Analytical solutions of stress field around lined rock caverns with yieldable concrete lining subject to high internal pressure and non-hydrostatic geo-stress field

This study develops an analytical framework for the stress field around Lined Rock Caverns (LRCs) for compressed air energy storage, subjected to high internal pressure and non-hydrostatic geo-stress. The model incorporates the yielding of concrete lining and the unique stress states of both lining and rock mass. Elastoplastic solutions were derived by combining the Mohr-Coulomb yield criterion with the equilibrium equation. Critical internal pressures for the yielding initiation of the concrete lining and the rock mass were formulated. The results reveal that under a non-hydrostatic geo-stress field, these critical pressures vary circumferentially. Designs based solely on hydrostatic assumptions underestimate the required pressure capacity along the major geo-stress direction, posing a failure risk. Concrete lining yielding significantly increases the radial stress transferred to the rock mass, an effect amplified by thicker linings. The stress transfer coefficient (interface radial stress to internal pressure ratio) decreases with lining thickness, friction angle, cohesion, and elastic modulus, but increases with internal pressure. Furthermore, elastic stress solutions were derived using the superposition principle, and an expression for the critical horizontal geo-stress inducing rock mass yielding during excavation was established. This work provides a crucial theoretical basis for the design and safety assessment of high-pressure LRCs.