<p>Under complex stress conditions, the spatiotemporal coupling between creep deformation and structural degradation of salt rock remains unclear. Traditional creep models mainly rely on macroscopic strain fitting, neglecting the intrinsic correlation between micro-damage and macroscopic structural evolution, which leads to ambiguous physical meanings, redundant parameters, and limited predictive capability. In this study, the microstructural evolution, acoustic emission response, and strain characteristics of salt rock during creep were analyzed to reveal the staged deformation mechanisms: in the initial stage, pores and microcracks gradually close; in the steady stage, microcracks independently nucleate and slowly propagate, marking the onset of new damage; and in the accelerated stage, deformation shifts from viscoelastic to instantaneous plastic compression. Accordingly, the total creep strain is decomposed into elastic, viscoelastic, and plastic compression components. Based on the fractional derivative Maxwell model, a nonlinear creep model incorporating a damage-attenuated Hookean element and a switch element was established to describe structural degradation and plastic compression. Creep tests on different types of salt rocks under various stress paths verified the model’s capability through staged parameter identification. A parameter sensitivity analysis was conducted for the plastic compressive strain model, further enhancing the convenience of model application. Based on the composition of creep strain, the strain evolution patterns of different types of salt rock under multiple stress levels were systematically analyzed, providing theoretical support for the precise characterization of time-dependent deformation and instability prediction of surrounding rocks in deep salt cavern reservoirs.</p> Graphical Abstract <p></p>