A Fractional-Order Creep Model of Water-Immersed Coal

The long-term stability of a coal pillar dam is a serious concern for coal mine underground reservoirs because of the creep behavior of coal in complex water immersion and mechanical environments. In order to investigate the characteristics of creep deformation of water-immersed coal and develop a proper creep model, this paper implemented a series of creep experiments of coal via multistage loading at various water-immersion times. The experiment data were analyzed, in terms of immersion-induced damage, elasto-plastic performance, creep behavior, etc., suggesting obvious mechanical properties' degradation of coal by water. The elastic modulus and peak strength of water-immersed coal decrease exponentially with the immersion time, while the creep rate of coal shows an upward tendency with the promoted immersion time. According to the remarked relationships of elastic, viscoelastic, and viscoplastic properties versus the stress levels and water-immersion time, a creep model based on conformable fractional derivatives is proposed, considering the influence of the water-immersion time and variable stress level. The proposed model was verified using the experiment data, showing a good capacity of the creep model for reproducing the creep process of water-immersed coal. This paper provides a fundamental model for further studying the stability of coal pillars and their influence on the safety of underground water reservoirs.