I wouldn't advise compost bins on concrete, they work best when worms can come up from the bottom and have a good old munch at the stuff you put in. I suppose people buy worms, but I don't.
Don't ever put ground elder in the bin as even half inch of root will grow.
I would suggest digging it out, by hand, tedious , but the only thing I find that works, then make sure you don't transfer any of it to your beds. I think a lot of people are plagued with ground elder, your not alone in this, I have loads of it, and am just taking it steady and digging it out.
Don't ever use a rotavator on it, you will just chop up the roots into more pieces and it will spread even more.