What I can't work out with your calcs above (and forgive my ignorance on
engineering loads) is how a 16 tonne load becomes 4 tonnes per pillar -
surely spreading the load reduces the overall load. This seems to add up
to
48 tonnes? This does show my complete lack of knowledge on this subject.

It is calculated on the centre pillars, which are loaded above average. I
also assumed 1.5m depth, giving a total water mass of about 24 tonnes. The
edge pillars will have only a small fraction of the worst case load.

Christian.