Abstract: To investigate the stability of roof-pillar systems in deep goaf groups, a three-dimensional mechanical model of the roof-pillar system was established that accounts for the high in-situ stress and lateral stress. Based on the accelerated creep behavior of rock pillars, a second-order dynamic model incorporating time-varying stiffness and damping degradation was developed. Catastrophe theory was introduced to propose an instability catastrophe criterion for the roof-pillar system, and a normalized sensitivity analysis was conducted to reveal the differences in the effects of various influencing factors. The results indicate that the pillar support area ratio, pillar elastic modulus, and uniformly distributed roof load have significant effects on system stability. The proposed model was verified against a deep iron mine case. Within two months after excavation completion, the theoretically predicted roof displacement was 2.5 mm, close to the monitored value of 2.1 mm. The model predicted that the system would remain stable for 15 months, with the roof boundary conditions remaining intact when instability occurred. This study provides a theoretical basis for stability evaluation and disaster early warning of deep goaf groups.

Key words: catastrophe theory, rheological theory, system stability, three-dimensional mechanical model