What in the world can you do with Georgia Clay?

We have a couple of areas around the house that are sloped and it just
erodes away. We can't get sod to anchor - rain water won't penetrate the
clay surface and anything on top eventually "slides" away...

It's the usual stuff - hard as concrete when it's dry, thick as firm gumbo
(for a half inch deep) when it's wet.

I'm thinking I could amend it with something and till it in. However, I
have no idea what amendment would be best to allow grass and plants a
fighting chance at establishing roots into the substrate.

I'm in the Atlanta area if that may shed any light. Whatever solution I
try will have to be done by me, and probably by hand. I do plan to rent a
tiller for that part.

I guess my questions a Presuming that if I can get grass/plants with
good deep root systems established, the erosion will slow or cease, what
type(s) of amendment, what quantity, when to amend it, how deep and how
well should it be tilled?

If anyone would be so kind as to share some wisdom in this area, I would
appreciate it.

Thanks,
J.D.Hood
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