A stacking-based machine learning framework for predicting the unconfined compressive strength of frozen soil with missing data imputation

Abstract

In cold-region engineering and artificial ground freezing applications, the unconfined compressive strength (UCS, σ_m) and failure strain (ε_f) of frozen soil are critical mechanical parameters for design and analysis. However, precisely predicting frozen soil mechanical behavior under complex conditions remains a significant challenge. This study compiled a dataset of 1,346 unconfined compression test records for frozen soils and addressed missing data via multivariate imputation by chained equations (MICE) utilizing a Random Forest (RF) algorithm. Leveraging Bayesian optimization (BO) and 10‐fold cross‐validation, we developed a stacked machine learning model combining three eXtreme Gradient Boosting (XGBoost) predictors for integrated classification and regression tasks. Compared to conventional empirical formulations, the proposed model demonstrates significant improvements in predictive accuracy for stress–strain curve types, σ_m, and ε_f. To enhance the model’s interpretability, we employed the SHAP (Shapley Additive Explanations) method to explain the impact of each feature on predictions. Furthermore, for scenarios with constrained data availability, two stacking models requiring fewer input features were constructed. Collectively, the stacking ensemble framework provides a robust and interpretable methodology for the accurate prediction of frozen soil mechanical properties under diverse and complex conditions.