Underground Pumped Hydroelectric Storage: A Feasibility Study

Thanks for asking. It's likely that the optimal design for a head height of a mile would use two stages. You would have an intermediate reservoir half a mile down. Reversible, Francis-type pump-turbines would likely be used. https://en.wikipedia.org/wiki/Francis_turbine

From my paper: " 8.1 PEPC Study: Two-Step Design with Reversible Pump-turbines The PEPC study’s optimized design called for single-stage reversible pump- turbines with identical layout and design. Each step consisted of three pump- turbine/motor-generator sets, each of 333-MW rating and each operating at 720 rpm under a nominal head of 762 m (2500 ft). With two steps combined, the overall nominal head was 1525 m (5000 ft). The study acknowledges that future technological development could significantly raise the head height or achieve the same head height in only one step. "

Or here is the original source for that info. Underground pumped hydroelectric storage Allen, R.D., Doherty, T.J., and Kannberg, L.D., for the Pacific Northwest Laboratory, sponsored by the United States DOE https://www.osti.gov/biblio/6517343