I don't have your species, but I have a lot of different Opuntias. Many times when we get big rains, the pads swell so much, and the plant will drop single pads or even huge branches because they get so heavy. To me this is normal. The ones on the ground will start growing right away. I think this is the way nature keeps it all going. You can let your pieces callous for a few days and then plant them for more plants.