Deformation energy of tectonic coal under hydrostatic conditions: A new calculation model based on critical state theory

The deformation energy (W_d) of soil-like tectonic coal is crucial for investigating the mechanism of coal and gas outbursts. Tectonic coal has a significant nonlinear constitutive relationship, which makes traditional elastic-based models for computing W_d unsuitable. Inspired by critical state soil mechanics, this study theoretically established a new calculation model of W_d suitable for the coal with nonlinear deformation characteristics. In the new model, the relationship between energy and stress no longer follows the square law (observed in traditional linear elastic models) but exhibits a power function, with the theoretical value of the power exponent ranging between 1 and 2. Hydrostatic cyclic loading and unloading experiments were conducted on four groups of tectonic coal samples and one group of intact coal samples. The results indicated that the relationship between W_d and stress for both intact and tectonic coal follows a power law. The exponents for intact and tectonic coal are close to 2 and 1, respectively. The stress-strain curve of intact coal exhibits small deformation and linear characteristics, whereas the stress-strain curves of tectonic coal show large deformation and nonlinear characteristics. The study specifically investigates the role of coal viscosity in the cyclic loading/unloading process. The downward bending in the unloading curves can be attributed to the time-dependent characteristics of coal, particularly its viscoelastic behavior. Based on experimental statistics, the calculation model of W_d was further simplified. The simplified model involves only one unknown parameter, which is the power exponent between W_d and stress. The measured W_d of the coal samples increases with the number of load cycles. This phenomenon is attributed to coal’s viscoelastic deformation. Within the same stress, the W_d of tectonic coal is an order of magnitude greater than that of intact coal. The calculation model of W_d proposed in this paper provides a new tool for studying the energy principle of coal and gas outbursts.