That would be a lot of steel. 100 meters of water is submarine territory. You need some thick walls to stem the radial pressure alone, probably at least 5 inches or 13 cm of steel (consider [0] and [1], this value also agrees with my intuition from engineering education). Assuming a barrel of 2 m radius and 3 m height (volume ~36 m³), that's 5 cubic meters (or 8 tons) of steel you'd need for the cylindrical hull alone, costing around 8000 USD in material [2] (varies wildly of course, but you're probably not using submarine grade steel). Per ~40 ton barrel. Would make about 40 million in steel costs alone for the number of barrels shown.

I have no idea what your air compression idea entails, but it doesn't sound more realistic. Concrete is pretty good at being stacked (source: look around you).

[0] http://www.madehow.com/Volume-5/Nuclear-Submarine.html

[1] https://en.wikipedia.org/wiki/Submarine_hull#Dive_depth

[2] https://www.wolframalpha.com/input/?i=steel+cost