Construction of Frozen Sandstone Creep Damage Model and Analysis of Influencing Factors Based on Fractional-Order Theory

During the construction of the freezing wall of the coal mine shaft, the long-term stability of the freezing wall is a key issue to control engineering safety. The creep deformation of frozen rock is one of the factors that cause the destruction of the frozen wall. Taking the Cretaceous saturated frozen sandstone as the research object, the creep mechanics test of frozen rock under different confining pressure conditions is carried out, and the strain–time curve clusters under different loading stress states are obtained. Based on the Riemann–Liouville-type integral function and borrowing from classic modeling ideas, a 5-element nonlinear creep damage constitutive equation considering low-temperature-damage-stress coupling is established, and the model verification is carried out. The results show: when the rock is in the elastic stage, the creep parameter \(E_{1}\) theory under each loading level should be exactly the same. But it shows a trend of increasing first and then decreasing, so the creep of frozen sandstone is a kind of nonlinear creep. The viscoelastic modulus \(E_{2}\) is a measure of the amount of deformation in the creep attenuation stage, indicating that it gradually decreases as the load factor increases. After the strain gradually increased to a certain fixed value, \(E_{1}\) remained basically constant. As the loading stress increases, the interior of the rock will undergo stages of compression, slippage, and recombination, and the friction between particles will increase, showing that the viscosity coefficients η₁ and η₂ gradually increase. The influence of the parameters \(\zeta\) and \(\gamma\) on the creep effect is analyzed through the results of the creep mechanics test. There is creep damage in the accelerated creep stage. As the load increases, the damage gradually expands. The same laws are shown under different confining pressure conditions. The research results can provide a theoretical model and the experimental basis for evaluating the instability and failure of the frozen wall induced by creep.