Remove the damaged concrete fastener from the concrete surface. Use a hand saw to cut off the head of the concrete fastener. Then drill the body of the fastener out of the concrete surface using an electric drill equipped with a high-speed drill bit.
Chisel out the hole to make it wider at the bottom than it is at the top, a process called undercutting. Tap the end of a chisel with a hammer, moving the chisel around at different angles to get a relatively smooth finish inside the hole.
Brush the inside of the hole with cement adhesive, then fill the hole with premixed concrete patch material. Put a small amount of concrete on a pointing trowel and press it down into the hole, making sure to fill the entire hole. Smooth the surface of the concrete with the side of the trowel and allow it to cure for three to seven days.
Replace the concrete fastener after three to seven days have passed. Allowing adequate curing time for the concrete helps ensure that the new fastener does not come loose or get damaged as easily.