Machine Learning-Based Prediction of Fracture Toughness of ISRM-Recommended CCNBD Rock Specimens Using ANN and Metaheuristic Optimizations

Accurate determination of rock Type-I fracture toughness ( K IC ) is crucial in geomechanics applications involving brittle or quasi-brittle rock fracturing. However, direct laboratory determination of K IC is often costly and time-consuming, while empirical and analytical approaches tend to over- or underestimate its value. Therefore, developing practical and cost-effective alternatives for K IC prediction is essential. This study employs machine learning (ML) techniques, including Levenberg-Marquardt algorithm-trained artificial neural network (ANN-LM), white shark optimization-tuned ANN (ANN-WSO), black widow optimization algorithm-tuned ANN (ANN-BWOA), and arithmetic optimization algorithm-tuned ANN (ANN-AOA), to predict K IC of chevron-notched cracked Brazilian disc (CCNBD) granite specimens. A dataset of 250 experimental results, comprising tensile strength and test specimens' geometrical parameters (radius, thickness, dimensionless thickness, dimensionless initial crack length, and final crack length), was used as input for model training. Six performance metrics, including the correlation coefficient (R), mean square error (MSE), root mean square error (RMSE), relative RMSE (RRMSE), mean absolute error (MAE), and variance accounted for (VAF), were employed to evaluate model performance. The cosine amplitude method (CAM) was used for input sensitivity analysis. Among the developed models, the ANN-LM 6-7-1 model demonstrated the highest prediction accuracy across training and testing datasets and was subsequently converted into a closed-form expression to enhance its interpretability and facilitate broader application. CAM analysis revealed tensile strength as the most influential parameter in K IC prediction. This research presents a reliable, efficient, and scalable methodology for predicting the K IC of CCNBD granite specimens, providing a practical alternative to traditional testing techniques across diverse geomechanical applications. • An ML method utilizing artificial neural networks (ANN) and metaheuristic optimization algorithms is introduced to estimate the Type-I fracture toughness ( K Ic ) of ISRM-standard CCNBD rock samples. • Model development was based on a comprehensive dataset comprising 250 laboratory-measured CCNBD specimens with six input parameters. • Geometrical properties, crack or notch characteristics, and geomechanical parameters of the rock specimens were utilized as model inputs. • The most accurate architecture was transformed into a clear and explicit mathematical expression to facilitate user-oriented execution, replication, and large-scale application. • The influence of individual predictor variables on K Ic was quantitatively assessed using the cosine amplitude method (CAM).