Study on Power-Law Singularity Precursory Characteristics of Catastrophic Failure of Deep Coal–Rock Under Real-Time Unloading

Deep coal–rock excavation under high stress may induce dynamic disasters. This study conducted real-time unloading tests on coal and sandstone using DIC and power-law singularity modeling. The results indicate that the evolution of strain rate consists of three stages; pre-catastrophe strain rate accelerates in a power-law manner (β→–1). Strain localization is the physical origin of singularity. Sandstone exhibits larger strain-rate amplitudes than coal, with distinct spatial distributions of β. These findings provide quantitative, lithology-sensitive precursory criteria for early warning of catastrophic instability in deep rock engineering. Compared with previous studies that applied power-law singularity analysis and DIC separately, mostly under quasi-static compression, the novelty of this work lies in (i) investigating the real-time drilling-unloading path of excavation on intact coal and sandstone specimens under high-stress holding conditions, (ii) combining the temporal power-law singularity analysis with a full-field strip-based strain-localization analysis to quantify both the temporal and spatial evolution of the singularity exponent β, and (iii) providing lithology-dependent β ranges as quantitative precursors. In summary, the study reveals the unloading mechanism and precursor characteristics of catastrophic failure in deep coal and sandstone excavation, providing valuable insights for failure analysis in deep geotechnical engineering.