Investigation on coal damage and fracture extension law of liquid nitrogen injection pre-cooling and fracturing under true triaxial stress

To more accurately describe the coal damage and fracture evolution law during liquid nitrogen (LN 2 ) fracturing under true triaxial stress, a thermal–hydraulic-mechanical-damage (THMD) coupling model for LN 2 fracturing coal was developed, considering the coal heterogeneity and thermophysical parameters of nitrogen. The accuracy and applicability of model were verified by comparing with LN 2 injection pre-cooling and fracturing experimental data. The effects of different pre-cooling times and horizontal stress ratios on coal damage evolution, permeability, temperature distribution, and fracture characteristics were analyzed. The results show that the permeability and damage of the coal increase exponentially, while the temperature decreases exponentially during the fracturing process. As the pre-cooling time increases, the damage range of the coal expands, and the fracture propagation becomes more pronounced. The initiation pressure and rupture pressure decrease and tend to stabilize with longer pre-cooling times. As the horizontal stress ratio increases, fractures preferentially extend along the direction of maximum horizontal principal stress, leading to a significant decrease in both initiation and rupture pressures. At a horizontal stress ratio of 3, the initiation pressure drops by 48.07%, and the rupture pressure decreases by 41.36%. The results provide a theoretical basis for optimizing LN 2 fracturing techniques and improving coal seam modification.