A Probabilistic Framework for Hydraulic Stability Assessment of Unlined Pressure Tunnels and Shafts

Unlined pressure tunnels and shafts are widely employed in hydropower projects where the surrounding rock mass is required to sustain the internal water pressure. Their hydraulic stability is governed by complex interactions among the three-dimensional in situ stress state, discontinuity geometry, rock mass properties, and operational water pressure. Conventional deterministic design approaches address these factors implicitly and provide limited information on the likelihood of hydraulic failure mechanisms, such as hydraulic jacking, hydraulic fracturing, and shear slip of discontinuities. This paper presents a probabilistic framework for assessing the hydraulic stability of unlined pressure tunnels and shafts, in which the governing failure mechanisms are explicitly formulated as limit states and key sources of uncertainty are systematically represented. The full three-dimensional stress tensor is rotated onto potential discontinuity planes to evaluate effective normal and shear stresses, and reliability-based methods are employed to quantify probabilities of failure. The methodology is demonstrated through a representative case study of a failed unlined pressure tunnel reflecting typical geological and stress conditions encountered in hydropower projects. The results show that variability in stress orientation and discontinuity characteristics has a strong influence on hydraulic stability and that commonly used deterministic criteria may not fully capture the associated failure risk.