A tire bead, the part of the tire that seats it securely onto the rim, must be air tight or leaking and tire failure will occur. In all instances of tire bead repair, if the cords or the tire bead are cut or sliced, they cannot be fixed and the tire must be replaced. But if the bead is intact, even if the cords are showing, then you can repair it.
Clean the tire rim and the bead thoroughly, then apply tire bead sealant to the bead. In many cases of bead failure, both the rim and bead are dirty or otherwise contaminated. Cleaning both will remove any debris that could prevent a tire bead from seating correctly. A tire bead sealant will slightly soften the bead rubber and make it conform tightly to the rim.
Apply an RTV silicone compound to the bead and allow it to dry for several days until it has completely cured. Cover the entire damaged area with the silicone and smooth it out so it conforms to the regular symmetry of the tire bead proper. Once dry, mount the tire and fill normally.
Spread an industrial style gasket maker onto the damaged bead, available at auto stores or farm stores. Allow the gasket maker to cure for approximately one minute before mounting the tire back onto the rim. Once mounted, fill with air.
Pry the tire away from the rim using a pry bar or heavy duty screwdriver, and hold it like this until the next step is completed.
Heat up the tire bead with a heat gun, and also heat the rim in the area where the bead is questionable. Heat the bead in this way until the rubber just begins to melt, then pull the pry bar or screwdriver quickly away and allow the tire to seat on the hot rim.
Immediately fill the tire up with air, as the molten rubber will fill in any compromised area of the bead, allowing the tire to seat properly on the rim.