Prepare the crumbling area for a coat of new concrete. Remove all of the crumbling concrete by hand, and then use a floor scraper to loosen any pieces that might be partially stuck but not completely crumbled. Vacuum the area after you are done to completely clean it and prep it for repair.
Create a slurry mixture by combining pure cement with water in a bucket. It should have a paint-like consistency. In another bucket mix up some concrete that you will use to finish the patch. Mix the concrete with a mason trowel, following the manufacturer's instructions. It should have a thick, creamy consistency.
Apply a coat of the cement slurry mixture on your previously crumbled area, using a paintbrush. Ensure that the slurry covers the entire area and penetrates any cracks. Paint it on from different directions to cover the surface completely. Work quickly, and don’t let the cement mixture dry. Apply more slurry if the initial coat starts to dry before you add your concrete.
Cover the cement slurry with some of your concrete mixture. Push the concrete around with your flat metal trowel from different angles until you have patched the old crumbled area completely. Smooth the new concrete with a flat trowel until it mirrors your existing concrete. Let the mixture dry for 72 hours before you allow traffic on it.