In order to address the safety construction issues of tunnels in karst areas, this study investigated the stability and instability time prediction of the roof of karst tunnels based on catastrophe theory. By establishing a discrimination equation for the sudden instability of the tunnel roof arch based on the elastic beam model and considering factors such as the self-weight of surrounding rocks and the position of caves, the calculation formula for the safety thickness of the roof of the karst tunnel was obtained. The study analyzed the impact of relevant factors on the safety thickness of the roof. Furthermore, a new method for predicting the instability of the tunnel roof arch was proposed, and it was validated through engineering examples. The results indicate that the water pressure in caves, the size of caves, the elasticity modulus of surrounding rocks, and the position of caves have extremely adverse effects on the safety of the arch roof. The calculation formula for the safety thickness of the roof of the karst tunnel derived from the theory of sudden change demonstrates feasibility and high accuracy in practical engineering applications. The established model for predicting roof instability can effectively forecast the time of roof arch instability in karst tunnels.

In this study, an experimental equipment is designed to simulate the mechanical boundary conditions of shield tunnels and test samples that exhibit varying degrees of initial damage fabricated through low-energy impact experiments. The fatigue damage characteristics of the initially damaged segments are examined under multistage cyclic loading. A comprehensive analysis of dynamic strain, mean strain, and strain amplitude time–history curves is conducted to derive damage evolution curves based on the degradation of elastic modulus. The average damage evolution rate is evaluated from these curves. The findings reveal that both initial damage and load level significantly influence segment performance evolution, potentially increasing the damage evolution rate by tenfold or more. Importantly, the results highlight a “memory effect” in damage evolution and identify a critical threshold that distinguishes between “stable” and “accelerating” damage evolution stages. Exceeding this threshold results in a substantial acceleration of the damage evolution rate, ultimately leading to failure. This research introduces the innovative concept of a stable damage limit and underscores the crucial role of initial damage in the nonlinear strain development of segmented concrete, providing valuable insights for improving fatigue design strategies in structural concrete elements.