Post-earthquake performance recovery models for shield tunnels based on semi-Markov process: development and application

To address the complexity and uncertainty inherent in the post-earthquake damage state recovery process of shield tunnels, a method for establishing performance recovery models based on semi-Markov processes is proposed, enabling quantitative assessment of seismic resilience. Initially, a detailed questionnaire was designed for the post-earthquake restoration process of shield tunnels, targeting experts worldwide in the fields of tunnel design, construction, inspection, maintenance and reinforcement, to obtain expert opinions on post-disaster decision-making time, selection of restoration tasks and restoration time. The optimal probability distributions for decision-making time and the duration of various repair tasks were determined through probability density function fitting. Based on this, the mathematical expression of the seismic resilience model was derived by fully considering the uncertainties in the structural damage, decision-making time, and restoration time, and characterizing the post-earthquake restoration of the shield tunnel as a semi-Markov process of damage state transitions. Finally, the method was applied to the seismic resilience evaluation of shield tunnels, revealing the evolutionary patterns of resilience indices across varying seismic intensities. The study demonstrates that the more severe the damage to shield tunnels, the longer the post-earthquake decision-making and restoration time. Additionally, the increasing seismic intensity leads to a nonlinearly decaying resilience index of shield tunnels, showing an initial acceleration and subsequent deceleration in degradation rate, with a significant increase in uncertainty.