Prediction of the mechanical behaviour of rocks using a multi-model stacking fusion

Abstract

Rock materials exhibit complex mechanical responses due to their heterogeneity and anisotropy, while traditional stress–strain models can only partially describe their behaviour and encounter limitations in handling complex nonlinear relationships. This study proposes a multi-model stacking fusion framework integrating random forest, LightGBM, and Extreme Gradient Boosting with Bayesian optimisation for stress–strain relationship prediction across five rock failure stages. The Stacking ensemble framework relies on the noise resistance of random forest to address overfitting and integrates the advantages of Extreme Gradient Boosting and LightGBM in capturing complex feature interactions, effectively overcoming the poor generalisation of single models. A dual-validation scheme (five-fold out-of-fold cross-validation combined with an independent validation set) was employed to generate unbiased meta-features and robustly assess model generalisation. Selected meta-learners (linear model, Lasso, and ridge) further integrate these base learner outputs to more precisely capture the complex relationships of rock mechanical behaviour. The proposed framework was trained and validated using a dataset comprising over 218,000 data samples collected from sandstone and mudstone samples from the Yuanzigou coal mine. Taylor-diagram analysis demonstrated the Stacking ensemble framework's superior robustness and improved generalisation. The Stacking-Lasso hybrid model demonstrates outstanding predictive performance of stress–strain relationship with R² of 0.942 (pre-peak) and 0.931 (post-peak), alongside mean absolute error of 0.0128/0.0565, mean squared error of 2.54 × 10⁻⁴/5.0 × 10⁻³, mean absolute percentage error of 0.051, and root mean square deviation of 0.0138/0.0707 in pre- and post-peak regimes, respectively. SHapley Additive exPlanations feature importance analysis reveals that axial stress ( σ_z ) and confining pressure ( σ_x/y ) constitute the most dominant features controlling rock mechanical behaviour. Additionally, a visual interactive tool for the Stacking ensemble is developed based on PyQt, enabling data upload, model training and result visualisation. This study confirms the framework as an innovative, reliable reference for advancing digital and intelligent rock mechanics modelling.