Renze
Elite Member
My personal tree downing record is 15" oak. That was before i had the frontloader. 
It is hard to get the lay of the land from your pics but.... making that 'gully' wide, shallow and armored with rocks may be the best option.
Another option might be to deal with the at least some of the water before it gets there. From the pic it looks like maybe the water follows the trail for a bit before crossing. Use of 'rolling grade dips' might help provide areas for it to cross before it starts to accumulate into a small stream.
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In the above pic you could put a grade dip about 1/3 of the way down on each side (near and far parts of the trail) (assuming there is someplace for the water to go on the downhill side). This would take any water that accumulates and wants to come down the trail and re-direct it off the trail. Then the center section only needs to deal with what water comes off the area above the center section between the grade dips.