New models for estimating pure shear fracture toughness of confined quasi-brittle PTS specimens: Empirical and machine learning framework

This study aims to create further empirical and machine learning (ML) models for predicting KIIc using a dataset of 223 experimental tests, encompassing igneous, metamorphic, and sedimentary rocks. This study outlines an innovative dual-approach framework that integrates conventional regression analysis with advanced hybrid machine learning methodologies, addressing the significant disparity between the limitations of laboratory testing and the practical engineering necessities for predicting fracture toughness under confining pressure. Three machine learning models are utilized in conjunction with meta-heuristic optimizers to enhance the reliability of predictions. Empirical models, on the other hand, are more rapid and effective methods of performing brief engineering assessments. Regression analysis is used to derive empirical models that include geometrical, mechanical, and loading condition parameters. The results show that CatBoost, coupled with the CSA, demonstrated superior performance during testing (R² = 0.946, RMSE = 1.172, and MAE = 0.858), whereas the RIME associated with XGBoost presented strong generalization capabilities (R² = 0.932, RMSE = 1.295, and MAE = 1.012). The empirical models, although computationally efficient, achieved an R² value of 0.75 for the ideal nonlinear regression, demonstrating a 15.38% enhancement compared to linear methods (R² = 0.65) while providing practical resources for initial design calculations. This effectively bridges the gap between lab work and field work. The practical implications include enabling the reliable prediction of fracture toughness in deep excavation, hydraulic projects, underground mining operations, and geotechnical engineering, thereby supporting informed decision-making in complex geological environments without compromising design safety or project feasibility.