges for different crowd conditions Adaptation of W.I.M. to pedestrian loads? Critical aspects: Pedestrians do not walk in lanes More than 1 pedestrian in the same deck cross-section Need to measure the lateral force component

33 Conclusions Footbridge serviceability under human-induced excitation is still an open research topic; Standard codes are still based on outdated assumptions, while design guidelines provide new design methodologies, load models and comfort criteria; Human-structure interaction is a complex phenomenon: it need further research to be deeply understood with contributions from different research fields Need for experimental tests to propose and validate load models statistichally characterise pedestrian walking behaviour (e.g. velocity, frequency, synchronisation, etc.)

34 A proposal for a different approach for SLE Description of the synchronous lateral excitation phenomenon through the proposal of a crowd-structure interaction model; model the crowd as a dynamical system instead of as a simple load. The model is based on: PARTITIONED APPROACH decomposition of the dynamic coupled system into two subsystems TWO-WAY INTERACTION t = t + t Crowd-to-Structure action STRUCTURE FORCE MODEL CROWD Structure-to-Crowd action VENUTI F., BRUNO L., BELLOMO N., Crowd dynamics on a moving platform: mathematical modelling and application to lively footbridges, Math. Comput. Model., n. 45, 2007

35 A proposal for a different approach for SLE F F ps + = VENUTI F., BRUNO L., P. NAPOLI, Pedestrian lateral excitation on lively footbridges: a new load model, SEI vol. 17 n.3, 2007 Force due to n pedestrians FORCE MODEL F pp + F s & z& Component due to n ps pedestrians synchronised to the structure n ps = ns ps Component due to n pp pedestrians synchronised to each other n pp = ns 1 S pp ( ps Component due to n s uncorrelated pedestrians n s = n n ps n function of the footbridge lateral acceleration and of the ratio between the step and the structure frequency pp ) function of the crowd density