I've been doing a bunch of work with floor tiles this weekend, and stumbled across a pretty quick and easy way to add some nice grout grunge to floor tiles using the standard filters available in Gimp. Here you go!
Start with a piece of floor tile, preferably with some sort of grout line drawn and in a separate layer. This is what I started with:
Start by selecting the grout lines by whatever means works for you. With a grout-only layer available, you can use Select by Color on the transparent area and invert, which is what I did. Once you have your selection, grow it a bit based on tile size. In this particular image, 30px equals one foot, and grout lines are 2px, so I did a grow by 2, giving me a 6px wide selection.
Create a transparent layer and call it Grout Grunge. Fill the selection with black or a very dark color of your choice. This is the basis of your dirt. Edit: Even better, use a dark soil or stone pattern, or another source texture that contrasts with the colors of your tiles well. Remove the selection and be sure this is your active layer.
Run a Gaussian Blur (Filters/Blur/Gaussian Blur) over this layer. I used a 7px blur, which is about quarter foot in scale.
Run the Cubism (Filters/Artistic/Cubism) filter over the result, adjusting size for your image. I used a 7px tile size and 1.5 for tile saturation.
Rerun the Gaussian Blur over the result, and you're done!
Here's the net result applied to my sample image:
The Cubism filter does a nice job of adding some randomness to the basic Gaussian blur, and re-blurring eliminates the straight lines it produces, leaving you with a nicely random set of noise that follows the edges of your tiles. Bear in mind this technique will create blur on all sides of your grout lines, so you may have to trim some of the grunge if it crosses wall lines or the like.
Hope this is useful! If you have improvements or questions, please comment.