The Mohs scale ranks minerals from 1 (talc) to 10 (diamond) by which one scratches the other. A tile surface is given the number of the hardest mineral that leaves no scratch on it.
Quartz, the main component of sand, has a hardness of 7. Grit carried in on shoes can therefore scratch a surface softer than that, which is why entrance mats protect glossy and polished floors.