Effective stress of gas-bearing coal and its dual pore damage constitutive model

The dual pore structure of coal and occurence of gas adsorption make gas-bearing coal different from other non-adsorptive porous materials, and therefore interactions between coal and gas cannot be accurately described by Terzaghi effective stress. Considering adsorbed-gas-induced swelling stress and erosion, and pore/fracture-induced damage and failure to coal skeleton, the new effective stress equation for three-phase medium composed of free gas, adsorbed gas and coal skeleton is established. It can be used to reveal the effects of the spatial and temporal distribution and evolution of coal pores/fractures under different stress conditions on coal's mechanical deformation and damage characteristics, and to quantify the erosion effects of adsorbed gas on coal from a physicochemical point of view. Based on the basic principles of irreversible thermodynamics, a dual pore elastic-brittle-plastic damage constitutive model of gas-bearing coal is established. The model is further verified through the full stress–strain experiments and the adsorption-induced swelling experiments of gas-bearing coal under different axial pressures, and compared with the elasticoplasticity model established based on Terzaghi effective stress. The results show that the dual pore damage constitutive model could better describe the gas–coal interaction mechanism, and solve the fluid–solid coupling problems in gas and coal engineering practices.