Coal creep deformation and pore-fracture evolution under cyclic loading–unloading using NMRI and fractal analysis

Understanding the creep deformation behavior and the evolution of pore-fracture structures (FPSs) in coal under cyclic loading–unloading is crucial for safe extraction and efficient methane utilization. Coal samples were subjected to cyclic loading–unloading creep experiments using online Nuclear Magnetic Resonance (NMR) and Nuclear Magnetic Resonance Imaging (NMRI) techniques. The results revealed the significance of instantaneous plastic and viscoplastic strains during creep, with creep failure modes analyzed using NMRI data and macroscopic fracture distribution. Viscoplastic strain was identified as a key indicator of accelerated failure, and NMRI revealed a transition from splitting–shear to V-shaped shear failure under increasing confining pressure. From a microscopic perspective, real-time T 2 spectra monitoring tracked the evolution of FPS at different loading levels, and the geometric mean of the pore structure ( T 2g ) quantitatively described the co-evolution of various pore types. A generalized model was developed to describe coal creep under cyclic loading–unloading, integrating microscopic and macroscopic deformation features and refined using fractal theory. These findings provide theoretical insights and practical guidance for coal extraction and methane management under cyclic loading–unloading creep.