If you do go the route of pouring concrete, I would pour deep footings so that a "gulley washer" doesn't undermine your hard work. (I'm not an engineer, and I don't play one on tv, so this isn't expert advice!) I have seen more than a few fords fail in snap thunderbursts that create a flash flood, almost always by the water getting under the ford...
That sixth power of speed law makes for some enormous earth moving powers as you get more water coming through. Water moving twice as fast has 64 times the sediment eroding and moving power...
If you can borrow material from somewhere else, large culverts might be a lot cheaper than concrete, unless your concrete is a lot cheaper than mine.
All the best,
Peter