Assessment of Soil Structural Stability of Coal Mine Roof Using Multidimensional Elliptical Copula and Data Augmentation

Roof instability in coal mines is one of the primary causes of mining disasters, casualties, and environmental damage. Accurately assessing its reliability is crucial for achieving safe production and sustainable development in coal mining. Based on 192 small measured samples from multiple domestic coal mines (including Anhui, Shanxi, Shaanxi, and Inner Mongolia), this study constructs multidimensional Gaussian Copula and t Copula models to characterize the complex correlation structure of mechanical parameters. The hybrid adaptive multi-method data augmentation (HAMDA) method with three distinct weighting strategies is proposed. Through Monte Carlo Simulation (MCS), systematic reliability assessments are conducted for different roof locations. The results indicate that multidimensional elliptical Copulas effectively simulate the correlation structure of highly variable multidimensional coal mine roof mechanical parameters. Roof system instability is primarily triggered by failure in the bottom zone, accompanied by sidewall instability in approximately 60% of cases, while the top zone remains relatively secure. This provides crucial insights for optimizing support design. The HAMDA method significantly overcomes the limitations of small sample data, with its expanded statistical characteristics closely matching measured data. Failure probability estimates vary across different HAMDA schemes: conservative programs may underestimate risks, while diverse programs tend toward conservatism in lateral zones. These results provide theoretical support for refined roof support design in coal mines, holding significant theoretical and practical value for advancing safety, environmental sustainability, and sustainable development in the coal industry.