A novel energy evolution-based method for brittleness evaluation of shale considering the deformation and failure process

Accurate evaluation of shale brittleness is critical for optimizing hydraulic fracturing design and predicting well productivity in shale gas development. Current brittleness indices often fail to comprehensively characterize rock brittleness throughout the deformation and failure process. To address this limitation, a novel quantitative brittleness index, which combines energy evolution with fuzzy analytic hierarchy process (FAHP) and grey relational analysis (GRA), is proposed. First, the stress–strain curve is divided into four characteristic stages, and a brittleness sensitivity index ( BSI i ) is defined for each stage based on its energy characteristics. Subsequently, FAHP and GRA are employed to determine the weight of each BSI i , thereby mitigating evaluation subjectivity and improving discriminatory power. Finally, a comprehensive brittleness index is established through weighted normalization. Verification through uniaxial and triaxial compression tests on shale specimens from the Chang 7 shale of the Ordos Basin, as well as on the Garau shale of the Lurestan Basin and the Longmaxi shale of the Sichuan Basin, demonstrates that the proposed brittleness index accurately captures the reduction in brittleness with increasing confining pressure. Furthermore, a comparative analysis against nine established brittleness indices confirms that the proposed method not only achieves superior accuracy but also demonstrates stronger adaptability across varying confining pressures. This research is of great significance for optimizing hydraulic fracturing design and predicting shale gas well productivity.