Scrape out the existing wood and other debris in the expansion joint with a large flat-head screwdriver. Remove as much debris as possible from the expansion joint by hand and placing it in the trash can.
Brush the length of the expansion joint with a stiff wire brush. This helps to remove any loose bits of concrete from the edges of the expansion joint.
Vacuum the debris from the expansion joint with a shop vacuum. Ensure that you remove all traces of debris from the joint.
Measure the length of the joint with a tape measure. Cut the expansion joint wood to the measurement with a hand saw. Measure the depth of the expansion joint and subtract 1/8 inch. Transfer the measurement to the face of the expansion joint wood. Rip cut the length of the wood with a circular saw and rip cutting blade.
Set the wood into the expansion joint. Tap the wood down into the joint with a mallet. The top of the wood should be 1/8 inch below the surface of the surrounding concrete. Place painters tape on the top of the two concrete slabs on each side of the joint.
Apply a bead of self-leveling compound over the wood with a caulk gun. The bead should cover the wood and even with the surrounding surface. Allow the self-leveling compound to cure for 24 hours and remove the rape from the concrete.