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/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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/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
T-bridge
Japan 1993
Millennium Bridge
London 2000 Passerelle Solferino
Paris 2000 Groves Bridge
Chester (UK) 1977
• Basse-Chaîne Bridge in Angers (FR,1850)
226 deaths
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/20 Introduction to footbridge human induced vibrations 4
High density of crowd (up to 10 ped/m2)
structural lateral vibrations
rumors about footbridge collapse
panic
stampede
347 deaths, 755 injuries
London Millennium Bridge, 2000
opening day Auckland Harbour bridge, 1975 Maori demonstration
Phnom Penh, Cambodia, 22nd Nov. 2010
Khmer Water Festival
Scores killed in Cambodia festival stampede, BBC News
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/20 5 Introduction to research and development activity .1
a growing scientific effort
and production
4% 4%
8%
19%
66%
0%
10%
20%
30%
40%
50%
60%
70%
1940 - 1970 1971 - 1980 1981 - 1990 1991 - 2000 2001 - 2010
years
% p
ub
lish
ed
pap
er
(non exhaustive survey over the
writers’ reference database)
different approaches
coming from distinct
scientific communities
Transportation
Engineering
20%
Biomechanics
9%
Base Sciences
20%
Structural
Engineering
51%
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?:
instrumented shoes (e.g. Simpex 2008, Ricciardelli & Pizzimenti 2010)
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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/20 14
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
• the model is popular
among Civil Engs. and it
is codified
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/20 Crowd-Structure Partitioned Modelling Framework 16
• decomposition of the
dynamic coupled
system into two
subsystems: approach
introduced since the
Eighties (e.g. Park and
Felippa 1983) for
coupled mechanical
systems;
• adapted to crowd-structure interaction by
Venuti et al 2005, 2007,
and hence developed by
Bodgi et al 2007, 2008, Bruno and Venuti
2009, Carroll et al 2012
Rk. The crowd model is a kinematic
one (ped position and velocity) It
should be complemented by a force
model (ped force)
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/20 Crowd-Structure Monolithic Modelling Framework 17
modelling as a SDoF/MDoF mechanical system(s)
• the human body of the single pedestrian
(e.g. walking pedestrians along a footbridge,
Macdonald 2008, Erlicher et al 2010)
• a group of standing people
(e.g. Jumping spectators in
stadia grandstand,
Pavic and Reynolds 2008,
Jones et al 2011)
• Nothing about walking
crowd.... Any candidate?
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/20 18 18
CODIFIED PRACTICES
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/20 19 Semi-probabilistic approach to crowd loading
Eurocodes adopt the so-called semi-probabilistic approach.
qk
g > 1
In general, the load qd to apply on the structure is defined as the product of:
the characteristic value of the load, which corresponds to the 5 %
probability of being exceeded (statistically well defined);
an empirical coefficient, which moves the design load towards higher
percentiles (socially and economically acceptable) even if the queues
are not precisely defined
qk = p
95
2s q
d = p
99,9999
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/20 20 Value of the pedestrian action
Scenarios for dynamic loading:
Single pedestrian
Group of N pedestrians
Crowd
ISO 10137, UK National Annex to EC1
ISO 10137, UK National Annex to EC1
ISO 10137, UK National Annex to EC1, Setra
FN = C N k Fp
Fp
FN
coordination factor reduction factor
the percentage of people in
the crowd who walk
synchronized
accounts for the probability of
occurrence of step frequencies within
certain frequency ranges
Equivalent static loading:
qk = 5 kN/m
2 represents the characteristic
action of a continuous dense crowd, with
dynamic amplification effects included
Eurocode 1 UNI EN 1991-2:2005 :
Actions on structures
Part 2: Traffic loads on bridges- Section
5: actions on footways, cycle tracks
and footbridges
Need to model the smooth transition from single pedestrian to crowd
Need to model intersubject variability Need to model synchronization
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/20 21
3 pedestrians do not
make a crowd…
What’s a “group”?
The sorites paradox (Eubulides of Miletus, 4th century b.c., from soros, ‘heap’)
1 pedestrian does not
make a crowd…
2 pedestrians do not
make a crowd…
Conceptually, wathershed values
cannot be set between single
ped, ped goup and crowd….
but most of the guidelines for
footbridge design set them….
UK National AnnexNA2.44 for
Eurocode EN1991-2:2003
Technical Guide Sétra/AFGC,
2006.
Sympex final report, - 2008
…100.000
pedestrians do not
make a crowd !
… …
7 pedestrians do not
make a crowd…
4 pedestrians do not
make a crowd…
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/20 22 22 Spatial distribution of the load
the distributed oscillating loading
has the same sign as the mode
shape configuration
worst case scenario Deterministic approach
The load should be applied on the footbridge deck in order to obtain the
most unfavourable effects on the structure
Dynamic load Equivalent static load
the distributed loading is applied
only in the unfavourable parts of
the influence surface
Need of a probabilistic approach to crowd distribution
inspired by crowd dynamics
Need of a fully semi-probabilistic approach
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/20 23 Some open issues
compact SLE models are justified by emergency engineering
conditions (e.g. Dallard et al. 2001), but in a scientific approach they
should results by reducing the order of rigorous, physically-based
models;
Some issues to account for:
Uncertainties in crowd towards probabilistic models
Initial or incoming position;
Intersubject variability
Itrasubject variability
Probability-based crowd distribution along the deck
Stop and go walking due to;
Excessive accelerations;
Attraction points (e.g. Panoramic point along the footbridge)
How to model the transition and the coexistence of individual and
collective phenomena (“pedestrian, group and crowd” in civil
engineering literature)?
