A gas-mechanical coupled constitutive equation for fractured coal containing gas

A gas-mechanical coupled constitutive equation is developed for coal containing gas or CO2 to predict the failure behavior based on fracture mechanics theory. A novel parameter of |∂cosα/∂Σ1| has been chosen as the failure characteristic parameter for coal containing gas. In addition, a closed-form gas-mechanical coupled constitutive equation is derived as σ1=σ3+fκ+fχpσtσcσtσcσ3+σc2. The effects of the coal friction coefficient f, the gas pore pressure p, Biot's coefficient χ and the fracture parameter κ have been coupled in the proposed model. Without considering the effect of pore pressure, the equation wonderfully coincides with the original Hoek-Brown Empirical Strength Criterion. Sensitivity analysis indicates that under a determining confining pressure, the failure stress is an increasing function of f, in contrast, a decreasing function of p, κ and χ. Due to the low tensile strength of coal, the effects of different fracture parameter κ from different fracture criterions can nearly be ignored when the pore pressure p is high. At last, in order to further verify the gas-mechanical coupled model proposed in this study, the comparison between some laboratory data and theoretical values for coal containing gas have been carried out. It seems that the new model is in good agreement with the existing experimental data.