Effect of Deviatoric Stress on Deformation Energy of Tectonic Coal: A Modified Energy Model Considering Nonlinearity

ABSTRACT The deformation energy stored in soil‐like tectonic coal plays a critical role in coal and gas outbursts. Unlike hard rocks, tectonic coal exhibits pronounced stress–strain nonlinearity, invalidating traditional elastic energy models. Based on critical state theory in soil mechanics, a nonlinear deformation energy model was developed and validated through hydrostatic and triaxial loading‐unloading experiments on intact and tectonic coal samples from five coal mines. Deformation energy variations were systematically analyzed using unloading curves, confirming the model's validity under hydrostatic and deviatoric stresses. The hydrostatic deformation energy model was simplified by consolidating parameters into a single term. To generalize it to all stress states, a deviatoric stress coefficient was introduced to represent the degree of stress deviation from hydrostatic conditions. Experimental results show that the deviatoric stress coefficient for intact coal is typically greater than 1, while for tectonic coal, it is often below 0.5 and can approach 0. The modified model provides a more accurate characterization of triaxial deformation energy–stress relationships compared to elastic models, as evidenced by both experimental and published data, owing to the stress‐dependent variation of Poisson's ratio and elastic modulus during loading. Both intact and tectonic coal exhibit a decreasing tangent modulus of elasticity and an increasing Poisson's ratio with progressive loading. At equivalent deviatoric stress levels, tectonic coal stores significantly more deformation energy than intact coal. However, at comparable ratios of deviatoric stress to material strength, their deformation energy becomes similar. This finding enhances the understanding of the energy mechanisms driving coal and gas outbursts.