Author

Jia-Zeng Cao

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Nov 2026

Uncertainty Modeling and Risk Analysis of Mechanical Properties in Warm Frozen Clay for Frozen Soil Roadbed Stability

Ignoring the uncertainty of mechanical properties in frozen soil roadbed stability analysis may cause uneven settlement and cracking. Therefore, evaluating the uncertainty of frozen soil mechanical properties is essential for reliable engineering design. Considering that temperature fluctuations and limited sample data affect the estimation of true statistical characteristics, this study investigates the dependence between the strength and elastic modulus of warm frozen soil using copula theory. Uniaxial compressive strength and elastic modulus data of warm frozen clay from the Beiluhe test section of the Qinghai–Tibet Railway at different temperatures are first statistically analyzed, and their bivariate joint distribution models are established. Second, the model's ability to characterize the uncertainty of bivariate parameter data is analyzed. This serves to verify the feasibility of judging the optimal function based on N -fold cross-validation. Moreover, the performance of different copula types in capturing parameter dependence is compared, emphasizing the effect of temperature and sample size on correct function selection for warm frozen soil. Finally, the simulation capability of the model is evaluated by the proportion of simulated data within the confidence interval of safety values. The results provide reliable parameter support for stability analysis and risk assessment of frozen ground engineering.

Hao Li, Tao Wang, Guo-Qing Zhou et al. · International Journal of Geo... · 0 citations

Open access Aug 2026

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.

Jianqiang Zhang, Jia-Zeng Cao, Tao Wang et al. · Applied Sciences · 0 citations