Dynamic strain evolution and thermo–mechanical damage model of coal under liquid-nitrogen injection–warming process in true triaxial stress fields

During cryogenic fracturing of low-permeability coal seams, the combined effects of temperature gradients, injection pressure, and in situ stress govern the thermo–mechanical response and crack propagation of coal. To investigate these interactions, true triaxial LN2 fracturing experiments were conducted under five vertical stresses and five injection pressures using a self-developed cryogenic system. Temperature, strain, and acoustic emission (AE) signals were continuously recorded to capture thermo–hydro–mechanical–damage (THMD) coupling during injection and warming. Results show that vertical stress suppresses, while injection pressure enhances, cryogenic propagation, deformation, and AE activity. Compared with the lowest-stress condition (7.35 MPa), peak and cumulative thermal stresses decreased by 94.37% and 54.30% as vertical stress increased to 17.15 MPa. In contrast, relative to 1.0 MPa injection pressure, both quantities increased by 9.98 times and 10.97 times at 3.0 MPa. Dissipated energy exhibited similar patterns, decreasing by 91.16% under high stress but rising by 10.67 times with higher pressure. AE responses consistently displayed a “double-peak” during LN2 injection and a single-peak decay during warming; cumulative AE counts decreased with stress yet rose with pressure. Coal damage also showed opposing trends—reduced by 89.14% at high stress but increased by 75.80% at high pressure. A THMD-coupled strain model reproduced these behaviors with relative errors of 0.15%–8.48%. The results clarify LN2-induced cryogenic fracturing mechanisms under true triaxial conditions and provide a quantitative basis for optimizing waterless stimulation in coalbed methane recovery.