Effectively controlling the adsorption and desorption of coal and mine gas is crucial to preventing harm to the environment. Therefore, this paper investigated the adsorption of coal and methane molecules from the perspective of microscopic energy through Gaussian simulation. Gaussian 09W and GaussView 5.0 software were used to construct and optimize the molecular model of four different metamorphic coals, namely lignite, sub-bituminous coal, bituminous coal, and anthracite, and their adsorption structure with methane as well as the energy, bond length, vibration frequency, infrared spectrum, and other data on the optimal structure were obtained. The binding energy of coal molecules and methane from large to small was as follows: sub-bituminous coal (7.3696 KJ/mol), lignite (6.6149 KJ/mol), bituminous coal (5.2170 KJ/mol), and anthracite (4.9510 KJ/mol). The equilibrium distance was negatively correlated with the binding energy, and the molecular structure and position of coal largely determined the binding energy. Additionally, adsorption was more likely to occur between methane molecules and hydroxyl groups. Many new vibration modes were observed during the adsorption of coal and methane molecules. This paper is of practical significance, as studying the adsorption of coal and mine gas can prevent and control mine gas outbursts and ensure safe production.

Cyclic high-pressure gas impact is a promising waterless stimulation method for enhancing permeability in deep low-permeability coal seams. However, the nonlinear fracture evolution, cumulative fatigue damage, and coupled fracturing mechanisms during repeated gas impacts remain insufficiently understood. In this study, cyclic high-pressure gas impact tests were conducted on unconfined synthetic rock-like specimens under gas pressures of 5 MPa and 7.5 MPa. The macroscopic crack networks induced by repeated impacts were quantitatively characterized using digital image processing and box-counting fractal analysis. Ultrasonic P-wave velocity measurements were used to reconstruct the spatial evolution of internal damage after each impact, and an empirical Weibull statistical damage model was established to describe the nonlinear fatigue degradation process. In addition, two-dimensional LS-DYNA numerical simulations were performed to reveal the transient stress wave propagation and stress-field evolution during cyclic impacts. The results show that fracture propagation under cyclic gas impacts exhibits a distinct nonlinear pattern, characterized by slow early-stage damage incubation followed by rapid late-stage crack coalescence. The fractal dimension of the surface crack network increased markedly after repeated impacts, reaching a maximum of 1.51 under the 7.5 MPa condition. Ultrasonic damage analysis further indicates that, based on path-averaged evaluations, apparent damage is more pronounced near boundaries at the lower pressure, whereas higher pressure induces severe structural degradation along the central measurement paths, with a maximum damage value of 0.47. The combined experimental and numerical results suggest that the initial impacts generate transient stress waves and cumulative microcracking, thereby progressively weakening the rock matrix. This progressive degradation subsequently enables quasi-static gas wedging to drive macroscopic crack propagation and coalescence. These findings provide a preliminary phenomenological baseline for understanding cyclic gas-induced cracking, providing a preliminary basis for understanding waterless reservoir stimulation by cyclic gas impacts.