Utilizing real-time acoustic emission monitoring data to predict the creep failure of salt rock has emerged as a crucial method for ensuring the smooth operation of salt cavern storage facilities. This article integrated real-time acoustic emission monitoring data from the creep process of salt rock to analyze the dynamic evolution of internal structural damage. It was discovered that the relationship between damage rate \(\dot{D}_{t}\) and cumulative strain closely resembles the Weibull distribution function. By incorporating the Weibull probability distribution function and Drucker–Prager strength criterion, a damage evolution model that considers elastic stress threshold and cumulative damage effect was established. Based on the damage evolution characteristics observed during the creep process of salt rock, the linear solution values of the damage evolution model were revised and validated. The cumulative damage \(D\) from the salt rock creep-acoustic emission test was integrated into deformation modulus \(E_{D}\) and viscosity coefficient \(\eta_{D}\) of the Maxwell creep model, thereby creating a new Maxwell creep model that considers compression-creep coupling and mutual feedback damage. This model was then extended to three-dimensional stress conditions. The research findings reveal that the new creep model adeptly describes the entire creep process of salt rock. The derivative order \(\beta\) of the model reflects the geometric structure state and creep strain participation rate \(\zeta\) of salt rock during the creep process. The sudden increase in strain during the accelerated creep stage of salt rock is attributed to the compressive strain resulting from rapid structural degradation.
