The scales of fluctuation of uncertain thermal parameters are the key to evaluating the spatial variability of artificially frozen soil, and it can directly affect the thermal engineering analysis of artificial frozen walls. In this study, the thermal conductivity, heat capacity, and thermal diffusivity at different temperatures (from −2.0 °C to 0 °C) are tested. Then the vertical and horizontal scales of fluctuation for the uncertain thermal parameters are estimated on the basis of the spatial recurrence method, curve fitting method, and correlation function method. A computational formula of the oblique fluctuation scale for the uncertain thermal parameters is proposed, and the oblique fluctuation scale for different angles is calculated and analyzed. The results show that the scales of fluctuation of uncertain thermal parameters calculated by the three methods are slightly different. The oblique fluctuation scale is larger than the vertical fluctuation scale, but is smaller than the horizontal fluctuation scale. The scales of fluctuation of uncertain thermal parameters are varied, and it is related to the temperature, water content, density, and depth. The results of the scale of fluctuation of uncertain thermal parameters in different directions reflect the spatial variability of artificially frozen soil, which has important reference significance for stochastic thermal analysis of artificial frozen engineering.

Limited by the actual investigation of coal mine engineering, the measured data obtained are often based on small sample characteristics. How to probabilistically de-integrate the prior information to obtain meaningful statistical values has received increasing attention from geotechnical engineers. In this study, an optimal copula function identification method for multidimensional geotechnical structures of coal mine roofs under the Bayesian approach is proposed. Firstly, the characterization method of multidimensional roof parameter correlation structures is proposed based on copula theory, and 167 sets of measured data from 24 coal mines at home and abroad are collected to study the measured identification results using the Bayesian method. Secondly, Monte Carlo simulation is utilized to compare the correct recognition rates of the commonly used AIC criterion and the Bayesian approach under different correlation structures. Finally, the influencing factors affecting the successful recognition rate of the Bayesian approach are analyzed. The results show that compared with the traditional AIC criterion, the Bayesian approach has more marked advantages in correctly recognizing the multidimensional parameter structures of roofs, and the number of measured samples, the strength of correlation coefficients, and the prior information have a major effect on the correct recognition rate of the optimal copula function under different real copula functions. In addition, the commonly used Gaussian copula has a better characterization effect in characterizing the multidimensional parameter correlation structure of the coal mine roofs, which can be prioritized to be used as a larger prior probability function in the evaluation process.