For repairs to Damaged Floor Joints to be Successful, the perimeter of the damaged concrete will need to saw cut, and then have all of the loose friable concrete removed.
The void, should then be filled with an Epoxy Mortar, and allowed to cure. Once cured, it is, Imperative to Retain the Original Joint Width, when Re-cutting the Joint.
The New Joint is then sealed. This will stop future Damage to the Joint Edges. If the New Joint is Not Sealed, then the Joint Edges will Break Down Again.