Accurate characterization of the joint influence of crack initiation position and groundwater is pivotal for the assessment and prediction of uplift stability in compressed air energy storage (CAES) caverns. Existing analytical models for cavern uplift failure generally do not incorporate these two factors concurrently, thereby leaving a theoretical gap. This study presents a rigorous limit analysis framework for evaluating uplift failure in circular rock caverns for CAES, with explicit consideration of crack initiation positions and the influence of groundwater. By integrating the Hoek–Brown (H–B) criterion and the upper-bound limit analysis, analytical solutions for the crack initiation angles \(\beta\) and limit internal pressure \(p_{{\text{u}}}\) are derived. Numerical validation via OptumG2 confirms the model’s superior accuracy. Parametric analysis reveals that the H–B material constants ( \(A\) , \(B\) ) and the uniaxial compressive strength of rock \(\sigma_{{\text{c}}}\) exert the most pronounced influence on \(f(x)\) , \(\beta\) , and \(p_{{\text{u}}}\) ; cavern burial depth \(H\) and radius \(R\) constitute secondary influences; while the pore water pressure coefficient \(r_{{\text{w}}}\) , groundwater table coefficient \(\eta\) , and the rock mass unit weight \(\gamma\) exert minor effects. In situ stress ratios ( \(\lambda > 1.2\) ) correlate with crack initiation near the cavern spring line, requiring 1.38–3.36 times higher \(p_{{\text{u}}}\) compared to crown–initiated failures under the coupled influence of \(A\) and \(B\) . A detailed, engineering-oriented set of design charts is provided to support preliminary design and rapid verification. The analytical solution provides a theoretical basis for anti-uplift stability assessment of high-pressure circular CAES caverns.
