How about a washable multi-stripe or pattern that is reversible? Pattern is less likely to show dirt.

or something like this one

Martha Stewart, still offers I believe, floor tiles by Flor that are placed in any combination with peel back adhesive. If one gets damaged, you just pull it off and replace. Seems a better alternative. Having said that, is this a budget consideration? Be it sand or snow, faux wood tiles would be easier to maintain.

Sorry about tile suggestion. I missed your FP picture... Sigh. I like a pattern idea to hide dirt, these are outdoor rugs. They sell them high end at sites like Frontgate and of course at the Depot etc. so I'm less concerned with showing you a picture here that you will actually want to get. Just trying to show you the wide range of styles now available!

Very traditional with some good color to brighten the room but dark enough to hide traffic patterns. This is going to wear like crazy because it's an indoor/outdoor rug. Pottery Barn $800 on line for a 9 x 12.