Construction of nonlinear creep damage model of frozen sandstone based on fractional-order theory

Abstract

The frozen wall of a coal mine vertical shaft undergoes creep deformation under long-term load, and excessive deformation induces damage to the frozen wall. The creep behaviour of frozen rock is key in controlling the long-term stability of frozen walls. In this study, Cretaceous saturated frozen sandstone was used as the research object to conduct creep mechanics tests under different confining pressure conditions. Based on the Riemann-Liouville-type integral function, a 6-element frozen sandstone nonlinear creep constitutive equation considering temperature–damage–stress coupling was established and verified by experimental data. The results show that: compared with the rock creep test at 20 °C, the creep process of saturated frozen sandstone also presents an attenuation creep stage, a steady-state creep stage, and an accelerated creep stage. A nonlinear creep damage equation is established based on the fractional-order theory. Comparing the theoretical formula with the experimental data, it was found that the agreement was higher. The research results can provide a theoretical and experimental basis for evaluating creep-induced instability and failure of frozen walls.