Damage and deformation control equation for gas-bearing coal and its numerical calculation method

• The effects of free and adsorbed gases in pores/cracks on crack evolution and coal deformation and failure.
• Numerical simulation and quantitative description of pores/cracks system of gas-bearing coal.
• The Spatial distribution and temporal evolution of cracks on the damage of coal.

The dual pore structure of coal and occurrence of gas adsorption make gas-bearing coal mechanical properties different from other non-adsorptive porous materials. Considering adsorbed-gas-induced swelling stress and erosion, and pore/fracture-induced damage and failure to coal skeleton, the new effective stress equation, damage deformation control equation and constitutive model for gas-bearing coal is established. Based on principle of statistics and fractal theory, we combined the macro- and micro-structure characteristics of coal, and established the control equation of fracture field distribution. According to fracture mechanics and mesoscopic damage mechanics, we also established the expansion and damage evolution control equation of mesoscopic cracks. Furthermore, we revealed the relationship between meso-scale crack extension damage and macro mechanical characteristics, set up the macro-mesoscopic numerical model and calculation method of fractured rock mechanic constitutive, and developed the stress–strain numerical calculation program of gas-bearing coal using Comsol Multiphysics partial differential equation module and MatLab software. The model and methods were further validated in field tests. The results showed that our equations could better describe the deformation and damage process of gas-bearing coal and solve the fluid–solid coupling problems in gas and coal engineering practices.