I do not know much about engineering this sort of things, but it seems to me that working against gravity is easier than working against elastic force (as you propose), because the force of gravity is independent of the amount of energy stored, while the elastic force depends on the amount on energy stored (when the air is already pressurized it is much harder to push in some new one). And in general I believe that it is more difficult to build a motor or a generator that are efficient independently of the force they have to work against/with.

Just random thoughts, though...

There are systems like that:

* old empty mine in Germany. They pump air into the mine and then heat it to get extra energy when letting it out.

* big underwater bags next to wind turbines. Wind turbine directly pumps air into nearby bags. When there is no wind, the air is used to rotate the same electric generator that the wind turbine uses.

Compressed air has been around for centuries, but:

""" While pumped hydropower storage has a charge/discharge efficiency of 70-85%, and chemical batteries reach 65-90%, the CAES plants in operation in Germany and the US have an electric-to-electric efficiency of only 40-42% and 51-54%, respectively """

http://www.lowtechmagazine.com/2018/05/history-and-future-of...

The disadvantage is that you have made a huge compressed air bomb in the event of failure. The concrete blocks would fail in a more local way by just falling down.

The compressed air would be located in deep inside abandoned mines. The volume and thus energy storage potential of such places is vast.

The idea has been around for decades, but no one has been able to really do it yet.

Rock isn't necessarily airtight more so in mines. A fractured host material for the ore is very desirable as it means less explosives and higher ore production numbers.

There are substantial thermodynamic challenges to scaling compressed air energy storage. You either need to perfectly insulate the pressure vessel or perfectly cool/heat the air as you compress/decompress it via passive radiators.

The compressed air systems anger the thermo gods though

Doesn't seem to have worked out so well for Lightsail Energy... http://energystoragesense.com/uncategorized/lightsail-anothe...

Think spent natural gas fields. Proven airtight, vast capacity.

This is an area of active and relatively promising research. Adibiatic heating and cooling is a concern.

It's definitely feasible IMHO:

http://www.lowtechmagazine.com/2018/05/ditch-the-batteries-o...

Compressed air storage is less efficient. I think practically they have an efficiency of about 50 %, due to thermal losses (e.g. compressing air creates heat).

Doesn't dropping a weight on a cable cause heat? What's the difference?

The article says that they can achieve an efficiency of 85 %. Which puts them in the ball park of hydro storage or lithium ion batteries. The problem with compressed air storage is that you are fighting with the fundamentals of thermodynamics i.e. compressing and decompressing air. The laws of thermodynamics try to ruin every good idea.