Interpretable prediction of uniaxial compressive strength for diverse rock materials: a stacking ensemble approach

Abstract

Uniaxial compressive strength (UCS) is critical for geotechnical design, yet conventional testing is costly and empirical formulas fail to adequately capture inherent nonlinearities. This study proposes an interpretable predictive framework that combines a two-stage heterogeneous stacking ensemble with SHapley Additive exPlanations (SHAP) for UCS estimation. Using 459 multi-lithology rock samples, four input variables were selected: point load strength index, Schmidt hammer rebound (SHR) value, compressional wave velocity, and porosity. Bayesian optimization rigorously tuned four base tree-based algorithms (Random Forest, XGBoost, LightGBM, and CatBoost), and their outputs were fused by a meta-learner, with Linear, Ridge, and Lasso regressions systematically compared. The optimal Stacking-Lasso architecture achieved robust generalization ( R 2 = 0.76, MAE = 15.39 MPa, MAPE = 19.51%) and effectively mitigated overfitting risks inherent in single-model approaches. SHAP analysis revealed that at the meta-learner level, the base learner most sensitive to SHR exerted the greatest influence on the final ensemble prediction. Local dependence analysis further uncovered a nonlinear threshold enhancement effect arising from the synergistic interaction of extremely low porosity and high SHR. This work offers a physically interpretable engineering paradigm for intelligent rock strength estimation under complex geological conditions.