In reply to Chris Craggs:
Very dim memory this, but I think it's Van de Waals bonds you break when the rubber tears due to crystals cutting through the surface - tearing the chains apart from each other rather than breaking the chains.
Less scientifically, the rubber sticks in at least 2 ways:
1. The tiny nobbles/crystals in the rock dig in and deform the rubber, so both surfaces are mechanically locked together
2. The rubber itself has a high friction factor, so even on smooth surfaces it has quite a lot of grip due to the weak chemical bonds the rubber forms with the other surface
There is also a 5th fundamental force which helps the rubber stick - belief. I don't think they've found a carrier for it yet, but it definitely exists, and without it the rubber is much less sticky.