Remove any dirt, leaves and other debris from the large joint with a hand brush. Use a wet-dry vacuum to suck out any remaining loose debris.
Cut foam backer rod to fit the length of the joint with a utility knife. The backer rod should be a little wider in diameter than the width of the joint. Lay the material over the top of the joint and push it to the bottom with a putty knife. Once in place, the top of the backer rod should be about one-quarter inch from the surface of the driveway.
Attach a tube of self-leveling urethane sealer to a caulk gun. Start at one end of the joint and fill the remaining joint with the sealer. Smooth the surface with the putty knife or a concave jointing tool. Block off the driveway so the joints can set for at least 24 hours.
Apply an even coat of concrete sealer over the driveway and expansion joints with a roller brush. The sealer repels water and stains. Wait a day full for the sealer to dry and plan to re-apply it every 2 or 3 years.