Enhancing shear strength predictions of rocks using a hierarchical ensemble model.

Shear strength (SS) parameters are essential for understanding the mechanical behavior of materials, particularly in geotechnical engineering and rock mechanics. This study proposes a novel hierarchical ensemble model (HEM) to predict SS parameters: cohesion ( ) and angle of internal friction ( ). The HEM addresses the limitations of traditional machine learning models. Its performance was validated using leave-one-out cross-validation (LOOCV) and out-of-bag (OOB) evaluation methods. The model's accuracy was assessed with R-squared correlation (R), absolute average relative error percentage (AAREP), Taylor diagrams, and quantile-quantile plots. The computational results demonstrated that the proposed HEM outperforms previous studies using the same database. The model predicted and with R values of 0.93 and 0.979, respectively. The AAREP values were 1.96% for φ and 4.7% for . These results indicate that the HEM significantly improves the prediction quality of and , and exhibits strong generalization capability. Sensitivity analysis revealed that σ_3maxσ3max (maximum principal stress) had the greatest impact on modeling both and . According to uncertainty analysis, the LOOCV and OOB had the widest uncertainty bands for the and parameters, respectively.