Believe me, it is 1000X easier to mix ANYTHING with sand than with pure clay (thick, heavy molasses when its wet, brick-hard when its dry).
When I first decided to dig up some of the backyard to put a raised garden in, my thought was to dig down a couple of feet, knowing that the clay would never drain and the plantings would drown. Shovel in hand, I started the project. This was in the spring and the clay was so heavy, that each shovel-full weighed in around 25 lb.! Bad back made worse - tender hands full of blisters. OK, that idea was shot down. Then I rented a commercial, extra-heavy duty tiller, a real monster of a thing. That baby beat me up so badly that my arms were bruised and my already-blistered hands re-blistered, It would only till 2-3" deep at most. After an hour of abuse (mine!) that idea collapsed as well. Finally I hired a landscape contractor who came in with a large back-hoe, lots of men with wheelbarrows, and a dump truck to haul the clay away. Success!!!!!!!!!!
The following year I decided to landscape my entire backyard lot-line, about 200' feet wide and 10' deep. That landscape contractor did the work, brought in a double-size dump truck (and filled it twice), and it was money well-spent.
Just ask me what I think of gumbo/concrete clay.....