When you sprint on carpet, I would expect to see particles of the carpet.
When I ran on the carpet, the particles I saw were the particles for the block underneath.
How to trigger:
1. Place carpet on any block. It's easier to see if you use a large area of carpet.
2. Run on the carpet. It's easiest to see in 3rd person view.
Note: Placing carpet on carpet of the same color and sprinting on the top one DOES show the correct particles.