Viscoelastic-plastic damage creep model for salt rock based on fractional derivative theory

Salt rock is widely used as an excellent material for energy storage owing to its low permeability, high safety, and stable mechanical properties. In this study, salt rock was subjected to a gradual loading creep test through the conventional uniaxial compression test. The loading time of each stage was approximately 14 days, and the total creep time exceeded five months. The steady-state creep rate of salt rock under different stresses and the corresponding creep strain law were positively correlated with the increase in stress and time. In addition, the long-term strength of the salt rock, determined via the isochronous stress-strain curve inflection point method, was 12 MPa. Furthermore, the viscoelastic-plastic damage-creep model of salt rock was established based on the theory of fractional derivatives. This proposed model was compared with the Nishihara model, and a sensitivity analysis of the parameters was performed based on the results of the nonlinear fitting of the fractional derivative. The rationality of the model was verified based on the results, especially for the accelerated creep phase. Moreover, the constitutive relationship of the model was straightforward and easy to apply. The proposed model provides a theoretical basis for future creep laws based on experimental data. The results reflected the creep law of salt rock to a certain extent and are expected to serve as a reference to studies on the long-term stability of deep salt rock.