Determining the Rock Brittle Index (BI) using multivariate regression (a case study)

Abstract

One of the geotechnical properties of rocks, which is particularly important in sensitive projects such as oil and gas extraction, nuclear waste disposal, and underground drilling, is their brittleness. Currently, here are no standards methods for direct measurement of rock brittleness. Different studies have used various indirect methods to predict rock brittleness index (BI). However, researchers have paid less attention to the prediction of BI using multivariate regression. Accordingly, this research has used the multivariate regression method to determine BI considering mechanical characteristics. Specifically, we sed uniaxial compressive strength (UCS), modulus of elasticity (E), pressure wave velocity (Vp), and shear wave velocity (Vs), and physical characteristics, including porosity (n) and density (ρ) to determine the BI. Statistical indicators, R square, results of ANOVA (Analysis of Variance) test, coefficients, beta statistics, and VIF were used in the first step to evaluate the regression relationships. Then, residual nalysis of each regression were performed. Finally, the correlation between the calculated and predicted BI values was investigated using each regression. The best results were obtained using UCS and E or UCS and Vs in the bivariate regression and UCS, E, and Vs in the three-variable regression. According to the results, increasing the number of variables in multivariate regressions leads to more accurate predictions of BI.