by Eugene J. OBrien, University College Dublin and Roughan & O’Donovan Innovative Solutions
To avoid unnecessary bridge strengthening, everybody is looking for more accurate safety calculations. But the focus is very much on evaluating strength; when there is a lot more to be gained by looking at the other side of the equation. Bridge traffic loading is the Cinderella of bridge assessment. It is poorly understood, and there are great potential savings if we can accurately quantify the conservatism in current methods of safety evaluation.
In simple terms, a bridge is safe if the load is less than the capacity to carry it. More precisely, a bridge is safe if the probability is very small that the stresses due to load exceed the capacities to resist them.
Calculating that probability is pretty straightforward on the capacity side – reliability theory is now well established. In simple terms, this means using statistical distributions for all the parameters – the strength of the steel, for example, can be represented by a distribution rather than by a single number.
This allows us to estimate the probability of failure and tends to be less conservative than conventional approaches. Generally, bridges are considered safe if the probability of failure is less than about one in a million in a given year.
Bridge traffic loading is at an earlier stage of development than capacity, but we have made a lot of progress in recent years. Over the past four or five decades, Weigh-in-Motion (WIM) has emerged – technologies of weighing trucks on the road while they are travelling at full traffic speed. There are now extensive databases available of WIM data, some of them with tens of millions of historical truck weight records.
Some people have objected to bridge loading studies on the basis that we can control truck weights – so why don’t we just assess the bridge for the heaviest truck out there? But there are several problems with this. Hauliers regularly use trucks that are illegally overloaded – some of them massively so.
So what is the heaviest truck out there? And, on longer bridges, should we design for the situation when the whole bridge is fully loaded with the heaviest possible trucks? This would simply not be practical.
Statisticians use return periods to quantify levels of safety. For example, the Eurocode for bridge loading specifies a return period of 1,000 years. So European bridges are designed for the level of loading that would typically be exceeded just once in 1,000 years. This is roughly equivalent to the level of loading that would be exceeded 10 per cent of the time in the 100-year life of the bridge.
For new bridges, being conservative is not expensive and it can even allow for possible future growth in the numbers and weights of trucks. For existing bridges on the other hand, conservatism is a real waste of resources as it can result in bridges being strengthened or even replaced prematurely – when they are still perfectly safe. Maybe for this reason, lower return periods are considered acceptable in assessment – 50 and 75 years are commonly assumed.
The Eurocode for bridge loading was one of the first codes to be calibrated using WIM data. It is a regular load model – there is a uniformly distributed load and a bogie – but the values used were derived using WIM data from France.
The process involved a lot of statistical calculations to find the characteristic maximum values of load effects – bending moments and shear forces – for a range of bridge types and spans. A notional load model was then found that gave a reasonable and conservative match to these characteristic values.
Finding characteristic maximum load effects involves some complicated statistics, but the principles are straightforward enough. It is usual to separate permit trucks from regular non-permit trucks.
Generally, the statistical calculations are done for non-permit trucks only on the assumption that permit trucks can be well controlled. (In practice, this is not so clear, as in some countries, trucks can have a long-term permit, can travel at full highway speed without an escort and are often found to have weights well in excess of the allowable.)
It is generally not possible to synchronise WIM data with vehicle permit data so it is not possible to say with certainty whether a truck has a permit or not. However, some good work has been done on identifying “apparent permit” vehicles, i.e. vehicles whose axle configurations suggest that they should have a permit. This works well and it has been shown that non-apparent permit trucks can be identified from their axle configurations and the corresponding characteristic maximum load effects can be found.
For short-span bridges, the governing condition is one or two trucks passing at full highway speed. While the static weight on the bridge may be less than when traffic is congested, the allowance for dynamics in most countries makes up for this and the overall effect is greater.
The simplest short-span bridge case is when there are two opposing-direction lanes. In this case, the traffic in each lane is statistically independent so each lane can be considered in isolation and the final probabilities multiplied.
Same-direction lanes, as would commonly occur in highways, are a much more difficult challenge as there are statistical correlations between the trucks in each lane. For example, a fast-lane truck is usually associated with a heavier (and therefore slower) truck in the adjacent slow lane.
The best approach in this case is “scenario modelling”, in which scenarios involving a group of vehicles in both lanes are extracted at random from the WIM database and stitched together to generate a multi-lane stream of simulated traffic.
For long-span bridges, the congested traffic case governs. This is particularly difficult to deal with as most WIM technologies do not operate effectively in congested traffic so finding data on vehicle weights, gaps between vehicles and the mix of cars and trucks is really difficult. Of course, assumptions can be made but traffic loading for long-span bridges is still a work in progress and current assessments are generally conservative.
In summary, the availability of WIM data has made it possible to now calculate characteristic maximum load effects in most bridges.
This means that we can get a much more accurate estimate of the probability of bridge failure that takes account of the actual load on the bridge as well as its condition. The result is that the lives of many existing bridges can be extended, without compromising the safety of the network.
