I just had my garage floor ground down to facilitate the installation of porcelain tile. The machine he used was called a "scarifier" (local equipment rental store) and it ground the floor and left a kind of rough finish on it, similar to when the city/county grinds residential sidewalks when they have "trip edges" sticking up. Then my floor guy used a self-leveler on the floor to reduce any low spots and fill the expansion joints. My floor is 40 years old BTW and stable. Then after the self-leveler he used a Schluter membrane that is rolled out and adhered to the floor with the same stuff he used to then install the porcelain tile. The result is a perfectly flat floor that looks terrific.