Fly ash (i.e. ash from industrial chimneys) is being used for this same purpose, as pozzolanic (volcanic ash) deposits are not that big or common around the world. The key here is, by the opinion of a cement researcher close to me, the availability of non-cristalline (i.e. an amorphous or vitreous form) silicon dioxide.

I've been slightly following the papers on roman concrete for a decade or so, and as far as I remember, they've been discovering different cristalline aluminosilicates that would explain the resilience of these concretes, so maybe there still is some need for pozzolanic, or for adding aluminium to fly ash.