Analytical Design and Stability Evaluation of 3D Seepage-Control Curtains for Deep Mine Shafts Under Extreme Hydrostatic Pressures

Mitigating catastrophic groundwater inrush hazards in deep underground engineering remains a challenge due to extreme hydrostatic pressures and complex hydrogeological conditions. To address this issue, this paper proposes an optimized analytical design methodology for three-dimensional (3D) seepage-control curtains in deep shafts. Structurally, the 3D system is decoupled into independent horizontal and vertical components. The required thickness of each component is conceptualized as the sum of a blasting-influenced zone and a stress-influenced zone. To ensure hydro-mechanical safety, the stress-influenced thickness is rigorously determined by evaluating both a seepage-based theoretical model and an elasto-plastic mechanical model, with the maximum value adopted as the design criterion. When applied to the 545 m deep main shaft of the Lianhuashan Phosphate Mine, the proposed dual-control model yields optimized thicknesses of 14 m and 20 m for the vertical and horizontal curtains, respectively, achieving a robust anti-heave safety factor of 1.90 under a confined water pressure of 4.46 MPa. The analytical design is successfully benchmarked and validated using 3D hydro-mechanical coupled numerical simulations based on Biot’s poroelasticity theory. Furthermore, multi-parameter sensitivity analyses reveal critical mechanical singularities, defining the strict physical capacity limits of the system. The theoretical derivations demonstrate a distinct functional divergence: the vertical curtain acts as a seepage-governed bottleneck highly sensitive to hydro-mechanical variations, whereas the horizontal curtain functions as a highly redundant, strength-governed structural plug. This comprehensive methodology provides essential theoretical insights and quantitative guidelines for effective groundwater hazard mitigation in deep-earth environments.