Nonlinear Prediction and Reliability Evaluation of Mechanical Parameters of Warm Frozen Soil Subgrade Based on Limited Survey Data

Agaist the backdrop of global warming, extensive areas of permafrost are degrading into warm frozen soil, posing severe challenges to the safe operation of transportation infrastructure in frozen areas. The warm frozen soil exhibits extreme sensitivity to temperature fluctuations, with even minor variations inducing significant changes in its mechanical properties, thereby affecting the long-term stability and bearing capacity of subgrades and foundations. Accurately characterizing the nonlinear correlations among mechanical parameters of warm frozen soil under limited survey conditions holds critical importance for the reliable design and risk assessment of transportation infrastructure in permafrost regions. This study utilized 150 sets of measured data from the Beiluhe test section of the Qinghai–Tibet railway. Through statistical analysis of the elastic modulus and strength of 150 warm frozen soil samples at different temperatures, the joint distribution function of elastic modulus and strength values for warm frozen soil was established. The nonlinear relationship between elastic modulus and strength was constructed using eXtreme Gradient Boosting (XGBoost), enabling the reliability analysis of nonnormal mechanical parameters associated with warm frozen soil. Results demonstrate that the constructed two-dimensional joint distribution model quantitatively describes the positive correlation between elastic modulus and strength in warm frozen soil. Both parameters exhibit decreasing trends with rising temperatures. The XGBoost-based prediction method effectively learns the distribution characteristics of the sample space, controlling prediction errors below 3% at high confidence levels (above 90%), significantly outperforming traditional Copula methods. This approach provides an effective technical pathway for evaluating subgrade bearing capacity, optimizing design parameters for frozen subgrades, and conducting reliability analyses in degraded permafrost regions of the Tibetan Plateau. It holds significant engineering application value for enhancing the resilience and climate adaptability of transportation infrastructure in permafrost zones.