Lime concrete, or limecrete, has been used since Roman times for massive structures such as bridges, docks, and even the dome of the pantheon in Rome. You can use it instead of cement concretes, in foundations, or to make a breathable floor.
You can use the same kinds of aggregate as with cement concretes – pebbles, small pieces of hardcore etc – but you can’t rely on carbonation for the set, as its thickness will mean that the middle won’t have access to CO2 from the air. You will either have to use hydraulic lime, or add pozzolans to a non-hydraulic lime – in the ratio of around 1:1 with lime.
So a typical lime concrete could be one part non-hydraulic lime putty, one part pozzolan, and six parts ballast / aggregate.
Limecrete is not as strong as cement concrete, and so it is not advisable to use it for big projects or where strength is very important.
At Ty Mawr they have a limecrete floor. With a concrete floor, moisture is not absorbed, so it is pushed to the walls, where it could possibly climb and rot timber etc. If you use limecrete you have a breathing floor. You can also put underfloor heating into the limecrete floor (but with plastic pipes, not copper, which will corrode).