Prediction of Mixed-mode I and II effective fracture toughness of several types of concrete using the extreme gradient boosting method and metaheuristic optimization algorithms

Complex sample preparation procedures, the necessity for highly accurate and sensitive in-struments, early sample failure, and brittle samples all contribute to the difficulty of measurement of concrete fracture toughness (CFT) in the laboratory. With such limitations on the measuring CFT, it is necessary to develop new and more effective tools. Machine learning (ML) methods are promising tools for non-linear time series prediction. In this study, six extreme gradient boosting (XGBoost)-based meta-heuristic algorithms, including standard XGBoost, XGBoost-particle swarm optimization (PSO), XGBoost-imperialist competitive algorithm (ICA), XGBoost-grey wolf opti-mization (GWO), XGBoost-shuffled frog leaping algorithm (SFLA), and XGBoost-genetic algo-rithm (GA) were developed to predict the effective fracture toughness (K_eff) of concrete, utilizing 560 datasets obtained from the central straight notched Brazilian disc (CSNBD) test. Additives of micro silica and powdered stone, which are the most widely used building materials were used in the concrete samples to investigate their effect on the physical and mechanical properties. Therefore, 10 different materials made from a combination of concrete and different percentages of additives, were used in the experiment. The datasets included six input parameters effective on the K_eff, including concrete type (ST), diameter (D), thickness (t), length (L), force (F), and crack angle (alpha). The XGBoost-based models' performances were compared with those of each other and with four other ML methods of Gaussian process regression (GPR), decision trees (DT), support vector regression (SVR), and K-nearest neighbors (KNN). The ML models' performance in the prediction of K_eff for both holdout and 5-fold methods from high to low is XGBoost-PSO, XGBoost-ICA, XGBoost-GWO, XGBoost-SFLA, XGBoost-GA, XGBoost, GPR, SVR, DT, and KNN. Considering the datasets utilized in this research, the feature selection method's sensitivity analysis revealed that, except for the parameter D, all other parameters considered in this study, significantly affect the K_eff. By developing the meta-heuristic methods, the ability of the XGBoost-based methods was significantly improved. Finally, this article recommends using the XGBoost-PSO hybrid model to predict the K_eff. This work's significance is that it allows geotechnical engineers to accurately estimate the K_eff of different types of concrete. In this way, the high time and cost required for the CSNBD test can be eliminated.