Creep–fatigue constitutive model of salt rock based on a hardening parameter

Salt rock has been recognized as an ideal medium for energy storage or oil and gas storage because of its good creep and self-healing characteristics. Accurate characterization and prediction of the complex mechanical behavior of salt rock is the basis for ensuring the safety of underground space utilization project of salt caverns. Based on proposed parameters of hardening and other characteristic factors, in this study, a new creep–fatigue constitutive model is developed for salt rock considering complex loading and unloading paths. Based on the dislocation mechanism of salt rock deformation, hyperbolic damping elements are introduced as state variables to characterize the degree of rock hardening. The influence of loading and unloading history on the deformation behavior of salt rock is considered according to the evolution of hardening parameters. Based on the stress–strain relation of the classical Norton model, a basic mathematical relation is established for the creep–fatigue constitutive model. By assuming the initial nucleation length and considering the material fracture toughness, the stress–strain relation is modified for the range of adjacent failure stage (accelerated deformation stage) based on a new introduced crack growth factor. In this manner, the proposed model can well predict the plastic deformation characteristics under complex loading and unloading paths, such as conventional creep, cyclic loading and unloading, lower-limit interval cyclic loading and unloading, and trapezoidal wave creep cyclic loading and unloading. The model can also better characterize the interaction between constant load creep and cyclic loading and unloading. Most of the model parameters have clear physical meanings in the new developed creep–fatigue constitutive model. Parameter a represents the relation factor between stress and deformation rate at the steady deformation stage of salt rock, parameter b determines the relation factor at the decelerated deformation stage of salt rock, and parameters $d_0$ and $\mu {}_{\text{d}}$ represent the initial crack nucleation amount and crack growth rate factor, respectively. The $d_0$ and $\mu {}_{\text{d}}$ jointly affect/modify the stress–strain relation at the critical failure stage of the model.