Saturday 10 June 2000 was a bad day for structural engineer Arup.
Monday 12 June was even worse. On the Saturday thousands of eager pedestrians crowded on to the ú18M ($26M) footbridge - dubbed a 'blade of light' by its codesigner, architectural superstar Sir Norman Foster - to mark its opening day. As the crowds built up, a strange phenomenon manifested itself. Groups of pedestrians, up to 100 or so at a time, began to march in step with each other in response to a build-up of lateral movement in the lightweight structure.
The more the structure swayed the more people joined in the 'syncopated shuffle', locking into the lateral movement and making it even worse.
In fact maximum horizontal displacements were never large - about 70mm at the centre of the main span - but accelerations were quite high at around 0.4g, and some pedestrians became alarmed.
Arup at first insisted the structure was safe, which in terms of the risk of catastrophic collapse was perfectly true. Although no one was hurt on the opening day, the client, the Millennium Bridge Trust, took the precaution of restricting access for two days.
Then, under a barrage of adverse publicity and expressed concerns over the safety of the elderly and infirm, the bridge was closed on the Monday evening, and has remained closed ever since.
An immediate investigation was launched, including detailed research into the lock-in so obvious on the video recordings of the opening day. Arup invested heavily in emergency research programmes at Sheffield and Southampton Universities and at Imperial College. Top experts in structural dynamics from the UK and overseas were asked to join the team.
Teams of researchers descended on the forlorn structure and began to shake and twist it, measuring its natural frequencies and modes of vibration, attempting to replicate the almost completely pure lateral movement that had caused the original problem.
In August a team of 100 Arup volunteers marched backwards and forwards across the bridge.
By late November Arup was sufficiently confident to apply for planning permission for a complex retrofit aimed to almost eliminate the sway without compromising the aesthetics.
These proposals featured a unique combination of viscous and tuned mass dampers tucked up under the deck, plus viscousdamped diagonal bracing at the piers. A complex viscousdamped tie will also tether the landward end of the southern span.
These proposals, which have been with the client's professional adviser WS Atkins since early September, appear to meet all original objectives. The landmark blade of light will look much the same, with access for pedestrians unrestricted. The wobble - particularly the lateral accelerations - is expected to be reduced to ultra-safe levels. But at an estimated ú5M, the cost of the retrofit will startle some, and there is still no agreement on who is going to come up with the cash.
Arup's original negotiating position appeared to be compromised by two main factors - its confident assertions before the opening day debacle that it had considered and eliminated all possible dynamic problems with the unusual design, and the discovery that at least three other large lightweight footbridges had suffered similar opening day sway problems.
Indeed, information on one of these, in Japan, was said to be readily available, and yet Arup had apparently not taken this potential problem into account.
A similar landmark crossing in Paris, the Passarelle Solferino, had also been closed shortly after its opening day because of a sway problem and Arup engineers had gone on record to insist that the Millennium Bridge could never behave in this way.
As the post-mortem proceeded it soon became obvious that the issues were less clear cut than they had seemed at the outset. The only common factor between the bridges which had developed opening day sway was their size and lightweight construction otherwise, in structural terms at least, they were very different designs. There were no video records of the incidents. Indeed, there is still some doubt that the same phenomenon was affecting all the bridges. And the research carried out by Professor Fujino Yozo of Tokyo University into the opening day sway problems on a large cable stayed footbridge had not explained exactly how and when lock-in occurred.
Nevertheless, the whole incident was a major embarrassment for the structural engineers. They had to come up with a retrofit solution to a problem which was little researched and which involved human psychology and physiology as much as structural dynamics.
There were several outspoken critics who blamed the whole debacle on the unorthodox design of the structure, a 'horizontal suspension bridge' which relied on cables under very high tension to work.
But any bridge at that site would have been an extreme structure. Restrictions on pier spacing and location in the navigable Thames, height restrictions designed to protect the sight lines to St Paul's Cathedral, and the client's expressed demand for a landmark crossing were bound to push bridge engineering skills to the limit.
And with Arup and Fosters' hitherto unblemished track record of producing extreme, innovative and highly exciting structures that worked, there was every confidence that the same team could turn the original blade of light concept into a memorable and fully practical working crossing of the Thames.
In an attempt to avoid further delay while the interested parties wrangle over the bill, Arup decided to fund a ú250,000 prototype trial programme on the bridge itself. Carried out immediately before Christmas last year, the trials assessed the performance of two sets of tubular steel 'chevron' braces and viscous dampers, plus a temporary tuned mass damper. Arup's detailed proposals for the total solution show around 30 of these chevron/viscous damper sets facing each other in pairs along the full length of the northern and central spans and the outer end of the southern span.
The outer ends of the braces are connected to the deck edge tubes. As the bridge sways and deforms, the resultant lateral movement of the point of the chevron is taken, via a horseshoe-shaped link, to the outer end of a viscous damper. This is mounted on the central transverse arm back to back with its equivalent on the adjacent bay.
It is the ability of these totally sealed dampers to work with piston displacements as low as 0.25mm that is at the heart of the Arup solution. They also come with a 35 year guarantee. Arup plans to combine these with 30 tuned mass dampers (TMD), each weighing around 2t, of which all but four are designed to damp out any excessive vertical movement. The other four, beneath the main span, will provide additional lateral movement damping.
For the trials, Arup fitted a single, temporary 5t TMD that could work both laterally and vertically if required. There was no attempt to try out the proposed diagonal viscous dampers at the piers.
However, the results of the trials seem to have strengthened Arup's argument that the 'lockin' phenomena was inadequately researched and documented and that there was no way the design team could have taken it into account from the outset. It now appears that any type of lightweight pedestrian crossing could start to sway in the same way - provided the density of the crowds on the bridge exceeds a key value.
Arup discovered that with 156 volunteers marching backwards and forwards on the northern span lateral sway was insignificant. Adding 10 more volunteers triggered excessive sway within seconds. This sudden transition from stability to sway depends only on the relationship between crowd density and the dynamic characteristics of the crossing, Arup claims.
'Highly delicate' negotiations were said to be close to success as NCEI went to press, but all parties to the project now accept there is no chance of the crossing being reopened before the anniversary of its closure on 9 June.
Once the viscous dampers are procured, installation should be relatively straightforward. The deck planks can be lifted individually to give access to the main bridge structure from above.
Some form of temporary access platforms will be needed, and the successful contractor may prefer to hang a full length access deck off the existing structure.
In all, Arup reckons, it will take three months to install the dampers and tiedown. Provided the all-important validation and testing period goes well, the bridge could be re-opened before the end of 2001.