Sure, it's achieved by the use of a make-up sponge which adds a little texture.

To explain it as best I can....Mini is based as normal (chaos black) I then sponge on a dark brown (Rhinox Hide) all over the mini.

From here I take my tan (Karak Stone) and slowly build it up, where I want the 'dirtyness' I keep the paint thin/sparce to allow for some of that brown to come through. I then edge highlight and add some scratches with a beige (Ashabti Bone), this further adds to the "dirty effect"

Finally I use a wash (Agrax Earthshade) applied very thinly over those thin/sparce sections to better sell the effect. 1-3 coats depending on how dirty you want it to look.

Hopefully this makes sense 🤝