What eishiya said, you need to make the tiles "puff-out", try to remove the corner rounding on the bottom of the tiles, and aggressively increase the rounding on the top of each tile, so their are more like pillows nailed to the ground on the bottom edges.
The bottom shading of each tile should probably be as rounded as the rounding on the top of the tiles, and the contrast should be lower to imply a less plastic/ceramic material.
Textile materials have a lot of subsurface scattering, like skin, that greatly reduces shading contrast.
Also, If the splotches are stains rather than folds and depressions, then are likely to be from organic stuff (blood, piss, healthcare daily life), so they might get some warmer colors, contrasting with the more pure grey of the actual shades which are not stains.