This paper analyzes the correlations between three regions of rheology and numbers of acoustic emission (AE) events with the application of the rheology-AE test for salt rock under the condition of uniaxial compression. On the basis of the relationship between AE events and loading time

which is obtained from Weibull distribution

the function of damage variable with time is proposed. By comparing the fitting results with data obtained from the rheology-AE test and the rheology-ultrasonic test of salt rock

it is found that the function of damage variable with time has an excellent applicability. In addition

this paper conducts the sensitivity analysis of parameters in the function of damage variable with time and reveals the effects of shape parameters and scale parameters on the damage variable of salt rock. The theories of fractional calculus and damage are introduced to build the constitutive model of the variable-viscosity Abel dashpot. By replacing the Newton dashpot in the Nishihara model with the variable-viscosity Abel dashpot

the fractional rheological model of salt rock is proposed. The fitting analysis of uniaxial rheological test curves of salt rock suggests that the fractional rheological model is evidently superior to Nishihara model in describing three regions of rheology

especially the accelerating one. Furthermore

the Nishihara model is proved to be a special case of the fractional rheological model.