Surrounded by concrete, I have a small 8 x 5 foot area with hard clay soil that only pools when it rains. I want to remover the top 2 to 3 feet of clay and replace with organic compost than top soil. I will only plant some Medicinal Herbs like Turmeric, Ginger, and Hawaiian Ti plants. Is this a bad Idea?
What you may have there is a no-longer-used septic tank; the size 8x5 is right for a tank and a concrete surround is what you would see if the top has been removed or caved in after the septic system was disconnected and filled. You can verify if this is an old tank by driving a rod down inside the surround and if it meets hard resistance at 5 feet then you have an old tank.
So part of the reason it is pooling there is maybe because there is no drainage, and good gardening says you should solve the drainage issue before attempting to improve the topsoil. However this raises issues: was the tank decommissioned properly and are you prepared to grow edibles in such a location? Normally the decommissioning would not further compromise the tank by breaking it due to residues left after pumping, and result in a grass surface. Check the history of the house and ask a few questions at the local health office to help your decision making.
I don’t think any of those plants will do well in clay. You want to make it more arable. Using a turf fork, you can break it up add mulch and this fall’s leaf drop into it. You might add some sand as well.
Alternatively if the clay pan is really deep, you can build raised beds above it, by elevating the soil this way will allow that soil to drain. Just make sure you put a hefty layer of crushed rock underneath the beds.