Nov 4

A few days ago, a bridge collapsed in Morbi, Gujarat, killing nearly 140
people. As if that wasn't enough of a tragedy, we've learned all kinds of
unsavoury details since - the company that refurbished the bridge was a
clock manufacturer; they reopened the bridge without official approval; the
hospital where plenty of the injured and dead were taken was spruced up
overnight - not because of the victims' arrival, but because the Prime
Minister arrived the next day to visit victims ...

... but how did this tragedy happen at all? There may be clues in how such
bridges behave when people walk across. That's what this column is about.
Please do let me know your thoughts.

The ground moves, beneath your feet,
https://www.livemint.com/opinion/columns/the-ground-moves-beneath-your-feet-11667494652439.html

cheers,
dilip

PS: Astonishingly, this was not the first great disaster in Morbi. In
August 1979, a dam over the same river this bridge spanned collapsed.
Unofficial estimates of the number of people killed go as high as 25,000.

---

The ground moves, beneath your feet


To start this column, I ask for a moment of silence and reflection. This is
in memory of the 140 people who died in the Morbi bridge collapse, and the
150 who died in the stampede in Seoul.

Done? Thank you.

One afternoon earlier this year, I used a pedestrian bridge to walk across
a wide river. Unlike in Morbi, nothing really happened as I walked. But
after Morbi, I've had occasion to remember the nickname pedestrians gave
that bridge. The Morbi bridge was popularly called "Julto Pul", or
"Swinging Bridge". The one I crossed last March is popularly called "Wobbly
Bridge".

An odd synchronicity in those names, right? The Wobbly Bridge's official
name is the Millennium Bridge, and it spans the River Thames in the heart
of London. It was opened on 10 June 2000. It was closed on 12 June 2000 -
yes, just two days later - and did not reopen for nearly two years, till 22
February 2002. In that time, it underwent significant structural changes.

Why were modifications necessary on a brand new bridge? Let me return to
that.

With suspension bridges, like Julto Pul and Wobbly Bridge, we've known for
a long time of a certain characteristic phenomenon. When a group of
soldiers march over it, the bridge can start swaying. This is because the
soldiers march in step, and this regular thumping of dozens or hundreds of
feet sets the bridge oscillating in synchrony. This can get quickly
dangerous. In 1850, a batallion of soldiers marched onto the Basse-Chaine
bridge in Angers, France. The bridge was already swaying with a
thunderstorm, and with these soldiers crossing, it swayed even more. The
cables holding it up snapped, and over 200 soldiers were killed as it
collapsed.

This is why soldiers on the march are told, when they come to a bridge like
this, to break formation and walk across any way they can. The more
disorganized, the better.

The day the Wobbly Bridge opened, about 90,000 people walked on it. At any
given moment, it carried about 2000. One theory about what happened then
goes like this. While walking, their natural gentle swaying motion caused
the bridge to sway slightly from side-to-side. This caused those on the
bridge, consciously or otherwise, to spontaneously fall in with the rhythm
of the bridge. That is, synchronously with the bridge's movement. This made
the bridge sway even more - the amplitude of its oscillations increased -
which in turn made the pedestrians sway more too ... and as the whole
swaying phenomenon was steadily reinforced, it soon was clear that the
bridge was dangerous.

Luckily, it was closed before a horrific disaster ensued.

In December of 2000, in an effort to understand how the bridge had behaved,
engineers carried out a "diagnostic wobble test". They sent pedestrians
onto the bridge a few at a time, slowly increasing their numbers until
nearly 200. As they walked and as the count rose, the engineers measured
the "wobble amplitude", meaning the distance the bridge sways.
Simultaneously, they also calculated the "order parameter", a measure of
how synchronized the pedestrians were in their walk. This measure goes from
0, meaning completely asynchronous, to 1, meaning in perfect lockstep.

They found something interesting indeed. "For small crowds, walkers are
desynchronized" - and thus the order parameter hovers close to zero. The
swaying of the bridge, too, is minimal. Almost certainly, the people on the
bridge did not notice any swaying. But "at a critical crowd size, the
bridge starts to sway and the crowd starts to synchronize, with each
process pumping the other in a positive feedback loop." That's a result of
each walker "impart[ing] an alternating sideways force to the bridge". In
turn, the movement of the bridge "alter[s] each pedestrian's gait."

That critical size is about 175 people.

The graphs that plot these two measures are eye-opening. At 175 people, the
wobble amplitude and the order parameter suddenly begin rising, themselves
in seeming lockstep. The former rises to over 5cm, the latter reaches about
0.7. (Numbers and quotes from "Crowd synchrony on the Millennium Bridge",
Steven Strogatz et al, Nature, 2 November 2005,
https://www.nature.com/articles/438043a).

What's also interesting about this model of the bridge's behaviour is that
it takes ideas about synchrony from biology. They describe, for example,
how individual fireflies manage to synchronize how they glow.

As ever with mathematics, though, there are doubts about this
synchronization explanation for what happened to the Millennium Bridge.

A more recent paper suggests that "any synchronisation of pedestrians' foot
placement is a consequence of, not a cause of the instability." For there's
very little evidence that the pedestrians synchronized their footsteps; in
fact, at most only 20% of those on the bridge were striding along in time
with the movements of the bridge. ("Emergence of the London Millennium
Bridge instability without synchronisation", Igor Belykh et al, Nature, 10
December 2021, https://www.nature.com/articles/s41467-021-27568-y).

The Physics Nobel Prize winner Brian Josephson made essentially this point
in a letter he wrote to The Guardian only days after the bridge was opened
and closed in 2000. The behaviour of the bridge, he pointed out, had
nothing to do with people walking in step. Instead, it is "connected with
what people do as they try to maintain balance if the surface on which they
are walking starts to move, and is similar to what can happen if a number
of people stand up at the same time in a small boat."

Josephson's point is borne out by a famous video of the crowds on the
Millennium Bridge when it opened in 2000. The structure is visibly moving,
yes. But the way the people are moving is decidedly awkward. Think of how
you might walk if the ground below your feet is moving. That's what you
see, in those pedestrians.

I have no idea if any such analysis could have been done for Julto Pul, or
if it would have saved those lives. But why not do it now, for other
pedestrian bridges?

Why not do it, in memory of the 140 we lost?


-- 
My book with Joy Ma: "The Deoliwallahs"
Twitter: @DeathEndsFun
Death Ends Fun: http://dcubed.blogspot.com

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