Abstract
During the operation of a compressed air energy storage (CAES) salt cavern, the surrounding rock experiences creep damage during the stages of constant internal pressure and undergoes fatigue damage due to the periodical injection-production. To describe the damage evolution of salt rock under creep-fatigue loading, a novel damage accumulation model based on the ductility exhaustion concept is proposed by applying a nonlinear summation method to represent the synergistic effect of creep and fatigue damage. Low-cycle fatigue (LCF) and creep-fatigue tests of rock salt were conducted under stress-control mode for various cycle stress amplitudes and hold times. Results show that the deformation of rock salt under creep-fatigue loading consists of initial, steady and accelerated phases. The proposed model matches well with the test data and can accurately describe the damage evolution as the applied stress amplitudes and dwell times change. The introduction of the hold times at the upper limit stress causes a strain increment and life reduction, which become more evident as the duration periods prolong and can be understood by the dislocation theory of crystals.
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Abbreviations
- D :
-
Total damage
- \(D_{C}\) :
-
Creep damage
- \(D_{F}\) :
-
Fatigue damage
- \(D_{N}\) :
-
Total damage at the end of \(N\) cycles
- \(\overline{\sigma }\) :
-
Deviatoric stress
- \(t_{H}\) :
-
Hold time per cycle
- \(L_{r}\) :
-
Life reduction ratio
- \(\dot{\varepsilon }\) :
-
Steady-state creep strain rate
- \(\varepsilon_{C}^{*}\) :
-
Multi-axial creep ductility
- \(\varepsilon_{C}\) :
-
Axial creep fracture strain
- \(\varepsilon_{F}\) :
-
Fatigue ductility
- \(\varepsilon_{p}\) :
-
Cumulative plastic strain at the end of \(N - 1\) cycles
- A, n :
-
Material- and temperature-dependent constants in Norton powerlaw
- S :
-
Load force
- a, b, c, f, m :
-
Material-dependent constants in Xu et al.’s plastic strain evolution formula
- \(W_{dN}\) :
-
Plastic strain energy of cycle \(N\)
- \(\sigma_{N}\) :
-
Stress amplitude of cycle \(N\)
- \(N_{F}\) :
-
Fatigue life in the proposed damage model
- \(N_{f0}\) :
-
Cycle numbers to failure in the LCF tests
- \(N_{cf}\) :
-
Cycle numbers to failure in the creep-fatigue tests
- \(N\) :
-
Cycle number
- \(p\) :
-
Creep-fatigue interaction damage exponent
- \(\sigma_{\max }\) :
-
The upper limit stress
- \(\sigma_{\min }\) :
-
The lower limit stress
- \(\sigma_{m}\) :
-
Mean stress
- \(\sigma_{eq}\) :
-
Equivalent stress
- \(R^{2}\) :
-
The coefficient of determination
- h :
-
Stress triaxiality in Cocks and Ashby model
- \(W_{d}\) :
-
Cumulative strain energy at the end of \(N\) cycles
- \(W_{0}\) :
-
Cumulative strain energy at the end of the final cycle
- \(k_{1}\), \(k_{2}\) :
-
Material-dependent constants
- \(\sigma_{1}\), \(\sigma_{2}\), \(\sigma_{3}\) :
-
Maximum, intermediate and minimum principal stresses
- \(\varepsilon_{N}\) :
-
Strain amplitude of cycle \(N\)
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Acknowledgements
The authors are sincerely grateful to Professor J. J. K. Daemen (Mackay School of Earth Sciences and Engineering, University of Nevada, USA) for his linguistic assistance during the preparation of the manuscript. The authors would gratefully like to acknowledge the financial support from the National Natural Science Foundation of China (Nos. 51874274, 51774266) and Youth Innovation Promotion Association CAS (Grant No. 2019324). The authors would like to thank the Science and Technology Research Project of Jiangxi Provincial Department of Education (Grant No. GJJ200634).
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Zhao, K., Ma, H., Yang, C. et al. Damage Evolution and Deformation of Rock Salt Under Creep-Fatigue Loading. Rock Mech Rock Eng 54, 1985–1997 (2021). https://doi.org/10.1007/s00603-020-02342-6
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DOI: https://doi.org/10.1007/s00603-020-02342-6