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Understanding salt rock creep properties is important for designing and operating salt caverns. Triaxial multistage creep test of salt rock and acoustic emission (AE) monitoring were conducted, revealing the influence of deviatoric stress on the creep and AE characteristics of salt rock. Based on the creep AE test of salt rock, the evolution characteristics of AE during the creep process of salt rock are revealed from a microscopic point of view. Previous constitutive models describing rock creep only considered the damage effect during the accelerated stage, and could not accurately depict the damage evolution during the creep process. Using AE characteristic parameters, a damage constitutive model was established, revealing an exponential increasing trend in damage evolution during salt rock creep process. Considering the damage effects during salt rock creep, a novel creep damage constitutive (CDC) model was constructed based on fractional derivatives, and expressions for one-dimensional and three-dimensional (3D) stress states were given respectively. The proposed model and the classical model were calibrated by the triaxial creep test data, indicating that the proposed model can better describe the nonlinear creep characteristics of salt rock. [ABSTRACT FROM AUTHOR]