Prediction of Mode-I Fracture Toughness of the ISRM-Suggested Semi-Circular Bend Rock Specimen Using ANN and Optimized ANN Models

A great understanding of the fracture behavior of rocks is very important for ensuring the successful and efficient design, implementation, completion, and structural stability of important large-scale mining, tunneling, oil and gas, and civil engineering projects. This study employed four soft computing models of an artificial neural network trained using the Levenberg–Marquardt algorithm (ANN–LM), grasshopper optimization algorithm-optimized ANN (ANN–GOA), salp swarm algorithm-optimized ANN (ANN–SSA), and arithmetic operation algorithm-optimized ANN (ANN–AOA) to predict the Mode-I fracture toughness (K_Ic) of rock. For this purpose, a database comprising 121 experimental datasets obtained from the K_Ic test on a semi-circular bend (SCB) rock samples were used to train and validate the models. Four important parameters affecting K_Ic, namely, the uniaxial tensile strength, disc specimen radius and thickness, and notch or crack length, were selected as the input parameters. The ANN–GOA 4-9-1 model was adjudged to be the optimum of the generated K_Ic models as determined by the error metrics used to evaluate model performance. The ANN–GOA 4-9-1 had the lowest error metrics and highest coefficient of correlation for the overall dataset, with R = 0.98498, MSE = 0.0036, VAF = 97.02%, and a20-index = 0.96694. To ensure easy implementation of the optimum ANN–GOA 4-9-1, the model was transformed into a tractable closed-form explicit equation. Furthermore, the impact of each of the four K_Ic effective parameters on predicted K_Ic is evaluated and the Brazilian tensile strength and rock specimen radius are determined to be the most sensitive parameters to K_Ic. Hence, the proposed models can provide a robust and functional reliable alternative to the laborious and costly experimental method for the determination of K_Ic of rocks.