Panniers stuck in tire spokes!
I once had this happen before by combining inexpensive saddle bags combined with a inexpensive rack.  The bags were not stiff enough for things like groceries and the rack provided no support to keep the saddle bags from twisting.   With the heavy weight the bags simply twist into the spokes while riding.

I now use higher quality expedition style panniers and racks (picture below). These have lots of side support to keep panniers/saddlebags from twisting. The panniers themselves also have stiff inserts to prevent twisting. I have put close to 120 lbs on the bike (front and back) after big grocery run with no such problems.



Also a photo of the rack and bag setup will help diagnose the problem.