The safety associated with the bearing capacity of pile foundations is intrinsically linked to the overall safety, stability, and economic viability of structural systems. In response to the need for rapid and precise predictions of pile bearing capacity, this study introduces a kernel extreme learning machine (KELM) prediction model optimized through a multi-strategy improved beetle optimization algorithm (IDBO), referred to as the IDBO-KELM model. The model utilizes the pile length, pile diameter, average effective vertical stress, and undrained shear strength as input variables, with the bearing capacity serving as the output variable. Initially, experimental data on pile bearing capacity was gathered from the existing literature and subsequently normalized to facilitate effective integration into the model training process. A detailed introduction of the multi-strategy improved beetle optimization algorithm (IDBO) is provided, with its superior performance validated through 23 benchmark functions. Furthermore, the Wilcoxon rank sum test was employed to statistically assess the experimental outcomes, confirming the IDBO algorithm’s superiority over other prevalent metaheuristic algorithms. The IDBO algorithm was then utilized to optimize the hyperparameters of the KELM model for predicting pile bearing capacity. In conclusion, the statistical metrics for the IDBO-KELM model demonstrated a root mean square error (RMSE) of 4.7875, a coefficient of determination (R²) of 0.9313, and a mean absolute percentage error (MAPE) of 10.71%. In comparison, the baseline KELM model exhibited an RMSE of 6.7357, an R² of 0.8639, and an MAPE of 18.47%. This represents an improvement exceeding 35%. These findings suggest that the IDBO-KELM model surpasses the KELM model across all evaluation metrics, thereby confirming its superior accuracy in predicting pile bearing capacity.

The hydrothermal properties of black soils in seasonal frozen regions are more complex during the freezing process. In the context of the freezing and thawing cycles of black soil within seasonal freeze–thaw regions, there is a limited application of mathematical models to characterize the interplay between water and thermal dynamics. Therefore, existing models for analyzing water and heat in black soil in seasonal frozen regions may not be applicable or accurate. The application of existing models to the water and heat problems of black soil in seasonal frozen regions is important and innovative. This study is grounded in Darcy’s law pertaining to unsaturated soil water flow and is informed by principles of mass conservation, energy conservation, and conduction theory. The research begins with the establishment of definitions for relative saturation and the solid–liquid ratio through mathematical transformations. Subsequently, a theoretical model is developed to represent the water–heat coupling in black soil, utilizing relative saturation and temperature as field functions. The model’s validity is confirmed through its integration with experimental data from a black soil freezing and thawing model test. Furthermore, the analysis delves into the distribution of the temperature field, water field, and ice content that arise from the phase change processes occurring during the freezing and thawing of black soil roadbed slopes. There is a theoretical basis for the prevention and control of disasters associated with black soil roadbed slopes in seasonal frozen areas.