Remove any remaining expansion joint material out of the crevices. Use a pry bar or large screwdriver to slowly work it up and out of the crack. Sweep the area clean with your broom.
Press foam backer rod into the crevice. Start at one end of the driveway and slowly work it into the crevice with a large screwdriver. The foam backer rod should be slightly wider than the crevice in the driveway you are filling and when installed should sit about 1/4 inch below the driveway's surface. Cut off any extra backer rod with your utility knife once you reach the other side of the driveway.
Load your silicone caulk tube into your caulk gun. Fill the crevice with an even bead of silicone caulk along its entire length.
Smooth out the caulk bead with a wet finger. Allow to cure for the recommended time stated on the caulk tube before walking or driving on the driveway.