Closed‐form stress solution and minimum safe burial depth correction for shallow‐buried large‐diameter energy storage chambers

Abstract

Shallow‐buried hard rock compressed air energy storage (CAES) chambers face critical safety risks due to gravity gradient and free surface effects, which are neglected by classical deep‐tunnel theories. This study proposes a modified closed‐form solution for the stress field around a circular shallow CAES chamber, explicitly incorporating the free surface effect, lateral pressure effect, and gravity gradient effect. Validated against ABAQUS simulations with a relative error below 5%, the modified solution accurately captures the distinct stress reduction at the crown or upper arch, which is a feature missed by both the Kirsch and Mindlin solutions. The solution further reveals that the location of minimum hoop stress shifts from the sidewall to the crown or upper arch as the relative burial depth Λ  =  d / r _i decreases, depending on the lateral pressure coefficient. Based on this, a closed‐form approximate corrected minimum safe burial depth formula (SBD‐Min‐AC) is derived, showing that conventional designs underestimate required depth by up to 17% for large‐diameter chambers. With this accuracy confirmed, the proposed solution offers sufficient reliability for preliminary engineering assessment while requiring only routinely available geological and design parameters. The proposed framework, therefore, offers an engineering‐ready analytical tool for the preliminary design and site selection of shallow CAES chambers.