I agree it's probably moles, especially if the ground over the trenches is very soft and spongy. BUT don't forget another possibility--crawdads. Those big red ones are very prevalent around where I live in Kentucky, and they can make some mighty big holes. They also make little mounds around the openings of the holes with what appears to be balls of dirt/mud about the size of a shooter marble. But this is not the right time of the year for them to be active, so I'd say you're looking at moles or ground squirrels.
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