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.