A new constitutive model for salt rock under cyclic loadings based on state variables

Underground salt rock caverns are ideal for national strategic energy storage, compressed air energy storage, and CO2 storage. Operation periods of salt cavern storage can be affected by periodic injection of gases during production/charging and discharging activities, thus causing fatigue damage to surrounding rock. It is therefore necessary to establish a model that can accurately characterize the evolution process of fatigue damage in salt rock under cyclic loading. This is a necessary input into the design of salt cavern storage systems and for the evaluation of their operation and safety. Relying on the rheological properties and cracks of salt rock and their effects on the bearing capacity of materials, this paper establishes a fatigue damage constitutive model of salt rock, using the rheological characteristics of rock and the deformation-crack expansion relationship. First, the time-varying state variable is introduced through the classical Norton model to characterize the degree of hardening; this is in order to modify the relationship between the stress deformation rate and the correlation of the historical path of loading and unloading of salt rock. Then, based on the relationship between crack damage and effective stress development under deformation conditions, a fatigue damage constitutive model of salt rock is established. Finally, using cyclic loading and unloading data of salt rock under different stress ratios or confining pressures, we verify and compare the model parameters. The results show that: (1) The model can accurately predict the fatigue deformation characteristics of salt rock under different cyclic loading and unloading paths and can better characterize the interaction between deformation and stress path; (2) In this model, parameter a affects stage II while parameter b affects stage I of salt rock fatigue deformation. This can be understood as the factor representing the relationship between stress and deformation rate of salt rock; (3) Parameter d0 characterizing the initial nucleation area and parameter mu d representing crack growth rate factor jointly affect/modify the stress-strain relationship in the critical failure stage or stage III of the model.