Predicting mode-I fracture toughness of rocks using soft computing and multiple regression

Mode-I fracture toughness (FT) is an important property to model fracture propagation in rocks and it has wide application in a plethora of rock mechanics problems such as hydraulic fracturing design, tunneling, geothermal energy extraction, CO2 sequestration, blasting and drilling activities, well-bore stability analysis etc. Determination of fracture toughness from different individual index geomechanical properties is an ongoing research area. Multiple past research have established simple regression relations between FT and individual mechanical parameters with various degree of success. But these were found to be rock and site specific and lack wide acceptance. In this paper, multiple regression analysis, and three types of soft computing methods (e.g. artificial neural network, fuzzy inference system, and adaptive neuro-fuzzy inference system) have been employed to predict mode-I fracture toughness from a set of common geomechanical properties. Based on Pearson's correlation coefficient, three index geomechanical properties, namely, tensile strength, P-wave velocity, and S-wave velocity were chosen to estimate the mode-I FT. As the results suggest, a single model is sufficient to estimate FT in all the sedimentary and crystalline rocks. Such model is capable of predicting fracture toughness irrespective of strength or compositional heterogeneity that is encountered in field. Statistical analysis of the predictions using correlation coefficient (R-2), root mean square error (RMSE), mean absolute percentage error (MAPE), and variance accounted for (VAF) show that all the soft computing methods performed better than the multiple regression models. However, among the soft computing methods, adaptive neuro-fuzzy inference system, which incorporates elements of both the artificial neural network and fuzzy inference system, constructs the best model for prediction. This is the first ever reported instance, where soft computing has been used to predict mode-I fracture toughness of dry rocks from the mechanical properties, and the results confirmed that this is an easier, efficient but highly accurate tool for prediction.