Increasing accuracy in predicting mode I fracture toughness of rock structures: a comparative analysis of the rock engineering system method

The investigation of crack initiation and expansion is vital for the stability of structures. The Mode I fracture toughness (K_Ic) of rocks is a key property used to predict crack propagation in tension and hydraulic fracturing. Various methods have been introduced to determine K_Ic, but results differ due to factors like sample dimensions, crack geometry, groove type, and loading conditions. The cracked chevron notched Brazilian disc (CCNBD) sample is commonly used in laboratory tests for its easy preparation. This study employs the rock engineering system (RES) technique to overcome the challenges of time-consuming and costly laboratory tests and the uncertainty in traditional methods (analytical, numerical, experimental, laboratory, regression). Using 88 CCNBD rock samples proposed by ISRM, input parameters include thickness of the disc specimen (B), uniaxial tensile strength (σ_t), initial crack length (α₀), radius of the disc specimen (R), crack length (α_B), and the length of the final crack (α₁). The RES-based model used 70 data points (80% of the dataset) for development, and 18 data points (20%) for evaluation. Regression analysis compared the performance of the RES method, using statistical indicators such as squared correlation coefficient (R²), mean square error (MSE), and root mean square error (RMSE) to measure accuracy. The RES-based method outperformed other regression techniques, demonstrating significantly enhanced accuracy. This highlights the effectiveness and superior performance of the RES method in estimating fracture toughness, particularly for CCNBD samples, showcasing its potential as a robust analytical tool.