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

• A new calculation model for deformation energy of tectonic coal based on critical state theory is proposed, which accounts for nonlinear constitutive behavior. • The relationship between deformation energy and stress follows a power law, with exponents close to 2 for intact coal and 1 for tectonic coal. • Coal viscosity and viscoelastic behavior significantly influence cyclic loading/unloading curves, leading to increased deformation energy with load cycles. • Tectonic coal exhibits deformation energy an order of magnitude higher than intact coal under the same stress, highlighting its role in coal and gas outbursts.