A fractional non-linear creep model for coal considering damage effect and experimental validation

• A fractional non-linear creep model for coal is proposed.
• The visco-elastic–plastic characteristics and the damage effect are considered.
• Experiments were carried out to validate the proposed model.
• The proposed model can predict the full creep stage of coal with better accuracy.
• The analysis of parametric sensitivity to creep strain is performed.

Accurate prediction of coal׳s creep behavior is of great significance to coalbed methane extraction. In this study, taking into account the visco-elastic–plastic characteristics and the damage effect, a fractional non-linear model is proposed to describe the creep behavior of coal. The constitutive and creep equations of the proposed fractional non-linear model are derived via the Boltzmann superposition principle and discrete inverse Laplace transform. Furthermore, uniaxial creep tests under different axial stress conditions were carried out to validate the proposed model. It is found that the present model can describe the experimental data from creep tests with better accuracy than classical models. Particularly, the present model can predict the accelerating creep deformation of coal which classical models fail to reproduce. Finally, the parametric sensitivity analysis is performed to investigate the effects of model parameters on the creep strain. It is verified that the introduction of fractional parameters and damage factor in the present model is essential to accurate prediction of the full creep stage of coal.