Fractional nonlinear creep constitutive model of salt rock

On the basis of a non-Newton fluid viscous damping element, fractional nonlinear dashpot element has been presented. Based on the definition of fractional derivatives, a theoretical expression for the element has been obtained. Its expression is consistent with that of the Abel dashpot. Through further comparison, it is found that the element can reflect the nonlinear acceleration characteristic of the creep curve. By introducing the element, new nonlinear creep constitutive model has been established. Based on the data from the creep experiments, fitting analysis has been conducted about the model. The results show that the nonlinear creep constitutive model agrees well with the data from the experiments and can clearly reflect the characteristics of the creep curves of the whole process, especially the nonlinear acceleration creep stage.