Damage quantification and failure prediction of rock: A novel approach based on energy evolution obtained from infrared radiation and acoustic emission

Rock failure under external force is a process of energy conversion between the external environment and the rock system. This study aims to quantify rock damage and predict failure from an energy perspective. Infrared radiation (IR) and acoustic emission (AE) technologies were used to monitor the failure process of red sandstone during uniaxial loading experiments in real time. The energy evolution law during the rock failure process was analyzed. Based on the Stefan–Boltzmann law, a quantitative parameter, average cumulative radiation energy increment ($\Delta ACRE$), was proposed for IR indicators. A coupling mathematical model between elastic strain energy and $\Delta ACRE$ was derived. The correlation between cumulative AE energy and dissipated strain energy was also analyzed. Results reveal that the rock failure process can be divided into four stages according to energy evolution: compaction, elastic, elastic–plastic, and failure stages. The proposed $\Delta ACRE$ can serve as a basis for dividing these stages. A cubic polynomial relationship was found between $\Delta ACRE$ and elastic strain energy. AE cumulative energy and dissipated strain energy showed similar variation trends. Furthermore, based on $\Delta ACRE$, AE cumulative energy, and energy evolution theory, a failure prediction indicator ($IRAEER$) was proposed. This indicator can effectively identify precursor points of rock failure. A quantitative indicator for rock damage evolution under combined IR and AE action was created using $IRAEER$ as the characterization parameter of the rock damage variable, demonstrating high reliability. This research provides strong support for estimating rock states and guiding the design of rock engineering structures.