Gravel.

Maybe you mean evergreen, not succulent? Possibly vinca would work, although it can take awhile to get established and will take just limited walking.

Why is it shady - from a building or fence nearby, or from a tree? Grass will grow in most places, so if you know why the grass won't grow then we may be able to be more helpful. How large an area is it? Pictures would help a lot, as well as knowing how many hours of sun it gets.

Ajuga is another possibility but mine got a mold and I had to pull it all out. (I am in Toronto.) Some ivies might also work but again they don't really like being walked on much.