1*your flow line (i.e. the bottom of the ditch) is the important thing.
2*(if you got CMP corrugated stuff, then its about half that)
1*That's just it- the bottom is to far down due to 40 years of eroding the sides and bottom of the ditch.
2*It's 15'' Double Wall Smooth Bore
You can cut the banks and fill in your ditch to a respectable grade but make sure you work the dirt in and pack it well. You don't want the water soaking under the culvert and finding a crack and starting to run under your newly installe culvert. So pack the bulk of the fill. The last few inches of dirt fill should be left loose where the culvert is going so the culvert lies in this soft dirt bed. That will allow the corrugations to fill up with soil as you cover it and lessen the chance of a washout.
I have installed culverts in ditches so deep that I had to use a dozer and push the dirt out each end, lay the culvert and then push it all back in to fill the trench. But that didn't mean I had to install a 20ft diameter culvert. The depth of the ditch has nothing to do with the size requirement of the culvert.
If you contact your county road crew and give them your drainage information, such as how many acres, how steep, type of terrain, they will tell you whether your culvert is big enough.
I never install a particular sized culvert simply because that's what I have on hand. Unless of course you want to install it again when it washes over the roadbed because it was too little, or hump up the roadbed to cover it because it was too large.
If you buy a culvert from your county road barn, a 15" double wall, smooth bore will cost you around $6.00 per foot. If you are installing a culvert under a double laned roadbed and not very deep, 30 feet of culvert is plenty. So we are talking about $180 here. Don't use your 15" culvert if it isn't the size required simply because you don't want to spend a couple hundred dollars for one that is. You'll spend that money quickly retrieving dirt to reinstall if it's the wrong size.