Abstract:In order to analyze the stability of the roof, the reliability theory and the theory of elasticity are used to construct the limit equilibrium equation of the empty roof. At the same time, the SPSS software is used to statistically analyze the relevant mechanical parameters obtained from the indoor rock mechanics test, and the probability distribution type and mathematical value are obtained. Using Mtlab software to obtain random numbers for Monte Carlo simulation, the probability of roof instability and reliable indicators are obtained. Applying it to a gold mine, the results show that the roof of the goaf of the gold mine is currently in a reliable state; Finally, using FLAC<sub><sup>3D</sup></sub> software to analyze the distribution of stress, displacement and plastic zone in the goaf, it shows that the roof is in a stable state as a whole, which verifies the correctness of theoretical calculation.
