Machine learning models for predicting rock fracture toughness at different temperature conditions

The rock fracture toughness (RFT) is significantly influenced by thermal treatments. Accurate evaluation of RFT at different temperatures holds great importance in the fields of geotechnical engineering. Current analytical and empirical models, based on our current but incomplete understanding of the fracture mechanics theory, are unable to produce a priori predictions of RFT. As a result, researchers have to rely on experiments, which are often costly and time-consuming, to understand external environment, internal factors and RFT links in rocks. This research explores the potential of employing machine learning (ML) models as an effective approach to address such challenges. Six ML models are presented, including support vector machine (SVM), random forest (RF), back propagation neural network (BPNN), back propagation-particle swarm optimization (BP-PSO), convolutional neural network (CNN), and radial basis function neural network (RBF). These models are applied using a dataset of 297 samples derived from previous studies involving semi-circle bend tests. The dataset encompasses 15 input variables, including sample radius, sample thickness, notch length, support span, inclination angle of the notch, tensile strength, uniaxial compressive strength, density, quartz content, feldspar content, gypsum content, clay content, other minerals, loading rate, and temperature. The results of three statistical metrics (root mean square error (RMSE), coefficient of determination (R2), and mean absolute error (MAE)) confirm that the ML models are able to predict the temperature-dependent RFT in modes I, II and III with high accuracy. The results demonstrated that the SVM model shows a better performance than the other five models. In the case of testing dataset, the RMSE, MAE and R2 values for SVM model are 0.1122 MPa·m1/2, 0.0829 MPa·m1/2 and 0.9506, respectively. Additionally, feature importance analysis highlights that the temperature and inclination angle are the most influential variables affecting the RFT.