With a few exceptions, it seems like newer bridge construction does not provide much in the way of nice pools. Maybe it is blind luck, or maybe new bridge pools need time to regenerate.
It's true that many old bridges and culverts form nice pools and most newer ones do not. It's not blind luck or a matter of time to regenerate. There is a logical explanation for it.
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Old bridges were usually built with narrow openings, to save money and because of the technology available then. A narrow opening concentrates flow causing high velocity, which excavates a pool. That pool does not fill in because during every high flow event high velocity flows dig the sediment out.
The high velocity flows and downcutting also threatens the supports for the bridge. And with a small bridge opening, water can back up above the bridge during floods, creating pressure that can cause bridge failures.
Because of these problems, when the bridge is replaced, the new bridges are typically built with much wider spans, to pass flood flows. And often the channels are dug wide with machinery. But this leads to a wide, flat channel with shallow water, rather than a "bridge pool."
It's similar with old fashioned culverts and their new replacements. The old culverts had a small opening and concentrated flow which carved out a pool. The new culverts are built much larger, and are often arched structures with flat bottoms. The advantages are that fish can migrate upstream now, and they often could not where there was a large drop from the culvert pipe down to the pool. And the larger opening passes flood flows better, and is less likely to get clogged up with trees.
The disadvantage is that no pool forms at the new style culvert. On some small streams, the bridge and culvert pools were the best pools on the streams. They were artificial habitat, but nevertheless they were the best pools, and much of the trout population in the small streams were in there. I think it's likely that many culvert replacement projects reduces the trout population in the stream for this reason.
Because our streams are mostly very highly altered, i.e. channelized, they tend to have limited pool formation, with far less pool habitat than they did originally, reducing the trout populations greatly from their original condition. So, all good pool habitat should be valued, whether it is naturally formed, or artificially created by bridges and culverts.
I think engineers could design bridges and culverts that meet all the usual civil engineering goals, AND also form good fish habitat, i.e. pools, and provide good grade control in the upstream direction.
But, in general, I don't think they've ever been ASKED to do that. If anyone knows of any efforts along these lines, please let us know.
I did see a recently built bridge on a small stream in Centre County, which may have been constructed with these goals in mind. It appears to have been designed large enough to pass flood flows, and to provide grade control in the upstream direction (to prevent incision), AND to create a deep pool under the bridge.
This bridge has a concrete "sill" running across the channel at the upper part of the bridge, and another "sill" across the channel at the lower part of the bridge. These "sills" provide grade control, stabilizing the channel in the upstream direction. And in the middle, between the sills, there is a moderately deep pool. It does not fill in with sediment because the water drops over the upstream sill and the velocity and turbulence keeps the sediment washed out. And the sills are low enough that fish can easily move over past them. I can't remember if the sills had slots or not, but slots could aid fish passage.
So, it is possible to create bridges that incorporate pool habitat for fish, if that is a design goal. It may cost a little more money, but those sills are probably a small percentage of the total cost. And they may not even have been thinking of fish habitat. They may have just built those sills for grade control, to prevent high velocity flows from undercutting of the bridge supports.