Could be used in abandoned mine-shafts.
In theory could be combined with geothermal energy. If you are going to drill a very deep hole of several kilometers anyway, you might as well make it wider and apply a massive concrete or iron “piston” of several tens of meters high and a few decimeter in diameter.
Example: borehole 2 km, diameter 50 cm. Use 10 cm for geothermal, leaving 40 cm. Length piston 30 m. Volume: that’s about 4 m3.
Density concrete: ca. 2.4 ton/m3
Density steel: ca. 8.0 ton/m3
Price steel: $700/ton
We’ll take steel.
Weight of our steel cylinder: 32 ton or $24,000
Energy storage capacity: mgh = 32,000 x 10 x 2,000 J = 640000000 J = 178 kWh
That’s surprisingly little. That’s 4 times the amount of the chemical energy in a car battery.
On an industrial scale we have already battery storage prices of $100/kWh or $17,800 for our 178 kWh “gravitricity”.
Gravitricity is a bad idea and has a 19th century coal mine smell about it.
For seasonal storage of energy, the last remaining missing link to guarantee a total victory of renewable energy, the solution will be either chemical energy storage (like hydrogen) or storage of heat in large water volumes or perhaps CAES.