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.

Artificial ground freezing technology is the most important construction method of complex water-bearing soft clay rock. The thermodynamic properties of soft clay rock are important evidence for the design and construction of space resources development, and the variable hydrothermal parameter can directly affect the uncertain thermodynamic properties of soft clay rock. In this work, an array of field experiments on the soft clay rock are carried out, and the anisotropic spatial variations of hydrothermal parameters of soft clay rock are obtained. The statistical variability characteristics of variable hydrothermal parameters are estimated. A stochastic coupling model of soft clay rock with heat conduction and porous flow is proposed, and the uncertain thermodynamic properties of soft clay rock are computed by the self-compiled program. Model validation with the experimental and numerical temperatures is also presented. According to the relationship between anisotropic spatial variations and statistical variability characteristics for the different random field correlation models, the effects of the autocorrelation function, coefficient of variation, and autocorrelation distance of variable hydrothermal parameters on the uncertain thermodynamic properties of soft clay rock are analyzed. The results show that the proposed stochastic analysis model for the thermal characteristics of soft clay rock, considering the spatial variability of frozen soil layers, is scientifically reasonable. The maximum standard deviation of average thickness is 2.33 m, and the maximum average temperature is 2.25 °C. For the autocorrelation function, the most significant impact comes from DBIN. For the coefficient of variation, the most significant impact comes from thermal conductivity. Different variations of hydrothermal parameters have different effects on the standard deviation of soft clay rock temperature. The biggest influence is the thermal conductivity, while the lowest influence is the specific heat capacity.