Saturday, September 17, 2011

The Infrastructure is Crumbling, but Don't Panic

As a Montreal resident, I sometimes wonder if the roads are as bad in other major cities.  It seems as though the roads within the province of Quebec suffer from a contagious disease constrained within its borders.  The disease transforms an otherwise developed nation into Colombia with snow.

The moment you cross the border into the United States, the crater-sized potholes vanish and the uneven surfaces become smooth.  If you listen closely, you can hear the suspension system of your car breathe a sigh of relief as you leave Quebec.  If you happen upon a road imperfection while driving in the states, it will be most certainly preceded by one or two warning signs.  If every hole in Montreal's roads were well-marked, there would be no space left for the speed limit signs (which we don't follow anyway, but that's another story).

In truth, dodging potholes and bouncing around in one's car is part of the quebecois experience; the locals have grown accustomed to it.  What the public will never come to accept, however, are falling overpasses and tunnels.  Over the past five years, several such incidents have occurred in the city of Montreal.  In the summer of 2011, reports of a major structure crumbling in some way seemed to become a weekly tradition.  Due to the local media coverage of these incidences, the average Montrealer now knows what a gusset is, and could probably submit a decent draft for our next bridge's design.

Let's first examine why structures fail, and then look at why so many are failing these days in particular.

An overpass or bridge is designed to support its own weight plus that of the cars and trucks that travel across it.  In addition, these spans must contend with high wind loads.  These external loads can be amplified if they are cyclical in nature, particularly if they happen to cycle at a similar rate as any of the natural frequencies of the structure itself.  At a minimum, the structure is designed to support all of these loads if they were to occur simultaneously.

The bridge is then sized with an additional safety factor.  A safety factor of two would imply that the external loading would have to be twice the worst-case-scenario that was assumed in order for the material limits to be exceeded.  This kind of failure is known as an ultimate failure.  It is very rare to find a structure that fails due to weight or wind loads, although the 1940 Tacoma Narrows bridge is one such exception.  A more common reason for why a structure's maximum strength might be exacerbated is due to surface vibrations, or earthquakes.  If all structures were designed to withstand a 9.0 earthquake, their cost would increase significantly.  In certain places of the world, such costs are necessary to undertake.

There is one other major form of stress that structures face: enforced displacement due to thermal expansion.  The amount of extension or compression experienced by a material is proportional to the change in temperature.  In Montreal, the temperature can change a lot over the course of a day.  Over the course of the year, the typical range of temperature is about 75 degrees Celsius.  It is even greater for dark substances, which absorb so much radiation from the sun.  Temperature gradients across structures cause them to deform, and crack.  When a crack is introduced into a material, its maximum load-carrying capacity drops dramatically.

Fortunately, structures are designed with such temperature fluctuations in mind.  Cracks are expected to occur, and corresponding decreases in material strength are anticipated and planned for.

Beyond these external loads placed on the structure as a whole, Montreal structures must survive the elements of the local environment.  While water, air, sun, ice and salt do not damage the insides of a bridge directly, they do affect the exposed surfaces.  Here, the alterations to the material are chemical in nature, rather than mechanical.  Still, a gradual chemical change can have serious effects on a material's functionality.  If the exposed surfaces are not maintained (painted every so often, for example), outer defects can propagate internally.  Scanning through the long list of defects for the Mercier bridge, one notices that every second word is "corrosion".

There is clearly a long list of threats to a structure's integrity, and they add up over time.  Time is in fact the key parameter for a well-designed structure.

The reason that a failure will eventually occur in every structure is due to the failure mode known as fatigue.  Like a person, when a material is pushed every which way enough times, it eventually loses it and cracks.  After enough back and forth expansion and contraction, not to mention vibration, a structure will fail at a much lower value than it would have when it was brand new.  Of course, engineers know a great deal about fatigue failure, and consider it very carefully when designing a bridge, tunnel, or overpass.

Fatigue failure is the reason why a city's infrastructure will one day fall to pieces unless it is carefully monitored.  Like food, all structures come with a "best-before date".  Once a bridge's life is extended beyond this period of time, the likelihood of it failing increases significantly. 

So, why is Montreal now experiencing so much failure at one time?  It is actually not so surprising.

Large supporting structures designed for a fairly extreme climate have a life expectancy in the area of fifty years with regular maintenance, while some can last up to one hundred years (it depends on the load-bearing material...Steel bridges outlast concrete ones).  That is not to say that such structures will immediately collapse on their fiftieth birthday, but around this time they will become statistically more likely to fail.

It turns out that a large quantity of the structures in Montreal are around five decades old.  This makes sense, as the city saw major infrastructure expansions in preparation for major events like Expo 67 and the Olympics in 1976.  In those days, these major investments were seen in a positive light, as they placed Montreal on the world stage, increased tourism, and allowed for the local population to grow.

Today, investments similar to those made half a century ago must be made again.  Unfortunately, these investments, made today, will not correspond to any economic growth; they will merely prevent the city from falling to pieces any more than it already has.

In summary, Montreal's many bridges, overpasses and tunnels are not poorly designed.  The soup we currently find ourselves in is the result of a big infrastructure boom many decades ago.  A large spike such as that will always call for a similar spike in the future; it is one consequence of rapid expansion.  If a city finds itself unprepared for an infrastructure overhaul, it amounts to a failure in city planning, not engineering.

As local defects within these structures are repaired - and certain bridges beyond saving are replaced altogether - the city must continue to function.  Its citizens should not drive around in a panic.  I have heard many people in this city express their fear of driving under or over their bridges to go to work.  Such fears are the result of much media attention, but they are statistically irrational.

The vast majority of car accidents would be averted if drivers were attentive, careful, and of course, sober.  The number of car accidents involving falling structures is tiny when compared to those involving reckless driving.  So, whether you are driving over a new bridge or an old one, the greatest threat to your safety remains the cars around you.

Still, given the state of Montreal's roads and bridges, no one can be faulted for muttering a small prayer upon entering a motor vehicle.

The more puzzling question than "Why are our bridges falling apart," is "Why do they cost more to tend to and replace in Montreal than anywhere else?"  The answer to that is likely attributed to our needlessly high number of bureaucratic jobs, but perhaps even more so to the troubling presence of organized crime in this city.  Sadly, efforts to repair these issues require more than duct tape and epoxy.


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The Engineer said...

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