Ok, I won't be so hasty about tree growth statements but they really do go up a little; I know from carving my initials in many, many trees in our woods growing up.
Buckeye, I read your post several times, very interesting. So you built your own beam by building up with oak planks. If I ever were to build a new bridge, a real bridge and not a culvert, I'd sure overbuild it. You know, a nice used M Kubota I want for banging around in the woods will sure weigh more than my L. Or a mini excavator. I would probably build it to carry seven to ten tons; a good safety margin. It's just a pond back there, never going to take a vehicle over the bridge.
He said now...
which begs the question, how strong are metal culvert pipes? How many feet of dirt would you need to pile on top to take, for example, a small bulldozer over, a nice D3. Like most guys, always wanted a bulldozer. Not very practical on my place but it sure would clear a trail nicely. So will a chainsaw and a pull chain. Now obviously culvert pipes are infinitely strong if built "properly", but if I dropped a five foot diameter pipe in a six foot ditch, with stone underneath, how much dirt has to go on top? I'm guessing that gravel goes on top first. Not an excavator guys, sorry if questions are stupid.
I'm really thinking that fixing this bridge up cosmetically and building something much stronger next to it or nearby makes the most sense. The bridge should last decades with just light use, say under a thousand pounds.