Document Type : Original Research Paper


1 Department of Geology, Yazd University, Yazd, Iran

2 Mining and Metallurgical engineering department of Yazd University, Yazd, Iran

3 Department of Petroleum Engineering, University of North Dakota, North Dakota



In this work, the machine learning prediction models are used in order to evaluate the influence of rock macro-parameters (uniaxial compressive strength, tensile strength, and deformation modulus) on the rock fracture toughness related to the micro-parameters of rock. Four different types of machine learning methods, i.e. Multivariate Linear Regression (MLR), Multivariate Non-Linear Regression (MNLR), copula method, and Support Vector Regression (SVR) are used in this work. The fracture toughness of mode I and mode II (KIC and KIIC) is selected as the dependent variable, whereas the tensile strength, compressive strength, and elastic modulus are considered as the independent variables, respectively. The data is collected from the literature. The results obtained show that the SVR model predicts the values of KIC and KIIC with the determination coefficients (R2) of 0.73 and 0.77. The corresponding determination coefficient values of the MLR model and the MNLR model for KI and KII are R2 = 0.63, R2 = 0.72, and R2 = 0.62,0.75, respectively. The copula model predicts that the value of R2 for KI is 0.52, and for KII R2=0.69. K-fold cross-validation testing method performs for all these machine learning models. The cross-validation technique shows that SVR is the best-designed model for predicting the fracture toughness mode-I and mode-II.