Elastoplastic analytical solutions for compressed air energy storage caverns under cyclic loading and unloading and non-hydrostatic in-situ stress

Compressed air energy storage (CAES) in hard-rock caverns involves excavation, support installation, first charging, and long-term cyclic charging and discharging. These engineering stages produce different elastoplastic mechanisms, especially under non-hydrostatic in-situ stress. A semi-analytical formulation is developed for a circular cavern under biaxial far-field stress. The solution distinguishes unloading-stage plasticity, an intermediate elastic state, and loading-stage plasticity, and derives the corresponding stress and displacement fields by combining the Kolosov–Muskhelishvili complex-variable elastic solution, the Mohr–Coulomb criterion, radial plastic equilibrium, and non-associated flow. Continuity of radial stress and displacement is enforced at the elastic–plastic (EP) interface, allowing excavation and pressurisation to be treated within one path-dependent formulation. The results show that the lateral pressure coefficient governs both plastic-zone extent and the direction in which yielding and deformation concentrate. Comparison between the loading-side Mohr–Coulomb shear threshold and the tensile cut-off pressure gives failure-initiation pressure envelopes for different confinement and strength conditions. A cyclic damage calculation is then used to estimate progressive degradation, residual displacement, and the maximum allowable operating pressure that considers accumulated damage during long-term operation.