It could be described as a tale of two videos. One, taken on the bridge's 10 June opening day, showed groups of pedestrians on the crowded £18M structure shuffling in phase with an alarming and unpredicted lateral sway. This was the first ever recording of a rare phenomenon that had apparently affected at least three other large, lightweight pedestrian crossings on their opening days.
Nearly six months and an intensive research programme later, Arup, the bridge's structural engineer, made another video recording. What it showed, Arup claims, is final proof that the sway which led to the bridge's closure only three days after it opened was completely unpredictable on the basis of engineering knowledge at the time the unorthodox structure was designed.
What Arup was attempting to do was establish a quantifiable and predictable relationship between pedestrian activity and structural movement. Previous Arup trials and laboratory research had suggested there would be some critical point at which pedestrians and structure would become locked into a feedback loop. The small sideways forces generated by individual walkers would eventually agglomerate until the structure responded and began to sway laterally. As it did, pedestrians would modify their stride pattern to compensate, placing their feet wider apart, gradually falling into phase with the movement and feeding ever larger forces into the bridge's motion.
Although some information on lateral forces generated by pedestrians and human response to lateral sway was available before the design began, none of it, says Arup, was of practical use to bridge designers. Even the emergency programme of laboratory research Arup commissioned last summer and the first series of trials on the bridge using small shakers and 100 Arup volunteers had failed to provide the definitive answer. There was enough data for Arup to devise an elegant retrofit solution (NCE 23 November 2000), but doubts remained over its likely effect on the bridge's behaviour.
More proof was needed. Arup commissioned a £250,000 prototype damper evaluation programme, and assembled no less than 300 volunteers. Lessons from the first set of trials were applied. Then, at 17.18hrs on 19 December, it happened.
Researchers had been gradually building up the numbers of volunteers circulating on the northern span, which was still in its original undamped state. As numbers increased, the needles on the battery of instruments monitoring the structure's lateral response hardly flickered.
Even with 156 volunteers patiently marching to and fro there was little change. Then, a further 10 person increment was added to the procession.
Within seconds the bridge began to sway. By the time the latest increment was approaching mid span the first signs of 'synchronised shuffling' were visible, with the sway approaching levels recorded on the opening day. The test was abruptly terminated - but the final piece of the puzzle was in place (see diagram).
Coupled with the results of similar tests on the central span with its array of prototype dampers and data from the university research programme, these crucial observations enabled Arup to formulate a classically simple theory to explain the original opening day debacle. The logic is compelling.
Each bridge, the theory says, has its own inherent damping, a specific resistance to horizontal sway.
As pedestrian numbers increase, this resistance is eroded. If numbers increase only a small increment beyond a key value, sway will begin and increase rapidly as pedestrians lock into the motion. This applies to all types of bridge with natural frequencies of motion in the range something below 0.5Hz up to 1.2Hz, but many will never be affected because it will be physically impossible to get enough people walking over the bridge at the same time to overcome its natural resistance.
Arup calculated that crowd density on opening day peaked at around 1.3 pedestrians/m 2, although many of these were stationary for much of the time. Its latest trials confirmed other researchers' findings that at densities of 1.7 pedestrians/m 2or so the crowd comes to a halt. So, concludes Arup, any large lightweight crossings which have so far escaped this phenomenon have probably done so simply because crowd densities have never been high enough. And it has developed a 'magic formula', which will make it possible for the first time for designers to check their structure's vulnerability to this effect.
There are some, of course, who would not be convinced unless a similar response could be induced in a crossing whose only similarity to the Millennium Bridge was its natural frequency of lateral movement. Such structures exist, in the UK and elsewhere. It remains to be seen if those in charge of such crossings would be willing to submit them to the sort of trials that took place in London before Christmas. The multi-million pound cost of the Millennium Bridge's anti-sway measures is likely to be a powerful deterrent.
A second finding was almost as controversial. Some experts believed pedestrians could lock in to vertical movements as well, although there was little hard evidence to support the theory.
Arup included a formidable array of tuned mass dampers (TMDs) in its retrofit proposals to take care of this possibility. In the event no signs of lock-in were observed. However, the trials did not provide definitive proof that vertical lock-in could never occur, so the TMDs have been retained.
These results seem to explain most of what was observed during the opening day. The greater sensitivity of the southern span is down to its natural 0.78Hz frequency being closer to the natural half pace walking rate than those of the central or northern spans. It also seems that the unusual design of the bridge, with its widely spaced, highly tensioned suspension cables, did not contribute significantly to the problem. And, says Arup, not only is vertical lock-in unlikely, vertical excitation from either static or dynamic loads, wherever applied, could not have caused a resonant lateral response.
Arup's conclusions and its retrofit proposals have been checked and approved by WS Atkins, the client's advisors. The ultimate fate of the bridge is now in the hands of its owners the Corporation of London and the London Borough of Southwark.