Creep-damage constitutive model based on fractional derivatives and its application in salt cavern gas storage

• A novel creep damage constitutive model based on fractional derivatives was proposed. • The proposed model can well describe the creep data lasting 21,000 and 15,876 h. • The creep damage constitutive model was numerically implemented in FLAC 3D . • The proposed model can evaluate the long-term deformation of salt cavern gas storage. The long-term stability of oil / gas salt cavern storage is still considered as a puzzle, which leads to enormous challenges in its construction and operation. To describe the creep behavior of salt rock more accurately, a new fractional derivative creep-damage (FDCD) constitutive model, based on a modified Mohr-Coulomb criterion, is established by coupling the Hooke body, Abel dashpot and viscoplastic damage body. Previous creep models, especially those coupled with creep and damage, are rarely verified by very long-term creep experimental data. By fitting the creep experimental data of salt rock lasting 21,000 and 15,876 h (875 and 661.5 days), it is found that the proposed model can well characterize the experimental data, especially in the accelerated creep stage. Compared with the classic Nishihara and Burgers models, the FDCD constitutive model has significant advantages, with fewer parameters and higher accuracy. Then the FDCD constitutive model is implemented in FLAC 3D with C++ language and applied to the deformation analysis of salt cavern gas storage. The deformation and volume shrinkage of salt caverns obtained by the numerical simulation are in good agreement with those measured by sonar. The FDCD constitutive model can be successfully applied to a numerical program for evaluating the long-term deformation of salt cavern gas storage.