Deformation Estimation and Failure Probability Analysis of Non-Circular Tunnels

Inherent defects in engineering rock masses inevitably lead to randomness in mechanical parameters and uncertainty in tunnel deformation and failure. To address these challenges, this study proposes a novel coupled analysis method that integrates complex function theory, physical model testing, and Monte Carlo simulation (MCS) for the deformation estimation and failure probability analysis of non-circular tunnels. Theoretically, this method provides a high-speed, high-accuracy analytical framework that overcomes the limitations of purely numerical approaches, particularly in handling continuous–discontinuous failure processes. Practically, it enables a more reliable and efficient stability assessment of tunnel systems under uncertain geological conditions. The proposed method is applied to a traffic tunnel at the Baihetan Hydropower Station. A series of uniaxial compression tests on 40 rock specimens are conducted to obtain statistical distributions of rock deformation parameters. An analytical solution for tunnel displacement is derived using plane elastic complex function theory, and the random displacement field is estimated via MCS. Physical model tests reveal that the elastic stage accounts for 83% of the overload failure process, based on which an elastic limit displacement function is established for tunnel arch settlement and surrounding rock convergence. The failure probability of the tunnel is then calculated, and the effects of the mean, coefficient of variation, and cross-correlation coefficient of rock deformation parameters on failure probability are discussed. The entire computational process is characterized by high speed and precision, offering a new and practical tool for tunnel stability evaluation and reliability-based design.