Modeling the visco-elastoplastic behavior of deep coal based on conformable derivative

The visco-elastoplastic deformation of deep coal poses a challenge for gas control in a high-stress environment. To investigate the mechanical response of deep coal to achieve better gas control, we establish a fractional visco-elastoplastic constitutive model by combining the fractional Burgers model based on conformable derivative with a nonassociated Drucker–Prager elastoplastic model. The fractional constitutive model is discretized within the implicit finite element method. The numerical model is verified against analytical solutions and subsequently calibrated and compared to experimental data of, e.g., triaxial compression tests. The numerical model is then used to analyze the rate-dependent stress–strain evolution of deep coal under triaxial compression. The results show that the numerical model can capture visco-elastoplastic phenomena and dilatancy of deep coal. In addition to triaxial stress paths, an engineering-scale finite element simulation of a roadway in a deep coal seam is carried out, and the deformation around the roadway is analyzed. This study provides theoretical support for understanding the visco-elastoplastic deformation of deep coal.