The differential distribution of original rock stress and stress concentration caused by the variation in coal seam depth in karst topography are critical factors influencing the selection of roof-cutting parameters. Based on this, this study explores a method to determine reasonable roof-cutting parameters by incorporating the characteristics of coal seam depth variation in karst mountainous areas. A mechanical model of the cantilever beam structure for roof cutting in gob-side entry retention (GSER) is constructed, and the critical values and reasonable ranges of roof-cutting height and angle under different burial depths are derived. Furthermore, the displacement and stress evolution characteristics of surrounding rocks in gob-side entry retention under different coal seam burial depths, roof-cutting heights, and roof-cutting angles within the reasonable range of roof-cutting parameters are analyzed. The results show that there is a positive correlation between roof-cutting height and tensile stress in the uncut portion of the main roof, while roof-cutting angle and coal seam depth are negatively correlated with tensile stress. From the perspective of impact, roof-cutting height has a greater impact than roof-cutting angle, followed by coal seam depth. As for the distribution characteristics of the reasonable roof-cutting parameter range, the fan-shaped area of reasonable roof-cutting parameters gradually decreases with increasing coal seam depth. Taking the geological conditions of Anshun Coal Mine as an example, when the burial depth increases from 350 m to 550 m, adjusting the roof-cutting height to 6 m, 7 m, and 8 m, respectively, and setting the roof-cutting angle at 10° can effectively achieve the stability of the surrounding rock in the GSER. The research findings can provide a scientific basis and engineering references for selecting roof-cutting parameters in mines with similar geological conditions.

Coalbed methane (CBM) development involves multiple interacting physical fields, and different coupling schemes can lead to distinctly different production behaviors. A thermo-hydro-mechanical model accounting for gas–water two-phase flow and matrix dynamic diffusion (TP-D-THM) is developed and validated, achieving an error rate below 10%. By embedding the numerically estimated reservoir physical parameters of the Qinshui Basin into the numerical model, multi-field couplings during CBM production, the evolution of physical parameters, and the depth-dependent effects on production characteristics were revealed. The main findings are as follows: The inhibitory effect of water on CBM recovery consistently exceeds the promoting effect of temperature. As burial depth expands, the inhibitory effect first diminishes, then intensifies, ranging from 19.73% to 28.41%, while the thermal promotion effect exhibits a monotonically increasing trend, fluctuating between 8.55% and 16.33% and stabilizing below 1000 m. Temperature and burial depth do not alter the trend in gas production rate. For equilibrium permeability, reproducing a decrease–increase–decrease rate pattern requires explicit inclusion of water and matrix-fracture mass exchange terms, which can explain why different scholars obtained varying gas production rate trends using the THM model. Matrix adsorption-induced strain is the primary control on permeability evolution, and temperature amplifies the magnitude of permeability change. The critical depth essentially reflects the statistical characteristics of reservoir petrophysical properties. A dimensionless critical depth criterion has been proposed, which comprehensively considers reservoir pressure, permeability, and a fractional coverage index. For burial depths ranging from 650 to 1350 m, the TP-D-THM model can be simplified to the gas-mechanical model accounts for matrix dynamic diffusion (D-HM) with an error below 5%, indicating that thermal and water effects nearly cancel each other.