Tail Risk Assessment of Coal Mine Roof Instability Under Small-Sample Constraints Based on D-Vine Copula and TVAE Modeling

Ensuring the stability of coal mine roofs is a critical technical prerequisite for safe underground operations and the structural stability of underground engineering systems in mining areas. However, roof instability is governed by the variability and dependence structure of multiple geotechnical parameters, including elastic modulus, Poisson ratio, cohesion, and internal friction angle. To address the challenges of insufficient modeling accuracy for multivariate joint distributions and the difficulty of tail-risk assessment under small-sample constraints, this study proposes reproducible data generation methods using the D-Vine Copula and Tabular Variational Autoencoder (TVAE) for assessing the reliability risk of coal mine roof structures from multiple sources. Based on 192 sets of measured data, the performance of both methods in simulating the multivariate joint distribution of geotechnical parameters is systematically compared. The results indicate that the key geotechnical parameters of the coal mine roof exhibit pronounced non-normal marginal distributions, nonlinear inter-variable dependence, and sparse data coverage in high-value regions. Both simulation methods are capable of effectively characterizing the asymmetric dependency structures among the parameters. Nevertheless, D-Vine Copula exhibits considerable statistical uncertainty in tail parameter estimation, resulting in substantial extrapolation of simulation samples for elastic modulus and cohesion. In contrast, TVAE provides a more robust statistical basis than the Copula approach for tail risk assessment under extreme parameter combinations. The proposed methodology offers a critical data foundation for stability analysis in complex geological conditions, thereby supporting disaster prevention and providing a reliable engineering basis for the structural design and risk control of underground mining systems.