A fractional order viscoelastic-plastic creep model for coal sample considering initial damage accumulation

In deep coal and rock mass engineering, extensive initial damage problems caused by excavation and unloading are critical to the long-term deformation and stability of underground projects. An innovative initial damage coal sample test method was proposed, and coal samples with different initial damage were prepared by the MTS pressure tester's circular displacement cyclic loading and unloading control. The creep characteristics of coal samples with different initial damages were tested by the staged loading creep test method. With the increase of initial damage, the coal samples' creep time became shorter, and the rate of accelerated creep damage increased sharply. The relationship between fractional viscosity coefficient and stress was introduced to describe the non-linear relationship of creep strain increase at each stage. The creep model in the acceleration phase was improved by establishing the relationship between the damage variable and the initial damage. Based on the fractional calculus theory, a viscoelastic-plastic model considering the initial damage of coal samples was established, and the fractional order model was verified. The coefficient of correlation between the experimental data and the creep model was higher than 0.95, indicating that the fractional creep model can better describe the creep characteristics of coal samples with initial damage. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).