Assessment method for determining rock brittleness based on statistical damage constitutive relations

The brittleness index of rocks is able to provide crucial guidance to the operation of the drilling and hydraulic fracturing. The definition and evaluation method of the rock brittleness has not yet been unified and standardized due to their diversity. We therefore develop an evaluation method of the rock brittleness based on statistical damage relation. A set of uniaxial compression tests on different rock samples are conducted, and corresponding experimental data is collected and analyzed. Then we establish piecewise damage constitutive models based on different combinations of statistical distribution functions, including power function distribution, Weibull distribution, lognormal distribution and logistic distribution. A new evaluation method of rock brittleness based on energy method and the piecewise statistical damage constitutive model is proposed, and the evaluation results show that the increase of damage variable of peak strain will undermine rock brittleness, and the mineral composition contents have influence on the brittleness of rocks. Comparison work between this proposed method and previous brittleness criteria shows that the brittleness index $B_{43}$ exhibits enhanced stability and consistency in rock brittleness. This study presents a novel method to studying rock brittleness, enhancing current evaluation methods and deepening our understanding of the rock index. Regarding practical application, some field operations involved with the process of drilling or fracturing lead the continuous damage evolution of rocks under loading conditions. The brittleness index from the proposed evaluation method is comparatively reliable and practical for on-site drilling and fracturing.