Prescription glasses getting dusty and greasy
An ex-coworker of mine got a pair of goggles that he could put over his prescription glasses.  In his case not so much because of dirt on the lenses, but because wind bothered his eyes.

A lot of the ones you'll find are the high-durability ones for mountain bikers (with thick heavy frames), but it is possible to find lightweight (and not so ugly ones) like these:



(Note that this is not a product recommendation; I don't recall the make of what he actually has, this is simply the closest in appearance that I can find in reasonable time.)