Settlement analyses of foundation soils are very important for the investigation, design, and construction of buildings. However, due to complex natural sedimentary processes, soil-forming environments, and geological tectonic stress histories, settlement properties show obvious spatial variability and autocorrelation. Moreover, measurement data on the physical and mechanical parameters of building foundation soils are limited. This limits the accuracy of formation stability analyses and safety evaluations. In this study, a series of field tests of building foundation soils were carried out, and the statistical physical and mechanical properties of the clay strata were obtained. A random field method and copula functions of uncertain geotechnical properties with limited survey data are proposed. A dual-yield surface constitutive model of the soil properties and a stability analysis method for uncertain deformation were developed. The detailed analytical procedures for soil deformation and stratum settlement are presented. The reliability functions and failure probabilities of variable settlement processes are calculated and analyzed. The impact of the spatial variation and cross-correlation of geotechnical properties on the probabilistic stability of variable land subsidence is discussed. This work presents an innovative analysis approach for evaluating the variable settlement properties of building foundation soils. The results show that the four different mechanical parameters can be regressed to linear equations. The horizontal fluctuation scale is significantly larger than the vertical scale. Copula theory provides a powerful framework for modeling limited geotechnical parameters. The bootstrap approach avoids parametric assumptions, leveraging empirical data to enhance the reliability analysis of variable settlement. The variability parameter exerts a greater influence on land subsidence processes than the correlation structure. The failure probabilities of variable stratum settlement for different cross-correlations of building foundation soils are different. These results provide an important reference for the safety of building engineering.

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.