Bruno, Venuti, Pedestrians, groups and crowds: structural effects on footbridges Dagli individui alla collettivia: folle e sciami,Roma, 15-16 Novembre 2012 /20 1 Pedestrians, groups and crowds: structural effects on footbridges phenomenological features, current modelling frameworks, codified practices, open issues Luca Bruno Fiammetta Venuti, Politecnico di Torino Department of Architecture and Design Dagli individui alla collettivia: folle e sciami photocredit Nakamura & Kawasaki (2006)
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Pedestrians, groups and crowds:
structural effects on footbridges
phenomenological features,
current modelling frameworks,
codified practices,
open issues
Luca Bruno
Fiammetta Venuti,
Politecnico di Torino Department of Architecture and Design
Dagli individui alla collettivia: folle e sciami
photocredit Nakamura & Kawasaki (2006)
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/20 2 Aims of this presentation
…. hoping to light the fire of curiosity
in mathematicians’ mind
The presentation does not aims at showing engineering
“math-practice” to mathematicians;
Goals of the presentation:
Introduce the math community to some engineering
problems:
1. Present the footbridge human-induced vibrations
2. Outline some phenomenological features
raise some doubts and open issues on the
engineering-problem-solving approach:
3. current modelling strategieframeworks,
4. codified practices,
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/20
Auckland Harbour
New Zealand 1975
3 Introduction to footbridge human induced vibrations
1- Footbridge collapses due to marching soldiers in resonance with the structure:
Attention focused on vertical vibrations
and ultimate limit state in the 20th century
2- Footbridge lateral vibrations due to unintentional synchronisation phenomena
• in Broughton (UK,1831),
20 injuries
Attention focused on lateral vibrations and serviceability limit state at the begginning of the 21th century
Rk. research fields usually segregated (multidisciplinary studies 2%);
In the last decade, increasing attention to human-induced vibrations
on footbridges testified by:
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/20 6 Introduction to research and development activity .2
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
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
European Project SINPEX
Specific international conference
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/20 7 Introduction to research and development activity .3
Deductive approach: from universal concepts and unified theories on
synchronisation phenomena, to applications to each specific problem
E.g.
Y. Kuramoto, Chemical oscillations, waves and turbulence, Springer, Berlin, 1984.
S.H. Strogatz, From Kuramoto to Crawford: exploring the onset of
synchronization in populations of coupled oscillators, Physica D 143 (2000).
S. H. Strogatz et al, Crowd synchrony on the millennium bridge, Nature
438 (3) (2005).
Inductive approach: from empirical observation of the single
phenomenon to ad hoc modelling (in emergency conditions…)
E.g.
Y. Fujino et al, Synchronization of human walking observed during lateral vibration
of a congested pedestrian bridge, Earthquake Engineering and Structural
Dynamics 22 (1993).
S. Nakamura, Field measurement of lateral vibration on a pedestrian
suspension bridge, The Structural Engineer 81 (22) (2003).
S. Nakamura, T. Kawasaki, Lateral vibration of footbridges by
synchronous walking, Journal of Constructional Steel Research 62 (2006).
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/20 8
SOME PHENOMENOLOGICAL FEATURES
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/20 9 How many synchronisations? .1
None lateral and vertical vibrations due to
parametric resonance and/or
autoparametric resonance, without
synchronisation process
Blekherman, J. Bridge Eng. (2007) Macdonald, Proc. Royal Soc. (2008)
Deck lateral motion triggers the synchronisation
between the structure and the pedestrian
widely accepted in literature since Dallard et al., Struct. Eng.(2001)
One: ped-structure interaction
Pizzimenti (2005)
t
lateral
ground
reaction
forces
t
energy
input
ttorso
displacement
t
deck velocity
displacement
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/20 How many synchronisations? .2 10
Self-excitation: The higher the amplitude of the deck motion,
the higher the torso displacement and the feet spread,
the higher the lateral force and the synchronisation
probability
Dallard et al. (2001)
lateral force [N]
Platform displacement [mm]
synchronisation CDF
Platform displacement [mm]
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/20 11 Does a stable synchronisation occur?
Pedestrians (active particles) desynch, hang on to
the handrails or stop walking when vibrations
exceed a threshold value
Pedestrians (non-local behaviour in time,
delayed agents) walk again only once a
stop-and-go time lag is elapsed
lock-delock limit cycle
“on spot”, unstable synchronisation
Nakamura & Kawasaki, J. Constr. Steel Res. (2006)
cm z
0
2
4
6
2
4
6
125 130 135 140
s t
girder torsopedestrian
synch desynch synch desynch
ntdisplaceme lateral
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/20 12 How many synchronisations? .2
How to measure walking frequency and phase angle?:
video recording and analysis (Seyfried et al 2005, Araujo et al 2009)
How ped-ped syncrhonisation interacts with ped-structure synchronisation?
can they coexist in a crowd?
the effect of former trigger the latter?
other psychological /social causes? (hand in hand, conversation, being part of a group…)
And/or an other one: ped - ped interaction in crowd synchronisation among pedestrians (active particles)
Seyfried et al (2005), Venuti et al (2005), Ricciardelli (2005)
Anisotropic, non local visual perception,
to avoid feet contact
shoulder-to-shoulder contact
How one-to-one synchronisation propagates in the crowd?
Rs
Fruin (1987)
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/20 13 How many scales?
Bearing in mind pedestrians are intelligent agents:
does individual and collective behaviour coexist?
which is the effects of the latter on the former?
E.g.:
single pedestrian acting in opposite trend
leaders driving the crowd behaviour
Individual behaviour always plays a role where
the analytical domain locally has a characteristic
length close to the single ped one
E.g.:
narrow walking platform;
pointwise obstacles (benches or light poles
along the span);
bottleneck or broken longitudinal axis…
How to model smooth transition, coexistence, local existence of single and
collective behaviour?
Some interesting ideas from Base Sciences, e.g. : E. Cristiani, B. Piccoli, A. Tosin. Multiscale modeling of granular flows with application to crowd dynamics, Multiscale Model. Simul., 2011
Does a smooth transition between individual
and collective behaviour exist?
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CURRENT MODELLING STRATEGIES
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/20 Source-Path-Receiver Modelling Framework 15
• structure-centred MF (i.e. the structure is the only dynamic
system, the crowd is not)
• the model is compact and simple: ped
force determined only once and off-line
(Živanović et al 2005, Racic et al 2009);
• significant difficulties in modelling collective behaviours